Stable nanocrystalline high-entropy alloys, and methods of making the same

Abstract

Herein provided are methods of forming stable nanocrystalline high-entropy alloys (HEAs). The method may include: processing a mixture of at least four or more principal elements in equiatomic or near-equiatomic ratios to form a single-phase solid solution HEA as a solvent; adding a solute element to the solvent, the solute element having a different crystal structure, an atomic size mismatch of at least 15%, and a higher melting point than the solvent; processing the solvent and the solute element until a single-phase solid solution HEA is formed; and annealing the single-phase solid solution HEA at 0.46 to 0.67 of the melting temperature of the HEA to form the stable grain-boundary-decorated nanocrystalline HEA. The nanocrystalline HEAs may be stabilized against grain growth and phase decomposition, including short and long- range orderings, at high homologous temperatures.

Description

STABLE NANOCRYSTALLINE HIGH-ENTROPY ALLOYS, AND METHODS OF MAKING THE SAME CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. provisional patent application no. 63 / 587,563, filed October 3, 2023, and which is hereby incorporated by reference. FIELD

[0002] The present disclosure relates generally to nanocrystalline (NC) materials. More particularly, the present disclosure relates to stable NC multicomponent alloys, also referred to as high entropy alloys (HEAs). BACKGROUND

[0003] Grain growth is prevalent in nanocrystalline (NC) materials at low homologous temperatures, thereby limiting their use in structural applications. Solute- element addition to offset excess energy that drives coarsening at grain boundaries (GBs) is an effective metallurgical means of stabilizing NC materials, albeit, mostly for simple binary alloy systems. This thermodynamic approach is considered complicated in multi- component alloy systems due to the possible complex pairwise interactions that could set on among the alloying elements. SUMMARY

[0004] It is an object of the present disclosure to obviate or mitigate at least one disadvantage of previous nanocrystalline high entropy alloy materials.

[0005] According to one aspect, there is provided a method of forming a stable grain-boundary-decorated nanocrystalline high-entropy alloy (HEA) comprising: a) processing a mixture of at least four principal elements in equiatomic or near-equiatomic ratios to form a single-phase solid solution HEA as a solvent; b) adding a solute element to the solvent, the solute element having a different crystal structure, an atomic size mismatch of at least 15%, and a higher melting point than the solvent; c) processing the solvent and the solute element until a single-phase solid solution HEA is formed; and d) annealing the single-phase solid solution HEA up to 0.46 to 0.67 of the melting temperature of the HEA to drive the solute and at least one of the solvent elements to the grain boundaries to form the stable nanocrystalline HEA.

[0006] Other aspects and features of the present disclosure will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments in conjunction with the accompanying figures. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Embodiments of the present disclosure will now be described, by way of example only, with reference to the attached Figures.

[0008] Fig. 1 is (a) a schematic of the conventional thermodynamic approach for binary alloy systems via mechanical alloying process; (b) a schematic of the pseudo-binary thermodynamic approach used in this study, where single-phase solid solution HEA is the solvent; (c) a Thermo-Calc calculated phase diagram for (CoCrFe)xAl1-x, where the concentration of Al increased from 0 to 25 at. %; (d) a Venn diagram illustration of the solute selection criteria: (I) contains the elements that have FCC and HCP crystal structures, (II) contains the elements that have an atomic mismatch ^ 15% with the Al25Co25Cr25Fe25, (III) contains the elements that have higher melting point than the Al25Co25Cr25Fe25HEA; and (e) a Thermo-Calc calculated phase diagram for (AlCoCrFe)xZr1-x, where the concentration of Zr increased from 0 to 20 at. %.

[0009] Fig.2 is the micro- and nano-structure of as-milled Al25Co25Cr25Fe25HEA in (a) X-ray diffractograms of the powders milled at different times, 0 to 40 hrs; SEM-EDS maps of powder at (b) 10 hrs, (c) 20 hrs, and (d) 40 hrs of milling; (e) STEM-EDS maps of lamella cross-section of powder at 40 hrs of milling; (f) HRTEM micrograph of HEA particle at 40 hrs of milling (the inset is the analyzed electron diffraction pattern); and (g) 3D atom maps of the analyzed needle volume showing the Al25Co25Cr25Fe25HEA after 40 hrs of milling, as well as the individual elements.

[0010] Fig.3 is the micro- and nano-structure of as-milled Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA powder in (a) X-ray diffractogram of the powder milled at different times, 20 to 40 hrs; (b) SEM-EDS maps of the powders at 40 hrs of milling; (c) STEM-EDS maps of lamella cross-section of HEA powder particle at 40 hrs of milling; (d) HRTEM micrograph of the HEA particle at 40 hrs (the inset is the analyzed electron diffraction); (e) APT 3D atom maps of the HEA showing the distribution of the alloying elements; (f) rectangular sub-volume of a region of interest in (e); and (g) 1D composition profile generated from (f) in the direction of the arrow.

[0011] Fig. 4 is the in-situ XRD patterns of the HEA with varying compositions of Zr, annealed at different temperatures. (a) Al25Co25Cr25Fe25; (b) Al24.9Co24.9Cr24.9Fe24.9Zr0.5; (c) Al24.7Co24.7Cr24.7Fe24.7Zr1.0; and (d) Al24.6Co24.6Cr24.6Fe24.6Zr1.5. The values indicated onthe profile are the holding time (in minutes) for each short scan. The “0” at the start of annealing of each sample connotes that the diffraction pattern was acquired at room temperature. The peaks labelled “0” at 873, 973, 1073, and 1123 K represent the last scan in the previous temperature.

[0012] Fig.5 is (a) instantaneous grain size as a function of annealing time for all alloy compositions during in-situ XRD annealing; (b) corresponding %increase in grain size as a function of annealing time for alloy compositions during in-situ XRD annealing.

[0013] Fig. 6 is STEM micrographs and EDS maps of Al24.7Co24.7Cr24.7Fe24.7Zr1.0HEA annealed at (a) 873 K and (b) 973 K. (a1) and (b1) are lamella cross-section of the HEA particle with corresponding HAADF-STEM and STEM-EDS maps of the alloying elements; (b1) shows evidence of phase decomposition—indicated by white arrows. (a2, a3), and (b2, b3) are BF-STEM images, showing the nanocrystalline matrix. Pt (platinum) is used as a protective layer against Gallium implantation, curtaining, and particle surface erosion during FIB sample preparation.

[0014] Fig. 7 is an APT reconstruction of the Al24.7Co24.7Cr24.7Fe24.7Zr1.0HEA annealed at 873 K. (a) 5 nm thin slice from a 3D atom map of the analyzed needle; (b) isocomposition surfaces showing the atomic concentration of each element at the GB. These values of the isocomposition surface highlight the segregation of Cr, Fe, and Zr, and the Zr-O phase at the GB edges; and (c) 1D concentration profile, generated from a region of interest in (a) in the direction of the arrow, quantitatively showing the segregation of Cr and Fe, and depletion of Al and Co (Fig.7 (c1)), and segregation of Zr and ZrO (Fig.7 (c2)).

[0015] Fig.8 is STEM micrographs and EDS of the HEA with varying amounts of Zr annealed at 973 K. (a) Al25Co25Cr25Fe25; (b) Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and (c) Al24.6Co24.6Cr24.6Fe24.6Zr1.5; (d) HR-STEM micrograph with line scan showing segregation of Zr at the GBs. The white and black arrows point at decomposed phases and Zr- decorated GBs, respectively.

[0016] Fig.9 is the nanostructure of NC-(AlCoCrFe)1-xZrxHEA heat-treated at 973 K for 4 h.5 nm thin slice from an APT reconstructed 3D atom map and 1D concentration profiles across GBs for (a) NC-Al25Co25Cr25Fe25; (b) NC-Al24.7Co24.7Cr24.7Fe24.7Zr1.0; and (c) NC-Al24.6Co24.6Cr24.6Fe24.6Zr1.5.

[0017] Fig.10 is stability maps for each of the constituent elements; (a) Co, (b) Cr; (c) Fe; and (d) Al based on Eqns. (5) and (6), where kγ is between 10 and 20 kJ / mol, and the Miedema estimates of ∆ ^^^^௫and ∆ ^^^^^and density functional theory calculations of ∆ ^^^^^^for compounds (obtained from the Open Quantum Materials Database) to observethe strength of correlation between the two axes of the stability map for the constituent elements.

[0018] Fig.11 is the (a) APT reconstruction (5 nm thin slice from a 3D atom map of the analyzed needle of Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA annealed at 973 K showing the GBs from which measurements were taken); and (b) enthalpy of GB segregation, ∆ ^^^^^of the constituent elements.

[0019] Fig. 12 is the (a) change in grain size with homologous temperature: a comparison of the stabilized NC-(AlCoCrFe)1-xZrxHEA with other NC-HEAs (AlCoCrFeNi, CoCrFeNiMn, FeCoNiCu, CoCrFeNiMnTi0.1, CoCrCuFeNi, Ni25Fe25Co25Cr25, Ni93Zr7, Ni29Fe23Co23Cr23Zr2, Ni25Fe23Co23Cr23Mo2Nb2Zr2, and Ni79.5Ta5.5Nb10W5); (b) Marked region in (a) clearly showing the growth trend; and (c) a simplified segregation model comparing the performance of bulk effect ^ ^^^^^ ^^^^, GB high entropy effect ^ ^^^^^ ^^^^, and their coupled effect, ^ ^^^^^ ^^^^, with the effects—self- ^ ^^௫∗) and coupled^ି௫ ௫∗self- and solute ^ ^^ ^^ )^ ^^^^; where element, ∗^^ element that self- ^^ solute ^^ and ^^ are 1,2, 3,….

[0020] Fig.13 is the X-ray diffractogram of the powder milled at different times, 20 to 40 h for (a) Al24.9Co24.9Cr24.88Fe24.9Zr0.5; and (b) Al24.7Co24.7Cr24.7Fe24.7Zr1.0.20 h*refers to the mixed 20 h milled-AlCoCrFe HEA plus 0.5 at. % Zr before further milling.

[0021] Fig.14 is the APT 3D reconstruction showing traces of oxygen (~1.4 at. %) at the atomic level in the as-milled AlCoCrFe sample.

[0022] Fig. 15 is the Ex-situ X-ray PDF profiles of the NC-HEAs in the as-milled state and annealed state at 973 K for 4 h: (a) Stacked PDF profiles from 1.5 to 30 Å for AlCoCrFe and (AlCoCrFe)98.5Zr1.5NC-HEAs in the as-milled and annealed states, and (AlCoCrFe)99Zr1NC-HEA in the annealed state; and (b-e) PDF profiles at lower r values from 1.6 to 3.6 Å for (b) AlCoCrFe NC-HEA in the as-milled and annealed states, (c) AlCoCrFe and (AlCoCrFe)98.5Zr1.5NC-HEAs in the as-milled state, (d) (AlCoCrFe)98.5Zr1.5NC-HEA in the as-milled and annealed states; and (e) AlCoCrFe, (AlCoCrFe)99Zr1, and (AlCoCrFe)98.5Zr1.5NC-HEAs in the annealed state.

[0023] Fig.16 is the APT data of (AlCoCrFe)98.5Zr1.5NC-HEA in the as-milled state: (a) detector hit map of 160 million ions impact after slicing the voltage curve which contains a low-density

[0100] crystallographic pole; (b) 3D atom map of ions of the constituent elements; (c) thin slice of elemental ions after calibrating the reconstruction, and it shows the atomic planes; (d) z-SDMs of same element pairs; and (e) z-SDMs of cross elements pairs.

[0024] Fig. 17 is the APT data of (AlCoCrFe)98.5Zr1.5NC-HEA sample after annealing at 973 K for 4 h: (a) detector hit map of 90 million ions impact after slicing the voltage curve which contains a low-density

[0012] crystallographic pole; (b) 3D atom map of ions of the constituent elements that shows GBs are decorated; (c) thin slice of elemental ions after calibrating the reconstruction and it shows the atomic planes; (d) z-SDMs of same element pairs; and (e) z-SDMs of cross elements pairs.

[0025] Fig.18 is the APT data of (AlCoCrFe)99Zr1NC-HEA after annealing at 873 K for 4 h: (a) detector hit map of 20 million ions impact after slicing the voltage curve which contains a low-density

[0121] crystallographic pole; (b) 3D atom map of ions of the constituent elements that shows GBs are decorated; (c) thin slice of elemental ions after calibrating the reconstruction; it shows the atomic planes; (d) z-SDMs of same element pairs; and (e) z-SDMs of cross elements pairs.

[0026] Fig.19 is the mixing enthalpy of the binary pairs, ΔHmix, of all the constituent elements of the NC-HEA.

[0027] Fig.20 is the PDF peak positions and their corresponding nearest neighbors and bond lengths. DETAILED DESCRIPTION

[0028] The present invention relates to a novel alloy design strategy for stabilizing nanocrystalline high-entropy alloys (HEAs) and other multicomponent alloy variants by coupling self-stabilizing and solute grain boundary segregation effects. The invention also relates to a method of synthesizing and annealing such alloys using mechanical alloying and heat treatment. The invention further relates to the use of such alloys for structural applications that require high strength, hardness, thermal stability, and resistance to grain coarsening and phase decomposition at high temperatures.

[0029] According to one aspect of the invention, a stable grain-boundary-decorated nanocrystalline high-entropy alloy (NC-HEA) is provided, comprising at least four principal elements in equiatomic or near-equiatomic ratios, and a minor amount of a solute element that preferentially segregates to the grain boundaries of the NC-HEA. The solute element is selected based on empirical and grain boundary segregation enthalpy considerations, such that the solute element has a different crystal structure, a large atomic size mismatch, and a higher melting point than the HEA. The solute element also has a low bulk solubility with the NC-HEA and does not form second phases or intermetallic compounds with the principal elements. The solute element reduces the excess energy at the grain boundaries and lowers the driving force for grain coarsening and phase decomposition.

[0030] According to another aspect of the invention, a method of synthesizing stable grain-boundary-decorated nanocrystalline high-entropy alloy (NC-HEA) is provided, comprising the steps of: (a) mechanically alloying a mixture of powders of at least four principal elements in equiatomic or near-equiatomic ratios to form a single-phase solid solution NC-HEA; (b) adding a minor amount of a solute element to the NC-HEA and further mechanically alloying the mixture to form a single-phase solid solution NC-HEA with the solute element; and (c) heat treating the NC-HEA with the solute element at different temperatures and holding times to drive the solute element to the grain boundaries of the NC-HEA.

[0031] According to yet another aspect of the invention, a structural material is provided, comprising a stable grain-boundary-decorated nanocrystalline high-entropy alloy (NC-HEA) as described above, having a grain size of less than 20 nm and a phase stability up to at least 0.64 times the melting temperature of the NC-HEA. The structural material exhibits high strength, hardness, thermal stability, and resistance to grain coarsening and phase decomposition at high temperatures. The structural material is suitable for various applications that require these properties, such as wear resistance, fatigue resistance, corrosion resistance, and magnetic properties.

[0032] In one aspect, there is provided a method of forming a stable grain- boundary-decorated nanocrystalline high-entropy alloy (HEA) comprising: processing a mixture of at least four principal elements in equiatomic or near-equiatomic ratios to form a single-phase solid solution HEA as a solvent; adding a solute element to the solvent, the solute element having a different crystal structure, an atomic size mismatch of at least 15%, and a higher melting point than the solvent; processing the solvent and the solute element until a single-phase solid solution HEA is formed; and annealing the single-phase solid solution HEA at 0.46 to 0.67 of the melting temperature of the HEA to form the stable grain- boundary-decorated nanocrystalline HEA.

[0033] The processing may be mechanically alloying or any other suitable method. The processing may include mechanically alloying, physical vapor deposition, electrodeposition, chemical vapor deposition, plasma-spraying, casting, or solidification.

[0034] The annealing may be done at any suitable temperature such as at 0.46 to 0.67 of the melting temperature of the HEA. The annealing may be done at 0.46 to 0.64 of the melting temperature of the HEA. The annealing may be done at 0.46, 0.47, 0.48, 0.49, 0.50, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.60, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, or 0.67 of the melting temperature of the HEA. The annealing may be done at 0.46 to0.50, or 0.50 to 0.55, or 0.55 to 0.60, or 0.60 to 0.64, or 0.60 to 0.67 of the melting temperature of the HEA.

[0035] The principal elements may be selected from the group consisting of Al, Co, Cr, and Fe. The principal elements may be any suitable elements. The Example provided herein utilizes Al, Co, Cr, and Fe as principal elements; however, it is understood that this approach could be used for alloys with differing principal elements.

[0036] The solute element may be selected from the group consisting of Zr, Hf, and Sc. For example, the solute element may be Zr, and the concentration of Zr may be between 0.5 and 1.5 at.%. The solute element may be different depending upon the HEA. For example, if the principal elements are not Al, Co, Cr, and Fe, then other elements may be chosen to satisfy the criteria of: the solute element having a different crystal structure, an atomic size mismatch of at least 15%, and a higher melting point than the solvent.

[0037] The mechanical alloying may be performed in a planetary ball mill with a ball-to-powder ratio of 10:1 and a process control agent of 1 wt.% ethanol.

[0038] The annealing may be performed in an inert gas environment with a heating rate of 50 °C / min and a holding time of 4 h per temperature step.

[0039] The solute element may segregate to the grain boundaries of the HEA, along with one or more of the principal elements with the highest average mixing enthalpy and melting point, to reduce the excess energy and the driving force for grain coarsening and phase decomposition.

[0040] The nanocrystalline HEA may be stabilized against grain growth, including short and long- range orderings, and phase decomposition at high homologous temperatures.

[0041] In one aspect, there is provided a nanocrystalline HEA obtained or obtainable by the methods herein disclosed.

[0042] The nanocrystalline HEA may have a body-centered cubic (BCC) crystal structure and an average grain size of less than 20 nm.

[0043] The nanocrystalline HEA may have a near-equiatomic composition of Al, Co, Cr, and Fe, wherein Zr is present in a concentration ranging from 0.5 to 1.5 at.%.

[0044] The nanocrystalline HEA may have a homogeneous distribution of the principal elements in the grain interior and a co-segregation of Zr, Cr, and Fe at the grain boundaries.

[0045] The nanocrystalline HEA may have Zr form a Zr-O phase at some of the grain boundaries.

[0046] The nanocrystalline HEA may have one or more of a high strength, hardness, wear resistance, corrosion resistance, and thermal stability.

[0047] In one aspect, there is provided a method of stabilizing nanocrystalline HEAs against grain growth and phase decomposition at high homologous temperatures comprising: processing a mixture of at least four principal elements in equiatomic or near- equiatomic ratios to form a single-phase solid solution HEA as a solvent; adding a solute element to the solvent, the solute element having a different crystal structure, an atomic size mismatch of at least 15%, and a higher melting point than the solvent; processing the solvent and the solute element until a single-phase solid solution HEA is formed; and annealing the single-phase solid solution HEA at 0.46 to 0.67 of the melting temperature of the HEA for a predetermined time to form the stable grain-boundary-decorated nanocrystalline HEA, wherein the solute element segregates to the grain boundaries of the HEA, along with one or more of the principal elements with the highest average mixing enthalpy and melting point, to reduce the excess energy and the driving force for grain coarsening and phase decomposition.

[0048] In one aspect, there is provided a pseudo-binary thermodynamic approach for designing stable grain-boundary-decorated nanocrystalline high-entropy alloys (HEAs) and other multicomponent alloy variants, comprising: a) selecting a single-phase solid solution HEA as a solvent, wherein the HEA comprises at least four principal elements in equiatomic or near-equiatomic ratios; b) selecting a solute element that meets the following criteria: i) the solute element has a different crystal structure from that of the solvent; ii) the atomic size mismatch between the weighted average atomic size of the HEA and the atomic radius of the solute element is at least 15%; iii) the melting point of the solute element is higher than that of the HEA; c) processing the solvent and the solute element until a single- phase solid solution HEA is formed; d) annealing the single-phase solid solution HEA at 0.46 to 0.67 of the melting temperature of the HEA for a predetermined time; e) wherein the solute element segregates to the grain boundaries of the HEA, along with one or more of the principal elements with the highest average mixing enthalpy and melting point, to reduce the excess energy and the driving force for grain coarsening and phase decomposition.

[0049] In one aspect, there is provided a nanocrystalline high-entropy alloy (HEA) or other multicomponent alloy variant designed by the pseudo-binary thermodynamic approach herein disclosed.EXAMPLES

[0050] Example 1: Design and development of stable nanocrystalline high-entropy alloy: coupling self-stabilizing and “solute” grain boundary segregation effects

[0051] Abstract

[0052] Grain growth is prevalent in nanocrystalline (NC) materials at low homologous temperatures, thereby limiting their use in structural applications. Solute- element addition to offset excess energy that drives coarsening at grain boundaries (GBs) is an effective metallurgical means of stabilizing NC materials, albeit, mostly for simple binary alloy systems. This thermodynamic approach is considered complicated in multi- component systems due to the possible complex pairwise interactions that could set on among the alloying elements. Guided by the empirical and GB segregation enthalpy considerations for binary alloy systems, we propose and develop a novel alloy design strategy referred to as the “pseudo-binary thermodynamic” approach, for stabilizing NC- high entropy alloys (HEAs) and other multicomponent alloy variants. Using Al25Co25Cr25Fe25as a model HEA to validate our approach, any of Zr, Sc, and Hf, are identified as the preferred solutes that would prefer to segregate at the HEA GB to stabilize it against grain growth. Using Zr, NC- Al25Co25Cr25Fe25HEAs with minor additions of Zr were synthesized, followed by annealing at different temperatures up to 1123 K. Using advanced characterization techniques—in-situ X-ray diffraction, scanning / transmission electron microscopy, and atom probe tomography, we report for the first time, nanograin stability in multicomponent HEAs up to substantially high homologous temperatures by coupling self- stabilizing and solute GB segregation effects. The self-stabilizing effect originates from the preferential GB-segregation of constituent HEA-elements that stabilizes NC- Al25Co25Cr25Fe25up to 0.5 Tm(Tm–melting temperature). Meanwhile, the solute GB segregation effect originates from the segregation of Zr to the GB of the solvent—NC- Al25Co25Cr25Fe25; this results in further stabilization of the phase and grain size (~14 nm) up to ~0.58 and ~0.64 Tm, respectively. These findings open a new way of designing stable nanocrystalline multicomponent HEAs for extreme service conditions.

[0053] Introduction

[0054] There is a lot of interest in nanocrystalline (NC) materials due to their many unique mechanical and functional properties such as high strength, superior wear resistance, super-plasticity and ductility, high fatigue resistance, excellent corrosion resistance, and good magnetic properties. More so, NC materials have a beneficial and unique combination of these properties that are sometimes mutually exclusive. Theseimproved properties, e.g., high strength and good wear resistance, benefit from a large volume fraction of grain boundaries (GBs) due to grain refinement to the nanometer range, and in turn, more barriers to dislocation slip. However, NC materials are generally thermally unstable even at low homologous temperatures because of the excess energy at GBs which is the driving force for grain coarsening—atoms at GBs are disorderly arranged, thus GBs exist in a high energy state and they contribute to the overall energy of the material system. The propensity for grain growth in NC materials significantly limits their use in various structural applications.

[0055] There are two established ways to address the thermal instability in NC materials. The first is the kinetic approach in which GB mobility is decreased by different GB-pinning ‘drag’ forces viz. solute drag, second phase drag, and chemical ordering. However, this approach is less effective due to its dependency on temperature. A more effective strategy is the thermodynamic approach, which depends on lowering the excess energy at the GBs through solute segregation. Thermodynamically, the change in Gibbs free energy, G, with reference to the GB area, A, is directly proportional to the GB excess energy, ^^, according to; ^^ ^^ ∝ ^^ ^^ ^^ (1)

[0056] Using the Gibbs adsorption isotherm as a starting point, Weissmuller noted that in the dilute limit, the GB energy, ^^, is lowered when solute atoms are segregated to the GBs via; ^^ ൌ ^^^െ Γ^Δ ^^^^^െ ^^ ^^ log^ ^^^^ (2) where, ^^^is the GB energy of a pure element, Γ is the solute excess at the GB, Δ ^^^^^is the enthalpy of segregation, ^^ is the Boltzmann constant, ^^ is temperature, and ^^ is the global solute concentration.

[0057] The classical McLean model which is premised on statistical mechanics, divides solute atoms among the matrix, and GB sites. McLean employed a regular solution approximation model where the driving force for segregation is the strain energy from solute misfit. The following relationship is used to determine the degree of solute atom segregation based on the McLean isotherm: ^ಸಳ ^ ೞ^^ൌ^^^ ^^ ^^^െ∆ு^ି^ಸಳ ^ି^^ ^் ^(3)w ^^ீ^is the is the atomic soluteconcentrations in and ∆ ^^^^^is the average GB segregation energy that can be obtained from the following equation; ∆ ^^^^^ൌ ^^^ீ^^^௨௧^െ ^^^^^^௨௧^(4)where ^^^ீ^^^௨௧^and ^^^^^^௨௧^are the energies of the solute at the GB and matrix, respectively. There have since been some modifications of the classical McLean model, including those of Kirchheim, Guttmann, and Schuh and co-workers. Due to its effectiveness, i.e., less temperature dependency, the thermodynamic approach has been used to design stable NC materials mainly for simple binary alloy systems. Some of the NC binary alloy systems include Fe-Zr, Pd-Zr, Ni-P, Ru-Al, Nb-Cu, Ti-Cu alloys, and those of Ni-W, Fe-Mg, and W- Ti alloy systems by Schuh and co-workers. There are three categories of solute interactions established in binary alloy systems that can influence the stability of GBs, namely co- segregation (where the segregation of an element with weaker GB interaction is due to the segregation of another element with stronger GB interaction because of the strong interaction between the two elements), site competition (where two elements, both having the potential to segregate at the GBs but are mutually repulsive, compete for site at the GBs, with the element having the strongest GBs interaction eventually occupying the site), and no interaction (where the addition of a solute element has no significant effect on GB segregation).

[0058] However, most engineering materials are multi-element alloys beyond the binary alloy systems, and they require a better understanding of GB stabilization due to the complex pairwise interactions that may exist among the constituent elements. High-entropy alloys (HEAs) are one of those complex multi-element alloys; these are concentrated solid solution alloys of at least four principal elements in equiatomic or near-equiatomic ratios typically within the range of 5 – 35 at. %. These alloys are characterized by high configurational entropy of mixing as compared to conventional alloys. HEAs possess remarkable properties such as high strength and hardness, good thermal stability, good ductility, excellent wear, oxidation, and corrosion resistance, as a result of their unique core effects. Grain boundary segregation has been observed in microcrystalline HEAs. For example, Li et al. studied the GB segregation in FeMnNiCoCr HEA and reported the segregation behavior of constituting elements at different GB characters: Ni and Mn co- segregated at high-angle GBs due to the large tendency for Ni and Mn to mix, while no segregation and slight segregation of Ni were observed at the twin boundaries and low- angle boundaries, respectively. Babicheva et al. analyzed short-range ordering and GB segregation in CoCrFeNi bi-crystals and Al (8 at. %)-CoCrFeNi HEAs using molecular dynamics and Monte Carlo simulations, and observed the segregation of Cr and Fe, and Al and Fe in CoCrFeNi and Al (8 at. %)-CoCrFeNi, respectively.

[0059] Recent work on NC-HEA observed the self-segregation of Cr and Fe in a model AlCoCrFe alloy, which stabilized the NC-HEA system even at high homologoustemperature (773 and 873 K) without the introduction of a solute element, as in the case of thermodynamic approach for binary alloy systems; a phenomenon that was termed as self- stabilizing effect. This work also shows that GB segregation competes with GB desegregation and phase decomposition, after which grain coarsening sets on. This points to an important hypothesis: further stabilizing GBs will delay phase decomposition and eventual grain growth. As a starting point, the objective of the current work is to determine the GB segregation and stabilization behavior of complex multi-element alloy systems like HEA, coupling the self-stabilizing and classical “solute” segregation effects (following a thermodynamic approach). We demonstrate for the first time that a thermodynamic GB segregation approach can still be tacitly used to stabilize multi-element NC-HEA using a pseudo-binary alloy system approach, in this case, single-phase solid solution HEA is the solvent, while a solute is carefully selected following the empirical and GB segregation enthalpy considerations.

[0060] Approach

[0061] In a thermodynamic GB stabilization approach for conventional binary alloy system via mechanical alloying process, a dilute solute element is added and milled with one principal element, followed by heat treatment to drive the solute to the GBs, as depicted in the schematic in Fig. 1 (a). Learning from this approach, we develop and propose an alloy design strategy for stabilizing NC-HEA and other complex multicomponent alloy variants; this is referred to as a pseudo-binary thermodynamic approach, and it is used to realize the objective of this work. An overview of this new approach is presented in Fig.1 (b): constituent HEA elements are first “forced-mixed” into a single-phase solid solution HEA through a mechanical alloying process—which serves as the solvent. Subsequently, a carefully selected solute is introduced into the single-phase HEA and further milled until a single-phase HEA forms; finally, the solvent (HEA)-solute system is heat-treated to drive the solute to HEA GBs.

[0062] We show that, as it is for binary alloy systems, where empirical considerations for solute selection would result in low bulk solubility of the system, these considerations can be followed for appropriate selection of solute that would segregate to the HEA-GBs. The empirical considerations that promote solute segregation at HEA-GBs include; (i) the solute should have a different crystal structure from that of the solvent— HEA,(ii) the atomic size mismatch, Δr, between the weighted average atomic size of HEA ( ^^^) and the atomic radius of solute ( ^^^) should be ≥ 15%, which can be calculated via: ^^ ^^ ൌ ^ଶ^^ಲି^ಳ^^ಲା^ಳ^, and (iii) the melting be higher than that of the HEA; the meltingpoint of or alloys can be estimated via: ^^^ൌ ∑^ಯೕ்^షೕൈ^^ൈ^ೕ∑^ಯೕ ^^ൈ^ೕ; where ^^^and ^^^are the atomic percentages of the ^^-th and ^^-th temperatures. This criterion isto GB upon solute segregation: high melting point elements increase bond strength, and their segregation to the GBs improves GB cohesion (enriched GB).

[0063] We used a quaternary BCC AlCoCrFe HEA (detailed design and development procedure in “Moses A. Adaan-Nyiak, Intekhab Alam, and Ahmed A. Tiamiyu, Powder Technology 427 (2023) 118766” and “I. Alam, M.A. Adaan-Nyiak, A.A. Tiamiyu, Intermetallics 159 (2023) 107919”) as a solvent to validate the approach described in Fig. 1 (b). As a starting point, we calculated the quaternary phase diagram of Al25Co25Cr25Fe25HEA using the CALculation of PHAse Diagrams (CALPHAD) approach via the Thermo- Calc 2023a software. The phase diagram in Fig.1 (c) confirms that a single-phase BCC crystal structure is expected. Considering that the crystal structure and melting point of Al25Co25Cr25Fe25HEA are BCC and 1673 K, respectively, a Venn diagram developed based on the solute-selection criteria (i)-(iii) above shows that only Zr, Hf, and Sc satisfy all the criteria, including Δr ^ 15% for these elements (Fig.1 (d)). Therefore, Zr was selected as the solute for this study due to its abundance and lower cost in comparison with Hf and Sc. In addition, the selected solute (Zr) should be in low bulk solubility with Al25Co25Cr25Fe25HEA, and this is confirmed in the calculated equilibrium phase diagram which shows only ~0.007 mole fraction of Zr (~0.7 at. % Zr) in solid solution with BCC Al25Co25Cr25Fe25HEA in Fig. 1e. Figure 1e also shows the possible presence of minor Laves phases—AB2intermetallic compounds that are in most cases deleterious—at lower temperature regime, which can be suppressed in a far-from-equilibrium process like mechanical alloying. However, a maximum of 1.5 at. % Zr—(AlCoCrFe)1-xZrx, x = 0, 0.5, 1.0, and 1.5—was used in this study to further suppress the chances of second phase formation and solute interactions at higher concentrations that oppose further GB segregation according to Fowler and Guggenheim.

[0064] Experimental Procedure

[0065] CALPHAD Simulation

[0066] The CALculation of PHAse Diagrams (CALPHAD) simulations were conducted on the Thermo-Calc software by utilizing the database–TCHEA6.1: High Entropy Alloy Database. Material to Material Calculator module was used for these simulations, where the calculations are only based on thermodynamic equilibrium.

[0067] As-received Powders and Mechanical Alloying Process

[0068] The details of the as-received Al, Co, Cr, and Fe powders have already been discussed in our previous work. Zr powder with 99.9% purity and 21 ± 3 µm average particle size was purchased from Nanografi. The Al, Co, Cr, and Fe powders were measured in an equiatomic ratio and milled in a planetary ball mill (PBM-04, MicroNano Tools). Using zirconia vacuum grinding jars with stainless steel jackets, the milling was conducted with stainless steel balls and 1 wt. % ethanol process control agent in an inert atmosphere. Milling was carried out at 350 rpm for up to 20 hrs where single phase BCC solid solution Al25Co25Cr25Fe25HEA formed—this is the solvent in the pseudo-binary thermodynamic approach. The choice of the processing parameters and further details of the milling environment and media can be found elsewhere. Subsequently, the solute—Zr was added to the Al25Co25Cr25Fe25solvent at varying concentrations of 0.0, 0.5, 1.0, and 1.5 at. %, and was milled further for 20 hrs at 350 rpm to obtain Al25Co25Cr25Fe25+ 0 at. % Zr (Al25Co25Cr25Fe25), AlCoCrFe + 0.5 at. % Zr (Al24.9Co24.9Cr24.9Fe24.9Zr0.5) AlCoCrFe + 1.0 at. % Zr (Al24.7Co24.7Cr24.7Fe24.7Zr1.0,), and AlCoCrFe + 1.5 at. % Zr (Al24.6Co24.6Cr24.6Fe24.6Zr1.5) alloys in solid solution. Note that the atomic percent of Al, Co, Cr, and Fe are approximations for convenience, i.e., Al24.875Co24.875Cr24.875Fe24.875Zr0.5, Al24.75Co24.75Cr24.75Fe24.75Zr1.0¸ and Al24.625Co24.625Cr24.625Fe24.625Zr1.5, are shortened to Al24.9Co24.9Cr24.9Fe24.9Zr0.5, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, Al24.6Co24.6Cr24.6Fe24.6Zr1.5, respectively, and the later description will be used throughout the manuscript. Alloy samples were taken out at 10 hrs intervals for characterization, and the 10:1 ball-to-powder ratio was maintained throughout the milling process.

[0069] Heat Treatment and Characterization of HEA Powder

[0070] The morphology and elemental distribution of the as-milled samples were determined using an SEM (Bruker Nano GmbH Berlin, Germany) coupled with a XFlash 5030 energy dispersive spectroscopy (EDS) detector and operating at 20 keV. To determine the phase evolution and grain size of the alloy powders, ex-situ XRD measurement was carried out using Bruker D8 Advance equipment with Cu Kα (λ = 0.15418 nm) radiation. We used 10o-90oas the range of scanning angle (2θ) at a constantscanning rate of 2.3o / min. DIFFRAC.EVA (Bruker) software was used for the post- processing the post-processing of ex-situ XRD results. In-situ XRD measurements were carried out so that the microstructural behavior of the HEA as a function of temperature could be evaluated. After mounting the as-milled samples on the DHS 900 heating stage, they were annealed in an in-house furnace inside the Bruker D8 Discover X-ray diffractometer with Cu Kα (λ = 0.15418 nm) radiation and high throughput, highly sensitive LynxEYE 1-D detector. During annealing, an inert nitrogen gas environment was maintained to prevent oxidation. The annealing and data acquisition scheme consisted of room temperature (30 ℃) and four sequential annealing steps: 500 ℃ (773 K), 600 ℃ (873 K), 700 ℃ (973 K), and 800 ℃ (1073 K) for Al25Co25Cr25Fe25, Al24.9Co24.9Cr24.9Fe24.9Zr0.5, and Al24.7Co24.7Cr24.7Fe24.7Zr1.0samples and 873, 973, 1073, and 1123 K for Al24.6Co24.6Cr24.6Fe24.6Zr1.5sample. A 50 ℃ / min heating rate was employed in between segments.21 consecutive diffraction patterns were collected at each temperature step: 20 narrow scans in the 40o–47.5o2θ range at 10 min / scan scanning rate and a wide scan in the 10o–90o2θ range at 40 min / scan scanning rate; these resulted in an annealing / holding time of 4 h per temperature step, and 16 h per sample. The narrow scans were aimed to determine grain and phase stability as a function of temperature. Scherrer equation was used to determine the grain size from the in-situ XRD patterns.

[0071] Based on the observation from the aforementioned in-situ XRD measurements, the heat treatment of as-milled powders was carried out at 773 and 973 K for Al25Co25Cr25Fe25, 873 and 973 K for Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and only 973 K for Al24.6Co24.6Cr24.6Fe24.6Zr1.5samples for 4 h hours at each temperature, using a LINDBERG SOLA BASIC+ tube furnace. An inert argon gas environment with a gas flow rate of 200 mL / min was maintained during the heat treatment process. After each heating cycle, the heat-treated samples were quenched in water at room temperature. For the scanning / transmission electron microscopy (S / TEM) analyses, the TEM lamella was prepared using the ThermoFisher Scientific Helios G5 Dual-Beam focused ion beam (FIB) following a standard in-situ lift-out process; lamella thickness was progressively reduced to ~50 nm, while gradually reducing the Ga+ beam voltage to 2 keV. The S / TEM analyses on both as-milled and heat-treated samples were carried out using a ThermoFisher Scientific X-FEG Talos 200X with a super-X EDS detection system, operating at an accelerating voltage of 200 keV.

[0072] An atom probe tomography (APT) technique was used for mapping the 3D-atomic distribution of constituent elements in the as-milled and heat-treated samples[1]. A ThermoFisher Helios 5 UC Duel-Beam FIB was used for needle sample preparationfollowing a standard in-situ lift-out procedure: randomly chosen particles were milled into a cantilever wedge by employing a micromanipulator arm and in-situ gas injection system (W source). Subsequently, the liftout wedge was joined onto the apex of prefabricated Si-posts from CAMECA Instruments and cut into separate segments. Then the segmented specimens were annular milled into needle-shaped microtips using a 30 kV accelerating voltage and successively lowering beam currents from 0.7 nA to 40 pA. To eliminate the material regions damaged by Ga-ion implantation, a final 5 kV milling step was used for the cleanup. CAMECA Local Electrode Atom Probe (LEAP) 5000 XS was employed to analyze the fabricated specimens. Field evaporation of each specimen was facilitated by applying a high electric potential to the tip under an ultra-high vacuum (10-11torr) and cryogenic conditions (~30 K). The evaporation of ions was controlled by pulsing a 355-nm-wavelength ultraviolet laser (20 pJ, 250 kHz) onto the apex of the specimen and gradually increasing the voltage to maintain an average ion detection rate of 0.005 ions per pulse (0.5%). The AP Suite 6.1 software from CAMECA was utilized for reconstructing the APT data.

[0073] Results

[0074] Micro- and nano-structural evaluation of the as-milled NC-(AlCoCrFe)1-xZrxHEA

[0075] The X-ray diffractograms of the milled Al25Co25Cr25Fe25powder show the onset of BCC single-phase solid solution after 10 hrs: only three BCC peaks—(101), (200), and (211) are evident at and above 20 hrs of milling, as shown in Fig.2 (a). The milling process was continued for an additional 20 hrs to produce a more homogenous phase and further reduce the powder’s final grain size to ~6 nm. The unmixed powder (0 hr) shows diffraction peaks that correspond to each of the constituents, Al, Co, Cr, and Fe. However, with prolonged milling, three notable changes are observed: a decrease in the intensity of elemental peaks, the disappearance of the elemental peaks, and peak broadening (see Fig.2 (a) inset)—an indication of grain refinement and increase in lattice strain due to lattice distortion. In agreement with the XRD results, and at least within their (XRD and EDS) resolution limits, the SEM-EDS maps in Figs. 2 (b-d) show uniform and chemically homogeneous distribution of the constituent NC-Al25Co25Cr25Fe25HEA elements at 20 and 40 hrs. Only the 40 hrs sample is further analyzed in the remainder of this section.

[0076] The cross-section of the high-angle annular dark field (HAADF)-STEM image and the corresponding energy dispersive X-ray spectroscopy (EDS) elemental maps of the NC- Al25Co25Cr25Fe25HEA after 40 hrs is shown in Fig.2 (e): it shows the chemical homogeneity of the as-milled HEA except for a few unmixed regions. The TEM bright field (BF) micrograph of the as-milled HEA is shown in Fig. 2 (f); the corresponding selectedarea electron diffraction (SAED) that confirms single phase solid solution with BCC crystal structure is shown as an inset. The HEA is nanocrystalline with an average grain size of about ~7 nm; which is close to ~6 nm grain size obtained from the XRD analysis. The APT three-dimensional (3D) atom maps of the alloying elements in the as-milled NC- Al25Co25Cr25Fe25HEA are shown in Fig.2 (g): they reveal the homogenous distribution of Al, Co, Cr, and Fe throughout the studied needle volume with no signature of segregation or clustering even at the atomic level. A minute trace of oxygen (~1.4 at. %) is recorded at the atomic level as shown in Fig.14.

[0077] Similarly, the microstructural evolution in the as-milled (AlCoCrFe)1-xZrx, using Al24.6Co24.6Cr24.6Fe24.6Zr1.5, is presented in Fig. 3. Figure 3 (a) shows the X-ray diffractograms of the HEA at 20 hrs of milling and just after the addition of 1.5 at. % Zr without further milling—represented as 20 hrs*. However, as milling progresses, the disappearance of the diffraction peaks corresponding to Zr occurs, and a complete single- phase solid solution with BCC crystal structure—(101), (200), and (211) peaks formed after 20 hrs of additional milling, i.e., 40 hrs of total milling time. A similar trend is observed for 0.5 and 1.0 at. % Zr samples as shown in Figs.13 (a) and (b). The grain size obtained from XRD analyses for Al24.9Co24.9Cr24.9Fe24.9Zr0.5, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5at 40 hrs of milling are ~8, ~7, and ~7 nm, respectively. The SEM image and the corresponding EDS maps of the Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA after 40 hrs of milling are shown in Fig.3 (b): it suggests complete alloying and the uniform distribution of Zr.

[0078] The cross-sectional STEM-EDS maps in Fig. 3 (c) further confirm the near-chemical homogeneity of the Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA. However, the TEM-BF micrograph and the corresponding SAED pattern in Fig.3 (d) reveal an extra (100) HCP ring in addition to those of BCC—(101), (200) and (211), which can be attributed to the fairly-unmixed Zr in Fig.3 (c). The grain size determined from Fig.3 (d) is ~7 nm, which is close to that of what was determined from XRD (6.7 nm). At the atomic level, all alloying elements including Zr are uniformly distributed with no evidence of GB segregation, as demonstrated by the APT 3D atom maps in Fig.3 (e). The uniform distribution of each of the constituent elements is further confirmed by analyzing a rectangular 11 × 6 × 5 nm3sub-volume in Fig. 3 (f), taken from a random region of interest in Fig. 3 (e). A one- dimensional (1D) composition profile is generated from the sub-volume in Fig. 3f in the direction of the arrow along the sub-volume's z-axis, as shown in Fig.3 (g), to demonstrate that the near-equiatomic composition of the Al25Co25Cr25Fe25HEA as well as the 1.5 at. % Zr was maintained after MA. There are no statistically significant concentration fluctuations.Despite milling in an inert environment, the interstitial element, oxygen, is observed in Fig. 3 (g), up to ~2 at. %. These results show the successful development of the NC-BCC solid- solution (AlCoCrFe)1-xZrx HEAs with no signature of GB segregation. In what follows, we assess the thermal stability of (AlCoCrFe)1-xZrxHEAs using in-situ XRD heat treatment at different temperatures.

[0079] In-situ Annealing of Nanocrystalline (AlCoCrFe)1-xZrxHEAs for Phase and Grain Stability Evaluation

[0080] The narrow scans from the in-situ XRD annealing are presented in Fig.4 to evaluate the effect of Zr addition on the thermal stability of NC-AlCoCrFe HEA. The in-situ annealing was done at different temperatures—773 K (~0.46 Tm), 873 K (~0.52 Tm), 973 K (~0.58 Tm), and 1073 K (~0.64 Tm) for Al25Co25Cr25Fe25, Al24.9Co24.9Cr24.9Fe24.9Zr0.5, and Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and at 873 K (~0.52 Tm), 973 K (~0.58 Tm), 1073 K (~0.64 Tm), and 1123 K (~0.67 Tm) for Al24.6Co24.6Cr24.6Fe24.6Zr1.5. For clarity, the minor additions of Zr do not alter the melting point of Al25Co25Cr25Fe25HEA significantly. For instance, the melting point for Al24.6Co24.6Cr24.6Fe24.6Zr1.5is 1678 K, hence, no impact on the homologous temperatures. Note that the specified temperature range is at or above the temperature where the grain boundary diffusion dominates, and grain coarsening should be anticipated. Phase stability is observed in the Al25Co25Cr25Fe25HEA up to 873 K—no new diffraction peaks evolved as shown in Fig.4 (a). However, new peaks emerged at 42.1°, 43.3°, 45.5°, and 46.6° 2θ angles when the annealing temperature was increased to 973 K, and subsequently 1073 K—indicating thermal instability at these temperatures. The new peaks have been identified to be AlCo in our prior work with the CrFe rich phase possibly subsumed in the main BCC peak. A similar trend is observed for Al24.9Co24.9Cr24.9Fe24.9Zr0.5, as shown in Fig.4 (b); hence, we safely conclude that the addition of 0.5 at. % Zr has no significant effect on the phase stability of NC-Al25Co25Cr25Fe25HEA. Increasing the amount of Zr to 1.0 at. % (Al24.7Co24.7Cr24.7Fe24.7Zr1.0) results in phase stabilization up to 973 K at lower annealing times, as shown in Fig.4 (c); new minor peaks start to appear at above 150 mins of annealing (denoted 150 in Fig.4c). At 1073 K, the evolution of the new XRD peaks—a signature of phase instability—can be clearly discerned. Intriguingly, increasing the amount of Zr to 1.5 at. % (Al24.6Co24.6Cr24.6Fe24.6Zr1.5) resulted in phase stability up to 1073 K below 50 mins, and complete instability at 1123 K, as shown in Fig.4 (d).

[0081] To assess the role of Zr addition on grain stability, the instantaneous grain size as a function of annealing time for each sample is presented in Fig.5 (a). While the grain size of all NC-HEAs in the as-milled state is ~6 nm, there is a slight increase in grain size at the start of each annealing temperature for all samples: for Al25Co25Cr25Fe25andAl24.9Co24.9Cr24.9Fe24.9Zr0.5HEAs, grain size increases up to ~8 nm at 773 K, and to ~10.0 nm at 873 K. The initial increase in grain size at the start of each annealing temperature is attributed to the alloy system finding a thermodynamically stable grain size at these temperatures. At and above 973 K, increase in grain size is recorded for these samples: grain size increases from ~10.0 nm at 873 K to about 14 (Al25Co25Cr25Fe25) and 12 nm (Al24.9Co24.9Cr24.9Fe24.9Zr0.5) at 973 K, and to a final grain size of 27.5 (Al25Co25Cr25Fe25) nm and 23 (Al24.9Co24.9Cr24.9Fe24.9Zr0.5) nm at 1073 K after annealing for a total time of 16 h. For Al24.7Co24.7Cr24.7Fe24.7Zr1.0, the grain size increases initially from 6 nm (as-milled state) to 8 nm at 773 K, and becomes significantly stable up to 973 K, followed by a subsequent nanograin coarsening to ~18 nm at 1073 K. Finally, for Al24.6Co24.6Cr24.6Fe24.6Zr1.5, the grain size increases initially from the as-milled state to 10 nm at 873 K, and becomes significantly stable up to 1073 K (14 nm) with no evidence of coarsening. The corresponding percentage increase in grain size as a function of annealing time for each temperature is shown in Fig. 5 (b). The maximum percentage increase in grain size occurs at the early stage of annealing at 773 K (873 K for Al24.6Co24.6Cr24.6Fe24.6Zr1.5) as arrowed in Fig.5 (b), followed by a slight increase at the start of other annealing temperatures for all samples. Increasing grain stability can be deduced from this plot when the slope approaches zero. Clearly, the incremental addition of 0.5 at. % Zr simultaneously increases the temperature limit of GB stabilization by 100 K: grain stability occurs up to 773, 873, 973, and 1073 K for NC- Al25Co25Cr25Fe25, Al24.9Co24.9Cr24.9Fe24.9Zr0.5, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEAs, respectively, in Fig.5 (b).

[0082] Although the selection of Zr was aimed at stabilizing GBs of NC-Al25Co25Cr25Fe25, these results point to the potential use of Zr as a thermal phase (beyond a critical threshold of 0.5 at. %) and grain size stability agent. In what follows, microstructural evolution and evaluation of Al25Co25Cr25Fe25, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5heat-treated at 873 and 973 K are presented to understand the mechanism of phase and grain stability in NC (AlCoCrFe)1-xZrxHEA.

[0083] Microstructural Evolution During Ex-situ Annealing of NC-(AlCoCrFe)1-xZrxHEA

[0084] To understand the mechanisms of nanograin stability in NC-(AlCoCrFe)1-xZrx, the Al25Co25Cr25Fe25, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5samples heat-treated at 873 and 973 K for 4 h are compared to the as-milled state in Figs. 2 and 3. Specifically, the effect of temperature at a fixed Zr content, and the effect of Zr addition at a fixed annealing temperature are evaluated in what follows.

[0085] Effect of Temperature on the Stability of NC-Al24.7Co24.7Cr24.7Fe24.7Zr1.0HEA

[0086] The STEM-EDS elemental maps and BF-STEM images of lamella cross-section of Al24.7Co24.7Cr24.7Fe24.7Zr1.0 particle heat-treated at 873 and 973 K are shown in Figs.6 (a) and (b), respectively. At 873 K, a homogenous phase—a characteristic of a stable phase that is consistent with the in-situ XRD result in Fig. 4 (c), can be seen in HAADF image and the corresponding EDS maps in Fig.6 (a1). At the same temperature, the BF-STEM images in Figs.6 (a2) and (a3) confirm a homogenous phase and dominant nanocrystalline structure with an average grain size of ~12 nm. However, at 973 K, HAADF image and EDS maps in Fig. 6 (b1) show the onset of Al24.7Co24.7Cr24.7Fe24.7Zr1.0decomposition into Al-Co and Cr-Fe rich regions, and the micro-sized Cr-Fe rich phase regions appear mainly as bright contrast regions in HAADF image in Fig.6 (b1). The BF- STEM images in Fig. 6 (b2) confirm the onset of phase decomposition (see arrowed regions) in NC-Al24.7Co24.7Cr24.7Fe24.7Zr1.0HEA after annealing at 973 K for 4 h, in agreement with the in situ XRD results in Fig.4 (c). Despite the onset of phase instability at 973 K, grain stability is still observed at this temperature (~13 nm grain size, which is close to 12 nm obtained at 873 K in Fig.6 (a)).

[0087] The mechanism of nanograin stability in Al24.7Co24.7Cr24.7Fe24.7Zr1.0HEA annealed at 873 K is evaluated by examining the APT 3D reconstructed atom map (5 nm thin slice taken from the center of the bulk needle down the z-axis) in Fig.7 (a). Unlike the observations in the as-milled APT results in Fig.3 (e) where no clear GBs are discernable, GBs can be clearly seen with evidence of segregation of some alloy constituent elements after annealing at 873 K (Fig.7 (a)). The map shows an average grain size of about 11 nm, which is close to the grain size determined from in-situ XRD data in Fig.5 (a). To determine which elements are segregating at the GBs, isocomposition surface analysis is performed using a threshold value of ~34.0 at. % Al, ~39.0 at. % Co, ~35.0 at. % Cr, ~30.0 at. % Fe, and ~0.2 at. % Zr as shown in Fig.7 (b): Cr, Fe, and Zr are co-segregating at the GBs, while Al and Co are mostly concentrated in the grain interior. Interestingly, some Zr are found to be preferentially oxidized at the GBs to form Zr-O phase, and they are identified with an isocomposition surface threshold value of ~1.4 at. %; we posit that the preferential oxygen picks up by Zr at the GBs is due to its lower enthalpy of oxide formation compared to those of Fe and Cr. This behavior is similar to what was observed by Xu et al. in NC Fe- Cr alloy stabilized by Hf, where Hf oxidized to contribute to the thermal stability of the alloy. The presence of Zr-O phase may contribute to the kinetic stabilization of the GBs via GB pinning.

[0088] The 1D composition profile generated from a cylindrical (height 144 nm and diameter 5 nm) sub-volume taken across a few grains (in Fig.7 (a)) quantitatively shows and confirms the level of segregation of the alloying elements as shown in Fig.7 (c). Similar to the segregation trend observed in NC-AlCoCrFe in our prior work—where high melting point elements, Cr and Fe self-segregated to GBs to provide stable nanograins, Cr and Fe still self-segregate at the GBs while Al and Co deplete at these regions as shown in Fig.7 (c1). This self-segregation in itself provides inherent stability to the NC-Al25Co25Cr25Fe25HEA at high homologous temperatures, compared to other NC-HEAs reported in the literature. Additionally, the segregation of Zr / ZrO phase at the GBs in Fig.7 (c2) validates the pseudo-binary thermodynamic approach proposed for the stability of the multicomponent alloy system. We therefore conclude that the addition of Zr provides extra stability to the HEA, and it explains the trend observed in the in-situ XRD results in Figs.4 and 5. However, at substantially high annealing temperature, phase decomposition and grain coarsening sets on in Al24.7Co24.7Cr24.7Fe24.7Zr1.0HEA at 973 K (Fig. 6) and 1073 K (Fig.5), respectively. In what follows, we assess the effect of Zr addition (0, 1, and 1.5 at. %) on the phase and grain stability at an annealing temperature of 973 K.

[0089] Effect of Zr Addition on the Thermal Stability of NC-(AlCoCrFe)1-xZrxHEA Annealed at 973 K

[0090] Figures 8 (a-c) show the BF-STEM images of lamella cross-section of the particles for Al25Co25Cr25Fe25, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEAs respectively, annealed at 973 K for 4 h. The STEM-EDS maps in Figs.8 (a1, b1, and c1) show that phase decomposition is dominant and ubiquitous in NC-Al25Co25Cr25Fe25HEA, as indicated by white arrows in Fig.8 (a2), moderate in NC-Al24.7Co24.7Cr24.7Fe24.7Zr1.0as seen in Fig.8 (b2), and significantly suppressed in Al24.6Co24.6Cr24.6Fe24.6Zr1.5as seen in Fig.8 (c2). Clearly, as the amount of carefully selected solute (Zr) increases from 0 to 1.5 at. %, phase decomposition is suppressed, in agreement with the in-situ XRD results in Figs. 4 (a) and (c). This phenomenon—phase stability with increasing Zr content— coincides with increasing grain stability in the investigated NC-HEAs, as seen in Fig.5: in Al25Co25Cr25Fe25HEA, the grain size increases from 10 nm to about 16 nm at 973 K (Fig.5 (a)), while, there is grain stability in Al24.7Co24.7Cr24.7Fe24.7Zr1.0and Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA at 973 K at an average grain sizes of ~13 and 12 nm, respectively (Figs.5, 8 (b2 and b3) and 8 (c2 and c3)). A STEM-EDS line profile scan across several grain boundaries in Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA annealed at 973 K for 4 h in Figure 8 (d) shows the fluctuations of Zr matches with these GBs as indicated by black arrows. This is a signatureof GB segregation by Zr, and a validation of our proposed pseudo-binary thermodynamic approach.

[0091] As it is the case of Al24.7Co24.7Cr24.7Fe24.7Zr1.0 HEA annealed at 873 K in Fig. 7, i.e., to validate the earlier established coupling of self-stabilizing and solute (Zr) segregation effects for stability in multi-component alloys, the APT reconstruction for Al25Co25Cr25Fe25, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5annealed at 973 K for 4 h are also presented in Fig.9. While there is self-segregation of Cr and Fe at the GBs of Al25Co25Cr25Fe25HEA (Fig. 9 (a)), Zr / ZrO also segregated in Al24.7Co24.7Cr24.7Fe24.7Zr1.0and Al24.7Co24.7Cr24.7Fe24.7Zr1.5for additional stability, as observed in the isocomposition surfaces (shown in Figs.9 (b2 and c2) and 1D concentration profiles in Figs. 9 (b3 and c3), respectively). In general, Fig. 9 not only shows the effect of our carefully selected solute (Zr) on nanograin stability, but it also shows consistency and the repeatability of the reported coupled effects. In what follows, we discuss these effects and their accompanying phenomena.

[0092] Discussion

[0093] In this example, we have developed a framework for thermodynamically stabilizing nanograins by GB decoration. Following a carefully outlined approach (Fig.1) and empirical considerations for solute selection, the results demonstrate that indeed the minor addition of the selected solute (Zr) up to 1.5 at. % to the NC-Al25Co25Cr25Fe25HEA results in GB segregation, alongside Cr and Fe, and the thermal stability of the materials system is significantly enhanced. Although the goal is to suppress grain growth, substantial phase stability accompanies this achievement—nanograin and phase stability are suppressed at high homologous temperatures up to ~0.64 Tm, where grain growth and phase decomposition rigorously occur in the undoped NC-Al25Co25Cr25Fe25HEA. The combined enhancement of both phenomena (phase and grain stability) may be connected to both being a diffusion-controlled process, so that the stability of one leads to the stability of the other. Interestingly, the onset of phase decomposition, preceded by Cr and Fe desegregation as established in other work, coincides with the onset of grain growth. The loss of phase stability through phase decomposition and consequently grain coarsening are common phenomena that have been observed in binary alloy systems after heat treatment at high temperatures. Unlike what is observed in Al25Co25Cr25Fe25HEA and at low concentration of Zr, Al24.9Co24.9Cr24.9Fe24.9Zr0.5(see Fig.4 (b)), the presence of Zr at the GBs tend to combat the compositional shift that thermodynamically supports phase decomposition while Zr is not taking part in the phase decomposition process itself. In whatfollows, we discuss the significance of the results in relation to the solute selection criteria, grain boundary segregation and correlation to stability of NC-(AlCoCrFe)1-xZrx.

[0094] Besides the empirical considerations for solute selection, as described above, GB segregation enthalpy calculations for binary alloy systems are another widely- used solute selection guide. We reassess the enthalpic consideration here for NC- (AlCoCrFe)1-xZrx, and justify its future exploration for other complex multi-element systems. From the work of Kalidindi and Schuh, a stable GB segregated state is achieved if the enthalpy of GB segregation, ΔHseg, of the solute exceeds that of the defect energy of the GB itself and other competing phases, e.g., second phase, to avoid forming solute-rich precipitate and intermetallic compounds according to the relation; ∆ ^^^^^^ ∆ ^^^^௫െ^௫ೞ^∆ ^^^^^^^ ^^ ^^ (5) where ∆ ^^^^௫is of the second phase, ^^^^is thestoichiometry of atoms in the compound, ∆ ^^^^^^is the enthalpy of intermetallic compound formation, and ^^ ^^ is the defect energy of the GB; ∆ ^^^^^^ ^^ ^^ is considered a metastability criterion.

[0095] Considering each HEA element singly as a solvent, and from Eqn. 5, the stability maps—∆ ^^^^^versus ∆ ^^^^௫െ^௫ೞ^∆ ^^^^^^plots for Co, Cr, Fe, and Al are shown in Figs.10a-d, where ^^ ^^ is 10-20 kJ / mol for typical grain boundary energies. The ∆ ^^^^^are calculated empirically using the Miedema approach, while the ∆ ^^^^^^vales which are determined by density functional theory, are obtained from the Open Quantum Materials Database. For clarity, only candidates (Zr, Sc, and Hf) that meet the three criteria in Fig.1 (d) are shown in the stability maps. Interestingly, these elements are located right in the stable or metastable regions for Co (Fig.10 (a)), Cr (Fig.10 (b)), and Fe (Fig.10 (c)); only Al falls in the unstable region in Fig. 10 (d). Despite Al being the outlier, we observe no formation of Al-Zr second phases and / or intermetallics in the HEA system, and we theorize that our approach to using a solid solution HEA suppresses any selective Al-Zr interactions. Also, considering the affinity for Al-Co interaction in the HEA system, we believe that the tendency for Zr to segregate in Co would most likely compensate for Al “deficiency”. While the observation in Fig.10 is interesting and it validates our design approach established above, we propose that the GB segregation enthalpy calculations for binary alloy systems can still be extended to reliably guide solute selection for complex multi-element alloy systems.

[0096] The GB segregation of Cr and Fe (self-stabilizing effect), and Zr (“solute” grain boundary segregation effect) which is responsible for the enhanced stability in this NC-HEA-Zr may also be driven by their enthalpies of mixing, ΔHmix, and enthalpies of GB segregation, ΔHseg. As we have established, the co-segregation of Cr and Fe at the GBs is due to their large enthalpy of mixing (as a result they have weak binding energy and can easily diffuse to GBs) compared to Al and Co that possess strong binding energies and higher activation barriers for diffusion, preferring the grain interior. This provides inherent thermal stability to the NC-AlCoCrFe HEA at relatively high homologous temperatures through the established self-stabilizing effect. In this example, the minor addition of the carefully selected solute (Zr) is due to its propensity to segregate at the GBs where the excess energy of the system would be further reduced to bring the system closer to a more thermodynamic equilibrium, hence dramatically enhancing nanocrystalline stability; the potency of Zr to stabilize binary and ternary systems is now observed in the present example for HEA.

[0097] The co-segregation of Cr, Fe, and Zr in the NC-(AlCoCrFe)1-xZrxcan be explained by their GB segregation enthalpies—defined as the energy difference between a solute atom at the GB site and the grain interior. The McLean treatment of GB segregation used for binary alloy systems can be tacitly used to estimate the equilibrium GB segregation in a multicomponent system by making the following assumptions: (i) that each of the segregating elements interact equally with all other elements in the system, and (ii) that the GBs are isotropic—the same site-type across the GB network. The oversimplification in McLean model, that all site types have the same segregation enthalpy value is addressed to some extent in this example by calculating the segregation enthalpy of several GBs (shown in Fig.11 (a)) and taking the average. The equilibrium GB segregation enthalpies of the segregating elements at the different GBs of the NC-(AlCoCrFe)1-xZrxHEA is experimentally determined by employing Eqn. 3, the McLean isotherm, with the atomic solute concentration at the GBs, ^^ீ^, and atomic solute concentration in the matrix, ^^^, from the APT measurements in Al24.6Co24.6Cr24.6Fe24.6Zr1.5 HEA annealed at 973 K.

[0098] The resulting segregation enthalpies for Al, Co, Cr, Fe, and Zr are approximately 16, 17, -23, -8, and -8 kJ / mol, respectively, as shown in Fig.11 (b). Although these values are averages, and not exact for each GB in Fig.11 (a) due to GB spectrality, they are not too far apart; for instance, Cr segregation enthalpies for GB1 to GB4 in Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEA are -27.0, -21.6, -25.5, and -20.4 kJ / mol, respectively. The negative segregation enthalpies of Cr, Fe, and Zr suggest that these elements have the tendency to segregate to the GBs of the NC-HEA. The large atomic size of the solute, Zr(with an atomic radius of about 1.6 Å [2]) compared to the HEA (with an average atomic radius of 1.3 Å) also partly contributes to its ability to segregate to GBs of the latter. The positive segregation enthalpies of Al and Co imply that these elements have less tendency to segregate to the GBs, and therefore, they have a significant presence in the bulk. The segregation of elements at the GBs may strengthen or weaken (embrittle) these interfaces; this depends on the atomic size of the segregating elements, their melting point, or the solute amount. Therefore, it is hoped that the segregation of Cr, Fe, and Zr, which have higher melting points among the alloying elements, will strengthen / enrich the GBs through the formation of stronger bonds at the interfaces to stabilize the GBs of the HEA.

[0099] To appreciate the significance and contribution of this work, we plot the grain size of the NC-(AlCoCrFe)1-xZrxHEAs at 4 hrs of annealing against their homologous temperatures, as shown in Fig. 12 (a-b); the literature data of other NC-HEAs are also included for comparison. It can be seen that Al24.6Co24.6Cr24.6Fe24.6Zr1.5NC-HEA exhibits the smallest and most stable nanograin size (with grain size of ~10 nm at 0.52Tm, ~12 nm at 0.58Tm, and ~14 nm at 0.64Tm), followed by Al24.7Co24.7Cr24.7Fe24.7Zr1.0with stable grain size of ~9 nm at 0.46Tm, ~10 nm at 0.52Tm, and ~12 nm at 0.58Tm; there are slightly coarse grains at 0.64Tmabout 18 nm. Slight grain coarsening in the Al25Co25Cr25Fe25and Al24.9Co24.9Cr24.9Fe24.9Zr0.5HEAs commenced at 0.46Tmand 0.52Tm, respectively (clearly shown in Fig.12 (b)). Compared with known HEAs, the present example exhibits improved grain stability at high homologous temperatures. Note that the grain size of the as-milled powder of this work is relatively smaller compared to the HEAs obtained from the literature, hence, rapid grain growth is expected in our alloy since grain boundary mobility is higher for smaller starting grain sizes than larger grains. On the contrary, grain growth is slower in the present work—evidence of the contribution of Zr addition to grain stability.

[0100] There was a recent study on nanograin stability of HEAs by Zhou et al. where bulk entropy and GB entropy effects were utilized to reduce GB energies; thereby reducing the thermodynamic driving force for grain growth at high temperatures. According to the authors, the bulk high entropy effect occurs in N-component system with multiple principal elements, M, and at least a segregating solute element, S, to achieve a high- entropy matrix, i.e., a case of ^ ^^^^^ ^^^^; i = 1, 2, 3,…,N-1). Similarly, GB high entropy effect occurs in a dilute multicomponent alloy in which GB energy reduces by increasing number of segregating solutes, i.e., a case of ^ ^^^^^ ^^^^, as represented in Fig. 12 (c). The approximated analytical expressions for the bulk and GB high entropies are presented in Eqns.6 and 7, respectively; ீ^^^െ2 ^^௫ ∆^ೞ^^.ష^^^.^^ െ ^^^^^^^^ ^^ ^^ ^^ ^1 ^ ^ ^^ െ 1^ൗ ௬^^ ^^ ^^ ൬െಿ^்^൨ (6)ೞ^^.ష^^^.^^ீ^െ ^^^^^ ^ 2 ^^^^^^ ^^ ^^ ^^^1 ^ ∑ே ∆^^ୀଶ^^ ^^ ^^൬െ ^^் ^ ൨(7)where ^^ீ^^^ is planar^^density of atoms, ∆g^^^.^ is free energy change of GB segregation by swapping an atom of the i-th element inside the grain with the 1stelement at the GB, T is temperature, k is the Boltzmann constant, n is the number of atoms per unit area in the atomic plane parallel to the GB, i=1, 2, 3,….(N-1), and ∆g^^^.ି^^௧.ே is the free energy difference between the segregation and precipitation authors found that the coupled effect of bulkand GB high entropies showed a reduction in GB energy compared to each of the two conditions, as shown in Fig.12 (c).

[0101] To put this example in context, we compare the final stabilized grain sizes with the experimental results of Refs. J. Luo, N. Zhou, Commun. Mater.4 (2023) 1–8 and N. Zhou, T. Hu, J. Huang, J. Luo, Scr. Mater.124 (2016) 160–163, where the bulk and GB high entropy models were established (open data points in Fig.12 (b)). As can be seen in Fig.12 (b), the self-stabilization effect ^ ^^^ି௫^^௫∗), and the coupled effect of self-stabilization and solute segregation ^ ^^^ି௫^^௫∗)^ ^^^^ show significant improvement in grain stabilization (and in turn, GB energy reduction) than the previously proposed coupled bulk and GB high entropy effects. This behavior is further represented in Fig. 12 (c), to delineate our observation from those of the aforementioned Refs.

[0102] We also assessed the short-range structure of the as-milled AlCoCrFe and (AlCoCrFe)98.5Zr1.5NC-HEAs and the associated changes with annealing temperature by analyzing the ex-situ X-ray PDF in real space as shown in Fig.15. The minor addition of Zr up to 1.5 at. % leads to slight damping of the peak intensity especially at higher r values (> 15 Å) in the as-milled state as shown in Fig.15a; this is characteristic of atomic correlation damping—loss of long-range order and crystallinity with Zr addition. There is no observable peak shift with Zr addition in the as-milled state. The PDFs at low r values (from 1.6 to 3.6 Å) containing the first eight coordination shells are further probed to discern the differences in peak intensity and to correlate the different bond pairs present in the NC-HEAs with the peak positions in the as-milled state and after annealing as shown in Figs.15b-e. The peaks within the selected r range are numbered from P1 to P8 for ease of description, and the bond lengths of all the binary pairs are presented in Table 1. We found that the addition of Zr into the NC-HEA which segregates at the GBs after annealing at 973 K for 4 h helps stabilize the bonds especially the nearest neighbor bonds corresponding to P4, P6, and P8. One unique feature of the PDF profiles in Fig. 15e is that P5 and P7 become more evident with increasing Zr content—1.5 at. % Zr exhibiting higher intensity followed by 1.0at. % Zr and lastly 0 at. % Zr. Following previous work interpretation in, this observation may typically be attributed to SRO of Al-Cr, Al-Fe, Cr-Fe or Co-Co, and Cr-Zr or Zr-Zr atoms that correspond to P5 and P7, respectively. Next, we investigated the presence of SRO in the synthesized NC-HEAs in the as-milled and annealed states using APT.

[0103] Figure 16a shows the 2D detector hit map of 160 million ions impact after slicing the voltage curve of the APT data of solid solution (AlCoCrFe)98.5Zr1.5NC-HEA in the as-milled state. A low-density crystallographic pole corresponding to

[0100] is observed. Regions that experienced significant trajectory aberrations are the low-density regions and these are areas where atomic planes can be imaged in the reconstructed APT dataset. The 3D atom map of the (AlCoCrFe)98.5Zr1.5NC-HEA is presented in Fig.16b. Figure 16c is a closed-up slice from the reconstruction in Fig.6b; the direction indicated by the arrow corresponds to the

[0100] direction and it contains BCC resolved planes. The z-SDM for Al- Al, Co-Co, Cr-Cr, Fe-Fe, and Zr-Zr pairs along

[0100] direction is presented in Fig.16d. One notable feature is that the z-SDMs for the same pair elements are identical—species peak- to-peak distances are equal for all elemental pairs, an indication that all the constituent elements have a strong tendency to occupy each other lattice sites. The z-SDMs for the cross-species elemental pairs are also shown in Fig. 16e; the peak-to-peak distance is identical and equal to the same pair of elements, and it shows the average distribution of one element atom relative to the other element atom along the

[0100] direction. These observations are an indication that a homogeneous solid solution—random distribution of all the constituent elements, rather than SRO, is achieved. Additionally, the peak intensities do not vary across the atomic planes except the central peak (which is normalized), which also confirms that there is no deviation from a random solid solution; deviation from a random distribution of the constituent elements is evidence of the presence of SRO in the NC-HEA.

[0104] A similar analysis is performed for the (AlCoCrFe)98.5Zr1.5NC-HEA sample annealed at 973 K for 4 h and the results are presented in Fig.17. The atomic planes of Al, Co, Cr, Fe, and Zr ions perpendicular to the

[0012] direction within the annealed (AlCoCrFe)98.5Zr1.5NC-HEA are clearly shown in Fig. 17c; atomic planes can clearly be visualized. The reconstruction is calibrated with an interplanar spacing of ~0.295 nm. Fig. 17d details the z-SDMs for the same element pairs—Al-Al, Co-Co, Cr-Cr, Fe-Fe, and Zr-Zr pairs. Similar to what is observed in the as-milled state, the interplanar spacing for all the same elemental pairs is equal, an indication that there is no deviation from the random distribution even after annealing—in the matrix, the elements are still uniformly distributed. Fig. 17e shows the z-SDMs for the cross-element pairs that are identical to the sameelement pairs. There is non-oscillating peak height across the atomic planes, except that which is between the central peak and the 1stpeak. This shows that even though Cr, Fe, and Zr are segregating at the GBs, the remainder (amount) of these elements present in the matrix are uniformly mixed with Al and Co which are significantly present in the matrix after annealing. The segregation of Cr, Fe, and Zr at the GBs after annealing suppressed ordering in the matrix; note that segregation can alter the SRO parameters in the matrix and this can change the matrix chemical potential. Similar trend is observed when the sample for (AlCoCrFe)99Zr1NC-HEA after annealing at 873 K for 4 h is also analyzed—the species peak-to-peak separation of the same element pairs and cross element pairs are identical after annealing as shown in Fig.18. Also, the peak intensities do not vary across the atomic planes. This confirms what is seen in Fig.17—there is homogeneous mixing in the matrix after annealing at 873 K.

[0105] In Fig. 19, the enthalpy of mixing of the binary pairs of the constituent elements are presented; the enthalpy of mixing significantly influences the formation of SRO as previously reported. While a more positive mixing enthalpy value favors GB segregation as established in our prior work, a more negative mixing enthalpy favors SRO formation. Based on the mixing enthalpy principle, the SRO formation tendency in this NC- HEA follows the order Al-Zr > Co-Zr > Fe-Zr > Al-Co > Cr-Zr > Al-Fe > Al-Cr > Co-Cr > Co- Fe > Cr-Fe as shown in Fig.19—Al-Zr pair has the potential to form SRO, followed by Co- Zr and in that order. However, the new peak in Fig.15e (P7) is a Cr-Zr bond length; this further supports the earlier observation that the evolution of the new PDF peak with increasing Zr amount up to 1.5 at. % at 973 K is as a result of segregation and not ordering, contrary to what is reported. These results show that the segregation of Cr, Fe, and Zr at the GBs suppressed ordering in the matrix.

[0106] Summary and Conclusions

[0107] In this example, we propose and develop a new alloy design strategy referred to as the “pseudo-binary thermodynamic” approach, for stabilizing NC-HEA and other variant of multicomponent alloys that is thought to be complex due to the possible complex pairwise interactions that could set on among the alloying elements. Using a pseudo-binary alloy system—single-phase solid solution HEA as the “solvent”, while a solute is carefully selected following empirical and GB segregation enthalpy considerations, we demonstrate that a thermodynamic GB segregation approach which is mainly used for binary alloy systems can still be tacitly used to stabilize multicomponent alloys. For the investigated alloy in this study (AlCoCrFe HEA), Zr, Sc, and Hf are identified as thepreferred solutes that would prefer to segregate at the GB of the HEA system to stabilize it against grain growth. Using Zr as solute, NC-AlCoCrFe HEAs with minor additions of Zr are synthesized by mechanical alloying, followed by annealing at different temperatures up to 1123 K. The micro- and nano-structural evolutions were investigated as a function of Zr content and annealing temperatures using advanced characterization techniques—in-situ X-ray diffraction, scanning / transmission electron microscopy, and atom probe tomography. The following conclusions can be drawn; - The average grain size of all as-milled NC-(AlCoCrFe)1-xZrxis ~6 nm with no signature GB segregation of any of the alloying elements, the incremental addition of 0.5 at. % Zr simultaneously increases the temperature limit for GB stabilization by 100 K, i.e., grain stability occurs up to 773, 873, 973, and 1073 K for NC- Al25Co25Cr25Fe25, Al24.9Co24.9Cr24.9Fe24.9Zr0.5, Al24.7Co24.7Cr24.7Fe24.7Zr1.0, and Al24.6Co24.6Cr24.6Fe24.6Zr1.5HEAs, respectively. - As the amount of Zr increases from 0 to 1.5 at. %, phase decomposition is suppressed; this phenomenon—phase stability with increasing Zr content— coincides with increasing grain stability in the investigated NC-HEAs. - The grain and phase stabilities are due to the combined segregation of Cr and Fe (self-stabilizing effect), along with Zr (“solute” grain boundary segregation effect) at the GBs to offset the excess energy that drives grain coarsening. - The enthalpy of segregation values are experimentally determined as 6, 17, -23, - 8, and -8 kJ / mol for Al, Co, Cr, Fe, and Zr, respectively; this shows that the large negative enthalpies of segregation for Cr, Fe, and Zr promote GB segregation and nanograin stabilization. - The onset of grain growth coincides with phase decomposition—direct dissolution of Cr, Fe, and Zr into the host lattice, and the gradual loss of phase stability.

[0108] Comparing the results of this example with other known NC-HEAs, the proposed pseudo-binary thermodynamic approach provides a novel route to stabilizing nanocrystalline HEAs at high temperatures. In addition to finding applications in the design of tailored functional materials, the novel alloy design strategy will find application in solid- state powder processes that require substantially high-temperature sintering for consolidation without grain coarsening.

[0109] In the preceding description, for purposes of explanation, numerous details are set forth in order to provide a thorough understanding of the embodiments. However, it will be apparent to one skilled in the art that these specific details are not required. In other instances, well-known electrical structures and circuits are shown in block diagram form inorder not to obscure the understanding. For example, specific details are not provided as to whether the embodiments described herein are implemented as a software routine, hardware circuit, firmware, or a combination thereof.

[0110] Embodiments of the disclosure can be represented as a computer program product stored in a machine-readable medium (also referred to as a computer-readable medium, a processor-readable medium, or a computer usable medium having a computer-readable program code embodied therein). The machine-readable medium can be any suitable tangible, non-transitory medium, including magnetic, optical, or electrical storage medium including a diskette, compact disk read only memory (CD-ROM), memory device (volatile or non-volatile), or similar storage mechanism. The machine-readable medium can contain various sets of instructions, code sequences, configuration information, or other data, which, when executed, cause a processor to perform steps in a method according to an embodiment of the disclosure. Those of ordinary skill in the art will appreciate that other instructions and operations necessary to implement the described implementations can also be stored on the machine-readable medium. The instructions stored on the machine-readable medium can be executed by a processor or other suitable processing device, and can interface with circuitry to perform the described tasks.

[0111] The above-described embodiments are intended to be examples only. Alterations, modifications and variations can be effected to the particular embodiments by those of skill in the art. The scope of the claims should not be limited by the particular embodiments set forth herein, but should be construed in a manner consistent with the specification as a whole.

Claims

WHAT IS CLAIMED IS:

1. A method of forming a stable grain-boundary-decorated nanocrystalline high- entropy alloy (HEA) comprising: a) processing a mixture of at least four principal elements in equiatomic or near-equiatomic ratios to form a single-phase solid solution HEA as a solvent; b) adding a solute element to the solvent, the solute element having a different crystal structure, an atomic size mismatch of at least 15%, and a higher melting point than the solvent; c) processing the solvent and the solute element until a single-phase solid solution HEA is formed; and d) annealing the single-phase solid solution HEA up to 0.46 to 0.67 of the melting temperature of the HEA to drive the solute and at least one of the solvent elements to the grain boundaries to form the stable nanocrystalline HEA.

2. The method of claim 1, wherein the principal elements are selected from the group consisting of Al, Co, Cr, and Fe.

3. The method of claim 1 or 2, wherein the solute element is selected from the group consisting of Zr, Hf, and Sc.

4. The method of any one of claims 1 to 3, wherein the solute element is Zr, and the concentration of Zr is from 0 to 1.5 at. %.

5. The method of any one of claims 1 to 4, wherein the processing comprises mechanically alloying, physical vapor deposition, electrodeposition, chemical vapor deposition, plasma-spraying, casting, or solidification.

6. The method of any one of claims 1 to 5, wherein the processing comprises mechanically alloying.

7. The method of claim 6, wherein the mechanical alloying is performed in a planetary ball mill with a ball-to-powder ratio of about 10:1 and a process control agent of about 1 wt.% ethanol.

8. The method of any one of claims 1 to 7, wherein the annealing is performed in an inert gas environment with a heating rate of about 50 °C / min and a holding time of about 4 h per temperature step.

9. The method of any one of claims 1 to 8, wherein the solute element segregates to the grain boundaries of the HEA, along with one or more of the principal elements with the highest average mixing enthalpy and melting point, to reduce the excess energy and the driving force for grain coarsening and phase decomposition.

10. The method of any one of claims 1 to 9, wherein the nanocrystalline HEA is stabilized against grain growth and phase decomposition at high homologous temperatures.

11. A stable nanocrystalline HEA obtained by the method of any one of claims 1 to 10.

12. The stable nanocrystalline HEA of claim 11, wherein the nanocrystalline HEA is stabilized against grain growth and phase decomposition, including short and long- range orderings, at high homologous temperatures.

13. The stable nanocrystalline HEA of claim 11 or 12, having a body-centered cubic (BCC) crystal structure and an average grain size of less than 20 nm.

14. The stable nanocrystalline HEA of any one of claims 11 to 13, having a near- equiatomic composition of Al, Co, Cr, and Fe, wherein Zr is present in a concentration ranging from 0.5 to 1.5 at.%.

15. The stable nanocrystalline HEA of any one of claims 11 to 14, having a homogeneous distribution of the principal elements in the grain interior and a co- segregation of Zr, Cr, and Fe at the grain boundaries.

16. The stable nanocrystalline HEA of any one of claims 11 to 15, wherein Zr forms a Zr-O phase at some of the grain boundaries.

17. The stable nanocrystalline HEA of any one of claims 11 to 16, having one or more of a high strength, hardness, wear resistance, corrosion resistance, and thermal stability.

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