Study of thermal properties of TiCNO by Debye-Einstein model and Debye-Grüneisen model

Abstract

The thermal properties of TiCNO are studied from the Debye-Einstein model based on the first-principle in combination with the special quasi-random structural model, meanwhile the derived result is compared with those obtained by the Debye-Grüneisen model. The present results show that Debye-Einstein model is excellent in predicting the thermal properties of multicomponent random structure materials due to consideration of the 3 n − 3 optical frequencies at the Γ point to represent the contributions of optic branches, although the Debye-Grüneisen models is also effective methods for predicting the thermal properties of multicomponent materials. The two methods show that when temperature rises, the thermal expansion coefficients of TiCNO first increase rapidly and then slowly, and Debye-Einstein predicts a stronger volume sensitivity to lower temperature due to the contribution of 3 n − 3 optic frequencies at Γ point. Although both models also predict a comparable temperature dependence of bulk modulus, the high temperature softening effect of TiCNO calculated by Debye-Einstein is gentler than that from Debye-Grüneisen, which demonstrates that the influence of optical branches cannot be negligible. With temperature increasing, the thermodynamic entropy predicted by both models increases due to the greater disorder degree of the system. Moreover, the thermodynamic entropy predicted by Debye-Einstein is larger owing to considering the optical frequencies at the Γ point. Due to the strong coupling between the acoustic and optical phonons lying in low frequency regime, both isobaric and isochoric heat capacities predicted by Debye-Einstein are larger than those predicted by Debye-Grüneisen at low temperatures. This work is a useful reference for predicting the thermal properties of multicomponent materials.