First-principles phonon calculations of thermal expansion in Ti3SiC2, Ti3AlC2, and Ti3GeC2

Thermal properties of ternary carbides with composition Ti3SiC2, Ti3AlC2, and Ti3GeC2 were studied using the first-principles phonon calculations. The thermal expansions, the heat capacities at constant pressure, and the isothermal bulk moduli at finite temperatures were obtained under the quasiharmonic approximation. Comparisons were made with the available experimental data and excellent agreements were obtained. Phonon band structures and partial density of states were investigated. These compounds present unusual localized phonon states at low frequencies, which are due to atomiclike vibrations parallel to the basal plane of the Si, Al, or Ge elements.