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

Abstract

Herein we report on the thermal expansions and temperature-dependent crystal structures of select ternary carbide Mn+1AXn (MAX) phases in the Ti–Al–C phase diagram in the 100−1000 °C temperature range. A bulk sample containing 38(±1) wt. % Ti5Al2C3 (“523”), 32(±1) wt. % Ti2AlC (“211”), 18(±1) wt. % Ti3AlC2 (“312”), and 12(±1) wt. % (Ti0.5Al0.5)Al is studied by Rietveld analysis of high-temperature neutron diffraction data. We also report on the same for a single-phase sample of Ti3AlC2 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(±0.1)×10−6 K−1 for Ti5Al2C3, 9.2(±0.1) ×10−6 K−1 for Ti2AlC, and 9.0(±0.1)×10−6 K−1 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.