Temperature dependent elastic and thermal expansion properties of W3Co3C, W6Co6C and W4Co2C ternary carbides

Abstract

W3Co3C, W6Co6C, and W4Co2C are known as η-phases of WC–Co materials that form at the expense of the Co phase, because Co allows C diffusion. Their intrinsic properties are generally poorly understood. We report here first-principles calculations of the temperature-dependent elastic and thermal expansion properties of these three phases. We calculated the elastic constants by using the strain–stress relations. The effects of temperature on the elastic properties were examined in the framework of Debye–Grüneisen theory with the quasistatic approximation. Using the results of the elastic properties, we examined the rigidness, brittleness, and ductility of the ternary carbides. In addition, we confirmed the reliability of our Debye calculations by comparing the results of previous experiments and phonon density of states with quasi-harmonic approximation. The results expand our understanding of the ternary carbides in the WC–Co system.