A Phenomenological Discrete Lattice Model for Simulating the Response of High-Entropy Alloys

High-entropy alloys (HEAs) are a class of materials with revolutionary applications as structural and functional materials. They are very strong and have high melting points. Moreover, they can retain their strength at high temperatures, even fairly close to melting points. This makes them particularly suitable for use in extreme environments such as in turbines and power stations.<br/>HEAs are essentially random alloys, typically containing five or more elements in approximately equal concentrations. The formulation of predictive theories for the strength of random alloys has been a topic of active research that has resulted into useful theories such as the effective medium theory. However, these theories are, in general, limited to low concentrations of the solutes and are not applicable to HEAs, in which the relative concentration of solutes is high.<br/>We propose a new, phenomenological discrete lattice model for the analysis and representation of measurements of HEA characteristics. Our model is essentially an atomistic version of the theory given by Varvenne, Luque, and Curtin [Acta Materialia <b>118</b> (2016) 164]. Instead of the usual continuum approximation, we assume a discrete Born von Karman model for the underlying lattice of the alloy. We define an effective monoatomic lattice, which has the same Bravais lattice structure and bulk elastic and thermal characteristics as the original alloy. In our model, each lattice site is assumed to be occupied by a hypothetical, effective atom, which is an ‘average’ of all the constituent solutes. Thus, instead of averaging over the field, we average over the solute atoms and replace each real solute by an effective atom.<br/>The next step is to locally replace one single effective atom by a real solute atom. This atom now becomes a defect, which distorts the host lattice. We calculate the lattice distortion by using the multiscale Green’s function (GF) method, developed in our group for general solids. The key point of the model (Varvenne et. al.), is that the dislocations in the solid interact with the local distortion field of each defect. This interaction is responsible for the characteristic hardness of the alloy.<br/>As an example, we apply our theory to a Ni-Co-Fe-Cr-Mn alloy. This alloy has been a popular choice in the literature and has an fcc Bravais lattice. The mass of each effective atom is the weighted average of all the solutes. For the interatomic interaction, we choose a two-exponential, four-parameter function, which extends up to second neighbors of each atom. The four parameters are determined using the literature values of the three elastic constants of the alloy, and its average binding energy, which also gives the effective lattice constant. Using this potential, we calculate the interatomic force constants, the phonon dispersion, and the phonon density of states by the method of the phonon GF. The interaction between the local distortion and dislocations is calculated by using the multiscale GF.<br/>The primary advantages of our GF method, compared to the previous methods, are the following:<br/>1. High computational efficiency. It can simulate a large crystallite (million atoms or more) in a few seconds even on an ordinary desktop. The computational expense of ordinary molecular dynamics generally limits the number of atoms that can be included in the model.<br/>2. Multiscale. It is valid at close range as well as at asymptotic distances from the defect. The GF accounts for the discrete lattice effects and nonlinear contributions in the near field. The GF reduces seamlessly to the macroscopic continuum values in the far field limit. This is crucial for modeling the interaction between the dislocations and the defects, which is absolutely essential for HEAs.<br/>3. Flexible model: It can be extended to include more distant neighbors, and more general potentials.<br/>4. The phonon GF can be used to calculate the relevant thermodynamic functions, such as the specific heat and the vibrational entropy.