Composition-dependent apparent activation-energy and sluggish grain-growth in high entropy alloys

ABSTRACT Experimental results reveal that the apparent activation-energy for grain-growth in an fcc-based AlxCoCrFeNi high entropy alloy (HEA) system increases from 179 to 486 kJ/mol when the Al content increases from x = 0.1 to 0.3. These unexpectedly high apparent activation-energy values can be potentially attributed to solute clustering within the fcc solid-solution phase that develops with increasing Al content in this HEA. Detailed microstructural analysis using atom-probe tomography and density functional theory (DFT) calculations strongly indicate the presence of such nanoscale clusters. This phenomenon can change grain-growth from a classical solute-drag regime to a much more sluggish cluster-drag based mechanism in these HEAs. GRAPHICAL ABSTRACT IMPACT STATEMENT First report on a composition dependent change in apparent activation-energy for grain-growth in high entropy alloys. A novel cluster drag effect inhibiting grain-growth kinetics is suggested.

Typically, the free energy of the system is reduced by grain-growth via boundary migration, resulting in a reduction in the total boundary area. The motion of grain boundaries involves 'short-range' jumps of atoms or ions across the grain boundary to align with the crystallographic orientation of the growing grain.
Typically, driving force for classical grain-growth in elemental materials is the boundary curvature determined by the internal pressure difference ΔP = α.γ GB G P is the difference in pressure between adjacent grains, α is the geometric factor, γ GB is the grain-boundary energy, G is the grain size.
The kinetics of classical grain-growth is often quantified by analyzing grain-size as a function of isothermal annealing time for different temperatures [3][4][5][6]. The local velocity of the grain boundary at any point is proportional to the local curvature and elastic strain effects are ignored.
For a given temperature, the grain diameter grows parabolically with time as: where d is the instantaneous grain size; d o is the initial grain-size; t is time; and k is a kinetic constant that depends on the temperature and grain-boundary energy. Equation (1) has often been generalized for solutecontaining systems, as: The value of n, varies from 2 to 7, determines the growth mechanism and k defines the diffusion processes [5][6][7]. Grain-growth in a number of carbon steels between 815°C and 1250°C have been studied and reported values for n ranging between 3 and 7 [3]. The deviation in the value of n from 2 was attributed by Grey and Higgins [8,9] to the clustered atoms inhibiting graingrowth because grain-boundary motion would now require these clusters rather than simply single atoms (classical solute-drag model) to be mobile. Additionally, small amounts of impurities have been shown to reduce grain boundary velocity by over an order of magnitude, which have been attributed to impurity atoms pinning grain boundaries and retarding their motion [7][8][9][10][11][12][13][14][15][16]. Furthermore, small particles of a second phase provide one of the most effective drag force in grain-boundary migration. The drag by particles on a moving grain boundary is usually considered in the Zener approximation, where the particles act as a stationary pinning center for the boundaries [14,15]. However, it is well known that inclusions in solids are not immobile and that particle mobility increases drastically with decreasing particle size. Therefore, small particles can move along with the boundary and severely constrain grain-boundary migration. Here, we analyze the influence of different levels of Al addition on grain-growth kinetics in an equiatomic quaternary alloy (CoCrFeNi), complementing experiments and DFT calculations. Based on the results of the grain-growth kinetics, the apparent activation-energy for grain-growth has been determined, as a function of Al content in these fcc Al x CoCrFeNi alloys. The results have been rationalized based on a possible cluster-drag based mechanism of grain-growth, eventually leading to the well-known Zener-pinning model, when second phase precipitates are formed at the fcc grain boundaries. A novel cluster drag phenomenon is suggested as the Al concentration increases.
Alloys with nominal chemical composition Al 0.1 Co CrFeNi, Al 0.2 CoCrFeNi and Al 0.3 CoCrFeNi were prepared by conventional arc melting, and microstructural characterization was performed using scanning electron microscopy (FEI Nova-NanoSEM 230 TM ) and atomprobe tomography (in Cameca Local Electrode Atom-Probe (LEAP) 3000X HR and 5000XS) 3D atom-probe. The atom-probe tips were prepared on FEI Nova 200 dual beam focused ion beam [17]. The arc melting chamber containing the raw materials was evacuated to ∼ 10 −3 Pa, flushed twice with pure Ar, and finally backfilled with Ar to a pressure of ∼ 5 × 10 4 Pa. The buttons were flipped and re-melted five times to ensure chemical homogeneity before finally casting into a cylindrical copper mold. The cast ingots were sealed in evacuated quartz tubes, homogenized at 1200°C for 24 h followed by water quenching (WQ). After grinding and cleaning the surfaces, the homogenized ingots were cold rolled along their long axis to a reduction in thickness ∼ 90% and aged at 950°C, 1075°C and 1150°C for various times, followed by water quenching. The grain-size measurement was done using ImageJ software taking five SEM micrographs from each condition covering at least 100 grains from each sample. The grain-size measurement was calibrated with electron back scattered electron diffraction (EBSD) orientation microscopy. Grain-size distribution vs annealing temperature/time is shown in Supplementary Table 1 and Supplementary Figure S1.
The isopleth section with varying Al content for the Al x CoCrFeNi system ( Figure 1) is calculated using a computational-thermodynamic (CALPHAD approach) [18]. The composition Al 0.1 CoCrFeNi, Al 0.2 CoCrFeNi and Al 0.3 CoCrFeNi are marked with vertical dotted lines on this isopleth, and the temperatures of 1150°C, 1075°C and 950°C are marked with a horizontal dotted line. While Al 0.1 CoCrFeNi and Al 0.2 CoCrFeNi alloys lie in the single fcc phase field in all three temperatures, the Al 0.3 CoCrFeNi alloy has fcc + B2 phases as equilibrium phases at 1050°C and 950°C. After annealing at different temperatures, Al 0.1 CoCrFeNi alloy shows completely recrystallized grains with no second phase precipitation ( Figure 1, left side). However, second phase grainboundary precipitates are clearly seen in Al 0.3 CoCrFeNi alloy at 950°C (Figure 1, right-side). SEM-EBSD and TEM investigations conclude that these grain-boundary precipitates have B2 structure, as shown in Supplementary Figure S2.
The grain-growth data obtained from the Al 0.1 , Al 0.2 and Al 0.3 Cocrfeni HEAs were modeled using Equation where k is rate-constant for grain-growth and depends on absolute temperature T (in Kelvin), A is the preexponential factor, E a is activation-energy, and R is universal gas constant.
Taking the natural-logarithm and rearranging the terms yields: The plots of ln k vs 1/T for Al 0.1 CoCrFeNi alloy is shown in Figure 2. Similar plots generated for    Figure 3(a), it is apparent that while all three points, corresponding to the three temperatures, lie on the same straight line in case of the Al 0.1 CoCrFeNi alloy, the situation is different in case of the Al 0.2 CoCrFeNi and Al 0.3 CoCrFeNi alloys. For these HEAs, containing higher amounts of Al, there is a distinct decrease in the slope between the latter two points (lower temperatures) as compared to the first two points, with the second point being a common one. Since the negative slope is directly proportional to the activation energy for grain growth, this difference is slope can be attributed to a change in activation energy resulting from a change in the grain growth mechanism at the lowest temperature (950°C) in case of Al 0.2 CoCrFeNi and Al 0.3 CoCrFeNi alloys. The precipitation of a second B2 phase on the grain boundaries at 950°C in case of these two alloys can change the grain-growth mechanism from a classical solute drag to a Zener-pinning like process. Hence, upon formation, B2 precipitates pin the grain boundaries and make the grain-growth extremely sluggish. Based on these experimental observations and restrictions imposed by the two-phase fcc + B2 mixture in case of the Al 0.2 CoCrFeNi and Al 0.3 CoCrFeNi alloys at 950°C, only the data from the two higher temperatures, 1150°C and 1075°C, have been used to calculate the apparent activation-energy for grain-growth for the three alloys, with all three exhibiting a stable single fcc phase based microstructure (Figure 3(b)).

Referring to
The slope of the linear fit to the data multiplied by R (gas constant) gives the apparent activation-energy that was computed to be 178.75, 321.75 and 486.37 kJ/mol for Al 0.1 , Al 0.2 and Al 0.3 , respectively. The activationenergy of most single-phase metals is in the range of 50-700 kJ/mol [18]. There are only a few published reports of activation-energies for grain-growth in HEAs. Liu et al. reported a value of 327 kJ/mol for FeCrNi-CoMn [19], and Juan et al. reported a value of 389 kJ/mol for HfNbTaTiZr [20]. The high activation-energy results in very sluggish diffusion in these high entropy alloys, which in turn hinders rapid grain-growth, as often observed in most single-phase HEAs. Figures 4(a,b) shows atom-probe tomographic (APT) reconstructions and respective data analysis results from the Al 01 CoCrFeNi and Al 0.3 CoCrFeNi HEAs, respectively, after these were subjected to annealing at 1150°C/60 min and subsequently water-quenched. The samples were lifted out from the regions close to (2-3 μm away) grain boundaries. All the atoms (ions) are displayed (different colors) in both reconstructions. While the raw atomic (ionic) maps look homogeneous in both cases, it should be noted that nanometer-scale short-range ordering/clustering tendencies cannot be statistically analyzed simply based on such pictorial depictions of the atomic-maps. A more statistical analysis of the randomness of the atomic distribution within such datasets involves dividing the dataset into bins of constant size (fixed number of atoms) and subsequently plotting a frequency-distribution plot of a number of bins versus the composition of the bin. If such a frequencydistribution plot exhibits a binomial distribution, then it represents a random distribution of the atoms within the analyzed volume [21-23-24]. The second set of figures in Figure 4(a,b), respectively, show the volumes employed for cluster analysis from the APT reconstructions of the Al 0.1 CoCrFeNi and Al 0.3 CoCrFeNi HEAs. The third set of figures (the extreme right set in Figure 4(a,b)) show the experimental frequency-distribution plot for Al atoms, as well as the simulated perfect binomial plot (representing random-distribution) for each alloy. While the experimental plot for the Al 0.1 CoCrFeNi HEA is in excellent agreement with the simulated binomial plot, indicating a true random distribution of the Al atoms, there is a significant difference in between the experimental and simulated plots for Al in case of the Al 0.3 CoCrFeNi HEA. Therefore, it can be concluded that in case of the Al 0.3 CoCrFeNi HEA, the Al atoms are not randomly distributed. Subsequently, a cluster-search algorithm was applied to the Al 0.3 CoCrFeNi dataset. The details of this technique can be found in the literature [17,23], and the step-by-step procedure is described in the IVAS TM 3.6.8 manual. After optimizing the parameters d max and N min , the actual cluster analysis was performed [23]. The d max was 0.84 nm, and N min was 33 ions. The number of clusters detected in the selected volume was 30, and cluster density was 8.33×10 −4 nm 3 /nm 3 , average volume of clusters was 88 nm 3 , average-diameter was 5.2 nm, and average-composition was 39Al-15Cr-14Fe-16Ni-16Co (at%). A visualization of these clusters in the Al 0.3 CoCrFeNi HEA is shown as an inset in the lower central part of Figure 4(b). The authors repeated the APT-experiments on two different generations on atom-probes 3000X HR and 5000XS. The results from both instruments compared well. The details of results from 5000XS are provided as the supplementary information ( Figure S5).
In order to provide more support on the experimentally observed clustering tendency of Al in Al x CoCrFeNi (HEA) alloy, a series of DFT calculations were performed. Our simulation methodology involves building an fcc supercell where all elements are randomly distributed and then constructing a hemisphere cluster domain inside this supercell which resembles the APT experimental chemical analysis of the clustering, which has approx. 38 at.% Al, and 14 at.% of each other element. There is energy scatter associated with various distributions of the elements within the supercell so, different random configurations of supercell were created with different hemisphere inside while maintaining the chemical concentration of the elements within the domain. The average energy of these configuration were calculated. The relaxed fcc supercell with the hemisphere domain cluster is illustrated in Figure 5(a), in addition to the hemisphere cluster illustrated in Figure 5(b).
Two supercells with 192 atoms have been used, one with fully random distribution of all elements and another one also with random distribution of the elements but with a constructed cluster inside it. Twenty different random configurations have been utilized to calculate the average ground state energies of these two supercells with full relaxation of ionic positions and cell volume and shape. These calculations showed that the system that contains cluster has an average of 30 meV lower ground-state energy than the system without a cluster. This confirms the clustering tendency of Al in this alloy, which agrees with APT analysis results.
Additionally, another experiment was carried out to investigate the tendency to form Al-rich clusters in case of the Al 0.3 CoCrFeNi alloy. Expediting and accentuating the formation of this short-range domain tendency is done by mechanically cold rolling this alloy followed by isothermal annealing at a lower temperature of 620°C for 1 h. The underlying rationale was that the cold-work will enhance the diffusion process while the lower annealing temperature will thermodynamically enhance the tendency to form Al-rich domains, due to the lower entropy contributions coupled with a stronger influence of the negative enthalpy of mixing of Al with the other constituent elements. The results of this cold worked and annealed samples are shown in Supplementary Figure S6. The TEM diffraction patterns, recorded from the [011] and [001] fcc zones, confirm the presence of a single fcc phase. However, the APT results from the same sample captured the strong tendency to form Al-rich domains, as shown in the APT reconstructions, with the Al atoms colored in yellow ( Figure S6, bottom).

Summary
Grain-growth at three different temperatures for three fcc-based HEAs, Al 0.1 CoCrFeNi, Al 0.2 CoCrFeNi, and Al 0.3 CoCrFeNi, exhibits a classical power law behavior (n = 3 exponent), with experimentally determined apparent activation-energies of 179, 321 and 486 kJ/mol, respectively. The power law exponent of 3 indicates that the grain-growth mechanism is largely controlled by the solute drag effect in addition to the interfacial tension at grain boundaries. Cluster analysis via APT clearly shows clustering/agglomeration of Al atoms in case of the Al 0.3 CoCrFeNi HEA, while it is not observed in case of the Al 0.1 CoCrFeNi HEA, Furthermore, DFT calculations confirm this tendency of Al in the Al 0.3 CoCrFeNi alloy, indicating that the extremely large value of activation-energy (486 kJ/mol) in this alloy, is most likely due to a cluster-drag mechanism, which drastically slows down the grain-growth kinetic. The neutron-diffraction experiments of Ma et al. [2] also experimentally showed the presence of Al-rich domains in fcc-based single-phase an Al-Co-Cr-Fe-Ni based HEA alloy, which further establish the propensity of formation of nano-domains in these concentrated solid solutions. Figure 5(c) schematically illustrates the cluster-drag phenomenon wherein clusters of atoms (showing in blue color) hinder the motion of the adjacent grain boundary. The sluggish grain-growth kinetics arises because grain-boundary motion requires a concurrent migration of these domains/clusters. Nano-clustering in singlephase HEAs can have a much broader impact. Previous reports have shown that the strengthening coefficient (k) in the Hall-Petch equation increased from 371 MPa.μm 0.5 [25] to 824 MPa.μm 0.5 [26] on increasing the Al content in the fcc solid solution from x = 0.1 to 0.3 in the AlxCoCrFeNi alloy system. Therefore, these nano-clusters can potentially influence the lattice friction (or Pierels-Nabarro stress), dislocation-motion, amenability for deformation-twinning, Hall-Petch coefficients for hardness and yield strength, etc., in these HEAs, which can in turn affect the mechanical properties of these alloys. Interestingly, another recent paper by the authors on the Al 0.3 CoCrFeNi alloy clearly shows the influence of more well-developed nano-clusters on extraordinary yield strengths in this alloy [18]. However, a fundamental understanding of the role of these nano-clusters on the deformation behavior and mechanical properties of these HEAs requires further detailed investigation. facilities, Talon2 and Stampede supercomputers at the University of North Texas and Texas Advanced Computing Center (TACC) at Austin for computational work.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
The work was supported by cooperative agreement between the US Army Research Laboratory and the University of North