Neutron Diffraction Measurements and First Principles Study of Thermal Motion of Atoms in Select M_{n+1}AX_n and Binary MX Transition Metal Carbide Phases

TL;DR

This study combines neutron diffraction and first principles calculations to analyze atomic thermal vibrations in MAX phases and binary carbides, revealing good qualitative agreement and insights into vibrational anisotropy and anharmonicity.

Contribution

It provides a comparative analysis of experimental and theoretical atomic vibrations in MAX phases and carbides, validating computational methods and exploring vibrational anisotropy and anharmonicity.

Findings

Good agreement between theory and experiment for binary carbides.

A element exhibits highest and anisotropic vibrational amplitude in MAX phases.

Computed Grüneisen parameters reveal anharmonicity in the systems.

Abstract

Herein, we compare the thermal vibrations of atoms in select ternary carbides with the formula Mn+1AXn ("MAX phases," M = Ti, Cr; A = Al, Si, Ge; X = C, N) as determined from first principles phonon calculations to those obtained from high-temperature neutron powder diffraction studies. The transition metal carbides TiC, TaC, and WC are also studied to test our methodology on simpler carbides. Good qualitative and quantitative agreement is found between predicted and experimental values for the binary carbides. For all the MAX phases studied - Ti3SiC2, Ti3GeC2, Ti2AlN, Cr2GeC and Ti4AlN3 - density functional theory calculations predict that the A element vibrates with the highest amplitude and does so anisotropically with a higher amplitude within the basal plane, which is in line with earlier results from high-temperature neutron diffraction studies. In some cases, there are quantitative differences in the absolute values between the theoretical and experimental atomic displacement parameters, such as reversal of anisotropy or a systematic offset of temperature-dependent atomic displacement parameters. The mode-dependent Gr\"uneisen parameters are also computed to explore the anharmonicity in the system.