High-temperature neutron diffraction and first-principles study of temperature-dependent crystal structures and atomic vibrations in Ti3AlC2, Ti2AlC, and Ti5Al2C3

Herein we report on the thermal expansions and temperature-dependent crystal structures of select ternary carbide MAX phases in the Ti-Al-C phase diagram in the 100-1000 deg C temperature range. A bulk sample containing 38 wt.% Ti5Al2C3, "523"), $32 wt.$_3$AlC$_2$for comparison. The thermal expansions of all the MAX phases studied are higher in the$c$direction than in the$a$ direction. The bulk expansion coefficients - 9.3 x 10^-6 for Ti5Al2C3, 9.2 x 10^-6 for Ti2AlC, and 9.0 x 10^-6 for Ti3AlC2 - are comparable within one standard deviation of each other. In Ti5Al2C3, the dimensions of the Ti-C octahedra for the 211-like and 312-like regions are comparable to the Ti-C octahedra in Ti2AlC and Ti3AlC2, respectively. The isotropic mean-squared atomic displacement parameters are highest for the Al atoms in all three phases, and the values predicted from first-principles phonon calculations agree well with those measured.

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