Elastic properties, thermal expansion coefficients and electronic structures of Ti 0.75X 0.25C carbides

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Elastic properties, thermal expansion coefficients and electronic structures of Ti 0.75X 0.25C carbides (X=W, Mo, Ta, Nb, V, Hf, Zr, Cr and Al) were systematically investigated using ab initio density functional theory (DFT) calculations. The calculated elastic moduli, electronic structures and thermal expansion coefficients α( T) of pure TiC are in good agreement with experimental data and other DFT calculations. Based on a phenomenological formula, the trends of elastic properties and ductile/brittle behavior of Ti 0.75X 0.25C were analyzed. It was found that alloying elements W, Mo, Ta, Nb, V and Hf can increase elastic moduli, while Zr, Cr and Al reduce moduli. The nearly free electron model and Debye approximation were applied in the evaluation of α( T). The anharmonic effect was taken into account by including volume-dependent elastic moduli and Debye temperature. Results show that alloying additions of 3 d V, 4 d Zr and Mo slightly reduce α( T), while 3 d Cr increases α( T), Al, 4 d Nb, 5 d Hf and W almost keep α( T) unchanged in Ti 0.75X 0.25C at high temperatures. The electronic structures of Ti 0.75X 0.25C were calculated and analyzed, and the electronic density of states was used to interpret variations of elastic properties and ductile/brittle behavior induced by alloying additions.