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

摘要

Herein, we compare the thermal vibrations of atoms in select ternary carbideswith 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 fromhigh-temperature neutron powder diffraction studies. The transition metalcarbides TiC, TaC, and WC are also studied to test our methodology on simplercarbides. Good qualitative and quantitative agreement is found betweenpredicted and experimental values for the binary carbides. For all the MAXphases studied - Ti3SiC2, Ti3GeC2, Ti2AlN, Cr2GeC and Ti4AlN3 - densityfunctional theory calculations predict that the A element vibrates with thehighest amplitude and does so anisotropically with a higher amplitude withinthe basal plane, which is in line with earlier results from high-temperatureneutron diffraction studies. In some cases, there are quantitative differencesin the absolute values between the theoretical and experimental atomicdisplacement parameters, such as reversal of anisotropy or a systematic offsetof temperature-dependent atomic displacement parameters. The mode-dependentGr\"uneisen parameters are also computed to explore the anharmonicity in thesystem.