SOLID PHASE PROCESSING OF NONCRYSTALLINE HIGH ENTROPY ALLOY COATINGS

Abstract

A method utilizes ball milling for coating a metallic alloy on a target surface. The method includes placing the target surface in a ball mill device. The method includes milling a mixture of powder with exposure to the target surface. The method includes forming an alloy comprising a first metal and a second metal. The method includes coating the alloy on the target surface of the object via a mechanical force of ball milling.

Description

BACKGROUND

Refractory high entropy alloy (RHEA) coatings, composed of multiple refractory metallic elements, exhibit high strength and have shown promise in enhancing the durability of components exposed to extreme conditions, significantly extending their operational lifespan. Melt-based processing of these coatings is challenging due to the large physical, thermodynamic and mechanical properties mismatches in the multiple principal elements. For example, the large difference in densities (from 6.49 g/cm3 for Zr to 19.25 g/cm3 for W) and melting points of refractory elements (from 1857° C. for Zr to 3422° C. for W) can result in unmelted or vaporized elements, microstructure coarsening and property instabilities during melting and solidification. Mechanically driven methods, due to their limited heat input and no melting or solidification, have the potential to minimize these issues.

Mechanical alloying has been applied to produce metallic coatings with mainly Face Centered Cubic (FCC) structure. While these metallic coatings entail high hardness, they are specifically suited for high temperature applications. The challenge of forming refractory coatings arises from the high strength and slow diffusion rates of refractory metallic powders, which hinder initial mixing and subsequent consolidation. This can result in the formation of heterogeneous multi-phase microstructures. For example, mechanically alloyed refractory W—Cu coatings entail multi-layered composite structures, albeit with most Cu dissolving into the W lattice. The chemical and microstructural heterogeneity in refractory high entropy alloys can become more pronounced as their formation mechanisms grow more complex, driven by the interaction among multiple principal elements. It has been reported that mechanically alloyed WMoNbTa and WMoNbTaV RHEA coatings exhibit heterogeneous microstructures, comprising a BCC solid solution and a Ta-rich phase. This phase separation is attributed to the reduced alloying rate and slow solid-state diffusion of Ta, resulting from its stronger atomic bonds and higher vacancy formation and migration energies. For the TiVZrTa RHEA studied in this work, its arc-melted counterpart was reported to entail multiple phases with Body Centered Cubic (BCC) crystal structure, indicating the microstructural heterogeneity of this alloy system. The current understanding of formation mechanisms in TiVZrTa and similar RHEAs such as TiVNbTa and TiVCrTa is predominantly limited to empirical observations at the micro- to nanoscale.

The formation mechanisms of mechanically driven RHEAs at the atomic scale remains difficult, mainly due to the inherently nonequilibrium nature of forced chemical mixing and thermal diffusion, typically requiring atomistic simulations for accurate representation. A kMC framework has been developed to study the chemical mixing and phase formation of metal pairs under mechanically driven conditions. However, this approach does not account for the influence of the microstructure and mechanical properties of the metallic elements. Another approach incorporated phase strength effects into the framework, but this approach remains limited to binary systems. In a multi-element system like quaternary RHEA, the chemical mixing process becomes more complicated as competitions of mixing rates and mechanisms in multiple elemental pairs occur simultaneously. Therefore, achieving a homogeneous, single-phase solid solution becomes more challenging due to the intricate interplay between forced chemical mixing and thermally activated recovery processes.

SUMMARY

In some embodiments of the system and methods describe herein, a coating on a steel substrate is mechanically driven using surface mechanical alloying and consolidation (SMAC). In some embodiments, the coating is a single-phase, nanocrystalline TiVZrTa RHEA. As will be discussed in more detail below, a kinetic Monte Carlo (kMC) simulation framework was developed, which incorporates four principal elements (Ti, V, Zr and Ta) to reproduce the atomic-level chemical mixing states and phase formation process, considering both phase strength effects and thermally driven recovery processes. The base formation mechanisms and mechanical properties of the RHEA coatings produced under room and cryogenic temperatures are described herein. Experimentally, a coating microstructure and phase evolution is described herein with scanning electron microscopy equipped with energy dispersive spectroscopy and X-ray diffractometer measurements. Additionally described herein, the hardness of the RHEA coatings are measured with nanoindentation tests and apply physically based models to analyze their strengthening mechanisms.

In some systems and methods described here, mechanical alloying (MA), X-ray diffraction (XRD), and kinetic Monte Carlo (kMC) simulations are combined to systematically study the interplay between the chemical pairing potential and the mechanical shearing during the formation process of mechanically driven complex concentrated alloys. The chemical and mechanical forces play a competing role in the mixing of ternary complex concentrated alloys with negative mixing enthalpies. The chemical driving force favors a chemically ordered atomic structure, while the mechanical force encourages a random atomic arrangement. The energetic basis of this competition is revealed as the gain and loss in mixing enthalpy and configurational entropy. Following this fundamental understanding, three types of mixing mechanisms and their corresponding steady-state phases are defined. It is shown that the molar content of the element with the lowest average mixing enthalpy governs the mixing mechanisms and thus determines the energetic stabilization of the steady-state phases. A theoretical phase prediction map is provided for an embodiment of the described alloy design. A nanocrystalline equiatomic NiCoCr coating is synthesized under the guidelines of the map, which presents exceptional mechanical properties achieved by the mechano-chemical mixing.

Mechanically driven alloys significantly differ from alloys produced by traditional melting-based methods in terms of phase formation mechanisms. In conventional melt-based processing, atoms of different elements diffuse to mix with each other in a liquid state and then solidify, during which the total free energy and cooling rate controls the steady-state phases. In contrast, mechanically driven alloys involve mixing elements in a solid state at relatively low homologous temperatures where thermal diffusion is suppressed and atoms are displaced from one phase to another by external forces to form new phases. The outcome of this process depends more on the ability to resist external shearing rather than on thermodynamic equilibrium state or cooling rate. The increasing kinetic shearing effect, combined with moderate thermal diffusion, can result in a synergetic [9-12] or competing effect of thermal and mechanical driving forces during the processing and formation of the driven alloys.

Previous research works have shown that in driven binary alloys, the mechanical driving force competes with the thermal driving force when the two elements have a positive mixing enthalpy. Bellon and Averback have shown the mechanical shearing force produces massive dislocations in the material, thereby introducing metallic bonds between atoms of different elements regardless of their positive mixing enthalpy (anti-bonding chemical potential). Their seminal kinetic Monte Carlo (kMC) simulations revealed that when the mechanical driving force overcomes the thermal driving force, atoms of different elements can be forced to mix into a randomly distributed solid solution through ballistic diffusion. In line with their results, binary immiscible elements such as Cu—Fe, Cu—Ag and Cu—Co have been reported forming single phase solid solutions under mechanical alloying.

However, some immiscible elements remain phase-separated even with abundant ballistic diffusion, suggesting restrictive factors of the forced mixing process. For instance, Cu—W and Cu—Ta do not gain chemical homogeneity even when mechanically alloyed at low homologous temperatures. With the observation that softer elements mix with Cu more easily than harder elements under mechanical alloying, the kMC model was extended by incorporating a hardness-dependent rate that controls the shearing events. It was found that when one phase is significantly softer than the other, shearing occurs preferentially in the soft phase, isolating the harder one. Therefore, the hardness mismatch between the two elements was proposed to determine whether they achieve a chemically random solid solution state or not.

On the other hand, for a binary system with a negative enthalpy of mixing, both thermal and mechanical driving forces should promote the mixing of two elements into a single-phase solid solution. A binary system with slightly negative mixing enthalpy yields a single-phase solid solution under mechanical alloying, which can be exemplified by Fe—Co forming a single uniformed BCC solution under high energy ball milling. With an even lower negative mixing enthalpy, an ordered phase can be developed due to the dominance of thermal diffusion. This is demonstrated by Ti—Ni which develops lamellar structures after 20 hours of mechanical alloying. In short, the extent of thermal diffusion also becomes a determinative factor of the chemical distribution in mechanically driven alloys with a negative mixing enthalpy.

The interplay between these two driving forces can be nontrivial in a ternary system with a negative mixing enthalpy and moderate hardness mismatch among elements. In binary systems with extremely low mixing enthalpy, ordered phases have been reported because the rapid diffusion process interrupted the repetitive mechanical shearing induced. In a ternary system with multiple elemental pairs having different chemical bonding potentials (pair-wise mixing enthalpies), compositional asymmetry may lead to a stronger tendency of chemical ordering or even phase separation; elements with a lower chemical pairing potential may easily bond to each other, leaving the third element in an isolated phase if it has a relatively high molar content in the alloy. Therefore, the uneven chemical bonding preference among neighboring atoms in ternary systems, which favors local chemical ordering or separated phases, can compete with the mechanically driven mixing process that favors a random atomic arrangement or a single phase. If the hardness mismatch between different elements is too large, the deformation is expected be preferentially accommodated only in the soft regions, and a single-phase random mixture may not be obtained.

The mechanical alloying approach have shown great potentials in producing single-phase solid solutions with various elements, breaking the miscibility constraints imposed by their mixing enthalpies. There is also growing research interest in mechanically driven complex concentrated alloys (CCAs) which are composed of more than three principal elements and relatively large concentrations and exhibit outstanding thermal and mechanical properties. Most previous research on mechanically driven CCAs has focused on equiatomic compositions and experimental characterizations while the phase evolution process during alloying has not been systematically understood. Understanding phase evolution in mechanically driven ternary concentrated systems with negative mixing enthalpies can provide insight into the mixing physics in compositionally complex asymmetric systems and support theory-enabled design of driven alloys.

It is desired to provide a fundamental understanding of the competition between chemical and mechanical driving forces and their energetics during the mechanical alloying process of ternary concentrated systems with negative mixing enthalpies. Described herein are the experimental characterizations with kinetic Monte Carlo (kMC) simulations. First, a kMC model is developed to explain the mixing mechanisms, energy interplays and resultant steady-state phases in mechanically driven ternary alloys with negative mixing enthalpy. In some embodiments, NiCoCr alloys were synthesized with varying Cr content by mechanical alloying and analyzed the phase evolution through X-ray diffraction. Combining simulation and experimental results, three distinct mixing mechanisms were identified and their corresponding phases, which are influenced by the molar content of the element with the lowest average mixing enthalpy. Secondly, an energetic criterion for single-phase formation is described, which is validated through simulations involving multiple ternary systems. Finally, a theoretical phase prediction map is described to guide future design of complex concentrated alloys (CCAs) using mechanical alloying methods. In some embodiments, an equiatomic NiCoCr coating was synthesized and characterized following the theoretical prediction, bridging the mixing mechanisms to mechanical properties.

These and other features of the present disclosure will become more apparent from the following description of the illustrative embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

FIG. 1a shows a comparison between VEC rules and experimental mechanically driven HEA phase compositions;

FIG. 1b shows a comparison between the 2-8 rules and experimental mechanically driven HEA phase compositions;

FIG. 2a shows a prediction of the phase composition after SMAC by a VEC model;

FIG. 2b shows a prediction of the phase composition after SMAC by a STDS model;

FIG. 3a shows the SEM images of the morphologies of Ti powder;

FIG. 3b shows the SEM images of the morphologies of V powder;

FIG. 3c shows the SEM images of the morphologies of Zr powder;

FIG. 3d shows the SEM images of the morphologies of Ta powder;

FIG. 4 shows elements and their strength in nanocrystalline states;

FIG. 5 shows the relationship between strength mismatch and the phase composition of mechanically driven HEAs;

FIG. 6 shows an established plane lattice;

FIG. 7 shows a schematic of four strength mismatch, while adjusting strategies upon initials strength configuration;

FIG. 8a shows the simulation process of mechanically driven HEA at low strength mismatch at the lattice plane conditions after 0 steps Monte Carlo simulation;

FIG. 8b shows the simulation process of mechanically driven HEA at low strength mismatch at the lattice plane conditions after 5000 steps Monte Carlo simulation;

FIG. 8c shows the simulation process of mechanically driven HEA at low strength mismatch at the lattice plane conditions after 10000 steps Monte Carlo simulation;

FIG. 8d shows the simulation process of mechanically driven HEA at low strength mismatch at the lattice plane conditions after 15000 steps Monte Carlo simulation;

FIG. 8e shows the simulation process of mechanically driven HEA at low strength mismatch at the lattice plane conditions after 20000 steps Monte Carlo simulation;

FIG. 8f shows the evolution of the SRO;

FIG. 9a shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 0 steps Monte Carlo simulation;

FIG. 9b shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 5000 steps Monte Carlo simulation;

FIG. 9c shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 10000 steps Monte Carlo simulation;

FIG. 9d shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 15000 steps Monte Carlo simulation;

FIG. 9e shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 20000 steps Monte Carlo simulation;

FIG. 9f shows the evolution of the SRO;

FIG. 10a shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 0 steps Monte Carlo simulation;

FIG. 10b shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 5000 steps Monte Carlo simulation;

FIG. 10c shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 10000 steps Monte Carlo simulation;

FIG. 10d shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 15000 steps Monte Carlo simulation;

FIG. 10e shows the simulation process of mechanically driven HEA at medium strength mismatch at the lattice plane conditions after 20000 steps Monte Carlo simulation;

FIG. 10f shows the evolution of the SRO

FIG. 11a shows the stacking bar chart of the SRO-strength mismatch plots of for the configuration shown in FIG. 7(a);

FIG. 11b shows the stacking bar chart of the SRO-strength mismatch plots of for the configuration shown in FIG. 7(b);

FIG. 11c shows the stacking bar chart of the SRO-strength mismatch plots of for the configuration shown in FIG. 7(c);

FIG. 11d shows the stacking bar chart of the SRO-strength mismatch plots of for the configuration shown in FIG. 7(d);

FIG. 11 e shows the relationship between MA-HEAs' ultimate phase compositions and strength mismatch of mixing elements;

FIG. 12a shows the steady state simulation at a strength mismatch of 2 in configuration (a);

FIG. 12b shows the SRO evolution of FIG. 12a;

FIG. 13a shows the steady state of simulation at strength mismatch of 2 in configuration (b);

FIG. 13b shows the SRO evolution of FIG. 13a;

FIG. 13c shows the steady state of simulation at strength mismatch of 2.25 in configuration (b);

FIG. 13d shows the SRO evolution of FIG. 13c;

FIG. 14a shows the steady state of simulation at a strength mismatch of 2.5 in configuration (c);

FIG. 14b shows the SRO evolution of FIG. 14a;

FIG. 15a shows the steady state of simulation at a strength mismatch of 2.5 in configuration (c);

FIG. 15b shows the SRO evolution of FIG. 15a;

FIG. 16a shows a block diagrams of the SMA process;

FIG. 16b shows a schematic of the SMAC process and its comparison with traditional mechanical alloying;

FIG. 17a shows a schematic illustrating the original powders of the SMAC process;

FIG. 17b shows a schematic illustrating an inside view of the vial containing premilled powders, milling balls, and steel substrates;

FIG. 17c shoes the initial placement of premilled powders and steel substrate;

FIG. 17d shoes the onset of coating formation;

FIG. 17e shows progressive coating build-up, resulting in increased thickness;

FIG. 18 shows the XRD patterns of the SMAC powders and SMACed coatings with different duration;

FIG. 19 shows the evolution of lattice strain and grain size during SMAC;

FIG. 20 shows a SEM image of the as-SMACed coating;

FIG. 21a shows a SEM image of the as-SMACed coating;

FIG. 21b shows a SEM image of cross-section of a nanocrstalline HEA after 20 h of SMA2T, where the HEA is adhered to Ni substrate;

FIG. 22a shows an EDS analysis of the as-SMACed coating;

FIG. 22b shows SEM and EDS images of the cross-section of one of an embodiments;

FIG. 23a shows a SEM images of the cross-section for RT;

FIG. 23b shows a SEM images of cryogenic milling;

FIG. 23c shows an EDS mapping of Fe for RT

FIG. 23d shows an EDS mapping of Fe for cryogenic milling;

FIG. 23e shows an EDS mapping of Ti;

FIG. 23f shows an EDS mapping of Ti;

FIG. 23g shows an EDS mapping of V;

FIG. 23h shows an EDS mapping of V;

FIG. 23i shows an EDS mapping of Zr;

FIG. 23j shows an EDS mapping of Zr;

FIG. 23k shows an EDS mapping of Ta;

FIG. 23l shows an EDS mapping of Ta;

FIG. 24a shows X-ray diffraction measurements for evolution of phases in TiVZrTa coatings processed at RT from original element powders (0 h powder), 6 h powder, 12 h powder, 24 h RHEA coating, and 36 h RHEA coating;

FIG. 24b shows X-ray diffraction measurements for evolution of phases in TiVZrTa coatings processed at cryogenic temperatures from original element powders (0 h powder), 6 h powder, 12 h powder, 24 h RHEA coating, and 36 h RHEA coating;

FIG. 25 shows the average compositions of near-equiatomic, Ta-rich and V-rich phases in the RT processed TiVZrTa RHEA coating;

FIG. 26a shows a TEM analysis of the as-SMAC coating and a bright field image of the coating;

FIG. 26b shows a TEM analysis of the as-SMAC coating and a HRTEM bright field;

FIG. 27a shows a map of hardness vs grain size of FCC HEAs produced by different methods;

FIG. 27b shows a calculation of strain rate sensitivity m;

FIG. 28 shows a map of the hardness vs grain size of FCC HEAs produced by different methods.

FIG. 29 shows the XRD patterns of the SMAC powders after 1 h of isochronal heat treatment (HT) under different temperatures;

FIG. 30a shows the XRD patterns of the SMAC powders after 8 h heat treatment under 450° C. temperatures;

FIG. 30b shows an XRD pattern of a sample after 20 h SMA2T showing only a single face centered cubic phase;

FIG. 31a shows XRD patterns of SMACed coating after one-hour isochronal heat treatment (HT) under different temperatures (grain sizes are shown);

FIG. 31b shows hardness of the coating after the heat treatment;

FIG. 32a shows an XRD pattern and phase analysis on a TaCrAlCo and NiCrCu1.5Ta;

FIG. 32b shows an XRD pattern and phase analysis on a TaCrAlCo coating on Ni substrates;

FIG. 33 shows the SRO evolution plot of CrMnFeCo's simulation;

FIG. 34 shows the comparison between the experimental datapoints and the strength model.

FIG. 35a shows mechanical test results for the RHEA coatings, and average hardness profile from the bottom to top layers of the room temperature (RT) processed coating, along with the average hardness for the cryogenic temperature (CT) processed coating;

FIG. 35b shows representative nanoindentation impressions across the cross-section from bottom to top layer for the RT processed coating;

FIG. 36a shows the evolution of grain size with heat treatment under different temperature;

FIG. 36b shows comparison of fractional increase of grain size with other Cantor-like HEA;

FIG. 37a shows the evolution of grain size and lattice strain with milling or SMAC time under RT processing conditions;

FIG. 37b shows the evolution of grain size and lattice strain with milling or SMAC time under CT processing conditions;

FIG. 38a shows the calculation of grain growth exponent n;

FIG. 38b shows the comparison between the grain growth exponents;

FIG. 38c shows the calculation of grain growth activation energy Q_act;

FIG. 39a shows a SEM image of a TiVTaZr coating SEM image;

FIG. 39b shows a XRD pattern of a TiVTaZr coating;

FIG. 40a shows kMC simulation results of the mechanically driven mixing process of the TiVZrTa RHEA coating processed at RT showing as the evolution of the simulation cell microstructure versus the Monte Carlo Steps from 0 to 3×105.

FIG. 40b shows kMC simulation results of the mechanically driven mixing process of the TiVZrTa RHEA coating processed at CT (b) showing as the evolution of the simulation cell microstructure versus the Monte Carlo Steps from 0 to 3×105.

FIG. 41a shows the evolution of chemical short-range order (CSRO) parameters of different metal pairs versus the MCS for RT processed samples;

FIG. 41b shows the evolution of chemical short-range order (CSRO) parameters of different metal pairs versus the MCS for CT processed samples;

FIG. 42a shows the evolution of chemical short-range order (CSRO) parameters versus the MCS of different metal pairs for the RT processed coating based on FIG. 37a, including Ta included pairs (TaTa, TaTi, TaZr, and TaV);

FIG. 42b shows the evolution of chemical short-range order (CSRO) parameters versus the MCS of different metal pairs for the RT processed coating based on FIG. 37a, including V included pairs (VV, VTi, VTa, and VZr);

FIG. 42c shows the evolution of chemical short-range order (CSRO) parameters versus the MCS of different metal pairs for the RT processed coating based on FIG. 37a, including Ti included pairs (TiTi, TiV, TiTa, and TiZr);

FIG. 42d shows the evolution of chemical short-range order (CSRO) parameters versus the MCS of different metal pairs for the RT processed coating based on FIG. 37a, including Zr included pairs (ZrZr, ZrTi, ZrTa, and ZrV);

FIG. 43 shows comparison of the theoretical and experimentally measured hardness of the TiVZrTa RHEA coating processed at both room and cryogenic temperature conditions, where ‘EXP’, ‘Theory-SS’, and ‘Theory-GSS’ represent experimental hardness, theoretical predicted solute strengthening, and grain size strengthening, respectively;

FIG. 44 shows a comparison of grain size, thickness, and hardness of refractory high entropy alloy coatings produced by SMAC and other deposition techniques including magnetron sputtering, thermal spray, electrodeposition, and laser cladding, where the average hardness of the RHEAs made by each method are color-coded;

FIG. 45a shows a cross-section view of selected (111) lattice plane in the Ni0.4Co0.5Cr0.1 cell after different MCS in the simulation of mixing process;

FIG. 45b shows stacking XRD patterns of Ni0.2Co0.2Cr0.6 powders before and after different durations of MA;

FIG. 45c shows the SRO evolution of different atomic pairs in Ni0.2Co0.2Cr0.6 during the simulation of mixing process;

FIG. 46a shows a cross-section view of selected (111) lattice plane in the Ni0.4Co0.5Cr0.1 cell after different MCS in the simulation of mixing process;

FIG. 46b shows stacking XRD patterns of Ni0.4Co0.5Cr0.1 powders before and after different durations of MA;

FIG. 46c shows the SRO evolution of different atomic pairs in Ni0.4Co0.5Cr0.1 during the simulation of mixing process;

FIG. 47a shows cross-section view of selected (111) lattice plane in the equiatomic NiCoCr cell after different MCS in the simulation of mixing process;

FIG. 47b shows Stacking XRD patterns of equiatomic NiCoCr elemental powders before MA and after different durations of MA;

FIG. 47c shows the SRO evolution of different atomic pairs in equiatomic NiCoCr during the simulation of mixing process;

FIG. 48a shows a NiCoCr phase map generated by kMC simulation;

FIG. 48b shows a contour maps of the ratio of entropy and enthalpy contribution;

FIG. 48c shows the Gibbs free energy distribution in a simulated NiCoCr system;

FIG. 49 shows six possible combinations of the chemical and mechanical mixing speed among elemental pairs in a ternary system, one example is given for each possible set, with selected transitional metals: Ti, V, Cr, Mn, Fe, Co, Ni;

FIG. 50a shows a NiCoMn phase map generated by kMC simulation;

FIG. 50b shows a contour map of the ratio of entropy and enthalpy contribution;

FIG. 50b shows the Gibbs free energy distribution in a simulated NiCoMn system;

FIG. 51 shows a phase prediction map for ternary systems, where the data points come from combination of any three among Ti, V, Cr, Mn, Fe, Co, Ni with varying atomic fraction;

FIG. 52a shows a cross-sectional SEM image showing the NiCoCr coating on the Ni substrate, where the green dashed line indicates the interface between the coating and the substrate;

FIG. 52b shows an EDS maps displaying the elemental distribution of Ni, Co, and Cr in the coating and substrate;

FIG. 53 shows the chemical composition of SMAC coating and substrate; and

FIG. 54 shows the relationship among coating thickness (μm), grain size (nm), and hardness (GPa) for various alloy coating processes, where the data points are color-coded to represent hardness;

FIG. 55a shows a Kinetic Monte Carlo simulation of competition between thermally activated diffusion and shear-induced mixing in a binary fcc system at an initial state of a fully separated system in which red and blue dots are for different atoms;

FIG. 55b shows a Kinetic Monte Carlo simulation of competition between thermally activated diffusion and shear-induced mixing in a binary fcc system at simulation results of processing after 60000 steps with lower simulated temperatures;

FIG. 55c shows a Kinetic Monte Carlo simulation of competition between thermally activated diffusion and shear-induced mixing in a binary fcc system at simulation results of processing after 60000 steps with higher simulated temperatures.

DETAILED DESCRIPTION OF THE DRAWINGS

For the purposes of promoting an understanding of the principles of the disclosure, reference will now be made to a number of illustrative embodiments illustrated in the drawings and specific language will be used to describe the same.

Described herein are systems and methods of a surface mechanical attrition and alloying treatment (SMA²T, in some embodiments) to make nanocrystalline high entropy alloy (HEA) coatings for structural applications. In some embodiments, a modified ball milling machine is used to exploit repeated plastic deformation to mix elemental powders such as Fe, Co, Cr, Mn, etc. down to atomic level, and at the same time, consolidate the alloy in the form of thick (more than 100 microns), defect free, high entropy coatings strongly adhered to a substrate material.

The HEA coating consists of a single-phase material with crystals of the size on the order of ˜10 nm making the alloy extremely strong and wear resistant. HEAs are a new class of alloys that—unlike conventional alloys—do not have a single major alloying element of high concentration (e.g., 90%) mixed with a number of minor alloying elements. HEAs, instead, are made by mixing equal or relatively large proportions of four, five or more elements. They offer a large lattice distortion coupled with significant solid solution strengthening and as a result are thermally more stable and mechanically stronger than conventional alloys.

Since the strength of alloys is inversely proportional with the square root of their crystal (grain) size, a nanocrystalline high entropy alloys could offer ultimate strength/hardness/wear resistance in the domain of structural materials. The processing of nanocrystalline HEAs is, however, challenging. Melt based processes, e.g., arc-melting can produce HEA but fails at making them nanocrystalline. That is, the crystal size of the arc melted material is usually on the order of 10-100 microns. Sputtering techniques, on the other hand could produce nanocrystalline HEAs but are limited only to thicknesses below ˜1 micron in size and therefore could not find a market in the domain of structural applications.

In some embodiments, a surface mechanical attrition and alloying technique is presented with which can be made several hundred-micron thick HEAs (shown in FIG. 21b), which will be discussed in more detail below. The HEA coating is unique because it offers large enough thicknesses for structural application and at the same time it is nanocrystalline. It was found that after 20 h of the described process (SMA²T), four elemental powder materials can be transformed into a single-phase high entropy nanocrystalline alloy and the same time achieve a full consolidation of the powders into a thick and adherent coating. The presence of a single phase and the nanoscale grain of the coating are both confirmed with X-ray diffraction analysis shown in FIG. 30b. The homogeneity of the elemental mixture down to the atomic level is confirmed with the energy dispersive spectroscopy analysis shown in FIG. 22b where all the elements are homogeneously distributed in the alloy with no indication of a second phase nor precipitates. Since the coatings are very thick, the approach can unlock the structural applications of nanocrystalline HEA coatings in a number of industries from automotive to naval to energy and biomedical.

The described approach is flexible in that it can work with all metallic powders and at any scale offering a large space for material design. Thus, a number of different industries can be targeted including automobile and aerospace for wear-resistant coatings, naval industry for corrosion resistance coatings, and fusion energy industries for the protection of fusion reactor walls against extreme thermomechanical and radiation conditions.

The current technologies used to make HEAs are either arc melting-based or sputtering-based. The former cannot produce nanocrystalline (thus very hard) HEAs and the latter is limited to coating thickness below ˜1 μm. In that sense, the proposed approach occupies a unique space in materials processing. It offers both very thick coatings with nanocrystalline grains. It is envision that the approach will be a competitive one compared to the existing processes. What is more, due to its solid-state character, it would produce a much smaller carbon footprint compared to the melt-based processes and would be much less expensive compared to the sputtering-based techniques.

As mentioned above, a challenge in the production of next-generation transformative materials is to develop manufacturing methods that can circumvent the constraints on chemistry and structure imposed by melt-based processing approaches. The systems and methods described herein utilize forced chemical mixing during extensive straining to fabricate mechanically driven high-entropy alloys in solid state. A large shear strain is introduced into the material, creating a mechanical-thermal coupling that facilitates diffusional processes without requiring the alloy to be melted. A competition between recovery processes, which work towards restoring the microstructure toward its equilibrium, and deformation processes, which push it away from equilibrium, governs the steady state microstructure. Kinetic Monte Carlo (kMC) simulations are used to understand this competition and to develop general design guidelines for mechanically driven high entropy alloys. In some embodiments describe hereinw, this concept is demonstrated by synthesizing a mechanically driven CrMnFeCo alloy, which indicates excellent strength as well as thermal stability.

The term “mechanically driven alloys” refers to the alloys that are in nonequilibrium conditions created by external dynamical forcing. In driven alloys, atoms are displaced not only by the traditional thermal induced diffusion, but also by plastic deformation to form certain microstructure. Mechanically driven alloys can bypass the current challenges for design of new materials, namely the limitations on chemistry and structure imposed by melt-based processing approaches.

One approach to make a mechanical driven alloy is mechanical alloying (MA). In this process, intensive shear strain created by the metal powders' collision with milling balls, with vial chamber, and with other metal powders results in the formation of new metallic bonds between different powders and eventually, the formation of new alloys in solid state.

Although mechanical alloying has been used to synthesize a large number of new alloys in the past decades, the evolution of the phases during mechanical alloying is not fully understood. Previously, a kinetic Monte Carlo simulation model had been proposed in which the shear induced alloying process was considered to be in competition with the thermally driven jumps of a vacancy in a face-center cubic (FCC) lattice of a binary system. This showed that, by adjusting the frequency of shearing with respect to that of thermal jumps, different steady state microstructures can be achieved. When shear-induced mixing dominates the response, atoms of different kinds tend to be fully mixed and achieve solid solution in the steady state. On the other hand, when the thermally activated jumps are the dominant mechanism, the system is driven by thermodynamics, and the steady state shows a phase separation.

The kinetic Monte Carlo model was later further extended to consider the phase strength effects in mechanical alloying. With the modification, it was then possible to observe something different in the steady states. It was reported that a large mismatch in the strength often results in phase separation, while a chemically homogeneous structure is usually obtained in the simulation with starting phase with similar strength in phases.

Recently, high entropy alloys (HEA) have received increasing attention in the domain of structural materials. HEAs are the alloys that formed by mixing equal or relatively large proportions of four, five or more principal elements. With their four core effects, HEAs are of great potentials in structural applications. Similar to normal alloys, HEAs could also be synthesized by MA and dozens mechanically-alloyed HEA have been previously reported.

But the conditions upon which a single phase high entropy alloy can be produced by mechanical alloying is not clear. It is known that HEAs fabricated by traditional casting methods show different phase compositions, and the phase composition shows great influence on an HEA's mechanical behavior. Based on physicochemical and thermodynamic understanding, several rules have been proposed to explain or predict HEAs' steady states, such as the VEC, Ω, and atomic size mismatch rules. Valence electron concentration (VEC) shows the electron concentration effect on the phase composition of HEAs, and the parameter Ω is the ratio of the multiplication of mixing entropy (ΔS_mix) and the melting temperature (T_m) to mixing entropy (ΔH_mix)m, as shown below:

$\Omega =\frac{T_m\Delta S_{\mathrm{mix}}}{\Delta H_{\mathrm{mix}}}$

The atomic size mismatch δ is the parameter describing the relationship between the weighted deviation of a concentration C_i, element's atomic radius (r_i), and the average atomic radius (r), as shown below:

$\delta =\sqrt{\sum _{i=1}^N{C}_i{\left(1-\frac{r_i}{\overline{r}}\right)}^2}$

According to the VEC rules, if the valence electron concentration of a HEA is larger than 8, then the HEA should be a single FCC phase. If 6.87≤VEC≤8, then a multi-phase microstructure would be expected. Lastly, if the VEC is smaller than 6.87, then the HEA is bound to show the body-center cubic (BCC) single phase composition. Typically speaking, higher parameters imply that the mixing elements would prefer having each other as nearest neighbors and form single solid solution phase. Lower also shows higher likelihood of forming single phase solid solution. But these rules of thumbs all fail when applied to mechanically alloyed HEAs. In FIG. 1a, the data points collected for mechanically alloyed HEAs have been populated into predictive maps constructed by these parameters. It can be seen from the figures that the phase compositions do not follow the VEC rules and different phase compositions are distributed everywhere. Meanwhile, shown in FIG. 1b, these two parameters also fail in prediction the conditions when applied to mechanically-driven HEAs.

The above demonstration highlights the need for design guidelines for mechanically-driven high entropy alloys. It is proposed the deviation in strengths of the mixing element controls the mixing results. A 2D lattice-based kinetic Monte Carlo simulation was conducted to support this proposal. Using the simulations, design guidelines were established for mechanically driven HEAs. In addition, this design is demonstrated by synthesizing a CrMnFeCo HEA.

FIG. 1a shows a comparison between the VEC rules and the experimental mechanically driven HEA phase compositions. The blue, green and red backgrounds are the BCC single phase (BCC SP), BCC+FCC multi-phase and FCC single phase (FCC SP) areas predicted by VEC rules. FIG. 1b shows the comparison between 2-8 rules and experimental mechanically driven HEA phase compositions. The blue and green backgrounds are the single phase and multi-phase areas predicted by the Ω-δ rules.

The previous criterions all fail in predicting steady state condition for mechanically driven HEAs. Inspired by previous reports on the phase strength effects in mechanical alloying of binary systems, a strength mismatch parameter is derived to dictate the steady state condition for mechanically-driven HEA, as shown below:

$\mathrm{StrengthMismatch}=\sqrt{\frac{{\sum }_{i=1}^N{C}_i{\left(S_i-\overline{S}\right)}^2}{\frac{\left(N^{\prime }-1\right){\sum }_{i=1}^N{C}_i}{N^{\prime }}}}$

in which the N and N′ are the number of elements and the number of elements that has non-zero concentration, respectively. C_i is the concentration of element i, S_i is the strength of element i and S is the weighted average of all the strengths of the elements present in the HEAs. In order to make the model close to the real mixing conditions, the strengths of elements were chosen in their nanocrystalline (nc) states, as shown in the table in FIG. 4.

The rational for the hypothesis is based on the expectation that softer phases should bear more deformation than the harder phases during the alloying process. If the deviation between the soft and hard phases is too large, the hard phases will not participate in the deformation-induced mixing and eventually, a multi-phase composition will be achieved. FIG. 5 is the plot showing the phase composition of mechanically driven HEAs and their corresponding strength mismatch. Interestingly, the strength mismatch can clearly distinguish the single phase alloys (denoted by “SP”) from multi-phase alloys (denoted by “MP”) with a transitional region where the two possibilities co-exist. As a general rule of thumb, larger strength mismatch (larger than 2) result in multi-phase HEAs. In addition both the SP alloys and MP alloys could co-exist in the transitional regime where the strength mismatch is between 1.5 and 2. In order to further understand the mixing process and to explain the transition observed in the map in FIG. 5, showing the relationship between the strength mismatch and the phase composition of mechanically driven HEA, lattice based kinetic Monte Carlo simulations have been conducted.

A Monte Carlo simulation is a computational technique used to approximate complex mathematical problems through random sampling. It involves using random numbers to model uncertainty in various systems and then running numerous simulations to derive statistical outcomes. The name ‘Monte Carlo’ suggests the use of random or chance sampling in obtaining numerical results. This method has found applications in diverse fields such as physics, finance, and engineering due to its ability to handle problems with intricate analytical solutions or multiple variables. Here, this method is applied to a 2D lattice-based model of 4 elements and their deformation-induced mixing process.

Shown in FIG. 6, in some embodiments, the lattice in the model is a plane lattice and a simplified version of a face-center-cubic (FCC) spatial lattice. As shown in FIG. 6, it represents one of the (111) planes in an FCC lattice. There are 48 atoms along each boundary of the lattice with the periodic boundary conditions being applied. More specifically, FIG. 6 shows an established plane lattice. The four different colors are referring to atoms from four different elements of the mechanically driven HEAs and a random lattice point is occupied by the vacancy, which is the black dot in the red area. The magnified plot shows the position arrangement of atoms in the lattice, three different slip lines are denoted by three red arrow lines.

In some embodiments, an adapted kinetic Monte Carlo (kMC) model is employed to simulate the chemical mixing process of TiVZrTa quaternary system with the individual elements' properties. Given that all the phases in the RT and CT processed RHEA coating exhibit a BCC structure, as shown in FIGS. 23 and 24, in some embodiments, a BCC lattice structure was used in the model. More specifically, atoms are simulated in a rhombohedron cell with the faces parallel to BCC {110} planes and 31 atoms along each edge.

In some embodiments, similar to previous Monte-Carlo simulations, one vacancy is introduced in a random position in the lattice. During the simulation, the jump could only happen between vacancy and one of its nearest neighbors. In some embodiments, the equation for the jump frequency is given by an Arrhenius model, shown below:

$w=\mathrm{vexp}\left\{-\frac{E_0+E_{\mathrm{XV}}^{\mathrm{act}}}{K_{B}T}\right\}$

where v is the attempted jumping frequency (10¹⁵ s⁻¹), E₀ is a configuration independent energy set equal to 0.8 eV, E_XV^act is the energy term provided by the local energy environment: E_XV^act=εn/2, n is the number of atoms with different kinds around the atom that is about to swap its position with the vacancy, and ε is an energy assigned with the variance caused by every surrounding different atoms, −0.533 eV. T is the temperature and K_B is the Boltzmann constant. In the following simulations and experiments the temperature is kept at 300K. A residence time algorithm is applied to select the next atom to be exchanged with the vacancy in the jumping step.

In some embodiments, mixing occurs through thermal diffusion and mechanical shearing, with either process taking place at each Monte Carlo step (MCS), depending on a residence time algorithm. In some embodiments, a single vacancy was introduced in the system and used the below equation to determine the thermal diffusion frequency, i.e., the switch of vacancy with one of its nearest neighbors:

$f_{\mathrm{jump}}=v_0\exp \left(-\frac{E_0+E^{\mathrm{act}}}{k_{B}T}\right)$

where ν₀=10¹⁵ Hz is the attempt frequency, k_B is the Boltzmann constant, T is set at 360K for room temperature milling based on the reported temperature ranges in a ball milling vial while the cryogenic milling temperature is set to be 77 K corresponding to the LN temperature. E₀=0.8 eV is a configuration-independent energy, E^act=Σ_i=1,j=1^Nn_ijE_ij is the activation energy which defines the energy configuration of each of the vacancy's nearest neighbors. E_ij=U_ij−0.5(U_ii+U_ij) is the energy change associated with the formation of ij bond in which U_ij is the energy of ij bond considered to be proportional to the mixing enthalpy ΔH_ij^mix. While lattice mismatch in RHEA could potentially decrease the diffusion rate, the increased defect densities and grain boundary areas under mechanically driven conditions can increase the diffusion rate by providing more diffusion paths. This counteracting effect supports the use of the above equation to calculate the thermal jump frequency in the formation of TiVZrTa RHEA.

In mechanical alloying process, powders randomly collide with milling balls, vial's chamber, and other powders, and therefore, either in real alloying or in modelling, the mixing resulted by deformation should be accomplished by different slip systems with a uniform probability distribution. In an FCC spatial lattice, the dislocations are moving in the 12 slip systems: three <110> slip directions with four 111 slip planes. In the discussed model, the dislocation movement can be seen as the shearing of one part of the lattice with respect to the other. And, considering the periodic boundary conditions, it could only happen on the materials between two parallel closest packed lines, which are in 60° with other sets of slip lines.

In some embodiments, in one shear event, the statistical selections are made in the following manner: slip lines and directions are chosen randomly, two parallel slip lines are selected by a probability distribution function that reflects the strength for a given line j:

$P_j=\frac{R_j}{\sum R}$

where R_j is calculated by:

$R_j=\exp \left\{\frac{x\left[950\times \sum F_{\mathrm{ij}}{H}_{\mathrm{ij}}\right]}{K_{B}T}\right\}$

where x is constant (2.4×10²² J), F_ij is the fraction of bond between atoms from element i and j in the slip line and H_ij is the fractional strength of the bond which is approximated by i and j's strength in FIG. 4 normalized by the strength of the strongest element. All the atoms between the two shearing lines are then displaced by one Burger's vector in one direction. And the frequency of the shearing event is set to 10³ s⁻¹.

In some embodiments, the mechanical shearing frequency is set as 10³ Hz to ensure that the effects of thermal diffusion and mechanical shearing remain comparable to those during the SMAC process. Since a series of parallel slip planes in the same slip system can be activated under external shear force, each mechanical shearing event causes all planes between two parallel ending planes to glide by one Burgers vector in a random slip direction. The two ending planes are selected from a random slip system out of the eight primary slip systems of BCC. The probability of a certain slip plane m to be selected, P_m, is inversely proportional to its planar hardness:

$P_m=\frac{R_m}{{\sum }_{k=1}^N{R}_k}$

where the denominator is the summation over all the slip planes (R_k) in a slip system, and the relative planar hardness R_m, the possibility of a dislocation move through a plane, is defined as:

$R_m=\exp \left(-\frac{\chi \sum N_{\mathrm{ij}}·H_{\mathrm{ij}}}{k_{B}T}\right)$

where N_ij is the number of ij bonds on the plane m, H_ij is the hardness of ij bond, and χ=2.4×10⁻²² J is constant; χΣN_ij·H_ij is the plastic work required to move a dislocation through plane m.

Before every step of the simulation, whether a jump or a shear would happen was determined by a residence time algorithm, and another round of calculation began after the preceding step was finished.

The model is based on the assumption that the strengths' distribution of the elemental materials dominates the steady state phase evolution, and softer phase will bear more deformation. However, if an improper initial phase configuration is chosen, the simulation result may be affected by the configuration itself rather than affected by mismatch in strength.

The approach to choose the initial configurations of the phases is described here. The lattice was divided into four areas horizontally with the same number of lattice atoms in every area. The two harder phases are distributed at top and bottom, and the softer phases is in between. By arranging the phases like this, the case that the soft phase self-shear is avoided. The goal of simulation is to observe if the local deformation would happen even if the shear was introduced to both strong and soft phases, which would really happen in the real mixing. Thus, a self-shear is definitely the thing that should be avoided. Material with the highest strength will be denoted as S4, the one with the second hardest strength is S3, second-to-last soft material is S2, and the softest material is S1 as shown in the initial phase configuration in FIG. 7.

In the real world, choosing an alloying element means assigning a phase with a certain strength, and different choices of HEAs will result in different strength mismatch. The simulation tests were also designed for showing this diversity. In the model four levels of strength are considered with three increment steps in a quaternary HEA. To cover the possibilities, while keeping the initial strength distribution the same strengths are carefully adjusted to cover a range of strength mismatch between 0.5 to 2.5 under four different scenarios which are also shown in FIG. 7: increasing all of the increment steps; increasing strength increment between S1 and S2 only; increasing strength increment between S2 and S3 only; increasing strength increment between S3 and S4 only. The change in strength values was limited to the normal values of nanocrystalline elemental material provided in FIG. 4.

FIG. 7 shows a schematic of four strength mismatch adjusting strategies upon the initial strength configuration. S1-4 is referring to the four materials with different strengths. The increment steps that marked with red are the strength being changed to adjust the strength mismatch in strategies.

After a sufficient number of steps, the simulations can predict the steady state microstructure by an updated lattice where the points are occupied by new atoms. From a quantitative point of view, short range order parameters (SRO) can be used to identify if a homogeneous solid solution is obtained, or the phase separation, namely the multi-phase structure, still exists. In some embodiments, for a binary ally system composed of atom A and B, the short range order parameter of A and B atoms with r distance away from each other is given bellow:

${\mathrm{SRO}}_{\mathrm{AB}}^{\left(r\right)}=1-\frac{p_{\mathrm{AB}}^{\left(r\right)}}{2X_A{X}_B}$

in which the p_AB^(r) is the probability to find a B atom around an A atom (or a B atom around an A atom, regardless of the order of finding which first) with r the distance apart, for which is often set to one in simulation. X_A and X_B are the concentration of A and B in the system. In a binary system, the SRO from 1 to 0 reflects an increasing number of dissimilar nearest atoms. The SRO evolution was calculated between two-by-two of the HEA elements and it was found that the SRO also follows the rules generally. For some cases, some SRO would drop to small numbers while for others the SRO can stay close to unity. This is reflecting of the two phases being mixed or remain separated otherwise, respectively. In the model, all SRO below 0.25 were considered as a fully mixed state.

In some embodiments, the chemical mixing state of the simulated system is evaluated with the Warren Cowley Chemical Short-Range Order (CSRO) parameter:

${\alpha }_{\mathrm{ij}}=1-\frac{X_{\mathrm{ij}}}{2c_i{c}_j}$

where α_ij is the CSRO parameter of ij pairs, X_ij is the probability of having ij nearest neighbors, corresponding to the proportion of ij bond, and c_i and c_j are molar fraction of element i and j respectively. For binary system, α_ij=1 represents full phase separation, α_ij=0 represents random single-phase solid solution, and α_ij=−1 signifies full decomposition. Similarly, in a multi-element system, a positive α_ij represents more separation of ij elemental pairs, while a negative α_ij indicates that element i and j are more segregated.

In some embodiments, to evaluate the thermodynamic stability of the systems, the steady state energy change ΔG of the simulation cell is calculated:

$\Delta G=\Delta H-T\Delta S$

where enthalpy change

$\Delta H=\frac{{\sum }_{i=1,j=1}^N{n}_{\mathrm{ij}}{E}_{\mathrm{ij}}}{M}$

is calculated as the total energy change associated with bond formation divided by the total number of atoms in the cell M. The configurational entropy change, ΔS, of a system with multiple principal elements is calculated with a cluster variation method (CVM):

$\Delta S=k_B[\left(Z-1\right){\sum }_i\left(c_i\ln c_i-c_i\right)-\frac{Z}{2}{\sum }_{i,j}\left(X_{\mathrm{ij}}\ln X_{\mathrm{ij}}-X_{\mathrm{ij}}\right)+\left(\frac{Z}{2}-1\right)$

where Z=8 is the number of nearest neighbors in a BCC system.

In each of the four types of simulations mentioned earlier, the strength mismatch values are adjusted for simulating at SRO=0.5, 1, 1.5, 2, and 2.5. Each simulation runs for 20,000 steps. If the SRO evolution curve still exhibits significant changes, the simulation then continues for an additional 20,000 steps until the curve reaches steady states. The steady states' SRO values for different elemental combinations are recorded. If there is a large increase in SRO values at the steady states (indicating a transition from a single phase to multiple phases in the simulation results), a new simulation is conducted before reaching this specific strength mismatch value to precisely determine the point where the simulated phase composition undergoes a large change.

In the simulations, different results are obtained before reaching a steady state at various steps. Here two typical simulations are considered with different strength mismatch from configuration (a) shown in FIG. 7 as examples to illustrate the data obtained during the simulation. FIGS. 8a-e are the evolution of the simulated lattice plane from step 5000 to 20000 at a strength mismatch of 0.5. As observed, these phases are soon mixed together because of the small differences in strength. Even the strongest phases are dispersed into the matrix after only 5000 steps (FIG. 8b) with an only small amount of segregation. After 20k steps, atoms from all phases are already distributed homogeneously in the lattice, implying a formation of solid solution single phase. The SRO evolution in FIG. 8f records the mixing process continuously, confirming the fully mixed steady state observed in FIG. 8e. The SRO between the softest material, S1 and S2 pairs drops most quickly, and the SRO for the pair contain the material with highest strength S4 (S1-S4, S2-S4 and S3-S4 pairs) drop the slowest, which prove the assumption that soft phases tend to bear more deformation in the alloying process.

FIGS. 9a-f show the simulation done at medium strength mismatch of 1.75. As shown, at 5000 steps (FIG. 9b), the stronger phases (red and yellow atoms) still exist as a segregated phase but are gradually subdividing and forming small clusters with continued shear. After 10000 steps (FIG. 9c), the state is similar to the state in FIG. 8b, while only the strong phases show small segregation.

At the end, all elements are also randomly distributed. The SRO dropping in FIG. 9f is slower compared to the it is in FIG. 8f, and the curves for different elemental pairs are more dispersed when dropping, implying a larger difference in deformation distribution. However, all of the curves converge at last, and a solid solution is obtained again.

FIG. 10a-f are from another simulation where even at the steady state, the lattice still remains unmixed, and it is found that from the beginning to the steady state, the shearing mainly occurs within the three softer phases with the strongest phase remaining unmixed. In reality, this final configuration illustrate a multi-phase case where mixing is only present among the soft phases. It can also be confirmed from the SRO evolution in FIG. 10e that phase composition has reached the steady state and dose not change with larger steps.

For every initial configuration shown in FIG. 7, by increasing the strength mismatch, the above analysis is repeated and the influence of configurations discussed individually. At the end, the stacked bar charts of the steady states' SRO at different configurations and different strength mismatch have been drawn in FIG. 11a-d. The aforementioned significant change points have been captured and projected onto FIG. 11e, demonstrating the relationship between phase composition of previous research MA-HEAs and strength mismatch.

FIG. 11a is the SRO-Strength mismatch plot of for configuration shown in FIG. 7(a) that all strength increments increase during strength mismatch adjusting. The stacking bar charts in FIG. 11 show the SRO-strength mismatch plots of four different initial strength configurations' simulation results (a-d, with the same order shown in FIG. 3) and the relationship between MA-HEAs' ultimate phase compositions and strength mismatch of mixing elements (single phase (SP) are symbolled as black square dots while the multi-phase (MP) are symbolled as red triangle dots).

As indicated, when the strength mismatch is below 2, the mixing results are always single phase solid solution, in which the SRO is in low levels. However, once the strength mismatch is higher than 2, the SRO soon increase to a much higher levels, implying a multi-phase steady state and persistence of the unmixed phases to remain separated. The steady state of the mixing at strength mismatch=2 has been shown in FIG. 12a and the corresponding SRO evolution is shown in FIG. 12b, from which it can be observed that the local deformation caused by shear as a result of large strength mismatch. A few harder atoms are dissolved into the green phase which has the lowest strength, and the rest of the lattice still remains unmixed. As the phase strength increases, fewer and fewer of atoms participate in the mixing process: the red strongest phase has the least number of atoms displaced by the deformation. It is reasonable to see that the lowest SRO in the high strength mismatch levels are always S1-S2 phase pair because these are the softer phases mixing the most in the simulations.

The SRO-strength mismatch plot for the configuration (b) where the strength increment is in between S1 and S2 is given in FIG. 11b. The first significant SRO change occurs when the strength mismatch is between 1.75 and 2.0. However, unlike other cases, the lowest SRO is no longer the yellow bar which is assigned to two of the softest phases, S1 and S2. Things would be clearer if the current configuration is considered: 4 strengths with one large increment between the S1 and S2. This means that all the strength values of S2, S3, and S4 are close to each other. Thus, when the softest S1 bears the most strain in the alloying process, rather than being sheared into the S2 area which will also cause the co-shearing of S2 or S3 inevitably, it would prefer being directly sheared in to the S4 area. This would cause the only co-shearing between S1 and S4. Therefore, the mixing shows the most homogeneous distribution between S1 and S4 (denoted as green bar) in this configuration.

FIGS. 13a and 13b show a steady state of simulation at strength mismatch of 2 in configuration (b) and its SRO evolution. FIGS. 13c and 12d show a steady state of simulation at strength mismatch of 2.25 in configuration (b) and its SRO evolution. The lattice for the steady state at strength mismatch of 2.0 and SRO curve are given in FIGS. 13a and 13b. Compared to the unmixed state in configuration (a), the unmixed extent in steady state of configuration (b) is lower because of the small differences between S2, S3 and S4, the soft phase would prefer shearing into the nearest S4 phase. And the alloying between S1 and S4 create a steady state with more distortion, since after the mixing, the strength of the slip line increase according to the equation. Clusters of red, blue and yellow phases are still very obvious but unchanged SRO evolution implies that it has reached its maximum mixing extent. Another interesting feature that should also be mentioned in the simulation with this configuration is the drop SRO when the strength mismatch reaches 2.25. The snapshot of it and the SRO curve is given in FIGS. 13c and 13d. The SRO curve drops very quickly, and this could also be explained by its unique strength configuration: under this configuration, the strength mismatch between S1 and the other three phases is so large that the deformation only localized in the S1 phase. Since the concentration of S1 is only 25%, the confined deformation in S1 cannot accommodate the applied strain and thus other phases must participate, which result in a co-deformation of all phases. Since the strength difference among the S2, S3, and S4 is so small, they soon reach a fully mixing steady state. Some similar experiments on TiZrNbMoTa and CrNbTiVZn also prove this observation.

FIG. 11c shows the plots for the configuration shown in FIG. 7c, where the increment is in between S2 and S3. This configuration gives the upper bound of SRO sudden increase point, which the strength mismatch is between 2.25 and 2.5. Such a high transitional boundary is again related to the initial strength configuration: from a mathematical point of view, under the same strength mismatch, the absolute range of strength produced by this configuration is the smallest, which implies a smallest strength mismatch among the mixing elements. FIG. 14 shows the steady state of simulation at strength mismatch=2.5 in configuration (c); and b: its SRO evolution. From the steady state at strength mismatch of 2.5 and its SRO curves in FIGS. 14a and 14b, the mixing behavior of the softest green phase can be noticed, the severe deformation even move the position of other phases, but the SRO still remain at high levels. In simulations and real mechanical alloying, HEAs with such configurations all show a higher tendency of mixing.

The last configuration is the one shown in FIG. 11d, in which the strength increment between S3 and S4 are adjusted to capture different strength mismatch. It shows the earliest change in the SRO that right after strength mismatch reaches 1.5, the sudden increase of the SRO bar indicates the phase separation of simulated result. The very small strength difference among S1, S2, and S3 provides sufficient material for the mixing that once the strength of S4 increases, the deformation will soon avoid going through it and accomplished by the rest of three, leaving a phase separation outcome. The steady state at strength mismatch of 1.5 and its SRO curves are given in FIGS. 15a and 15b. Both of the lattice and the curves are different from the others. First of all, the strongest red phase stands alone as the unmixed state, but the other three phases are all dissolved and form a solid solution phase. Previously mentioned sufficient soft mixing material and avoiding of the hard phase work together, creating a two-phase structure in steady state. Secondly, the SRO curves also capture this phenomenon: all the pairs contain material that has the strength of S4 remain at a pretty high level, while the curves for the other pairs drop quickly and soon converge, which also show the different mixing behavior between S4 and S1, S2, S3.

The data collected from mechanically driven HEAs' phase composition and their corresponding strength mismatch is shown in FIG. 11e. The overlaying of SP and MP areas is now can be explained: the transition area created by experimental datapoints matches the area created by lower and upper bounds for the SRO significant changes considering all possible configurations. The transitional zone demonstrates that even under the same strength mismatch, the choice of the mixing elements and their strengths could still affect the alloying results. And this match validates the successful simulation and prediction of the Monte Carlo model to the real experiments, showing its potentials to be used as a guideline for MA-HEAs design beforehand.

In another example embodiment, the classical Bellon-Averback kinetic Monte Carlo (kMC) model was extended to depict the atomic movements during alloying and the steady-state atomic arrangement. The model mainly describes two types of mixing events, namely the thermally activated vacancy diffusion and the deformation-induced slip plane shearing. A rhombohedral simulation cell has been used in the described model with all faces of the cell parallel to {111} planes in face-centered cubes (FCC) and 30 atoms along each side. Periodic boundary conditions were applied. One vacancy was introduced into the system initially.

At each Monte Carlo step (MCS), either the vacancy can swap its position with one of its 12 nearest neighbors, or a series of {111} slip planes are sheared by one Burgers vector. For the vacancy jump event, the jump frequency is determined by Eq. 1, where f is the jump frequency, ν is the atomic vibrational frequency (10¹⁵ s⁻¹), k_B is the Boltzmann constant, T is the temperature, E₀ is the chemical-independent atomic migration energy (0.8 eV), and Fact is the total activation energy based on pairing potentials. The values of ν and E₀ are selected from literature. T is set to constant at 300K to be in line with the experiments. Fact is further defined with the below equation, where n_ij is the number of i-j bonds to break during the swap event, and ∈_ij is the pairing potential (in eV). In the below equation, only atomic pairs of different elements need to be counted (i≠j) since the pairing potential is theoretically defined as the change in chemical potential when forming one i-j bond while breaking a pair of i-i and j-j bonds. In this work, experimentally measured mixing enthalpy were adapted at their critical temperatures to convert ∈_ij. A residence time algorithm was applied to determine which neighbor site the vacancy would jump to. The acceptance probability (P_i) of a swap attempt between the vacancy and atom i is calculated from the chemical activation energy before (E_i^before) and after (E_i^after).

$f=v·\exp \left(-\frac{E_o+E^{\mathrm{act}}}{k_{B}T}\right)$ $E^{\mathrm{act}}=\sum n_{\mathrm{ij}}·{ϵ}_{\mathrm{ij}}$ $P_i=\exp \left(-\frac{E_i^{\mathrm{after}}-E_i^{\mathrm{before}}}{k_{B}T}\right)$

On the other hand, the frequency for a deformation-induced shear in a Monte Carlo step (φ) is set to constant at 10³ s⁻¹ to capture the external mechanical force on an atomic scale. A shearing event was simulated by the following steps adapted from Cordero et. al. First, one of the four {111} slip systems was selected randomly, and an Arrhenius form shearing energy barrier R_j is defined as Eq. 4 and assigned to individual slip plane j. Here χ is a constant (2.4×10⁻²² J/bond) capturing the amount of work needed to glide a dislocation across a plane j and n_ij is the number of i-j bonds on the plane j (including both i=j and i≠j). H_ij is the relative hardness of i-j pair defined as

$\left(\frac{H_i+H_j}{2·H_{\max }}\right),$

with H_i and H_j being the measured strength of i and j nc elemental powders and H_max being the largest strength value among all elements in the ternary system. The strength of nanocrystalline elemental Ni, Co and Cr powders is shown in FIG. 4. P_j gives the probability distribution function of a slip plane j to be sheared in the selected system, and N is the total number of planes in the selected {111} slip systems. Then, two slip planes were selected under a residence time algorithm to be the initial and ending plane of the shearing event. The distribution function was recalculated after selecting the initial plane. Eventually, all parallel slip planes between the two selected ones were sheared by one Burgers vector.

$R_j=\exp \left[-\frac{\chi \left(\sum n_{\mathrm{ij}}·H_{\mathrm{ij}}\right)}{k_{B}T}\right]$ $P_j=\frac{R_j}{{\sum }_{i=1}^N{R}_i}$

In some embodiments, for every step in the simulation, the frequency of vacancy jump is compared to that of planar shear, and the rejection sampling method is used to decide which event would happen. With accumulated atomic motions, the system gradually changes its chemical distribution, which is further quantified by the Warren-Cowley short range order parameter (WC-SRO). As shown in the below equation, α_ij¹ means the SRO between ij elements on their 1^st nearest neighbor site, c_i and c_i are the molar fractions of element i and j, and p_ij is the fraction of i-j bonds in the simulation cell (i≠j). This WC-SRO parameter α shows how far is the current system away from its statistically random state. A zero SRO means that the system is perfectly random. When α>0, the microstructure is ordered; when α<0, the microstructure is decomposed. Applying this parameter to the mechanical alloying process, a positive α means that the atoms are inadequately mixed, and a negative α means that the particles are overly mixed. The degree of mixing is thereby traced by plotting the revolution of α with respect to the Monte Carlo steps.

${\alpha }_{\mathrm{ij}}^1=1-\frac{p_{\mathrm{ij}}}{2c_i{c}_j}$

When the SRO curves reach a stationary stage, it is considered that the system has reached its mixing limit. The energy landscape of the system is further characterized by its configurational enthalpy and entropy values. In the below equation, individual atoms and binary pairs are considered as the compositional units that contribute to the entropy; Z is the number of nearest neighbor atoms, and X_i, X_j and X_ij are the molar fraction of element i, j and i-j pairs (including i=j) in the simulation cell [49]. The average mixing enthalpy contributed by an element i is defined as shown below.

$\begin{array}{cc}{H}_{\mathrm{conf}}=\sum n_{\mathrm{ij}}·{ϵ}_{\mathrm{ij}}& \mathrm{Eq}.7\end{array}$ $S_{\mathrm{conf}}=-k_B\left\{\left(Z-1\right)\sum \left(X_i·\ln X_i-X_i\right)-\frac{Z}{2}\sum \left[X_i{X}_j·\ln \left(X_i{X}_j\right)-X_i{X}_j\right]+\left(\frac{Z}{2}-1\right)\right\}$ $\begin{array}{cc}\stackrel{\_}{{ϵ}_{\iota }}=\frac{\sum {ϵ}_{\mathrm{ij}}}{\left(\#\mathrm{of}\mathrm{elements}-1\right)}& \mathrm{Eq}.9\end{array}$

In the above example embodiment, how the driving forces contributed to the steady-state phases was analyzed by examining the relative mixing paces of Ni—Co, Cr—Ni, and Cr—Co pairs. While the mechanical driving force works towards a chemically random mixing state in a single phase through mechanical shearing, the chemical driving force promotes preferred low potential bonding and thus an ordered elemental distribution through thermal diffusion. According to the above equation, a lower enthalpy of mixing for a pair (ΔH_ij) leads to faster mixing under chemical driving forces. Conversely, a lower relative hardness of a pair (Δ_ij) results in faster mixing under the mechanical driving force. For NiCoCr, the mixing order of elemental pairs has an exactly opposite trend under either driving force: in chemical mixing, the mixing speed order is Cr—Ni>Cr—Co>Ni—Co, whereas in mechanical mixing, the order is Cr—Ni<Cr—Co<Ni—Co. Three types of mixing mechanisms and their corresponding steady-state phase(s) are defined according to their characteristic relative speed of mixing among elemental couples.

In view of the above described examples, under the guidance of Monte Carlo model and data collection, a new kind of mechanically driven HEA was designed: equiatomic CrMnFeCo HEA coating with a modified mechanical alloying approach, which is referred to as Surface Mechanical Alloying and Consolidation (SMAC). The simulation shows that such element choice will produce a single solid solution HEA and the goal is to validate it with experiment and probe the properties of this alloy.

SMAC centers around the synthesis of nanocrystalline high entropy alloy (nc-HEA) coatings for structural applications. In system and methods described herein, repeated impact-induced plastic deformation is utilized to force mixing-alloying and consolidation of elemental metallic powders into thick nc-HEA coatings concurrently. There is no other known approach that could produce coating with similar properties with similar efficiency.

SMAC is based on a mechanical alloying method called “ball milling.” FIG. 16 shows the schematic of the SMAC process and the block diagram of it. A milling vial is composed of vial, cap, lid, milling media, and so on. Shown in FIG. 16b at the bottom, before the mechanical alloying, the metal powders and milling media, such as milling balls, are loaded into the vial and sealed by lid and cap. During the alloying, the milling vial will be shaken by the milling machine with high energy and at a high frequency. With the collision among the powders, milling media, the powder particles are broken and grain size decreases. Meanwhile, different powders are alloyed together to form a new nc alloy powder. For example, the powders are trapped between the milling media and sheared repeatedly, mixed into HEA powder, and consolidated into a coating strongly adhered to a substrate.

Differently, instead of just obtaining the powder, SMAC requires some modifications to the milling vial. As shown, the lid of the vial is changed by a metallic substrate. The substrate is the material that one wants to make coating on. In addition to simple alloying, the milling media (also known as milling balls) would peen the alloyed material onto the substrate and consolidate it into a coating more than 100 μm. The modification one needs to do with the milling vial is minimal: first one needs to make his target substrate into a disc that has the same dimensions as the lid. Additionally, there should be sealing rings between the substrate disc and the milling vial to prevent leaking. In exemplary experiments the high entropy alloys (alloys that have four or more principal elements) coating was successfully synthesized onto a nickel substrate and a stainless steel substrate. CoCrFeMn HEAs coating is used as an example herein to show the synthesis procedure.

In an example embodiment, the modification was done on a SPEX 8001 milling vial, and is demonstrated in a schematic in the figures. As shown in FIG. 16b, the traditional SPEX 8001 milling vial is composed of a vial, a lid, and a cap. In the shown experiments, the lid is taken out and and replaced with a own metallic substrate, which is a nickel disc (99.6% purity, 48 mm in diameter and 3 mm in thickness). A rubber ring is added between the disc and vial to secure leak proofness.

In an example embodiment, the principal elements used to process RHEA coatings are Ti, V, Zr and Ta powder particles with high purity (≥99.9 wt. %). In an example embodiment, Zr was purchased from Sigma-Aldrich, and Ti, V and Ta were purchased from Changsha TIJO Metal Material Co., Ltd. China. The morphology of these powder particles is shown in FIG. 3a (Ti powder), FIG. 3b (V powder), FIG. 3c (Zr powder), and FIG. 3d (Ta powder). Ti, V, and Ta powders show a spherical shape, and Zr powder exhibits an irregular shape. The nominal particle sizes of Ti, V, and Ta powders are in the same range spanning from 50-150 μm, and Zr powders are smaller than 149 μm (−100 mesh). A total of 3 grams of equiatomic Ti, V, Zr and Ta powders were mixed with 30 grams of 440 C stainless steel milling balls (with diameter of ˜4 mm) in a hardened stainless-steel vial and sealed in a glove box with a highly purified argon atmosphere.

In an example embodiment, a Retsch ball milling machine (Verder Scientific, Inc.) was used to mix these powders. The original Ti, V, Zr, and Ta powders were pre-milled for 12 hours with a shaking frequency of 30 Hz (˜1800 rpm) (FIG. 17a). This shaking frequency (or ball milling speed) was also used during the SMAC process at both room and cryogenic temperatures. After premilling, disk-like (10 mm diameter and 5 mm thick) ferritic/martensitic steel substrates (ASTM A387 Grade 91, American Alloy Steel, Inc.) were placed inside the vial in Ar atmosphere (FIGS. 17b and 17c). This steel was selected for its optimal combination of strength, ductility, and toughness, attributed to its tempered martensitic microstructure. The ball charge ratio is initially ˜8% and increases to 11% during the SMAC process. For room temperature milling, to minimize the temperature rise within the vial, milling was conducted for 10 minutes followed by a 5-minute room temperature cooling. For cryogenic milling, liquid nitrogen (LN) is used to cool the vial continuously throughout the entire premilling, milling, and cooling processes. A 10-minute milling time is maintained for each cycle for cryomilling, while the cooling time was reduced to 0.5 minutes due to the superior cooling efficiency of liquid nitrogen. As the vial shaking begins, coating formation initiates (FIG. 17c). With continued SMAC processing, coating thickness progressively increases due to layer build-up (FIG. 17d).

The phases of the powders and coatings are characterized using X-ray diffraction (XRD) technique (Bruker-D8-Powder-Diffractometer). XRD measurements were performed using a Cu Kα source (wavelength ˜1.54 Å) with a scanning rate of 0.001 rad/s, under 25 kV voltage and 40 mA current. The RHEA coating sample is then cross sectioned and characterized the microstructures with a scanning electron microscope (SEM, Tescan Mira) equipped with energy disperse spectroscopy (EDS). The hardness of the RHEA coating cross-section was measured using an Alemnis Berkovich nanoindenter at a strain rate of 0.1 s-1 and a nominal displacement of 1 μm. For the RT processed RHEA coatings, nanoindentation tests were conducted at distances of 20 μm, 50 μm, and 80 μm from the interface, with five repetitions performed at each location. For the CT processed RHEA coatings, five repetitions were conducted at a position 40 μm from the interface. Each repetition for both RT and CT processed coatings was spaced 20 μm apart.

In another example embodiment, mechanical alloying is used to produce nc NiCoCr alloy powders. Elemental powder of Ni (˜50 μm), Co (≤105 μm) and Cr (≤74 μm) were loaded into a milling vial along with stainless-steel milling balls at 10:1 ball-to-powder weight ratio. The vial was then shaken by a ball milling machine (Cryomill, Restch) at a 30 Hz constant frequency. The processing was conducted at room temperature, with the machine stopped for 5 minutes after each 10-minute MA to avoid excessive heat. During and after MA, X-ray diffraction (XRD) was used with D8 Bruker diffractometer to determine the phase evolution process and its steady state. Samples were examined after every 30 minutes of processing from 1 hour to 6 hours. Grain sizes and lattice strains were calculated by Williamson and Hall method.

HEAs with single or multi-phases will behave differently in terms of mechanics, thermodynamics, and other areas. Therefore, the prediction of phase composition about HEA is always an appealing topic in the HEA area. There are plenty of papers discussing the fabrication of HEA by traditional casting methods, and one will find out that in those literatures most of the phase prediction rules for casting will fail when it comes to HEA fabricated by Mechanical alloying (MA), and by the described method, SMAC. For example, according to Valence electron concentration (VEC) rule, if the valence electron concentration of the high entropy alloy (HEA), which is defined as VEC=Σ_i=1ⁿc_i(VEC)_i where the c_i and (VEC)_i are the concentration and VEC for individual element i, respectively, is larger than 8, single face-center-cubic (FCC) phase exists. If it is smaller than 6.87, then a single body-center-cubic (BCC) phase exists. An FCC+BCC dual phase will be obtained if VEC falls in between 6.87 and 8. However, the VEC plot of MAed HEA and the described SMACed HEA coating shows no rules, which is given in FIG. 2a. FIG. 2a shows prediction of the phase composition after SMAC by a VEC model: red, green, and blue areas are the areas that will produce FCC single phase, FCC+BCC multi-phase, and BCC single phase areas, respectively. FIG. 2b shows prediction of the phase composition after SMAC by a STDS model: red, gray, and blue areas are the areas that will produce multi-phase, multi-phase or single phase, and single phase areas, respectively. Dots are experimental datapoints. Stars are for data points a first trial: the equiatomic CoCrFeMn nc-HEA coating on nickel substrate and another two additional verifications.

Based on the understanding of MA and SMAC, the rules for melting-based HEA may only focus on the equilibrium states but ignore the kinetic behavior in MA. Provide here a semi-empirical method, standard deviation of strength (STDS), for users to roughly extrapolate the phase composition of HEA before doing experiments. The STDS, compared with VEC and other methods, serves better in phase prediction of not only SMACed HEA coatings, but also of all MAed HEAs. The equation of STDS is given as follows:

$\mathrm{STD}=\sqrt{\sum _{i=1}^n\frac{\frac{{c_i\left(S_i-{\stackrel{\_}{S}}_w\right)}^2}{\left(n-1\right){\sum }_{i=1}^n{c}_i}}{n}}$

in which c_i is the concentration of individual element i, the n is the total number of elements added into the ball milling vial, S_i is the strength of the elemental material i at nanocrystalline state, and the S_w is the weighted average strength of HEA calculated by Σ_i=1ⁿc_iS_i. This theory is based on previous research probing the influence of difference between Hardness of two materials in a binary MA system. The fundamental idea is that during the ball milling, if the discrepancy between hardness of milled metal is too large, then only the softer phase will bear the total deformation, and single-phase solid solution can never be achieved due to the strain localization. Standard deviation of strengths shows how the strengths of elemental material deviate from the average value and therefore, to some extent, can also predict the deformation situation in MA of HEA Data was collected from literature about MAed HEA and a STDS plot was drawn in FIG. 2b.

A trend may be noticed that nearly all of multiphase MAed HEAs are distributed in the area where STDS is larger than approximately 1.44, and all Single phase MAed HEA, no matter if they are BCC or FCC, are distributed in the area in which STDS is smaller than approximately 2.05. The area in between is the so-called transition area, where the phase composition may not be dominantly controlled by the STDS and either single or multi-phase results will be obtained. To further validate the proposed model, two SMAC experiments have been done on the same nickel substrate but with different elements powder: equiatomic TaCrAlCo powders and NiCrCu1.5Ta. VEC calculation shows that this HEA would produce a single BCC phase alloy and FCC alloy, respectively, but the STDS model predicts that multi-phase coatings should be synthesized. XRD analysis supported the latter model: there were two BCC main phases in TaCrCoAl alloy, and four main phases in the NiCrCu1.5Ta alloy, respectively, after the same 20 hour SMAC.

In an example embodiment, after finalizing the powered for SMAC based on the STDS model and design application requirements, how much powder does one need for coating synthesis is the next question. In order to obtain a coating of more than 100 μm in thickness, it was determined the mass of the powder in the milling vial should be around 2-3 times of coating's mass on the material. Here a first trial, the equiatomic CoCrFeMn nc-HEA coating on nickel substrate, is used to describe the operation steps. In an example experiment, the coated area is around 11.3 cm² on the substrate. Based on the approximation of the density of the expected CoCrFeMn coating, the calculated mass of powder needed is around 2˜3 grams.

In an example embodiment, in order to obtain a coating of more than 100 μm in thickness by SMAC in a SPEX 8001 milling vial, the mass of the powder in the milling vial should be around approximately at least 2-3 times of coating's mass on the material. In one example, a cantor-like combination (equiatomic CoFeCrMn on a nickel substrate) is used to probe the formation process and properties of SMACed nc-HEA coating. For the example case, the coated area is around 11.3 cm². The approximation of HEA's density is calculated simply by

ρ_app=Σc_iρ_i

in which c_i and ρ_i are concentration and density of elemental powders, respectively. Therefore, the total amount of powder needed is expected to be approximately 2-3 grams. Metal powders with the same stoichiometry were loaded into the milling vial in a glove box in a total amount of approximately 3 g: 0.76 g cobalt powder (99.9% purity, ≤150 mesh), 0.72 g iron powder (99% purity, ≤200 mesh), 0.71 g manganese powder (99.6%, 140-325 mesh), and 0.68 g chromium powder (99.94%, ≤200 mesh). The milling balls were added into the vial with a ball to powder ratio of 10:1. Then, the lid of the milling vial was replaced by a nickel substrate disc (99.6%, with a diameter of 48 mm and a thickness of 3 mm). The surface was grinded by sandpapers with different grits (120-400-600-800-1200) to a mirror-like surface for oxidation and dirt removement. A robber O-ring was added between the vial and the disc for sealing and finally the cap was screwed tightly.

In an example embodiment, a SPEX 8000M mixing machine was used to shake the milling vial. During the SMAC, the powders collide with each other, with milling balls and with vial's chamber, finally alloying and being adhered onto the substrate. To reduce the potential influence from the temperature, increase during milling, when every 10 minutes' milling was finished, the machine was stopped for 5 minutes. After 30 hours, a nc-HEA coating on substrate SMACed for 20 hours was achieved. Also, 5 h, 10 h, and 15 h's SMACed coatings are collected for characterization.

In an example embodiment, coated specimens were cut by the Allied TechCut5 Precision High Speed Saw into small pieces for characterization experiments. Samples were first analyzed by X-ray diffraction (XRD, Cu-Kα radiation, Bruker D8 Advance ECO powder diffractometer) for phase and microstructure information obtaining. The grain size and lattice strain were analyzed by the Williamson-Hall method. The cross-section of the samples was grinded by sandpapers with 120, 400, 600, 800 and 1200 grits and then polished by diamond suspension with 3 and 0.5 μm and by silica colloidal with 0.08 μm on an Allied Multi-prep polisher. Scanning electron microscope (Tescan Mira3 SEM) and energy-dispersive spectrometry (Bruker XFlash EDS) were applied to characterize the morphology and the elemental composition of the coating, respectively. The mechanical properties of the coating were tested on polished cross-section of the samples by nano-indentation with a Berkovich tip. The tests were strain rate control (0.1, 1, 10 and 100 s-1) and the indentation-depth was set to 1 μm.

The strain rate sensitivity (SRS) of the coating was calculated by the equation

$m=\frac{\partial \ln \sigma }{\partial \ln \stackrel{.}{\epsilon }}$

in which the flow stress σ was substituted by hardness and {dot over (ε)} is the strain rate.

In some embodiments, the strength of the alloying elements shows influence on the phase composition of the SMACed sample. It was found that TaCrAlCo and NiCrCu1.5Ta coating on Ni substrates after SMAC with the same parameters are multi-phase structures (see FIG. 32), which were already predicted by standard deviation of strength model. FIG. 32a shows the XRD pattern and phase analysis on the TaCrAlCo and FIG. 32b shows the NiCrCu1.5Ta coating on Ni substrates. From this, multi-phased structure is confirmed.

In an example embodiment, SMACed specimens were heat treated isochronally at various temperature from 300 to 900° C. for 1 h and isothermally at 900° C. for 1, 2, 3 and 4 h for thermal stability probing. Heat treatments were done in a vacuum furnace, for example, a Lindberg High Vacuum Furnace in some embodiments, and specimens were left in the furnace for cooling down.

XRD patterns of the SMAC powders and SMACed coating with different durations are shown in FIG. 18. The X-ray diffraction (XRD) patterns in FIG. 18 show the evolution of phases during the SMAC process. As shown, the process starts with distinct multi-element phases in the form of a mixture of elemental powders. The repeated impact-induced plastic deformation during SMAC mixes the elemental powders to the extent that after 20 hours, a single FCC HEA phase is left. The analysis of the X-ray results shows that grain size in the HEA alloy is ˜25 nm and the lattice constant is around 3.60 Å, confirming that the coating is indeed nc-HEA. In particular, as shown in the plot, before the SMAC, there are peaks of elemental powders (CoFeCrMn). After 5 h SMAC, a lot of peaks disappeared and there are two phases remaining, which are the high entropy alloy peaks and Nickel phase peaks, suggesting the ongoing mixing. With the increase of the SMAC duration, the intensity of the nickel peaks decreased, and the HEA peaks got broaden, which are connected to the thickness increase of the coating and its grain refinement, respectively. After 20 h SMAC, the nickel phase peaks disappeared, leaving a single-phase FCC HEA coating on the surface. The evolution of lattice strain and grain size during SMAC is shown in FIG. 19. The ultimate state of the coating has a nano-crystallite grain size of approximately 25 nm, and a lattice constant as approximately 3.60, which is exactly the same as the Cantor HEA alloy.

Considering the detecting depth of X-ray is below 100 μm, the gradual disappearance of nickel phase peaks in the XRD patterns could be reasonably explained by the SEM plots. As proof of concept, FIG. 20 shows the SEM image of a CoCrFeMn nc-HEA coating realized through the SMAC process. As can be seen in the figure, the thickness of the coating is more than 100 μm, and the coating is basically defect free. From the images the crystal structure cannot be seen, confirming the nanoscale grain size proved by XRD analysis.

The EDS analysis of the as-SMACed coating, as show in FIG. 22, illustrates the uniform distribution of the elements and confirmed the single-phase microstructure. All four elements are randomly distributed into the coating. The interface of substrate and coating is wavy, showing the sever plastic deformation during SMAC. The chemical mapping of the coated alloy using energy dispersive X-ray spectroscopy shows complete mixing with no chemical segregation.

FIG. 23a shows the cross-sectional microstructure of an example embodiment of a TiVZrTa RHEA coating processed at RT, which is dense and around 100±20 μm thick. As show, a wavy interface was observed between the RHEA coating and the steel substrate due to the heterogeneous plastic deformation by stochastic collisions during the process. FIG. 23c shows a small amount (˜1 vol. %) of Fe which results from the fragments of the steel substrates brought about by the severe mechanical shearing. Due to the relatively smaller amount of Fe, the discussion is limited to the major phases associated with Ti, V, Zr and Ta in the following sections. FIGS. 23e, 23g, 23i and 23k show the distribution maps of the major refractory elements which confirm layered welding of the material enriched in one of the primary elements such as Ti, V Zr, and Ta, respectively. As the coating was built up, it was observed that better mixing of the powder exhibited by a decrease of the concentration areas of individual elements.

In the example embodiment, the CT processed coatings are also dense and entail a thickness of 50±20 μm (FIG. 23b). The smaller thickness compared to the RT processed counterparts is probably due to the slower consolidation of powders and the high tendency of the fracturing in already formed coatings under much lower temperatures. Although some microcracks were observed in the outermost layer of the coating (FIG. 23b), no significant microcracks were detected in other regions of the cross-section. The studied cross-section of the CT processed coatings entails a ˜4 vol. % of Fe which might come from the shearing of steel substrates, stainless steel milling balls and/or the steel vials. Despite the presence of Fe, the CT processed TiVZrTa coatings exhibit more homogeneous mixing from the interface to the top layer (FIG. 23b) compared to those processed at room temperature. The EDS mappings shown in FIGS. 23f, 23h, 23j, and 23l further confirm this higher level of elemental homogeneity as no major elemental islands were observed, unlike the RT processed RHEA coatings. It is believed this is the first demonstration of a mechanically driven TiVZrTa RHEA coating that achieves near-homogeneity.

Show in FIG. 26, a TEM analysis was also applied to the as-SMAC materials. FIG. 26a is TEM bright field image, the contrast comes from the different orientation of the grains, showing their nanoscale size. The not obvious boundaries is because of the grain's severe deformation. FIG. 26b is a HRTEM bright field image. Corresponding SAED image is shown in the insert. For large grain samples, the SAED plots will contain plenty of dots, illustrating the arrangement of lattice planes in reciprocal space. The appearance of rings implies diffraction of lots of grains and thus, a fine grain structure. The distribution of the ring demonstrates an FCC lattice structure in the HEA and every one of the rings is assigned a specific lattice plane.

Nanoindentation is used to measure the strength of the fcc nc-HEA coating processed with SMAC. FIG. 28 compares the strength of an example embodiment of the material with HEAs processed with other techniques. In the exemplary plot, it is noted that HEA processed with SMAC possesses the highest hardness: 8.85±0.2915 GPa Using nanoindentation, a hardness of 8.85±0.29 GPa was measured at quasi-static state (0.1 s-1) for the nanocrystalline HEA coating. Another example figures, FIG. 27, shows a map of the hardness vs grain size of FCC HEAs produced by different methods, and calculation of strain rate sensitivity m. The comparison with FCC HEA alloys synthesized by other methods demonstrates its excellent strength (FIG. 27a). And the SRS calculation shown in FIG. 27b gives a relatively low value of approximately 0.118.

FIG. 27A compares the strength of he material with HEAs processes with other techniques. The strength of the material is larger than cast and magnetron-sputtered HEAs by factors. Second, although it only slightly outperforms the cast followed by high pressure torsion (cyan) family and the mechanically alloyed (blue) family of materials, it is noted the following significant advantages in the material. Both casting followed by high pressure torsion and mechanical alloying requires at least two energy intensive steps (Mechanical alloying will get you only powder so an additional consolidation step is needed) whereas SMAC is a single step process. A slightly better performance has been achieved consuming much less energy per unit mass of the product. The SMAC has already consolidated the powder into a coating again offering a significant advantage on the readiness front for structural applications.

The relative excellent mechanical performance is also sustainable under different conditions: in order to probe the thermal stability of SMACed coating, one-hour isochronal heat treatments at 300° C., 450° C., 500° C., 600° C., 800° C. and 900° C. were applied on an example embodiment of the material. As shown in FIG. 31a, XRD patterns demonstrate that the grain size of the SMACed HEA is still in nano-size and that in addition to the high entropy alloy phase, there are also several diffracted signals coming from segregated phases: when temperature is below 500° C., a weak signal for a second body center cubic (B.C.C.) phase was detected. When temperature increases to around 500° C., a tetragonal σ second phase arose in the patterns. The second phases strengthen the material such that the hardness even increases with the heat-treating temperatures instead of drops due to the heat-induced recovery, as shown in FIG. 31b, and these phenomena have been reported from the research of bulk similar nc-HEAs. Nevertheless, when temperatures is larger than 500K, the softening effect eventually outcompeted the hardening coming from second phase, and the hardness dropped down to 5.59±0.38984 GPa after the 900° C. heat treatment.

The XRD patterns of the example heat treated samples after 1 h of isochronal heat treatment (HT) under different temperatures are shown in FIG. 29. It demonstrates that in addition to the high entropy alloy phase, there are also several diffracted signals coming from segregated phases after annealing: when temperature is 450° C., a weak signal for a second body center cubic (BCC) phase was detected (The peaks become more obvious when the duration was elongated to 8 h under 450° C., for which the XRD result is shown in FIG. 30). When temperature increases to around 500° C., a tetragonal σ second phase arose in the patterns. Both of the above second phases are found to be Cr-rich phases. The existence of the σ phase continues to the 800° C. heat treatment. When the temperature is higher than 900° C., all second phases are redissolved into the matrix and a new carbide phase arise, which is attributed to the contamination of carbon from the milling vial's stainless steel vial.

Another example embodiment is shown in FIG. 24. FIG. 24a demonstrates the XRD measurements of an example embodiment of the RT processed coatings including the phase evolution from original powders to the stabilized multi-phase RHEA coating after SMAC up to 36 h. A gradual alloying coupled with the annihilation of individual elemental peaks was observed. After 6 hours, the Ti and Zr peaks begin to diminish. By 12 hours, all Ti peaks and most of the Zr and V peaks have disappeared. Following an additional 12 hours, the Zr peaks vanish completely. The Fe peak corresponds to the small amount (˜1 vol. %) of steel fragments coming from the substrates as shown in FIG. 23b. At 36 hours, the phases begin to stabilize, forming a multi-phase structure consisting of a near-equiatomic phase, a Ta-rich phase, and a V-rich phase, with their average compositions provided in FIG. 25. The average phase fractions for the stabilized near-equiatomic, Ta-rich, and V-rich phases were calculated to be 68%, 11%, and 21%, respectively. A comparable multiphase structure has also been observed in arc-melted TiVZrTa RHEAs, though with variations in phase compositions.

In the example embodiment shown, while three BCC phases were also observed in arc melted TiVZrTa RHEA, the lattice parameters are quite different from what was achieved in this work. Here, the V-rich phase (lattice parameter of 3.033 Å) results from the incomplete dissolution of V exhibiting high hardness. The lattice parameter of the near-equiatomic phase (3.310 Å) and the Ta-rich phase (3.303 Å) are very similar to that in pure Ta powders (3.301 Å) but much larger than those in original Ti (2.951 Å), V (3.03 Å), and Zr (3.232 Å) powders. It is possible that most of the Ti, V and Zr atoms are absorbed into the Ta lattices to become solid solutions. Transmission Electron Microscopy (TEM) will be used to further confirm this in future studies. This occurs for two reasons, i.e., first, Ti and Zr have a higher thermal diffusion rate into the Ta lattice compared to the reverse; second, the higher hardness of Ta results in a much slower shear-induced diffusion into other softer elements (Ti, V and Zr).

FIG. 24b shows that under cryogenic temperatures, the peak evolution from the initial powders to 12 hours of milling closely mirrors the trend observed in room temperature processing, with a somewhat accelerated dissolution rate at 12 h. The CT processed RHEA coating at 24 h demonstrates a single-phase BCC solid solution plus some small amount of Fe which is in contrast to the multiple BCC phase structure formed in the RT processed coatings at 24 h and 36 h. This single-phase structure in 24 h CT processed coating is justified by the XRD peak deconvolutions showing no valid peaks other than the single-phase BCC. The formation of single-phase BCC solid solution is attributed to the more homogeneous mixing under cryogenic conditions as shown in FIG. 23b. However, after an additional 12 hours of milling (36 h coating), part of the BCC solid solution decomposed into multiple phases including Zr, V and V₂Zr. This decomposition under cryogenic conditions can be attributed to the extensive lattice distortion or solid-state diffusion caused by severe plastic deformation which results in the breakdown of the supersaturated BCC single phase solid solution.

As predicted by the previous Monte Carlo model, in some embodiments, a single solid solution phase of CrMnFeCo HEA may be achieved during the alloying process. As described above, it can be observed that HEA phase was also attached onto the nickel substrate and became thicker and thicker during 5-20 h SMACing. The Monte Carlo simulation then could explain how the HEA phase formed during the first 5 h milling.

From the example embodiment of the SRO evolution plot of CrMnFeCo's simulation, shown in FIG. 33, it can be seen, the SRO of the softest couple, the Co—Mn pair, drops first and most swiftly among the SRO curves, and SRO of other couples that contain the soft materials also go down quickly. This result implies that at the first stage of the SMAC, the deformation was mainly borne by the soft materials. But later, hardest Cr phase was finally mixed by the continued shear. In the dropping SRO, the pairs with harder Cr or Fe elements are the last to drop. This also aligns with the fact that in the simulated plots, the Cr atoms are the final phase that eliminates segregation and dissolve into the solid solute matrix. During the first 5 h of SMAC process, all metal powders are fused into the matrix in ascending order of hardness and form single phase solid solute HEA. In the following 5 to 20 hours, the HEA phase gradually thickens on the substrate until it exceeds the detection range of XRD, reaching a thickness of over 100 μm.

In order to understand the reason behind the ultra-high strength of the coating, the contribution of different strengthening mechanisms will be discussed. Normally, a single phase nc-HEA shows the following strengthening mechanisms: grain size effect and solid solution strengthening. Here a strength model is adopted proposed by R. B. Figueiredo et. al and Varvenne et. Al:

$\sigma ={\sigma }_{\mathrm{ss}}+{\sigma }_{\mathrm{gs}}={\sigma }_0\exp \left(-\frac{\mathrm{RT}}{0.51\Delta E}\ln \frac{{\stackrel{.}{\epsilon }}_0}{\stackrel{.}{\epsilon }}\right)+\sqrt{\frac{3{\mathrm{GK}}_{B}T}{2\times 1.67{\mathrm{db}}^2}\ln \left(\frac{{\stackrel{.}{\epsilon }\left(1.67d\right)}^3}{10\delta D_{\mathrm{gd}}}+1\right)}$

The first term in the equation is the contribution of solid solution hardening σ_ss and second one is attributed to the nano grain size effect σ^gs. The σ₀ is the solid solution strength at 0K, ΔΣ is the activation energy of the barrier, {dot over (ε)}₀, is a reference strain rate, G is the shear modulus, dis the grain size calculated from XRD analysis, b is the grain size, δ is the thickness of grain boundaries and D_gd is the grain boundary diffusivity. The basis of σ_ss is that the overcoming of dislocation to the solid solute atom follows an Arrhenius model:

$\stackrel{.}{\epsilon }={\stackrel{.}{\epsilon }}_0\exp \left(-\frac{\Delta E\left(\sigma \right)}{\mathrm{RT}}\right)$

and the σ_ss is based on the assumption that in the nanocrystalline regime, the speed of dislocation generation due to grain boundary sliding should be the same as the speed as it climbs along the opposite grain boundary and gets annihilated.

It is noted that, in some embodiments, the assumption was made that the Hardness is around 3 times the flow stress. In the as-SMACed sample, the change of the strain rate of the nano-indentation test could verify the model from {dot over (ε)} angle but the influence of grain size d could not be validated. Therefore, it was decided to heat treat the as-SMACed coating and get samples with different grain sizes for the validation. Based on research on the thermal stability of cantor HEA, the multi-phase region in the cantor-like HEA was carefully avoided and finally the heat treatment parameters were chosen as 1100° C. with 2 min and 45 s. After the heat treatment, the sample was left in the furnace for cooling down. XRD analysis demonstrated a single HEA phase, and the grain size was calculated to be approximately 164 nm. The comparison plot between the strength model and the experimental values from both samples was then plotted, as shown in FIG. 34.

Comparison between the example model embodiment shown and experimental datapoints demonstrates an excellent prediction ability: the mechanical behaviors under the changes of both grain size and strain rate could be well-predicted by the model, which implies that the grain size effect and solid solution strengthening are the two main mechanisms in the hardness of second-phase free nc-HEA. According to the equation, the grain size shows no influence on calculation of the solid solution hardening. Therefore, for both of the HEAs with different grain size, the solid solution hardening contribution to the hardness should be the same: at 0.1, 1, 10, 100 s⁻¹: 321.7 MPa, 358.0 MPa, 400.7 MPa, and 446 MPa, which is similar to the data in literature. Compared to the total hardness, the contribution from solid solution hardening is not large, but it is a stable hardening effect, regardless of the change of grain size.

Strain rate sensitivity (SRS) of strength reflects the deformation mechanisms in materials. Through calculation, the SRS of the second-phase free nc-HEA coating with 25 and 164 nm grain sizes are 0.0118 and 0.0123, respectively. The model's prediction gave the similar result: 0.0116 and 0.0127, respectively. Small SRS implies that the coating mechanical behavior is insensitive to strain rate change and the increasing trend of the SRS is also different from other traditional single phase FCC materials. The abnormal values and trend of the SRS in FCC single phase HEA has been noticed and widely discussed. An assumption was adopted from that it is due to the sluggish diffusion in the solid solution. The strong solid solute effect in the HEA makes the dislocation movement to be sluggish, creating a wavy dislocation and slowing down its velocity. Meanwhile, the dislocation moving in ultra-fine or nano grains meet less obstacles, such as dislocation forests, cell structures, etc., and will be ab-sorbed directly by the grain boundary on the opposite side. The absorption of the dislocation at grain boundary could be described as a probability event:

$P_{\mathrm{dis}}={\left[1-{\left(1-e^M\right)}^N\right]}^J$

M is a constant mobility factor, N the number of attempted jumps by atoms within dislocation core to grain boundaries during an average time, and J the total number of atoms on the dislocation core jumping into grain boundaries. The slow dislocation velocity secures sufficient time for the grain boundary to absorb dislocations, resulting in large P_dis at the same strain rate compared to dilute alloys and as a result, less dislocation impinges at the same unit time. Therefore, for a given strain rate interval, the strengthening effect in FCC nc-HEA is weaker. But when the grain size increases, the obstacle-free pathway for dislocation to move to grain boundary does not exist anymore, the dislocations interact with each other more and more often and less with grain boundary and thus SRS increases.

In some embodiments, through Williamson-Hall analysis, the evolution of grain size with the heat treatment under different temperature was calculated, shown in FIG. 36a. Through comparison of fractional increase of grain size to other thermal stability research on HEAs, such as other Cantor-like HEA with pure Ni, as shown in FIG. 36b, it can be seen that the mechanically driven alloy possess an excellent thermal stability. The appearance of different second phase shown previously is considered to be the main barriers for the grain growth in addition to HEA's own sluggish diffusion effect. To quantify the rate of grain growth, an exponential grain growth model has been applied:

$D^n-D_0^n=K_0\exp \left(-\frac{Q_{\mathrm{act}}}{\mathrm{RT}}\right)t$

where D, D₀, are the current and initial grain size, respectively. K₀ is a pre-exponential constant, _act is the grain growth activation energy. R is the gas constant. T is the temperature and t is the time. Using the data from 900° C. isothermal heat treatments mentioned above and ignoring the initial grain size, the grain growth exponent could be obtained by n=∂ ln t/∂ ln D. As shown in FIG. 38a, which shows the calculation of grain grown exponent n, the grain growth exponent is approximately 3.91. The comparison among grain growth exponents of different materials and the meaning of different n values is shown in FIG. 38b. Usually, an exponent around 4 is the implication of second phase retarding the grain growth and the previous XRD patterns confirmed the calculation, reaffirming the contribution of second phase to the thermal stability. Once the grain growth exponent is finalized, the value _act is then available. When time is fixed (namely the isochronal heat treatment), through linear fitting of ln(D_n−D₀ⁿ) over 1/T, FIG. 38c demonstrate the calculation process of grain growth the activation energy _act. Similar to other thermal stability research on HEA, two different _act have been calculated: for low temperature regime, the _act is often low associated with a rearrangement of unstable grain boundary configurations without significant grain growth and a 27.4 kJ/mol _act for the material from 300-600° C. coincides with this statement. When in terms of high temperature regime, the energy barrier to overcome is no longer a relaxation process. The 118 kJ/mol value is lower than the similar alloys (˜300 kJ/mol) which the grain growth is often controlled by the bulk diffusion. Nonetheless, it is closer to the grain boundary diffusion energy. Therefore, this low level of _act is attributed to the carbide phase precipitation and coarsening along the grain boundary.

The exceptional mechanical and thermal performance of the nc-HEA coating presented here stems from the characteristics of the SMAC process. SMAC is a solid-state deformation-based approach to making materials. The repeated shearing events at the atomic scale happening during the process force elemental metals to mix. At the same time, the accumulation and multiplication of dislocations (carries of plastic deformation) result in grain refinement down to the nanoscale. The extremely small grain size in the material renders it mechanically strong and the severe distortion of the lattice and the small amount of second phase emergence at high temperatures slow down diffusional processes and thus grain coarsening. No other processing routes or even combination of processing routes can produce HEAs with these attributes at a competitive level of normalized cost or energy spent.

In some embodiments, applying the Williamson-Hall equation on the XRD curves, as shown in FIGS. 24a and 24b, is used to calculate the evolution of grain size and lattice strain with increasing milling or SMAC duration, as shown in FIG. 37. The results indicate that as milling time increases, grain size decreases and lattice strain increases under both RT (FIG. 37a) and CT processing conditions (FIG. 37b). With the same milling time, CT processing results in a more substantial reduction in grain size and a greater increase in lattice strain in powders or coatings compared to RT processing. Notably, the TiVZrTa coating exhibits a significantly higher lattice strain (˜2.6% at room temperature and ˜3.0% at cryogenic temperature) compared to the original Ti, V, Zr, and Ta powders, which show an average lattice strain of only ˜0.03%. This suggests significant lattice distortion occurs following the milling or SMAC process.

In the example embodiment shown, the grain size of the CT processed RHEA coating at 24 h is ˜5.6 nm which is 30% smaller than that of the RT processed sample at 36 h (˜11 nm). This grain refinement can be supported by a dislocation model proposed in which the minimum grain size achieved during ball milling is a result of the equilibrium between the dislocation structures introduced by the severe deformation and thermal recovery. That is, lower mechanical alloying temperatures lead to smaller nanocrystalline grain sizes, following a relationship between minimum grain size, d_min, and the mechanical alloying temperature, T, through:

$d_{\min }\propto \frac{e^{-\frac{\beta Q}{4\mathrm{RT}}}}{T^{0.25}}$

where β is a constant (0.04), Q is the self-diffusion activation energy, and R is the gas constant. Using this equation, for the shown example embodiment, the theoretical ratio of stabilized grain size of coatings processed at room and cryogenic temperatures is calculated to be ˜2.2 which is close to the experimental ratio of ˜2.0.

The nanocrystalline grain sizes should result in a high hardness in TiVZrTa RHEA coatings processed at both room and cryogenic temperatures. Nanoindentation tests for some embodiments show that the average hardness of RT processed coatings was measured to be 10.2±1.4 GPa, while the CT processed RHEA coating exhibits a much higher hardness (13.1±0.6 GPa) (FIG. 35a). The higher hardness in the RHEA coating processed at cryogenic temperatures is caused by the much smaller grain size and more homogeneous solid solution. While higher hardness could potentially increase the brittleness, no obvious cracks were observed in the CT processed RHEA coating close to the substrate. The large standard deviation of hardness shown in the RT processed RHEA coating is due to its inhomogeneous multi-phase structure. A gradual increase of average hardness was obsevered through the thickness direction corresponding to a gradual decrease of white Ta-rich phases from bottom to top layer (FIG. 35b). Because each phase is submicron in size, while the nanoindenter tip used is much larger (˜10 μm), accurately measuring the hardness of individual phases is challenging. These measured hardnesses are comparable to those reported in a nanocrystalline film of NbMoTaW RHEA (12 GPa). What is more, the hardness of the CT processed TiVZrTa RHEA is ˜75% higher than that of its as-cast counterpart (7.4 GPa) due to the much larger grain sizes and high microstructural heterogeneity found in the latter (FIG. 35b).

The example experimental results shown and described above demonstrate that, in some embodiments, the RT processed TiVZrTa coating exhibits a multi-phase structure while the CT processed counterpart is composed of a nearly homogeneous single phase BCC solid solution. It is expected that the formation of multi-phase structure in RT processed coating is due to the dynamic competition between mechanically forced chemical mixing and thermally activated diffusion. SMAC at ambient temperature generally promotes thermally activated diffusion and recovery due to the local temperature rise caused by repetitive collisions between milling balls and powders. While the temperature rise might be small compared to the melting temperatures of the Ti, V, Zr and Ta principal elements, this enhanced thermal recovery retards the forced chemical mixing, increasing the likelihood of forming multiple phases. However, when the SMAC was performed under cryogenic conditions, the recovery processes are expected to be significantly suppressed, resulting in more significant mechanical shearing and homogeneous mixing.

In some embodiments, to reveal the phase formation mechanisms at the atomic scale for TiVZrTa coatings processed at room and cryogenic temperatures, a kinetic Monte Carlo atomistic simulations with combined mechanical shearing and thermal diffusion was conducted. FIG. 40a shows the simulated microstructure evolution of the RT processed TiVZrTa RHEA. After 105 MCS, the diffusion of Ti and Zr elements into the Ta domain was observe, which corresponds to the XRD data in FIG. 24a. Meanwhile, interface roughening between different elements under shear breaks the domains and forms islands of four elements in a multi-element matrix, corresponding to the Ti-, V-, Zr-, and Ta-rich phases in the bottom layer of the coating (FIG. 23a). The size of the elemental islands decreases as the mixing proceeds, pushing the composition towards a near-equiatomic state. A steady state is reached after about 3×10⁵ MCS, as indicated by the disappearance of elemental islands in FIG. 40 and stable CSRO curves in FIG. 41a. However, the large variations in CSRO parameters between different metal pairs shows that the equilibrium state of the RT processed coating is not a single-phase random solid solution. This corresponds to the multi-phase structures shown in FIGS. 23a and 36 h results in FIG. 24a.

In some embodiments, to further confirm the formation of three major phases in the RT processed RHEA coating, the CSRO parameters of metal pairs associated were compare with each principal element. FIG. 42a shows that the CSRO curve of TaTa pair reaches a steady state with the CSRO parameter varying between −0.02 and −0.04. This large negative deviation reveals the formation of a Ta-rich phase. Similarly, FIG. 42b shows that a V dominant phase can form which is supported by the significant negative deviation of VV pairs (−0.04 to −0.06). The larger negative deviation of CSRO parameter from zero in VV pair than that in TaTa pair corresponds to the larger fraction of V-rich phase (21%) compared to Ta-rich phase (11%). This aligns with the larger V islands shown in FIG. 40, indicating a lower mixing rate for V. FIGS. 42c and 42d show that the CSRO curves of Ti- and Zr-included pairs converge without significant negative deviation from zero, indicating the formation of a phase with a near equiatomic composition, slightly enriched in both Ti and Zr. Furthermore, the total energy change at the steady state is −3.45±0.01 kJ/mol, much lower than the energy change associated with a random single phase solid solution (−3.32 kJ/mol) calculated with a randomized equiatomic cell. This suggests that the multi-phase state is more thermodynamically stable in the RT processed sample. These observations are consistent with the three phases observed experimentally in the coating microstructure (FIGS. 23a and 24a).

FIG. 40b shows the evolution of an example embodiment of simulation cell microstructure for RHEA coatings processed at cryogenic temperatures. The steady state is reached after 5000 MCS, as manifested by the lack of apparent elemental islands. The CSRO parameter curves in FIG. 41b show that all the metal pairs reach a steady state with minimal deviation (less than 0.01) from zero CSRO parameter, indicating the formation of homogeneously mixed single phase. The single-phase formation is further corroborated by the stable energy change observed at 77 K (−1.88±0.02 kJ/mol), which closely aligns with the calculated value for a random single-phase solid solution at this temperature using (−1.88 kJ/mol). Compared to the RT case, the simulated microstructure for the 77 K case reaches the steady state more rapidly. This rapid and homogeneous mixing at 77 K corresponds to the observations that the RHEA coating processed at cryogenic temperature reaches a single-phase BCC at 24 h (FIG. 23 and FIG. 24b), while the RT processed RHEA coating at 36 h still shows multi-phase structure (FIGS. 23 and 24a).

In some embodiments, the ratio of thermal jumps to shearing steps is key to understanding the significant differences in mixing and phase formation under the two processing conditions (RT vs. CT). This ratio serves as an indicator of the competition between thermal recovery and mechanically driven mixing. A higher ratio suggests greater thermal recovery relative to mechanical mixing, favoring the formation of a multi-phase structure. Conversely, a lower ratio indicates suppressed thermal recovery compared to mechanical mixing, promoting the formation of a homogeneous single-phase structure. Specifically, the ratio of thermal jump to shearing steps is about 15:1 at RT, with the average thermal jump frequency being about 1.6×10⁴ Hz. However, this ratio is nearly zero at 77 K, as the rate of thermal jump is highly temperature dependent and thermal diffusion is negligible at cryogenic temperatures. Moreover, it takes ˜40% fewer shearing steps to reach a steady state for coatings processed at 77 K (˜3000 shearing steps) when compared to the coatings processed at RT (˜5000 shearing steps). This is because more shearing steps are needed to accommodate the thermal recovery at higher temperatures. Therefore, the suppressed thermal diffusion at cryogenic temperatures not only facilitates single-phase formation, but also accelerates mixing.

In some embodiments, the continuous forced chemical mixing and plastic straining result in the formation of supersaturated solid solution and nanocrystalline grain structure in the RHEA coating which contribute to a high hardness for coatings processed at both room and cryogenic temperatures. These high strengths suggest that the primary strengthening mechanisms for this RHEA coating are likely nanocrystalline grain boundary strengthening and solute strengthening.

In some embodiments, for grain size strengthening, a physically based model was used which considers the grain size strengthening is thermally activated. This model assumes that grain boundary sliding is the rate-controlling flow mechanism, without the formation of major dislocation substructures like dislocation cells and subgrain boundaries within the grains. External shear stresses cause extrinsic dislocations at grain boundaries to glide, leading to grain boundary sliding and activating dislocation sources at triple junctions. Dislocations then slip in neighboring grains, pile up at opposite boundaries, and build up stresses, which in turn activate dislocation climb. The yield stress of BCC RHEAs using this model can be calculated through:

${\sigma }_{\mathrm{gs}}=\sqrt{\frac{3\mu k_{B}T}{2{\mathrm{db}}^2}\ln \left(\frac{\stackrel{.}{\epsilon }{d}^3}{10\delta D_{\mathrm{gb}}}+1\right)}$

where μ is the shear modulus, b is the magnitude of Burgers vector, T is the temperature, dis the grain size, {dot over (ε)}=0.1 s⁻¹ is the strain rate during the nanoindentation tests, δ=2b is the grain boundary width, δD_gb is the coefficient for grain boundary diffusion.

In some embodiments, besides grain size strengthening, the interaction between solutes and edge dislocations in the HEAs is another primary contribution to the total strength of the HEAs. Curtin developed an analytical theory to calculate the edge dislocation based solute strengthening in BCC HEAs. This theory posits that each alloying element acts as a solute interacting with dislocations in a hypothetical homogeneous ‘average’ alloy, reflecting the macroscopic properties of the actual random alloy. The uneven distribution of solutes causes local potential energy variations, prompting dislocations to form low-energy wavy structures. Plastic flow in the RHEA thus requires thermal activation, assisted by temperature and stress, to move dislocations from these low-energy areas, overcoming significant barriers created by adjacent high-energy environments along the glide plane. This theory defines the yield strength of BCC RHEAs as a function of strain rate and temperature:

${\sigma }_{\mathrm{ss}}\left(T,\stackrel{.}{\epsilon }\right)={\sigma }_{y0}\exp \left[-\frac{1}{0.55}{\left(\frac{k_{B}T}{\Delta E_b}\ln \frac{{\stackrel{.}{\epsilon }}_0}{\stackrel{.}{\epsilon }}\right)}^{0.91}\right]$

in which

${\sigma }_{y0}=3.067A_{\sigma }{\alpha }^{-\frac{1}{3}}{\mu \left(\frac{1+v}{1-v}\right)}^{\frac{4}{3}}{\left({\sum }_i\frac{c_i\Delta {V_i}^2}{b^6}\right)}^{\frac{2}{3}}$ $\Delta E_b=A_E{\alpha }^{\frac{1}{3}}\mu {b^3\left(\frac{1+v}{1-v}\right)}^{\frac{2}{3}}{\left({\sum }_i\frac{c_i\Delta {V_i}^2}{b^6}\right)}^{\frac{1}{3}}$ $\Delta V_i=V_{0i}-V=V_{0i}-\sum _i{c}_i{V}_{0i}$

where σ_y0 is the zero-temperature stress, ΔE_b is the zero-stress energy barrier, {dot over (ε)}₀ is the reference strain rate (10⁴ s⁻¹), c_i is the solute concentrations, V_0i is the atomic volume of the refractory elements, ΔV_i is the misfit volume of the type-i solute in the average alloy, μ and ν are the isotropic alloy elastic constant, α= 1/12 is a fixed line tension coefficient, A_σ=0.040±0.004 and A_E=2±0.2 are coefficients for BCC HEAs based on materials properties (elastic constants, misfit volumes, and line tension). The total predicted yield strength can then be obtained:

${\sigma }_{\mathrm{Theory}}=\sqrt{\frac{3{\mathrm{Gk}}_{B}T}{2{\mathrm{db}}^2}\ln \left(\frac{\stackrel{.}{\epsilon }{d}^3}{10\delta D_{\mathrm{gb}}}+1\right)}+{\sigma }_{y0}\exp [-\frac{1}{0.55}{\left(\frac{k_{B}T}{\Delta E_b}\ln \frac{{\stackrel{.}{\epsilon }}_0}{\stackrel{.}{\epsilon }}\right)}^{0.91}$

In FIG. 37, the theoretical predicted hardness (H_Theory=3σ_Theory) and the experimentally measured hardness for an example embodiment of coatings processed at both cryogenic and room temperatures are compared. A relatively good match is observed between the theoretically predicted hardness and the experimentally measured hardness for coatings processed at both room and cryogenic temperatures. The small difference between theory and experiment can be ascribed to heterogeneous microstructures in RT processed coating. this difference can be attributed to a number of mechanisms not considered in the model, including the short-range order, solute-solute interactions, and dislocation-dislocation interactions for coatings processed at cryogenic temperature. Nevertheless, the agreements between theoretical and experimental results indicate that the grain size and solute strengthening are indeed the major strengthening mechanisms for the mechanically driven TiVZrTa RHEA coating processed at both cryogenic and room temperatures.

The mechanically driven nanocrystalline TiVZrTa RHEA coatings in the example embodiment manufactured in this work exhibit not only high hardness (˜13 GPa) but also considerable thickness, up to 100 μm. This unique combination of nanocrystalline microstructure, high hardness and large thickness has not been reported in the coatings made by other methods in the literature. FIG. 44 shows that most of the reported refractory RHEA coatings exhibit a hardness (grain size)-thickness tradeoff. For instance, magnetron sputtering can achieve higher hardness due to the nanocrystalline structures it produces, but coatings made by this method are limited to a few micrometers in thickness. In contrast, laser cladding, thermal spray, and electrodeposition can produce thick refractory coatings, but their hardness is generally around 40-50% lower than that of coatings produced by magnetron sputtering due to their coarse-grained, heterogeneous microstructures. The mechanically driven TiVZrTa RHEA coatings overcome the traditional microstructure-hardness-thickness tradeoff, presenting a promising strategy for designing metallic coatings with potential enhanced surface wear resistance and irradiation tolerance.

In some embodiments a dense TiVZrTa refractory high-entropy alloy coating was synthesized using surface mechanical alloying and consolidation, achieving thicknesses of approximately 50 μm under cryogenic conditions and 100 μm at room temperature. The SEM images and EDS mapping results show that RT processed coating exhibits a multi-phase microstructure with elemental-rich phases such as V-rich and Ta-rich phases. The formation of the elemental-rich phases is attruibuted to the high strength and low shear-induced diffusion rates of both Ta and V. The XRD measurements confirmed that these phases entail a BCC crystal structure with an average grain size of ˜11 nm. For the CT processed RHEA coating, the mixing is more homogeneous, and a nearly single BCC phase with grain size of ˜5.6 nm was formed within 24 hours of milling. Nanoindentation tests show that RT processed coating exhibits a gradient hardness distribution from the interface to the top layer with an average hardness of ˜10 GPa. However, the average hardness for the CT processed sample is ˜30% higher due to more pronounced grain size strengthening and solute strengthening.

A kMC simulation framework was also developed to reproduce the chemical mixing states and phase formation of the TiVZrTa coating in some embodiments. A decreasing size of elemental islands in the simulation cell microstructures is shown, which corresponds to the experimentally characterized cross-sectional microstructure. For RT processed RHEA, a large negative deviation in the CSRO parameter was observe from zero values in the TaTa and VV pairs, indicating the formation of Ta-rich and V-rich phases. On the other hand, the CSRO curves of the CT processed samples show minimal deviation from zero and achieved steady state in less MCS steps compared to the RT processed counterparts. This minimal CSRO deviation indicates a greater milling efficiency and tendency to reach single phase solid solution under cryogenic processing temperatures. The described SMAC technique and kMC simulation framework are instrumental in designing thick, high-strength, and single-phase RHEA coatings for applications demanding high surface wear or irradiation resistance.

In addition to being mechanically ultra strong, the nc-HEA of some embodiments shows relative exceptional thermal stability at high temperatures. The 1-hour isochronal heat treatment shows no phase decomposition up to 623 K. Only small amounts of Cr-rich and carbide phases appear at 873 and 1173 K respectively (carbon was introduced by the steel milling vial). What is striking, however, is that under isothermal annealing at 1173K nc-HEA retains its nanosized grains for up to 4 hours. The analysis of the grain growth kinetics reveals a grain growth exponent n of ˜3.9 in this nc-HEA. This is a slower rate when compared to other metals or to alloys and even to the HEAs processed with other techniques (see FIG. 28). Based on the mechanism controlling regime, the 3.9 value of the grain growth exponent illustrates the grain stabilizing effects from both strong solid solution drag and the precipitation pining effect. The present nc-HEA outperforms available HEAs by lowering the rate of grain growth by ˜30% at temperature beyond 1000K. The fact that the nc-HEA alloy can retain its nanocrystalline (and thus the improved properties) for a longer time makes it a compelling candidate for application in extreme conditions.

Other than nc-HEA coating CoCrFeMn, some other HEA coating was also synthesized on other substrate. TiVTaZr was named as “refractory high entropy alloy” because of its excellent thermal stability. In one example, TiVTaZr coating was synthesized by SMAC: the substrate material is ASME SA 387-91 F/M steel. Equal molar amount of Ti, V, Ta and Zr powder were loaded into the vial. Milling balls were added into the vial with a ball to powder ratio of 10:1. It has been found that only after 12 h of SMAC, powders form a thick coating (shown in FIG. 39a) on the steel substrate and the coating is mainly composed of BCC phase (shown in FIG. 39b). The hardness tested by the nanoindentation with a Berkovich tip is ˜9.72±0.5 GPa.

TiVTaZr was named as “refractory high entropy alloy” because of its excellent thermal stability. In a lab setting, TiVTaZr coating was synthesized by SMAC: the substrate material is ASME SA 387-91 F/M steel. Equal molar amount of Ti, V, Ta and Zr powder were loaded into the vial. And 4 mm milling balls were added into the vial with a ball to powder ratio of 10:1. It has been that only after 12 h of SMAC, powders form a thick coating (shown in the SEM plot) on the steel substrate and the coating is mainly composed of BCC phase (shown in the XRD plot). The hardness tested by the nanoindentation with a Berkovich tip is ˜9.72±0.5 GPa.

The two components of alloying and consolidation are achieved concurrently and in solid state setting SMAC apart from currently available HEA synthesis technologies that require either phase transformation (e.g., melting and solidification) or chemical reactions (e.g., electro-deposition). The former is an energy intensive approach with no ability to make nanocrystalline materials and the latter favors the formation of undesired chemically ordered and brittle compounds. SMAC on the other hand offers an environmentally friendly pathway to the synthesis of truly random concentrated solid solutions that are also nanocrystalline. The mechanical strength of the thermal stability of the alloys processed by SMAC are of top level compared to those processed by the currently available techniques.

SMAC is flexible in that it can work with an exceptionally wide range of metallic powders and at any scale offering a large space for material design. Thus, a number of different industries can be target including automobile and aerospace for wear-resistant coatings, naval industry for corrosion resistance coatings, and fusion energy industries for the protection of fusion reactor walls against extreme thermomechanical and radiation conditions.

Looking at another example embodiments, Ni_0.2Co_0.2Cr_0.6 represents the mixing with high Cr contents, which induces a high thermal jump frequency and gives the chemical driving force a leading role. Atomic arrangement at different mixing stages were observed from diagonal {111} cross-sectional planes (FIG. 45a). During the first 2×10⁵ MCS, Cr—Ni mixing occurs noticeably faster than for the other two pairs with stripes of Cr and Ni along <111> directions forming across the phase boundaries, which is attributed to the mechanical shearing process. Ni—Co mixing is poor from the beginning to 10⁶ MCS indicated by very few contact interfaces between “islands” of Ni and Co. After 10⁶ MCS, distinct boundaries between phases were roughened due to the thermal diffusion process, while small “islands” of Ni and Co remained isolated. This observation is in line with a major BCC phase (with higher diffraction intensity) and a minor FCC phase (with lower diffraction intensity) being formed after 1 hour of MA and persisting after 6 hours of MA. This can be explained by significant Ni mixing into Cr leading to the Cr-dominant BCC phase, while a smaller amount of Ni mixes into Co, forming the FCC phase (FIG. 45b). The evolution of the SRO curves shown in FIG. 45c corroborates the formation of these two phases. The Cr—Ni SRO parameter decreases significantly faster than the other two pairs and reaches a negative value, corresponding to the Cr—Ni rich BCC phase, while both Ni—Co and Cr—Co SRO values persist above 0.5, corresponding to the Co-rich FCC phase (FIG. 45c).

Since Cr—Ni has the lowest (most negative) mixing enthalpy and the highest hardness, sufficient mixing of Cr—Ni as demonstrated by Ni_0.2Co_0.2Cr_0.6 can be attributed to the chemical driving force. The crossing point between the Cr—Co and Ni—Co SRO curves at 10⁵ MCS indicates that the chemical driving force overcomes the initial mixing trend influenced by the mechanical driving force and dominates in the later mixing and steady stages (FIG. 45c). This type of mixing behavior is defined as the chemically dominated mixing, which is characterized by the fastest mixing of Cr—Ni pairs and the slowest mixing of Ni—Co pairs during the main mixing stage. The chemical mixing mechanism is typically observed in high Cr content compositions, resulting in a steady-state microstructure that usually exhibits dual phases (BCC and FCC). In Ni_0.2Co_0.2Cr_0.6, the BCC phase shows a lower lattice strain (˜0.27%) compared to the FCC phase (˜0.69%), indicating that the former is obtained by thermal diffusion and the latter is achieved by mechanically forced mixing.

Ni_0.4Co_0.5Cr_0.1 exemplifies the alternative situation with low Cr contents and suppressed thermal diffusion, where the mechanical driving force governs the mixing. In the cross-section of the simulated microstructure for Ni_0.4Co_0.5Cr_0.1, Cr disperses into mainly isolated Ni and Co regions in the starting 10⁴ MCS, and the Ni—Co mixing occurs gradually until 5×10⁵ MCS (FIG. 46a). The simulated mixing process is again supported by XRD patterns (FIG. 46b). A Co-rich HCP phase forms alongside the FCC matrix after 0.5 hour of MA, which can be attributed to the insufficient mixing of Ni—Co in the initial 10⁴ MCS. This HCP phase then vanishes after 1.5 hours of MA and a single FCC phase persists in the steady state, as demonstrated by all three elements having extensive contact with each other after 5×10⁵ MCS in the simulated atomic arrangement. Correspondingly, the Ni—Co SRO parameter is higher than the other two pairs in early mixing stage when the HCP phase exists, and its bypasses the other two at 2×10⁵ MCS as the HCP phase vanishes (FIG. 46c).

The fact that Cr predominantly appears as isolated atoms and Ni and Co appear as stripes suggests that the thermal jump (diffusion) process assists Cr in mixing into the matrix, while the mechanical shearing process facilitates the mixing of Ni and Co. On the other hand, the initial SRO decrease for Cr—Ni and Cr—Co pairs can be attributed to fast diffusion during the early stages, and the more rapid SRO drop for Ni—Co during the major mixing stage indicates that the mechanical driving force surpasses the chemical driving force eventually. Indeed, the mechanical driving force facilitates the HCP phase mixing into the matrix, resulting in a single-phase solution in the steady stage (FIG. 46b), with all three SRO curves converging to a near zero value after 5×10⁵ MCS (FIG. 46c). In the zoomed-in view of the steady-state SRO curves, the three curves fluctuate around the same level and frequently intersect, indicating the formation of a single-phase chemically random solution. From XRD analysis, this steady-state phase has a high lattice distortion (˜0.49% lattice strain) and nanometer scale grain size (˜82 nm). This mixing behavior was identified as the mechanically dominated mixing, which is typically observed with low Cr contents.

Inspired by the previous two mixing mechanisms associated with high and low Cr content extremes, a third mechanism is anticipated at moderate Cr contents, with significant roles of both chemical and mechanical driving forces. The mixing of equiatomic NiCoCr was thereby simulated. In FIG. 47a, all three elements mix almost simultaneously and are averagely distributed on stripes and roughened interfaces, suggesting that both thermal jump and mechanical shearing facilitate mixing. Also, the SRO curves do not intersect throughout the mixing stage (FIG. 47c). All SRO curves fluctuate around distinct values near zero and do not intersect, and this is expected to be a single phase with minor chemical ordering, which features no superior of neither chemical nor mechanical driving force. In general, such a mixing process characterized by a similar mixing pace of all pairs is defined as mechano-chemical mixing. A single-phase solution with local chemical ordering is expected at the ultimate stage of mixing under this mechanism.

The stacked XRD patterns of powder samples with different durations of MA (FIG. 47b) support the mixing process demonstrated by SRO curves. After 1 hour of MA, three different phases were detected: 1) an FCC phase with the highest intensity, identified as the matrix, 2) minor peaks for a hexagonal close packed (HCP) phase, and 3) a body centered cubic (BCC) phase with relatively weaker signals. The formation of HCP and FCC phase can be associated with insufficient Ni—Co mixing, and the formation of the BCC phase can be attributed to poor mixing between Cr and the other two elements. After 4 hours of MA, the intensity of both HCP and BCC patterns decreases, suggesting their dissolution into the FCC matrix, and only an FCC phase was detected eventually. The dissolution of HCP and BCC phase corresponds to the gradual decrease in SRO parameters towards near zero values. The calculated lattice strain of equiatomic FCC phase falls in-between that of the two other FCC phases formed under mechanically dominated and chemically dominated mixing.

Based on the three possible mixing mechanisms discussed above, steady-state phases formed under the MA process are expected to be dependent on mixing mechanisms and vary with the molar content of each element. To systematically investigate the steady-state phases, the mixing result of NiCoCr was simulated with atomic content of each principal element varying from 10% to 80%. The energetic stabilization of the steady-state phases was then analyze using mixing enthalpy and configurational entropy. Eventually, the rationale was extended regarding composition, mixing mechanisms, steady-state phases, and mixing energetics from NiCoCr to various ternary systems involving transition metals with negative mixing enthalpies.

The simulated NiCoCr phase diagram suggests that the steady-state phase(s) are primarily determined by Cr content (FIG. 48a). Below 25% Cr, a single random phase forms. Between 25% and 35% Cr, a single ordered phase appears. Above 40% Cr, separate phases persist. These three phase regimes correspond to the mechanically dominated mixing, mechano-chemically mixing, and chemically dominated mixing mechanisms, respectively. The dependency of the mixing mechanism and the degree of ordering in the steady-state atomic arrangement on Cr content is attributed to the lowest average mixing enthalpy of Cr. Higher Cr content increases the average thermal jump frequency, resulting in phase separations under the chemical mixing mechanism, whereas low Cr content results in a thermal jump frequency lower than the mechanical shearing frequency, forming a single phase under the mechanically dominated mixing mechanism.

The influence of average mixing enthalpy on mixing process and outcome suggests an energetic basis of mixing mechanisms regarding the interplay between enthalpy and entropy. Extensive discussions on configurational entropy and mixing enthalpy in CCAs have highlighted their controlling effects on phase formation. The competition between driving forces can be explained in the formation of driven CCAs within these frameworks. Preferable bonding between elements with low mixing enthalpy under the chemically dominated mixing can energetically stabilize the system. In contrast, the microstructure with low SRO formed under the mechanically dominated mixing results in a high configurational entropy that energetically stabilizes the system. From a thermodynamic perspective, the competition of chemical and mechanical driving forces corresponds to the competition of mixing enthalpy and entropy in the steady-state phase stabilization respectively. The fraction of configurational entropy increases as the mechanical driving force gradually exceeds the chemical driving force with decreasing Cr contents (FIG. 48b), and an entropic fraction roughly above 0.35 is needed to maintain a single-phase solution after MA. Nevertheless, the total free energy of mixing is highest in the single-phase random solution regime and reaches a minimum in the multi-phase regime (FIG. 48c), which is in line with previous understanding that near-equiatomic transitional CCAs are in metastable states at medium to low temperatures.

As previously mentioned in the result section, the numerical feature of pairing potentials and hardness in NiCoCr gives an opposite mixing order among three elemental pairs under either chemical or mechanical driving force, which helps to identify which driving force dominates during mixing through the relative decreasing speed of SRO values. Nevertheless, it introduces some level of intrinsic symmetry to the mixing kinetics. Since the compositional asymmetry in mixing process and atomic arrangement is the key feature that distinguishes the ternary systems from binary ones, it is essential to validate the above discussion with systems having completely asymmetric trends of mixing. For an arbitrary ternary system A_xB_yC_(1-x-y), there are six possible relative mixing trends in total as listed in the table in FIG. 49. Selective compositions from the six example ternary systems are simulated and analyzed to reach a general understanding of the mixing mechanisms and energetics.

Steady-state phases and energies of mixing for NiCoMn that represent completely asymmetric cases were simulated in the same manner as the NiCoCr system. In NiCoMn, Mn contributes most to the negative mixing enthalpy, and it was observed the cutoff lines between phase regimes roughly align with Mo contents, similar to the role of Cr in NiCoCr. The boundary between single- and multi-phase regimes is roughly along the 25% contour line of Mn content, with the former obtained by mechanically dominated mixing and the latter obtained by chemically dominated mixing (FIG. 50a). A transitional behavior from entropically stabilized low SRO atomic arrangement to enthalpically stabilized high SRO atomic arrangement occurs with increasing Mn content, and the critical ratio of

$❘\frac{T\Delta S}{\Delta H}❘$

for NiCoMn is around 0.35 (FIG. 50b). Additionally, the single-phase regime has a higher total free energy of mixing compared to the multi-phase regime (FIG. 50c). These trends and cutoff values are consistent with what have been observed in NiCoCr, indicating a universality.

Combining the above analysis of NiCoCr and NiCoMn, the following principles regarding the mixing physics of mechanically driven ternary alloys are proposed. The mechanical driving force pushes the system towards a lower-ordering atomic arrangement (single-phase random solution) to obtain a high configurational entropy that compensates the loss in mixing enthalpy and stabilizes the microstructure. The chemical driving force pushes the system towards a higher-ordering atomic arrangement (multi-phase solution) to achieve a low mixing enthalpy that stabilizes the microstructure. When the two driving forces compete on a comparable scale, the system develops an atomic arrangement with moderate level of local ordering to stabilize the microstructure from both enthalpic and entropic perspectives, with which a low total free energy is possibly achieved. The mixing mechanism, resultant steady-state phase(s), and the energetics for a specific composition are determined by the molar content of the element that provides the largest (absolute value) of mixing enthalpy.

Comparing the results described herein with previous research, there are two points that are of note. First, the competition between the two driving forces investigated in described system and methods is different from what has been previously discussed. Previous models focused on binary systems with positive mixing enthalpy. They described the competition between chemical and mechanical driving forces as the former prevents any mixing between the two elements while the latter works to break the anti-bonding barrier. In contrast, the method described herein studied systems with negative mixing enthalpies, for which the two driving forces both promote the formation of new bonds between different elements. Nevertheless, due to the difference in pairing potential of each pair of elements in the asymmetric ternary system, mixing under merely chemical driving force cannot reach a random distribution of all elements. It is therefore argued that, for a system with positive mixing enthalpy, the mechanical driving force directly opposes the anti-bonding chemical driving force. On the other hand, for a system with negative mixing enthalpy, the mechanical driving force works to correct the asymmetric bonding tendency introduced by chemical driving force to a random bonding stage.

Secondly, the critical ratio of

$❘\frac{T\Delta S}{\Delta H}❘$

described here (˜0.35) is far lower than the well-known critical Ω criterion (˜1.1) [50,59-63]. The lower critical ratio is explained herein by the difference between traditional melt-base process and MA process: in the melt-base processes, large amount of thermal heat is introduced to the system such that a global thermodynamic equilibrium must be achieved in the melted solution; however, during MA, the extensive mechanical work traps the system in a metastable energy stage under room temperature. The energy diagram suggests that a highly random atomic arrangement is allowed to form under MA process even when the fraction of configurational entropy is lower than the mixing enthalpy, and the free energy is allowed to be higher than the global minimum value. Conclusively, this lower cutoff ratio reveals a more generous thermodynamic constraint on forming multi-principal element solutions with the MA process.

The high tolerance of metastable phase formation under the MA process opens a broad possibility of compositions for ternary concentrated alloys. Cordero has defined miscibility criterion simply based on hardness mismatch for binary systems with a constant positive mixing enthalpy because in that case the thermal driving force is always anti-mixing. For a ternary system with two driving forces both contribute towards mixing but developing different bonding preferences, a two-dimensional phase prediction map is proposed, taking into account both hardness and mixing enthalpy. First, the relative hardness mismatch parameter (H_ijk) of a ternary system is defined by the below equation. Same as in section 2, H_ij is the relative hardness of an i-j bond and X_ij is the molar fraction of ij bonds, with both i=j and i≠j being counted. When the mismatch of pairwise hardness is larger than a certain value, the system is expected to be non-miscible into a single phase. Secondly, it is assumed that H_ijk is below the critical hardness mismatch value and examine whether an atomic structure with near zero SRO can be stale under thermal jump and mechanical shearing events. An average thermal jump frequency (f_avg) is defined based on zero SRO (Eq.11) and compared with constant shearing frequency (φ=10³). Phase separation is expected if f_ang>φ, similar to the chemically dominated mixing; otherwise, the single phase is stable similar to the mechanically dominated mixing.

$H_{\mathrm{ijk}}=\sqrt{\sum {X_{\mathrm{ij}}\left(H_{\mathrm{ij}}-\sum \left(X_{\mathrm{ij}}·H_{\mathrm{ij}}\right)\right)}^2}$ $f_{\mathrm{avg}}=\left(-\frac{E_o+\sum 2c_i{c}_j{E}_{\mathrm{ij}}}{k_{B}T}\right)$

Combining the hardness and jump frequency criteria, the simulated steady-state phases were mapped to FIG. 51, where the x-axis represents the bond strength mismatch parameter (H_ijk), and the y-axis represents the ratio of jump frequency to the shear frequency (f_avg/φ). Simulation data points were selected from the six representative systems listed in the table in FIG. 49. A chemically random single-phase structure can be achieved and stabilized under room temperature when the hardness mismatch is smaller than ˜0.15 and the jump frequency is no larger than a magnitude above the shear frequency. A single-phase structure with moderate local ordering is anticipated to be stabilized with the hardness mismatch being smaller than ˜0.15 and jump frequency being approximately a magnitude higher than shearing frequency. Phase separation is expected with larger hardness mismatch values or higher thermal jump frequencies.

Although, in the described example embodiment, a constant temperature at 300K has been used for all data points in FIG. 51, the threshold values for H_ijk and f_avg/φ should be valid for a broad temperature range from cryogenic to below melting points. On one hand, changing the temperature affects the jump frequency according to the above equations, introducing higher jump frequency (f_avg) at elevated temperatures. On the other hand, elemental powder becomes softer with rising temperatures, thereby reducing their hardness mismatch (H_ijk). With the same composition alloyed at higher temperatures, the higher jump frequency and lower hardness mismatch will incline to the chemically dominated mixing and form phase(s) with larger SRO. Conversely, mechanically dominated mixing is more favored at cryogenic temperatures. The mechano-chemical competition breaks down when reaching the lowest melting point of principal elements, where mixing mechanisms in traditional melt-based processes dominate.

With rising molar content of the element with the lowest mixing enthalpy, the total free energy tends to decrease while the jump frequency tends to increase and form multiple phases. In the example embodiment, to form a single-phase solution while maintaining the lowest possible free energy, the single-phase solution with moderate SRO is expected to be the most desirable solution. This indicates that compositions falling along the two cutoff lines on the map are thereby expected to have good properties. There are indeed ternary CCAs coatings reported with exceptional wear and corrosion resistance that have H_ijk and f_avg/φ values aligning with the critical values proposed. Particularly, NiCoCr CCAs are often designed with near-equiatomic compositions, and the simulated equiatomic NiCoCr point described herein lies on the intersection of the cutoff lines on the map.

Furthermore, the microstructure of the coating falls beyond the thickness-grain size trade off among coatings produced by other traditional alloy coating synthesis process (FIG. 54), which gives rise to a high hardness. Shown by XRD results, the phase evolution stages during mixing are similar to FIG. 47b, and the coating grain size is calculated around 20±4 nm. Nanoindentation tests were conducted at 0.1 s⁻¹ strain rate with a Berkovich tip reaching fixed maximum test depth at 1 μm, and the hardness is measured to be 7.8±0.6 GPa. The nanocrystallinitiy is achieved by confined thermal diffusion path length with moderate thermal jump frequency (f_avg/φ below 10), and the homogeneity and thickness benefit from the high deposition rate induced by intensive mechanical shearing (H_ijk below 0.15). Resultantly, the grain size effect and strong solid solution strengthening together lead to a hardness that ranks among the highest in all alloy coatings [97,98]. These features of equiatomic NiCoCr effectively demonstrate that the mechano-chemical competition quantified by the kMC model and phase prediction map can provide insights into mechanical properties beyond microstructures.

In summary, MA process produces single-phase CCAs in a complete solid state under a unique interplay of thermal and mechanical driving force. Previous theoretical works have not explained the atomistic mixing mechanism under MA for compositionally asymmetric systems with negative mixing enthalpies. Described herein, a theoretical framework is provided to explain the mixing physics and guide alloy design through integration of experimental characterizations with kMC simulations. Three types of mixing mechanisms are defined based on the degree of competition between the mechanical and chemical driving forces, namely the mechanically dominated mixing, chemically dominated mixing, and mechano-chemical mixing. The system was found to reach a single-phase random solution, a single-phase ordered solution, or inclining to phase separation under the three mixing mechanisms respectively.

It was a further demonstrated that the mixing mechanism varies according to the molar content of the element that has the lowest average mixing enthalpy in the system. The chemical driving force promotes a high SRO atomic arrangement to obtain low mixing enthalpy. Conversely, the mechanical driving force favors a low SRO atomic arrangement to achieve a high configurational entropy. The competition between the two driving forces can be thermodynamically interpreted as the gain and loss in mixing enthalpy and configurational entropy and thereby determines the steady-state phases. When the ratio of

$❘\frac{T\Delta S}{\Delta H}❘$

is larger than 0.35, a single-phase solution is achieved and stabilized.

Based on the mechanistic and energetic understanding, it is suggested the hardness mismatch parameter (H_ijk) and thermal jump to shear frequency ratio (f_avg/φ) as the mechanical and chemical constrains to form a single-phase solution under MA. With simulations among six ternary systems exemplifying all six possible relative mixing trends, it is concluded that a single phase is likely to form when H_ijk is smaller than 0.15 and f_avg/φ is lower than 10. Additionally, it was found that compositions with comparable amount of all three elements have their H_ijk and f_avg/φ parameters close to the threshold values and present the lowest free energy. Good material performance is expected with a single-phase microstructure and rfelatively low total free energy. Equiatomic NiCoCr coating was synthesized and demonstrated its superior hardness resulting from the mechano-chemical mixing mechanism.

Equiatomic NiCoCr coating was sythensized to study its expected outstanding mechanical performances. Elemental powders were loaded into the milling vial together with a polished Ni substrate to achieve surface mechanical alloying and consolidation (SMAC) simultaneously at room temperature. With cross-sectional scanning electron microscopy (SEM), it was observed that elemental powders consolidated to form a thick and adherent coating exceeding 200 μm after 10 hours of processing (FIG. 52a). Ni, Co and Cr elements are shown to be randomly distributed in the coating without observable signs of segregation or precipitation by energy dispersive spectroscopy (EDS) (FIG. 52b). The chemical composition of the coating measured via EDS and presented in the table in FIG. 53, closely aligns with the initial equiatomic concentration. The microstructure characterization proves the successful synthesis of a uniform thick coating with chemical homogeneity as predicted by the kMC model.

The described system and methods may also be applied to the processing side. The current technologies to make HEAs are either arc melting-based or magnetron sputtering-based. The former cannot produce nanocrystalline (thus very hard) HEAs and the latter is limited to coating thickness below ˜1 μm with a deposition rate of ˜1 Å/s. In that sense, the proposed approach occupies a unique space in materials processing. That is, it is the only approach that offers both very thick HEA coatings with nanocrystalline grains. Slow grain growth rate under a large working temperature mentioned previously secure that SMACed coating will retain its splendid mechanical properties to a very high temperature. It is envision that the proposed approach will be a competitive one compared to the existing processes. With the provided guideline and the STDS model, one can easily approximate and synthesize the nc-HEA coating that meets his or her own requirements. What is more, due to its solid-state character, it would produce a much smaller carbon footprint compared to the melt-based processes which need a large amount of both expensive raw materials and energy to melt the components. It would also be much less expensive and far more efficient compared to the sputtering-based techniques.

Given the above, the new kinetic Monte Carlo approach is proposed to simulate the steady state microstructures in the mechanically driven HEA fabrication process considering the strength of the mixing elements. The result of the model align well with the data collected from literature. In addition, a modified mechanical alloying experiment was conducted under the guidance of the model. A CrMnFeCo HEA coating was fabricated, and its phase composition was predicted by the kinetic Monte Carlo simulation. The mechanical behavior of the SMACed HEA have been studied both theoretically and experimentally. And its excellent thermal stability have been discussed. From the above, the following conclusions can be drawn: (1) The 2D kinetic Monte Carlo simulation shows a good ability to predict the phase composition of the mechanically driven HEA after the alloying process. Its robustness has been validated both by data from previous literature and by example conducted experiments. The success demonstrate a new concept, the strength mis-match, shows a significant influence on the mechanically driven high-entropy alloys and can be considered as a guide line for alloy design. (2) The SMACed CrMnFeCo HEA shows nanocrystalline microstructure, single FCC solid solution phase, and excellent hardness. A strength model considering both the solid solution strengthening and grain size effect shows good prediction of the hardness of the tested samples, confirming the main two contributions of the hardness. The different SRS from traditional FCC alloy could be well explained by an established theory. Moreover, slow grain coarsening kinetics, and a low activation energy for grain growth have been shown in comparison analyzed by isochronal and isothermal experiments. In addition to the sluggish diffusion effect that slows down the grain growth rate, the described mechanically driven HEA's microstructure is also stabilized by the appearance of second phase.

Nanocrystalline alloys are usually stronger than their coarse-grained counterparts but are often brittle. Coarse-grained alloys are more ductile but their strength remain at low level. The high entropy alloy coating solid phase processing technic enables us to produce composite material which combines both a strong and wear resistant coating and ductile matrix. There is SMAT (Surface mechanical Attrition Treatment) for surface strengthening, arc-melting technic for making bulk HEAs, and for surface coating, magnetron sputtering is another option. But these approaches have shortcomings and are not as valuable as the method and systems described herein: without adding powder to form alloy coating, the strength of SMATed materials is lower than counterparts made by the described approach, the bulk HEAs are extraordinarily expensive both in producing and in purchasing raw materials, and magnetron sputtering could only produce film on substrate for several micrometers, which is nearly ignorable compared to ˜200 μm coating produced by hours of solid phase processing.

The method and systems described herein greatly improve the strength of material, increase surface hardness and wear resistance. High entropy alloy is a kind of alloy that is synthesized by mixing equal or relatively large proportions of four, five or more elements. It is famous for its cocktail effect: the performance, especially mechanical performance of it is often better than its components'. Compared to coarse-grained bulk high entropy alloy produced by arc-melting, it is an economical alternative which has nearly the same strength because of nanocrystalline grains on the surface. Nanocrystalline HEA coating provides ultra-strength while the coarse matrix secures the ductility. Higher practical application value due to its thick coating (several hundred micrometers) than several micrometers thin film made by magnetron sputtering.

To achieve the solid phase process, a traditional milling vial is modified: first, the lid of the milling vial should be replaced by the target substrate disc. Then some leak proofness measures need to be taken to prevent powders coming out of the vial. More than four kinds of element powders with nearly the same atomic percentage should be added to the vial. A long ball milling process will eventually create HEA coating on the surface with a gradient structure from the interface to the interior of the substrate disc.

In ball milling, temperature increase is always a phenomenon that researchers want to avoid: it will impede the particle and grain size reduction process and recrystallization caused by high temperature will produce powders that have larger grains and particle size than the initial state. In the solid phase process, high temperature is also detrimental to the coating bonding with substrate: forced mixing effect will be outcompeted by the phase separation process due to thermo-driven atomic diffusion and large metal powders will have higher difficulty to be peened into the substrate. Therefore, a cryogenic ball milling machine could be used for the process, there will be no such problems stated above, and it will definitely improve the efficiency.

The method and systems described herein approach are flexible in that they can work with any metal and at any scale. Thus, a number of different industries can be targeted fincluding automobile and aerospace for wear-resistant coatings, naval industry for corrosion resistance coating, and fusion energy industries for the protection of reactor walls against extreme thermomechanical and radiation conditions.

A future objective may be to significantly extend the HEA alloys compositions that can be processed with SMAC. This may be done in a systematic manner, focusing on 5-element high entropy alloys CoCrNiMnX where the 4 elements are fixed to be Co, Cr, Ni, and Mn and vary the fifth element. It may be shown how the physical and thermomechanical properties of X affect the processability of the alloy. In particular, the effect of X could be studied on whether a single phase or a multiphase alloy is produced and how X changes the extent of consolidation. Then a 5-element high entropy alloys CoCrNiXY could be studied, where the 3 elements are fixed to be Co, Cr, Ni and vary the fourth and fifth elements. This may provide a benchmark for ˜30-40 compositions to be able to produce processing guidelines.

Furthermore, the underlying basis of the SMAC process is the shear-induced mixing at the atomic scale. Recovery/diffusional processes that are thermally activated compete with shear-induced mixing during the process. To suppress the recovery processes and to achieve an enhanced level of mixing and grain refinement, it is proposed to develop a cryogenic SMAC. A liquid nitrogen chamber may be integrated within the discussed setup and conduct cryogenic SMAC on a subset of compositions explored in aim 1. The alloy will be characterized by X-ray diffraction, Electron Microscopy and Energy Dispersive Spectroscopy.

Additionally, the alloy benchmark created at room temperature and cryogenic temperatures could be used to develop processing maps for the SMAC process. Processing maps can be used to guide materials selection for the development of new nc-HEAs/nc-HEA coatings. The initial data screening suggests that the smaller the strength deviations of the elemental powder, the higher the probability of developing single phase nc-HEA during SMAC. This hypothesis could be studied with kinetic Monte Carlo and Molecular Dynamics Simulations. The kinetic Monte Carlo model has already been developed for a binary (two elements) system (FIG. 55) and plan to extend it to include more than two elements. The central idea is to understand the competition between the shear-induced mixing and the thermally activated diffusion at the atomic level for a solution that contains multi-principal elements. The atomic level simulations will help us predict the saturated (final) state of mixing during the SMAC process which may be verified with the benchmark created in the first two aims.

While the disclosure has been illustrated and described in detail in the foregoing drawings and description, the same is to be considered as exemplary and not restrictive in character, it being understood that only illustrative embodiments thereof have been shown and described and that all changes and modifications that come within the spirit of the disclosure are desired to be protected.

The present disclosure may comprise one or more of the following features and combinations thereof.

A method of using ball milling for coating a metallic alloy on a target surface includes placing the target surface of an object on at least a portion of an interior surface of a ball mill chamber of a ball mill device. The method includes milling a mixture of powder with exposure to the target surface, wherein the mixture of powder comprising a first powder material of a first metal and a second powder material of a second metal. The method includes forming an alloy comprising the first metal and the second metal. The method includes coating the alloy on the target surface of the object via a mechanical force of ball milling.

In some embodiments, a mixture of powder materials comprises at least three, four, five, six, or seven different powder materials or at least three, four, five, six, or seven different metals.

In some embodiments, the alloy is a high entropy alloy, or a alloy comprising of five or more elements with relatively high concentrations. In some embodiments, the allow is a medium entropy alloy, or a alloy comprising of three or four elements with relatively high concentrations).

In some embodiments, the alloy comprises at least four or at least five different metals. Each metal may have at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 w.t %, or at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 vol % or mol %.

In some embodiments, the alloy has component metals substantially uniformly disturbed in a coating layer.

In some embodiments, a component of the mixture of powder is selected from Ag, Al, Au, Be, Cd, Co, Cr, Cu, Fe, Mg, Mn, Mo, Nb, No, Pd, Si, Ti, V, W, Zn, or Zr.

In some embodiments, each component of the mixture of powder is selected from a group I metal, a group II metal, a group III metal, a group IV metal, or a transition metal.

In some embodiments, the coated alloy is a single phase, multiphase, or any combination thereof.

In some embodiments, two or more essential component metals in the mixture of powder have a strength mismatch of less than 1.5. In some embodiments, the formed alloy is substantially a single-phase alloy.

In some embodiments, two or more essential component metals in the mixture of powder have a strength mismatch of at least 2. In some embodiments, the formed alloy is substantially a multi-phase alloy.

In some embodiments, two or more essential component metals in the mixture of powder have a strength mismatch of between 1.5-2.0. In some embodiments, the formed alloy is substantially a single-phase alloy or a multi-phase alloy.

In some embodiments, the ball milling process is a dry ball mill process (e.g. substantially free of binder or solvent).

In some embodiments, the ball milling process operates at less than 300° C., less than 200° C., less than 100° C., less than 50° C., less than 25° C., less than 10° C., less than 4° C., less than 0° C., less than −10° C., less than −18° C., or less than −80° C.

In some embodiments, the ball milling process operates in a cryogenic ball mill device (e.g. having a cryogenic chamber or liquid nitrogen chamber).

In some embodiments, an average particle size of the first powder material, the second powder material, optionally more powder materials, and/or the average particle size of a mixture of the powder materials is 1 micron to 1000 microns including any value therewithin or any subranges therebetween.

In some embodiments, an average grain size of the alloy is smaller than an average particle size of a mixture of the powder materials.

In some embodiments, an average grain size of the alloy is less than 1 micron, less than 100 nm, less than 50 nm, or less than 30 nm, e.g. 5 nm-100 nm, including any value therewithin or any subranges therebetween.

In some embodiments, the coating layer is substantially free of non-metal materials.

In some embodiments, the coating layer has a hardness higher than the coating layer formed by spraying, cladding, casting, sputtering, vapor deposition, or electrodeposition methods (with the same or substantially same element/component metals).

In some embodiments, the coating layer has a hardness of at least 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 GPa, or a hardness of 5-20 GPa including any value therewithin or any subranges therebetween.

In some embodiments, the loading the ball mill device is 10 vol %-50 vol % including any value therewithin or any subranges therebetween.

In some embodiments, a lid or cover of the ball mill device is at least a portion of the object to be coated having the target surface exposed to milling media and a mixture of the powder materials.

In some embodiments, the method comprises a leak proofness measures to prevent a mixture of the powder materials coming out of the ball mill chamber.

In some embodiments, the ball mill chamber further comprises milling media having a size of 1 mm to 500 mm, including any value therewithin or any subranges therebetween.

In some embodiments, the object (e.g. a substrate) is lid fixed on top of the ball mill chamber.

In some embodiments, one or more surfaces of the object (e.g. a substrate) forms an interior wall, a top surface, a bottom surface, or any combination thereof the ball mill chamber and configured to be removable or disassembled after coating.

In some embodiments, the object (e.g. a substrate) is fixed inside the ball mill chamber.

In some embodiments, the object (e.g. a substrate) is placed inside the ball mill chamber and configured to be movable or rotatable during ball milling process.

In some embodiments, the coating layer is rough or substantially uneven in microscale on the target surface after ball milling coating.

In some embodiments, the coating layer has a roughness of greater than 1, 2, 3, 4, 5, 10, 20, 30, 40, or 50 microns on the target surface.

In some embodiments, the method comprises a post-processing treatment to reduce the roughness of the target surface.

In some embodiments, the method comprises a heat treatment on the coating layer or to the object after ball milling coating.

In some embodiments, a metal alloy coating layer is formed by a method of using ball milling for coating a metallic alloy on a target surface includes placing the target surface of an object on at least a portion of an interior surface of a ball mill chamber of a ball mill device. The method includes milling a mixture of powder with exposure to the target surface, wherein the mixture of powder comprising a first powder material of a first metal and a second powder material of a second metal. The method includes forming an alloy comprising the first metal and the second metal. The method includes coating the alloy on the target surface of the object via a mechanical force of ball milling.

In some embodiments, an object having at least a portion of a surface coated by a method of using ball milling for coating a metallic alloy on a target surface includes placing the target surface of an object on at least a portion of an interior surface of a ball mill chamber of a ball mill device. The method includes milling a mixture of powder with exposure to the target surface, wherein the mixture of powder comprising a first powder material of a first metal and a second powder material of a second metal. The method includes forming an alloy comprising the first metal and the second metal. The method includes coating the alloy on the target surface of the object via a mechanical force of ball milling.

In some embodiments, a system for coating a metallic alloy on a target surface includes a ball mill chamber to hold a mixture of powder and ball mill media wherein the ball mill chamber comprises one or more openings (e.g. an open top surface and/or an open bottom surface) such that one or more target surfaces (e.g. a led) fit and cover the one or more openings to seal the ball mill chamber. The system includes one or more fixation elements configured to fix the one or more target surfaces to the ball mill chamber to seal the ball mill chamber. The system includes one or more actuators configured to rotate the ball mill chamber for ball milling coating.

In some embodiments, the system comprises a leak proofness measures to prevent a mixture of the powder materials coming out of the ball mill chamber.

Claims

1. A method of using ball milling for coating a metallic alloy on a target surface comprising: placing the target surface of an object on at least a portion of an interior surface of a ball mill chamber of a ball mill device;milling a mixture of powder with exposure to the target surface, wherein the mixture of powder comprising a first powder material of a first metal and a second powder material of a second metal;forming an alloy comprising the first metal and the second metal; andcoating the alloy on the target surface of the object via a mechanical force of ball milling.

2. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the mixture of powder comprises at least three, four, five, six, or seven different powder materials or at least three, four, five, six, or seven different metals.

3. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the alloy comprises of five or more elements with relatively high concentrations or the alloy comprises of three or four elements with relatively high concentrations.

4. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the alloy comprising at least four or at least five different metals, each one of the different metals having at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 w.t %, or at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 vol % or mol %.

5. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the alloy has component metals substantially uniformly disturbed in a coating layer.

6. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein a component of the mixture of powder is selected from Ag, Al, Au, Be, Cd, Co, Cr, Cu, Fe, Mg, Mn, Mo, Nb, No, Pd, Si, Ti, V, W, Zn, or Zr.

7. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein each component of the mixture of powder is selected from a group I metal, a group II metal, a group III metal, a group IV metal, or a transition metal.

8. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the coated alloy is a single phase, multiphase, or any combination thereof.

9. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein two or more essential component metals in the mixture of powder have a strength mismatch of less than 1.5 and the formed alloy is substantially a single-phase alloy.

10. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein two or more essential component metals in the mixture of powder have a strength mismatch of at least 2 and the formed alloy is substantially a multi-phase alloy.

11. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein two or more essential component metals in the mixture of powder have a strength mismatch of between 1.5-2.0 and the formed alloy is substantially a single-phase alloy or a multi-phase alloy.

12. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the ball milling process is a dry ball mill process.

13. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the ball milling process operates at less than 300° C., less than 200° C., less than 100° C., less than 50° C., less than 25° C., less than 10° C., less than 4° C., less than 0° C., less than −10° C., less than −18° C., or less than −80° C.

14. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the ball milling process operates in a cryogenic ball mill device.

15. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein an average particle size of the first powder material, the second powder material, and/or the average particle size of a mixture of the powder materials is 1 micron to 1000 microns including any value therewithin or any subranges therebetween.

16. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein an average grain size of the alloy is smaller than an average particle size of a mixture of the powder materials.

17. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein an average grain size of the alloy is less than 1 micron, less than 100 nm, less than 50 nm, or less than 30 nm, e.g. 5 nm-100 nm.

18. The method of claim 5, any other suitable claim, or any other suitable combination of claims, wherein the coating layer is substantially free of non-metal materials.

19. The method of claim 5, any other suitable claim, or any other suitable combination of claims, wherein the coating layer has a hardness higher than the coating layer formed by spraying, cladding, casting, sputtering, vapor deposition, or electrodeposition methods.

20. The method of claim 5, any other suitable claim, or any other suitable combination of claims, wherein the coating layer has a hardness of at least 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 GPa, or a hardness of 5-20 GPa.

21. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the loading the ball mill device is between 10 vol %-50 vol %.

22. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein a lid or cover of the ball mill device is at least a portion of the object to be coated having the target surface exposed to milling media and a mixture of the powder materials.

23. The method of claim 1, any other suitable claim, or any other suitable combination of claims, further comprising a leak proofness measures to prevent a mixture of the powder materials coming out of the ball mill chamber.

24. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the ball mill chamber further comprises milling media having a size of 1 mm to 500 mm.

25. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the object is lid fixed on top of the ball mill chamber.

26. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein one or more surfaces of the object forms an interior wall, a top surface, a bottom surface, or any combination thereof the ball mill chamber and configured to be removable or disassembled after coating.

27. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the object is fixed inside the ball mill chamber.

28. The method of claim 1, any other suitable claim, or any other suitable combination of claims, wherein the object is placed inside the ball mill chamber and is configured to be movable or rotatable during ball milling process.

29. The method of claim 5, any other suitable claim, or any other suitable combination of claims, wherein the coating layer is rough or uneven in microscale on the target surface after ball milling coating.

30. The method of claim 29, any other suitable claim, or any other suitable combination of claims, wherein the coating layer has a roughness of greater than 1, 2, 3, 4, 5, 10, 20, 30, 40, or 50 microns on the target surface.

31. The method of claim 30, any other suitable claim, or any other suitable combination of claims, further comprising a post-processing treatment to reduce the roughness of the target surface.

32. The method of claim 5, any other suitable claim, or any other suitable combination of claims, further comprising a heat treatment on the coating layer or to the object after ball milling coating.

33. A metal alloy coating layer formed by the method of claim 1, any other suitable claim, or any other suitable combination of claims.

34. An object having at least a portion of a surface coated by the method of claim 1, any other suitable claim, or any other suitable combination of claims.

35. A system for coating a metallic alloy on a target surface comprising: a ball mill chamber to hold a mixture of powder and ball mill media wherein the ball mill chamber comprises one or more openings such that one or more target surfaces fit and cover the one or more openings to seal the ball mill chamber;one or more fixation elements configured to fix the one or more target surfaces to the ball mill chamber to seal the ball mill chamber; andone or more actuators configured to rotate the ball mill chamber for ball milling coating.

36. The system of claim 35, any other suitable claim, or any other suitable combination of claims, further comprising a leak proofness measures to prevent a mixture of the powder materials coming out of the ball mill chamber.