How Atoms of Polycrystalline Nb 20.6 Mo 21.7 Ta 15.6 W 21.1 V 21.0 refractory High-Entropy Alloys Rearrange during the Melting Process

The Nb 20.6 Mo 21.7 Ta 15.6 W 21.1 V 21.0 RHEAs was investigated by the molecular dynamics (MD) simulation using the 2NN MEAM potential. For the single crystal RHEA, the density profile displays an abrupt drop from 11.25 to 11.00 g/cm 3 at temperatures from 2910 to 2940 K, indicating all atoms begin significant local structural rearrangement. For polycrystalline RHEAs, a two-stage melting process is found. In the first melting stage, the melting of the grain boundary (GB) regions firstly occurs at the pre-melting temperature, which is relatively lower than the corresponding system-melting point. At the pre-melting temperature, most GB atoms have enough kinetic energies to leave their equilibrium positions, and then gradually induce the rearrangement of grain atoms close to GB. In the second melting stage at the melting point, most grain atoms have enough kinetic energies to rearrange, resulting in the chemical short-ranged order (CSRO) changes of all pairs.


Introduction
Materials used in the extreme working environments such as high temperatures or pressures are in an urgent need for industrial application. For example, to improve the efficiency of gas turbine engines in the aerospace industry, increasing engine operating temperature is one of the most effective ways [1]. However, the most commonly used hightemperature structural material, nickel-based superalloy, has its own melting point of about 1300 °C, which limits the maximum operating temperature. Thus, it is very important that the material has a high enough melting point [2]. High entropy alloys (HEAs), also known as multi-principal-element alloys (MPEAs), are composed of major element types more than four [3].
Among all HEAs, the refractory high entropy alloys (RHEAs) generally have one or more compositional refractory elements such as W, Mo, Ta, Nb, Zr, and Re [13].
Accordingly, RHEAs display excellent high temperature resistance, high melting point (>2000 °C), and higher high temperature strength, which has wide potential for applications in high temperature equipment. For examples, in 2010, the first RHEA, NbMoTaW RHEA, was fabricated by Senkov [14]. The yield strength of NbMoTaW RHEA at 1600 °C is 405 MPa, and the working temperature limit of 1600 °C is much higher than that of nickel-based high temperature alloys about 1300 °C. The poor phase stability and low plasticity at high and medium temperatures are two bottlenecks to restrict the application of HEAs at high temperatures. Thus, In Nie's study [1], the HfMoScTaZr RHEAs were prepared by vacuum arc melting equipment. By adding Sc element, the density of the alloy becomes lower, and the strength and plasticity of HfMoScTaZr RHEAs were significantly improved. The yield strengths of HfMoScTaZr RHEAs at room temperature, 800 °C, 1000 °C and 1200 °C are 1778, 1118, 963 and 498 MPa, respectively.
At 1200 °C, the yield strength of HfMoScTaZr RHEA is about 4.3 and 6 times higher than those of the traditional classic superalloys, Inconel 718 and CMSX-4. Besides the compositional element types and their related fractions, the material properties of HEAs or alloys are significantly affected by the extent of crystallinity. For examples, In Lin's study [15], the melt-ball milling-hot pressing process was adopted to fabricate the Cu 3−x Ni x SbSe 4 (x = 0~0.03) alloys with different average grain sizes. The influences of average grain size on the microstructure and thermoelectric properties of Cu 3−x Ni x SbSe 4 were observed.
Because of the grain refinement and Se defect increase, the lattice thermal conductivity decreases from 3.3 Wm −1 K −1 to 2.4 Wm −1 K −1 at room temperature when the fraction Ni fraction decreases from x=0.03 to 0. In Sun's study [16] [17], they found the steady-state creeping rate of Cu0.5Ni0.5 alloy speeds up dramatically under the elevated stress and temperature as well as the decreasing grain size. The lattice and grain boundary diffusion play a critical factor of creeping deformation mechanism of the NC Cu0.5Ni0.5 alloy. Giang studied the melting stages of 2D confined germanene in both perfect crystalline and polycrystalline states by MD simulation [18]. The temperatures from solid to liquid phase transition are about 1670 K and 1540 K for the crystalline and polycrystalline models, respectively. In Noori's study [19], the MD simulation was utilized to realize the effect of grain size on the melting temperature of Al nanocrystals. Their results show that the melting temperature becomes lower when the grain size is smaller.
The pre-melting and melting at grain boundary regions does not take place instantly, and the melting of the polycrystalline Al occurs within a certain temperature range, rather than at a specific temperature.
The systematic investigation on how atoms rearrange for a single crystal and polycrystalline RHEAs during the heating process is still lacking. In order to explore the melting mechanism, the single crystal Nb 20 behaviors of different elements at grain boundaries and within grains were also investigated, and variations of affinity between any two element type pairs were investigated by the chemical short-ranged order (CSRO) during the heating process.

Simulation model
The second-nearest neighbor modified embedded atomic method (2NN MEAM) was used to describe the interactions among Nb, Mo, T, W, and V atoms. Table 1 lists the parameters of all single elements [20], and Tables 2 and 3 show all cross-element and ternary-element parameters of 2NN MEAM potential, parametrized by the reference data prepared by the density functional theory (DFT) calculation. The detailed parametrization process can be seen in the supplementary file of our previous study [21]. The ATOMSK package [22]was adopted to build the structures of polycrystalline  RHEAs were investigated by the MD temperature elevation process from 300 to 3600 K.
The heating process was processed in the increasing temperature by 10 K increment, and each increment was accompanied by a relaxation process in 10 ps before the subsequent temperature increases. For maintaining the constant temperature under the free stress during the temperature elevation process, the TtN method was utilized [24]. This method combines the Parrinello-Rahman variable shape size ensemble with the Nosé-Hoover thermostat. For the heating simulation, the periodic boundary conditions (PBCs) were used in all dimensions. Large-scale atomic/molecular massively parallel simulator (LAMMPS) was utilized to perform all MD simulations, which was developed by Plimpton et al. [25].
The OVITO package [26] was used to do all visualization and post process of all simulation results. nm. In Fig. 1, according to the CNA results, atoms within the GB and grain are arranged in the undefined type and the BCC type, respectively. When the average grain size becomes smaller, the surface area to volume ratio of grains becomes higher. Accordingly, the fraction of GB atoms surrounding grains significantly increases, resulting in the increase of atoms at the GB/grain interface. Atoms at GB/grain interface possess higher local stresses and higher binding energy, so the atomic binding energy of GB, grain, and system decrease parabolically when the grain size increases from 5.2 to 25.3 nm as illustrated in

Results and Discussion
where is the CSRO parameter of the i-type referenced atom relative to j-type atom, N ij is the partial coordination number (CN) for the i-type referenced atom relative to j-type atom obtained from the predicted structure, and c j and N i are the fractions of j-type atom within the alloy and the average CN of i-type atoms, respectively. The value of c j by N i is an ideal partial CN for the referenced i-type atom relative to the first neighbor j-type atom, and this value completely depends on the respective atomic composition fraction of ) for the i-type reference atom to its first neighbor j-type atom. If this ratio is larger than 1, it means the affinity of j-type atom to i-type atom in the predicted structure is higher than that in the ideal structure. On the other hand, if this ratio is lower than 1, the affinity of j-type atom to i-type atom in the predicted structure is lower than that in the ideal structure. If the ratio is close to 1, it infers the affinity of j-type atom to i-type atom in the predicted structure is close to that in the ideal structure. Consequently, the positive and negative values of CSRO indicate the lower and higher affinity of the element type pair, compared with their ideal affinity.    whereas the negative value indicates the affinity of an element type pair becomes stronger.
In Fig. 8(b), one can see the CSRO differences of the same element type pairs are negative, indicating the affinity of the same element undergoes significant change at temperatures higher than the melting point. Figure 9 shows the atom distributions of Nb, Mo, W, Ta Fig. 8(b), most of their CSRO differences are positive, indicating these element pairs become less affinity after the structural rearrangement after the melting. increase linearly with the increasing temperature from 2100 to 2800 K and from 2100 to 2670 K. Then binding energies of grain and GB display parabolic increase from 2800 to 2920 K and from 2670 to 2820 K, respectively. At temperatures higher than 2800 K for grain and 2670 K for GB, SD values begin to rise dramatically, indicating the local structural rearrangement occurs at these temperatures. It can see the temperature for GB structural rearrangement is relatively lower than that of grain. Consequently, at 2820 K, most GB atoms have enough kinetic energies to leave their equilibrium positions, and then these GB atoms gradually induce the rearrangement of grain atoms close to GB.
Consequently, the temperature of 2820 K can be regarded as the pre-melting temperature, at which the melting of GB has been completed. When the temperatures continuously increase from 2920 K to 3100 K for grain and from 2820 K to 3100 K for GB, the binding energies decrease with the increasing temperature, and it indicates atoms of the same element types have a higher opportunity to contact each other. It should be noted the temperature, 2920 K (very close to the melting point obtained from enthalpy profile), is located at the binding energy peak of grain atoms, and it indicates most grain atoms have enough kinetic energies to rearrange. At temperature higher than 3100 K, the binding energies of grain and GB also illustrate linear increase with the increasing temperature.
The average CSRO square profiles of the case with the average grain size of 25.3 nm during the heating process were shown in Fig. 12 (melting point), and 2920 (binding energy peak of grain atom) K are illustrated in Fig. 13.
At the pre-melting temperature, 2820 K, the GB atoms and some grain atoms close to GB have undergone significant local structural arrangement, leading to the CSRO changes of these atoms. The CSRO value variations of different element pairs at temperatures higher than the pre-melting temperature are very similar to those of single crystal Nb 20.6 Mo 21.7 Ta 15.6 W 21.1 V 21.0 RHEA at temperatures higher than that with the minimum of average CSRO square as shown in Fig. 8(a). The structure at 2000 K was used as the reference for calculating the atomic displacement vectors. The atom positions of the structure at 300 K were used as the reference, and the vectors were colored according to the length of a vector. In Fig. 18(a), GB atoms and grain atoms close to GB have longer displacement vector sizes (marked in red and green), as compared with those at the cores of grains (marked in blue). At 2540 K as shown in Fig.   18(b), more grain atoms have large displacement vector lengths and the melting occurs toward the cores of grains. At 2700 K, the displacement vectors in Fig. 18       The square displacement (SD) and enthalpy pro les of system, Nb, Mo, W, Ta, and V during the heating process for the single crystal Nb20.6Mo21.7Ta15.6W21.1V21.0 RHEA. The insert shows SD pro les at temperatures lower than the melting point of 2940 K.   The distributions of Nb, Mo, Ta, W, V, and all elements within the single crystal Nb20.6Mo21.7Ta15.6W21.1V21.0 RHEA at 3110 K.  The binding energy and square displacement (SD) pro les of system, Nb, Mo, W, Ta, and V of (a) the grain atoms and (b) the GB atoms for the case with the average grain size of 25.3 nm during the heating process.  The CSRO distributions for the Nb20.6Mo21.7Ta15.6W21.1V21.0 RHEA with the average grain size of 25.3 nm at four characteristic temperatures, 2780 (minimum of average CSRO square), 2820 (pre-melting temperature), 2900 (melting point), and 2920 (binding energy peak of grain atom) K.

Figure 14
The atomic displacement vectors of 25.3 nm at (a) 2820 K, (b) 2920 K, and (c) 3100 K, respectively. The atom positions at 300 K were used as the reference positons for the displacement vectors.

Figure 15
The binding energy and square displacement (SD) pro les of system, Nb, Mo, W, Ta, and V of (a) the grain atoms and (b) the GB atoms for the case with the average grain size of 5.2 nm during the heating process.

Figure 16
Average CSRO square pro les of the same and different element type pairs for the Nb20.6Mo21.7Ta15.6W21.1V21.0 RHEA with the average grain size of 5.2 nm. The texts (I) and (II) indicate the minimum of average CSRO square of the same element pair at 2340 K and the melting point at 2540 K.

Figure 17
The CSRO distributions for the Nb20.6Mo21.7Ta15.6W21.1V21.0 RHEA with the average grain size of 5.2 nm at 2340 (minimum of average CSRO square), 2460 (pre-melting temperature), and 2540 (melting point and the binding energy peak of grain atom) K.