On Sluggish Diffusion in Fcc Al – Co – Cr – Fe – Ni High-Entropy Alloys : An Experimental and Numerical Study

High-throughput measurement using the numerical inverse method combined with the diffusion multiple technique was employed to determine the composition-dependent interdiffusion coefficients in fcc Al–Co–Cr–Fe–Ni high-entropy alloys at 1273, 1323, and 1373 K. The reliability of the obtained interdiffusion coefficients was confirmed by comparing the model-predicted composition/interdiffusion flux profiles with the experimental data. The tracer diffusivities of the components were then predicted based on the obtained interdiffusion coefficients and the simplified thermodynamic description. The diagonal interdiffusion coefficients in the present high-entropy alloys were comprehensively compared with those in conventional fcc alloys. Therefore, the sluggish diffusion effect does not apply for all the elements in the present fcc Al–Co–Cr–Fe–Ni high-entropy alloys. A similar result was also observed for the evaluated tracer diffusivities.


Introduction
The high-entropy alloys (HEAs) (or multi-principle element alloys (MPEAs)) initially proposed by Yeh and Huang in 1995 [1] have drawn increasing attention because of their comprehensive beneficial mechanical, magnetic, and electrochemical characteristics.These characteristics render these HEAs suitable for numerous potential uses.These applications include structural materials for transportation, heat-or wear-resistant coatings, and other uses in energy and nuclear industries [2,3].Distinct from conventional alloys, HEAs were originally defined as alloys consisting of more than four principal metallic elements, and exhibiting high mixing entropy when they are in a high-temperature solid solution or liquid state [4].
The aforementioned outstanding properties are usually directly attributed to the four core effects on HEAs [2,5].Among these effects, sluggish diffusion is identified as the one responsible for many distinct characteristics of HEAs [6], such as the deceleration of grain growth, exceptional thermal stability, and formation of nanostructures.Most recent findings [7] suggest that, within the past ten years, the number of studies on diffusion in HEAs has grown from three papers to 30 papers each year.Moreover, a significant number of studies on the measurement of diffusivities in HEAs have also been conducted [8][9][10][11][12][13], aimed at verifying the occurrence of sluggish diffusion in HEAs.Table 1 summarizes all available experimental measurements of diffusivities in different HEAs in the Vaidya et al. [12] recently measured the tracer diffusivities of Ni in the equiatomic Co-Cr-Fe-Ni and Co-Cr-Fe-Mn-Ni alloys and argued that at any given absolute temperature, the diffusion rate of Ni in the Co-Cr-Fe-Mn-Ni alloy was even faster than that in the Co-Cr-Fe-Ni alloy.This difference indicated that the so-called sluggish diffusion in HEAs was not inevitable.Chen and Zhang [13] recently measured the composition-dependent interdiffusion coefficients in the Co-Cr-Fe-Mn-Ni quinary system.Comparison of the results revealed that, for Co-Cr-Fe-Mn-Ni HEAs, the sluggish diffusion feature was plausible for the interdiffusion coefficients rather than the tracer diffusivities.In addition, Verma et al. [14] reported on interdiffusivities in the Co-Cr-Fe-Mn-Ni quinary system; however, their purpose was to emphasize the importance of diffusional interactions in controlling interdiffusion in the Co-Cr-Fe-Mn-Ni HEA rather than examine the sluggish diffusion in HEAs.Several investigations on diffusivities in HEAs have been reported, but whether the diffusion in HEAs is sluggish remains unclear.Thus, more experimentally measured diffusivities, including the Al-Co-Cr-Fe-Ni quinary system which seems to be ignored, compared with the Co-Cr-Fe-Mn-Ni system, need to be provided.
The concentration-dependent interdiffusion coefficients in alloy systems, mainly ternary systems, could be determined by combining the single-phase diffusion couple/multiple technique and the previously developed numerical inverse method by the present research group [15][16][17].With the numerical inverse method, the interdiffusion coefficients along the entire diffusion paths of the diffusion couple(s)/multiple can be efficiently obtained based on the experimentally measured composition-distance profiles.The advanced feature of this type of numerical inverse method is attributable to its applicability in different multi-component solid solution alloys, such as binary alloys, ternary alloys, and HEAs.Moreover, the presence or absence of the thermodynamic description for the target alloy exerts no influence on the quality of the evaluated interdiffusion coefficients [16].This numerical inverse approach has thus been successfully used to evaluate concentration-dependent interdiffusion coefficients in different alloys, including fcc Cu-Ag-Sn alloys [18], fcc Ni-Al-Ta [19], and Ni-Al-Mo [20] alloys, bcc Fe-Mn-Si alloys [21], and fcc Co-Cr-Fe-Mn-Ni HEAs [13].Their reliability was also verified by direct comparison with the Metals 2018, 8, 16 3 of 14 determined results by using the traditional Matano-Kirkaldy method and the reported data in the literature.
Thus, in the present study, high-throughput measurement of the composition-dependent interdiffusion coefficients in fcc Al-Co-Cr-Fe-Ni alloys at different temperatures is to be conducted by combining the recently developed numerical inverse method with the efficient single-phase diffusion multiple technique.The model-predicted composition profiles and interdiffusion fluxes with the experimental data are to be comprehensively compared to verify the reliability of the obtained interdiffusion coefficients.Moreover, the corresponding tracer diffusion coefficients of each component are estimated and compared with the literature data in fcc pure elements and lower-order alloys from which the sluggish diffusion effect is analyzed.

Experimental Procedure
Starting materials include pure aluminum (purity: 99.99 wt %), cobalt (purity: 99.98 wt %), chromium (purity: 99.95 wt %), iron (purity: 99.98 wt %), and nickel (purity: 99.995 wt %).(in at %, denoted as Alloy 3)-which were scrupulously chosen according to recent thermodynamic predictions [22], were arc-melted under an argon atmosphere by a non-consumable tungsten electrode.All samples were re-melted more than four times to enhance their homogeneities.The ingots were subsequently cut into blocks approximately measuring 4 mm × 4 mm × 8 mm and homogenized at 1373 K ± 3 K for 168 h after being placed in evacuated and sealed quartz tubes, followed by quenching in water.All annealed alloys were subjected to X-ray diffraction measurements (Bruker D8 Advance, Bruker, Germany) and confirmed to be located within the fcc single-phase region, as shown in Figure 1.Three diffusion multiples were subsequently prepared by stacking the polished and cleaned blocks up in the sequence, as schematically shown in Figures 2-4, in a vacuum hot-pressing furnace under a load of 5 MPa for 2 h at 1273 K, 1323 K, and 1373 K.The three diffusion multiples were ground to remove surface contamination and then annealed for another 46 h at 1273 K, 1323 K, and 1373 K, followed by quenching in water.Finally, the concentration profiles of the diffusion multiples were measured using electron probe microanalysis (EPMA, JXA-8230, JEOL, Tokyo, Japan) on the polished section made by standard metallographic preparation.For each component, the variations in alloy compositions were limited to 0.5%.
Metals 2018, 8, 16 3 of 14 coefficients [16].This numerical inverse approach has thus been successfully used to evaluate concentration-dependent interdiffusion coefficients in different alloys, including fcc Cu-Ag-Sn alloys [18], fcc Ni-Al-Ta [19], and Ni-Al-Mo [20] alloys, bcc Fe-Mn-Si alloys [21], and fcc Co-Cr-Fe-Mn-Ni HEAs [13].Their reliability was also verified by direct comparison with the determined results by using the traditional Matano-Kirkaldy method and the reported data in the literature.
Thus, in the present study, high-throughput measurement of the composition-dependent interdiffusion coefficients in fcc Al-Co-Cr-Fe-Ni alloys at different temperatures is to be conducted by combining the recently developed numerical inverse method with the efficient single-phase diffusion multiple technique.The model-predicted composition profiles and interdiffusion fluxes with the experimental data are to be comprehensively compared to verify the reliability of the obtained interdiffusion coefficients.Moreover, the corresponding tracer diffusion coefficients of each component are estimated and compared with the literature data in fcc pure elements and lower-order alloys from which the sluggish diffusion effect is analyzed.

Experimental Procedure
Starting materials include pure aluminum (purity: 99.99 wt %), cobalt (purity: 99.98 wt %), chromium (purity: 99.95 wt %), iron (purity: 99.98 wt %), and nickel (purity: 99.995 wt %).Three different Al-Co-Cr-Fe-Ni alloys-i.e., Co25.33Cr25.77Fe24.53Ni24.37 (in at %, denoted as Alloy 1), Al4.88Co29.53Cr18.58Fe19.62Ni27.39 (in at%, denoted as Alloy 2), and Al6.64Co23.82Cr23.66Fe23.01Ni22.87 (in at%, denoted as Alloy 3)-which were scrupulously chosen according to recent thermodynamic predictions [22], were arc-melted under an argon atmosphere by a non-consumable tungsten electrode.All samples were re-melted more than four times to enhance their homogeneities.The ingots were subsequently cut into blocks approximately measuring 4 mm × 4 mm × 8 mm and homogenized at 1373 K ± 3 K for 168 h after being placed in evacuated and sealed quartz tubes, followed by quenching in water.All annealed alloys were subjected to X-ray diffraction measurements (Bruker D8 Advance, Germany) and confirmed to be located within the fcc singlephase region, as shown in Figure 1.Three diffusion multiples were subsequently prepared by stacking the polished and cleaned blocks up in the sequence, as schematically shown in Figures 2-4, in a vacuum hot-pressing furnace under a load of 5 MPa for 2 h at 1273 K, 1323 K, and 1373 K.The three diffusion multiples were ground to remove surface contamination and then annealed for another 46 h at 1273 K, 1323 K, and 1373 K, followed by quenching in water.Finally, the concentration profiles of the diffusion multiples were measured using electron probe microanalysis (EPMA, JXA-8230, JEOL, Japan) on the polished section made by standard metallographic preparation.For each component, the variations in alloy compositions were limited to 0.5%.

Numerical Inverse Method
The determined concentration profiles at different temperatures were used to retrieve the composition-and temperature-dependent interdiffusivity matrices in fcc Al-Co-Cr-Fe-Ni alloys by using the recent numerical inverse method [15][16][17].In an N-component phase, the composition of component i changes according to Fick's second law: where t is the diffusion time, x is the diffusion distance, ci is the composition of component i, and The interdiffusivity ( , , ,..., 1) where T is the temperature, and R is the gas constant.On the right-hand side of Equation ( 2), the second term indicates the vacancy-wind effect.The contribution of this effect can be monitored by the parameter s equaling either 0 or 1.In the present study, s is equal to 0; that is, the vacancy-wind

Numerical Inverse Method
The determined concentration profiles at different temperatures were used to retrieve the composition-and temperature-dependent interdiffusivity matrices in fcc Al-Co-Cr-Fe-Ni alloys by using the recent numerical inverse method [15][16][17].In an N-component phase, the composition of component i changes according to Fick's second law: where t is the diffusion time, x is the diffusion distance, c i is the composition of component i, and The interdiffusivity D N ij (i, j = A, B, . . ., N − 1) can be in relation to mobility M i by Manning's random alloy model expressed as where T is the temperature, and R is the gas constant.On the right-hand side of Equation ( 2), the second term indicates the vacancy-wind effect.The contribution of this effect can be monitored by the parameter s equaling either 0 or 1.In the present study, s is equal to 0; that is, the vacancy-wind effect is disregarded.A 0 is one parameter only depending on the crystal structure, and for fcc crystals, it equals to 7.15.Φ N ij is the thermodynamic factor being expressed by where µ i is the chemical potential.The value of µ i can be derived based on the corresponding thermodynamic descriptions.In the numerical inverse method [15][16][17], the degree of fit of the model-predicted composition/interdiffusion flux profiles to the experimental ones determines the quality of the obtained interdiffusion coefficients.To evaluate the atomic mobility, the thermodynamic factor is needed.For the numerical inverse method, the mobility parameters and the thermodynamic factors can be treated only as the numerical parameters with no physical meaning under the condition that the thermodynamic description is absent for the target alloy [15][16][17].In the CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) formalism, the mobility M i in a phase composed of N components can be expanded as where ∆G j i is the end-member for the diffusion of component i in component j, and ∆G j,k i and ∆G j,k,l i are the interaction parameters in the binary and ternary systems, respectively.Thus, the concentration profiles of component i can be readily simulated by combining Equations ( 1)-( 4).
In accordance with the study by Chen et al. [16], the more sensitive interdiffusion flux is also considered.According to Fick's first law, the interdiffusion flux of component i in an N-component phase is whereas the experimental interdiffusion flux of component i can be obtained on the basis of the experimental concentration profiles, as follows: where ) is a normalized composition variable, and c R and c L are the compositions of component i on the far right and far left of the diffusion couple, respectively.During the evaluation of interdiffusion coefficients, the computed interdiffusion coefficients are used to simulate the composition profiles of the components according to Fick's second law.An optimal set of model parameters in Equation ( 4), such as ∆G j i , ∆G j,k i , and ∆G j,k,l i , is evaluated by iterative fitting until the error between the calculated and the experimentally measured concentration and interdiffusion flux profiles is minimized: where c cal ij and J cal ij are the calculated concentration and interdiffusion flux of component i at the jth point, and c exp ij and J exp ij are the analogously experimental ones.Num denotes the number of experimental data.w c and w J represent the weights of concentration and interdiffusion flux during the minimization.In general, they both are set to 0.5.Thus, the composition-dependent interdiffusivities in the target can be evaluated using Equations ( 1)-( 7), and the composition-dependent interdiffusion coefficients in the target can be computed using Equation (2) on the basis of the optimal set of model parameters.

Results and Discussion
The composition profiles of the components in the three diffusion multiples measured by EPMA are presented in Figures 2-4.The corresponding interdiffusion fluxes evaluated using Equation ( 6) are also shown in the plots.All experimental data are denoted by symbols in Figures 2-4.As can be seen from the figures, the simulated composition profiles are in good agreement with the experimental results.For the interdiffusion flux profiles, however, there exist relatively large deviations between the experimental results and the corresponding simulated ones.In the present work, all the interdiffusion flux points were directly evaluated from the raw experimental concentration points.No extra smooth and fitting treatments were used in order to stick to the original experimental information, because the interdiffusion flux is related to the gradient of composition, and thus is greatly sensitive to the uncertainty of the composition profiles over the diffusion region, which cause relatively large uncertainty for the present quinary high-entropy alloys.Besides, for the numerical inverse method, the experimental composition profiles are used as the primary observation for the first step, and then the additional "experimental" interdiffusion flux information that are sensitive to the optimization parameters can be considered for speeding up the numerical convergence [15][16][17].Moreover, the position and value of the peak for the interdiffusion flux are much more important than the values outside the diffusion region, which should be 0 theoretically.Thus, the relatively large scattering values for the interdiffusion flux outside the diffusion region will not influence the quality of the evaluated interdiffusivities.By using the numerical inverse method [15][16][17], the concentration-dependent interdiffusion coefficients along the diffusion paths in the three diffusion multiples were effectively determined based on the experimentally measured concentration profiles.The average relative uncertainty for all the interdiffusion coefficients was evaluated to around 30% by using the error propagation method [18][19][20][21].In the current study, Ni is regarded as the dependent component for interdiffusivity notation.In fact, the dependent component can be chosen arbitrarily, and different notations of interdiffusivities with different dependent components can be equivalently converted into each other [13].The fcc phase in the quinary Al-Co-Cr-Fe-Ni system was simply considered as an ideal solution during the evaluation of the interdiffusion coefficients.In this case, the thermodynamic factor Φ N ij (i, j = N) is equal to 0 if i is not j and is equal to 1 when i is j.Moreover, Φ N Nj (j = N) is equal to −1.In addition, the parameters of the end-members in all sub-binary systems shown in Equation ( 4) are from Refs.[23][24][25][26][27][28][29][30], as listed in Table 2.These parameters are fixed during the evaluation.Different sets of interaction parameters were then adjusted to best fit the experimental concentration/interdiffusion flux profiles measured from the 3 diffusion multiples.On the basis of the final optimal set of model parameters, the concentration-dependent interdiffusivities in fcc Al-Co-Cr-Fe-Ni alloys at different temperatures can be calculated using Equation (2).The obtained diagonal interdiffusivities D Ni Al Al , D Ni CoCo , D Ni CrCr , and D Ni FeFe along the diffusion paths in the 3 diffusion multiples are presented in Figures 2-4, and all of the digital files are provided in the electronic Supplementary Materials.The obtained diagonal interdiffusion coefficients are in the same order of magnitude as those limited data obtained by Kulkarni and Chauhan [10] and Chen and Zhang [13].As shown in the figures, all of the diagonal interdiffusivities for the 3 diffusion multiples are positive, which is expected.The complete interdiffusivity matrices over the investigated composition and temperature ranges may be acquired using the numerical inverse method.The large quantities of off-diagonal interdiffusivities and the comparison among the interdiffusivities for each component in both situations-i.e., with Ni as the dependent component and Fe as the dependent component-are all presented in the electronic supplementary materials.As shown in the figures, when Ni is considered as the dependent component, the off-diagonal interdiffusivity ()  To assess whether diffusion is sluggish in the present HEAs, the diagonal interdiffusivities (Ni is regarded as the dependent component) D Ni Al Al , D Ni CoCo , D Ni CrCr , and D Ni FeFe in the current 3 Al-Co-Cr-Fe-Ni alloys are first compared with those in the other lower-order fcc alloys [32][33][34][35][36] with similar elements available in the literature.As presented in Figure 7, for Al, Cr, and Fe, all diagonal interdiffusivities in the present 3 HEAs at 1273, 1323, and 1373 K are lower than those in the lower-order alloys (i.e., Al 6 Ni 94 [32], Al 3.76 Co 14.7 Ni 81.54 [33], Al 7.7 Cr 9.7 Ni 82.6 [34], Fe 40 Ni 60 [35], and Co-Cr-Fe-Ni [10] alloys).Meanwhile, sluggish diffusion for Co exists only at 1273 K-i.e., the sluggish diffusion effect can be observed only for Al, Cr, and Fe in the present HEAs.Subsequently, for further analysis, the tracer diffusivities of the 5 elements in the present fcc Al-Co-Cr-Fe-Ni alloys as well as in different fcc elements and conventional alloys with similar elements available in the literature are plotted against the inverse homologous temperature T m /T and the inverse temperature T −1 , as demonstrated in Figure 6.As shown in Figure 6a [11], and Al 20 Co 20 Cr 20 Fe 20 Ni 20 [11] alloys).Therefore, no significant sluggish diffusion is observed for Al, Co, and Ni in the present Al-Co-Cr-Fe-Ni HEAs.Meanwhile, the tracer diffusivities of elements Cr and Fe in the present Al-Co-Cr-Fe-Ni HEAs are lower than those in the other pure elements/alloys (i.e., pure Fe [41], pure Ni [42,43], Fe-15Cr-20Ni [40] [11], and Al 20 Co 20 Cr 20 Fe 20 Ni 20 [11] alloys).With reference to Figure 6a, when the inverse absolute temperature T −1 is used for comparison, sluggish diffusion can be observed only for Fe and Cr in the present HEAs.When the comparison is made against the inverse homologous temperature T m /T, as shown in Figure 6b alloys also coincide.Obviously, when comparison is made against the inverse homologous temperature T m /T, the result is the same as that when the comparison is made against the inverse absolute temperature T −1 , that is, the diffusion is sluggish only for Fe and Cr in the present HEAs.[38], pure Fe [41], Al in Ni [37], Co in Ni [44], Cr in Ni [42], Fe in Ni [43], pure Ni [39], Fe-15Cr-20Ni [40], Co25Cr25Fe25Ni25 [12], Co20Cr20Fe20Mn20Ni20 [12], Co22.22Cr22.22Fe22.22Mn11.12Ni22.22 [11], Al20Co20Cr20Fe20Ni20 [11] plotted as a function of (a) the inverse absolute temperature and (b) the inverse homologous temperature.[38], pure Fe [41], Al in Ni [37], Co in Ni [44], Cr in Ni [42], Fe in Ni [43], pure Ni [39], Fe-15Cr-20Ni [40], Co 25 Cr 25 Fe 25 Ni 25 [12], Co 20 Cr 20 Fe 20 Mn 20 Ni 20 [12], Co 22.22 Cr 22.22 Fe 22.22 Mn 11.12 Ni 22.22 [11], Al 20 Co 20 Cr 20 Fe 20 Ni 20 [11] plotted as a function of (a) the inverse absolute temperature and (b) the inverse homologous temperature.Al6Ni94 [32], Al3.76Co14.7Ni81.54[33], Al7.7Cr9.7Ni82.6 [34], Co40Ni60 [35], Fe40Ni60 [35], Co5Ni95 [36], Co-Cr-Fe-Ni [10].

Conclusions
In summary, the composition-dependent interdiffusion coefficients in fcc Al-Co-Cr-Fe-Ni HEAs at 1273 K, 1323 K, and 1373 K were evaluated by using the recently developed numerical inverse method combined with concentration profiles from diffusion couples and multiples.The reliability of the obtained interdiffusion coefficients were verified by comparing the simulated composition/interdiffusion flux profiles with the corresponding experimental ones.The tracer diffusivities of the components were also evaluated based on the interdiffusivities and the simplified thermodynamic description.The comprehensive comparison between the diagonal interdiffusivities (Ni is regarded as the dependent component) in the present HEAs and those in fcc conventional alloys shows that sluggish diffusion can be observed only for Al, Cr, and Fe in the present HEAs.The results of the comparison of the tracer diffusivities indicate that the significant sluggish diffusion is only observed for Cr and Fe in the present HEAs.Therefore, the sluggish diffusion effect is not true for all the elements in the present Al-Co-Cr-Fe-Ni alloys.

Supplementary Materials:
The following are available online at www.mdpi.com/link.

Figure 2 .
Figure 2. Comparison between the experimental and simulated concentration profiles/interdiffusion fluxes of diffusion couples annealed at 1273 K for 46 h as well as the evaluated diagonal interdiffusivities.Symbols are due to the experimental measurements.

Figure 2 .of 14 Figure 1 .
Figure 2. Comparison between the experimental and simulated concentration profiles/interdiffusion fluxes of diffusion couples annealed at 1273 K for 46 h as well as the evaluated diagonal interdiffusivities.Symbols are due to the experimental measurements.

Figure 2 .
Figure 2. Comparison between the experimental and simulated concentration profiles/interdiffusion fluxes of diffusion couples annealed at 1273 K for 46 h as well as the evaluated diagonal interdiffusivities.Symbols are due to the experimental measurements.

Figure 3 .Figure 3 .
Figure 3.Comparison between the experimental and the simulated concentration profiles/interdiffusion fluxes of diffusion couples annealed at 1323 K for 46 h as well as the evaluated diagonal interdiffusivities.Symbols are due to the experimental measurements.

Figure 4 .
Figure 4. Comparison between the experimental and the simulated concentration profiles/interdiffusion fluxes of diffusion couples annealed at 1373 K for 46 h as well as the evaluated diagonal interdiffusivities.Symbols are due to the experimental measurements.

Figure 4 .
Figure 4. Comparison between the experimental and the simulated concentration profiles/interdiffusion fluxes of diffusion couples annealed at 1373 K for 46 h as well as the evaluated diagonal interdiffusivities.Symbols are due to the experimental measurements.
The diagonal interdiffusivities D Ni Al Al and D Ni CoCo vary significantly with alloy compositions, whereas the variations in D Ni CrCr and D Ni FeFe with alloy compositions are relatively weak.Within the investigated composition and temperature ranges, the diagonal interdiffusivity D Ni Al Al is the largest, followed by D Ni CoCo , D Ni CrCr and D Ni FeFe , indicating that the component sequence with the fastest diffusion rate (the highest interdiffusion coefficient) to the slowest is Al > Co > Cr > Fe in the present fcc Al-Co-Cr-Fe-Ni high-entropy alloys.In addition, all diagonal interdiffusivities D Ni Al Al , D Ni CoCo , D Ni CrCr , and D Ni FeFe increase from 1273 K to 1373 K. Fe is also considered as the dependent component for comparison among the diagonal interdiffusivity of Ni and those of the other components in the 3 diffusion multiples.The results presented in Figure 5 show that the diagonal interdiffusivity D Fe NiNi is close to D Fe CoCo .the component sequence with the fastest diffusion rate (the highest interdiffusion coefficient) to the slowest is Al > Co > Cr > Fe in the present fcc Al-Co-Cr-Fe-Ni high-entropy alloys.In addition, all diagonal interdiffusivities K to 1373 K. Fe is also considered as the dependent component for comparison among the diagonal interdiffusivity of Ni and those of the other components in the 3 diffusion multiples.The results presented in Figure 5 show that the diagonal interdiffusivity Fe NiNi D is close to Fe CoCo D .

Figure 5 .
Figure 5.Comparison among the evaluated diagonal interdiffusivities for Al, Co, Cr, and Ni in the diffusion multiples annealed for 46 h at 1273 K, 1323 K and 1373 K, respectively, where Fe is taken as the dependent component.

Figure 5 .
Figure 5.Comparison among the evaluated diagonal interdiffusivities for Al, Co, Cr, and Ni in the diffusion multiples annealed for 46 h at 1273 K, 1323 K and 1373 K, respectively, where Fe is taken as the dependent component.

Table 2 .
List of the assessed mobility parameters during evaluation of the composition-dependent interdiffusion coefficients in fcc Al-Co-Cr-Fe-Ni HEAs at different temperatures.
[12]e tracer diffusivities of Al, Co, Cr, and Fe in the present quaternary HEA Co 25.33 Cr 25.77 Fe 24.53 Ni 24.37 are lower than those in the present quinary HEAs Al 4.88 Co 29.53 Cr 18.58 Fe 19.62 Ni 27.39 and Al 6.64 Co 23.82 Cr 23.66 Fe 23.01 Ni 22.87 .The temperature-dependent tracer diffusivities of Al in the present 3 HEAs are higher than the tracer diffusivity of Al in Ni [37].Co in the present HEA Al 6.64 Co 23.82 Cr 23.66 Fe 23.01 Ni 22.87 has the highest tracer diffusivities, whereas pure Co[38]has the lowest tracer diffusivities.Moreover, all tracer diffusivities of Ni in the present 3 HEAs are higher than those of Ni in the other fcc pure elements and alloys (i.e., pure Ni[39], Fe-15Cr-20Ni[40], Co 25 Cr 25 Fe 25 Ni 25[12], Co 20 Cr 20 Fe 20 Mn 20 Ni 20[12], Co 22.22 Cr 22.22 Fe 22.22 Mn 11.12 Ni 22.22 , Co 22.22 Cr 22.22 Fe 22.22 Mn 11.12 Ni 22.22 , the 2 curves of the tracer diffusivities of Al in the present Co 25.33 Cr 25.77 Fe 24.53 Ni 24.37 and Al 6.64 Co 23.82 Cr 23.66 Fe 23.01 Ni 22.87 alloys coincide; the 2 curves of the tracer diffusivities of Co in the present Al 4.88 Co 29.53 Cr 18.58 Fe 19.62 Ni 27.39 and Al 6.64 Co 23.82 Cr 23.66 Fe 23.01 Ni 22.87