  In this study Mo-Nb-Ta-W refractory high-entropy alloys (R-HEAs) have been
studied for their phase stability for a wide temperature range (100 K to 2000
K). The equilibrium thermodynamic phases are determined by the changes in
enthalpy and entropy. The enthalpy changes at any temperature are simulated by
embedded atom method (EAM) potential based hybrid Monte Carlo molecular
dynamics (MC/MD) simulations. Configurational entropy was calculated by
quasichemical method. The EAM potentials were all calculated based on the
physical input parameters of elements like atomic volume, cohesive energy,
elastic constants etc. It was found that the MC/MD evolved equilibrium
structures and the degree of local chemical short-range order/clustering
(SRO/SRC) largely depend on the ordering enthalpies for various temperatures.
The ordering transition temperature is close to 700 K, which is also
substantiated by the experimental powder X-ray diffractions done in synchrotron
beam. Large increase of degree of next-neighbor B2-type ordering of Mo-Ta pairs
and decrease of that Nb-W pairs were observed. This was also expected from the
trends of density functional theory (DFT) based ab-initio simulations done in
the literature and discussed in this work. The simulated diffraction pattern
and changes in scattering intensity due to the chemical SRO and SRC was
investigated. The diffraction trends were explained with the help of the
features of the evolved nanostructure morphology. The developed methodologies
may be helpful in prior prediction of long-term phase stability in
multi-element alloys by reducing the number of costly experiments.
