Hightemperature neutron diffraction and firstprinciples study of temperaturedependent crystal structures and atomic vibrations in Ti_{3}AlC_{2}, Ti_{2}AlC, and Ti_{5}Al_{2}C_{3}
Abstract
Herein we report on the thermal expansions and temperaturedependent crystal structures of select ternary carbide M_{n +1}AX_{n} (MAX) phases in the TiAlC phase diagram in the 1001000 °C temperature range. A bulk sample containing 38(±1) wt. % Ti_{5}Al_{2}C_{3} ("523"), 32(±1) wt. % Ti_{2}AlC ("211"), 18(±1) wt. % Ti_{3}AlC_{2} ("312"), and 12(±1) wt. % (Ti0.5Al0.5)Al is studied by Rietveld analysis of hightemperature neutron diffraction data. We also report on the same for a singlephase sample of Ti_{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(±0.1)×10^{6} K^{1} for Ti_{5}Al_{2}C_{3}, 9.2(±0.1) ×10^{6} K^{1} for Ti_{2}AlC, and 9.0(±0.1)×10^{6} K^{1} for Ti_{3}AlC_{2}—are comparable within one standard deviation of each other. In Ti_{5}Al_{2}C_{3}, the dimensions of the TiC octahedra for the 211like and 312like regions are comparable to the TiC octahedra in Ti_{2}AlC and Ti_{3}AlC_{2}, respectively. The isotropic meansquared atomic displacement parameters are highest for the Al atoms in all three phases, and the values predicted from firstprinciples phonon calculations agree well with those measured.
 Publication:

Journal of Applied Physics
 Pub Date:
 May 2013
 DOI:
 10.1063/1.4803700
 arXiv:
 arXiv:1304.0068
 Bibcode:
 2013JAP...113r3519L
 Keywords:

 ab initio calculations;
 aluminium alloys;
 carbon;
 crystal structure;
 neutron diffraction;
 phase diagrams;
 thermal expansion;
 titanium alloys;
 vibrations;
 61.66.Dk;
 61.05.F;
 81.30.Bx;
 65.40.De;
 Alloys;
 Neutron diffraction and scattering;
 Phase diagrams of metals and alloys;
 Thermal expansion;
 thermomechanical effects;
 Condensed Matter  Materials Science
 EPrint:
 doi:10.1063/1.4803700