Vibrational mode analysis and heat capacity calculation of K_2SiSi_3O_9-wadeite

摘要

The phonon dispersions and vibrational density of state (VDoS) of the K_2SiSi_3O_9-wadeite (Wd) have been calculated by the first-principles method using density functional perturbation theory. The vibrational frequencies at the Brillouin zone center are in good correspondence with the Raman and infrared experimental data. The calculated VDoS was then used in conjunction with a quasi-harmonic approximation to compute the isobaric heat capacity (C_ P) and vibrational entropy (S~0_ 298), yielding C_ P(T) = 469.4(6) - 2.90(2) × 10~3 T~ (-0.5) - 9.5(2) × 10~6T~(-2) + 1.36(3) × 10~9T~(-3) for the T range of 298-1,000 K and S~0_ (298) = 250.4 J mol~(-1)K~(-1). In comparison, these thermodynamic properties were calculated by a second method, the classic Kieffer's lattice vibrational model. On the basis of the vibrational mode analysis facilitated by the first-principles simulation result, we developed a new Kieffer's model for the Wd phase. This new Kieffer's model yielded C_P(T) = 475.9(6) - 3.15(2) × 10~3T~(-0.5)-8.8(2) × 10~6T~(-2) + 1.31(3) × 10~9T~(-3) for the T range of 298-1,000 K and S_(298)~ 0 = 249.5(40) J mol~(-1)K~(-1), which are in good agreement both with the results from our first method containing the component of the first-principles calculation and with some calorimetric measurements in the literature.