High-temperature neutron diffraction and first-principles study of temperature-dependent crystal structures and atomic vibrations in Ti_3AlC_2, Ti_2AlC, and Ti_5Al_2C_3

摘要

Herein we report on the thermal expansions and temperature-dependent crystal structures of select ternary carbide M_(n+1)AX_n (MAX) phases in the Ti-Al-C phase diagram in the 100-1000℃ temperature range. A bulk sample containing 38(±1) wt. % Ti_5Al_2C_3 ("523"), 32(±1)wt.% Ti_2AlC ("211"), 18(±1)wt.% Ti_3AlC_2 ("312"), and 12(±1)wt.% (Ti_(0.5)Al_(0.5))Al is studied by Rietveld analysis of high-temperature neutron diffraction data. We also report on the same for a single-phase sample of Ti_3AlC_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(±0.1) ×10~(-6)K~(-1) for Ti_5Al_2C_3, 9.2(±0.1) ×10~(-6)K~(-1) for Ti_2AlC, and 9.0(±0.1) ×10~(-6)K~(-1) for Ti_3AlC_2-are comparable within one standard deviation of each other. In Ti_5Al_2C_3, the dimensions of the Ti-C octahedra for the 211 -like and 312-like regions are comparable to the Ti-C octahedra in Ti_2AlC and Ti_3AlC_2, 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.