Phonon broadening in high entropy alloys

Fritz Körmann,Yuji Ikeda,Blazej Grabowski,Marcel H F Sluiter

doi:10.1038/s41524-017-0037-8

Abstract

Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation high-temperature applications. At high temperatures, materials properties are strongly affected by lattice vibrations (phonons). Phonons critically influence thermal stability, thermodynamic and elastic properties, as well as thermal conductivity. In contrast to perfect crystals and ordered alloys, the inherently present mass and force constant fluctuations in multi-component random alloys (high entropy alloys) can induce significant phonon scattering and broadening. Despite their importance, phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys. We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys, from binaries up to 5-component high entropy alloys, addressing the key question of how chemical complexity impacts phonons. We find that it is crucial to include both mass and force constant fluctuations. If one or the other is neglected, qualitatively wrong results can be obtained such as artificial phonon band gaps. We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities, specifically the vibrational entropy. Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations. The set of studied alloys includes MoTa, MoTaNb, MoTaNbW, MoTaNbWV, VW, VWNb, VWTa, VWNbTa, VTaNbTi, VWNbTaTi, HfZrNb, HfMoTaTiZr.

Highlights

On the basis of our results, we address the following fundamental questions: How strongly are phonon spectra affected in high entropy alloys by chemical disorder induced scattering? What is the detailed contribution due to mass and force constant fluctuations? Are both important or could one or the other be neglected?
The 2- and 5-component alloys, the phonon spectra based on the virtual-crystal approximation (VCA, black solid lines in Fig. 1 and black dashed lines in Fig. 2), where we replaced the force constants with averaged values according to the crystal symmetries and the atomic masses with averaged i.e. VW and VWNbTaTi, reveal qualitatively different phonon broadening their ΓM parameters are similar (0.32 vs. 0.29)
For energies and constitute a very effective frequency range quantitative predictions force constant fluctuations cannot be for such a selective filter

Summary

INTRODUCTION

High entropy alloys (HEA) are of great technological interest due to their excellent mechanical[1, 2] and electronic properties.[3]. The longwavelength limit (region close to Γ) is unaffected, i.e., no broadening is visible and the spectral function is sharply peaked as exemplified in the two 3D insets (e) and (f) for MoTaNbW and MoTaNbWV This long-wavelength behavior is a consequence of the Rayleigh law (~ ω4) for impurity scattering.[35] For the mid- and high-frequency region (above ~ 4 THz), the broadening turns out where the broadening sets in, the averaged dispersions fail in capturing the correct physics. The 2- and 5-component alloys, the phonon spectra based on the virtual-crystal approximation (VCA, black solid lines in Fig. 1 and black dashed lines in Fig. 2), where we replaced the force constants with averaged values according to the crystal symmetries (i.e. by not distinguishing the different constituents) and the atomic masses with averaged i.e. VW and VWNbTaTi, reveal qualitatively different phonon broadening their ΓM parameters are similar (0.32 vs 0.29). Insets e and f provide 3D representations of the long-wavelength phonon spectra for MoTaNbW and MoTaNbWV npj Computational Materials (2017) 36

Ta-Ta 181 u

DISCUSSION