Vibrational mode analysis and heat capacity calculation of K2SiSi3O9-wadeite

• Published in: Physics and chemistry of minerals Vol. 40; no. 7; pp. 563 - 574
• Main Authors: Chang, Linlin, Liu, Xi, Liu, Hong, Kojitani, Hiroshi, Wang, Sicheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.07.2013; Springer Nature B.V
• Subjects: Brillouin zones; Computer simulation; Crystallography and Scattering Methods; Density; Earth and Environmental Science; Earth Sciences; Entropy; First principles; Geochemistry; Mineral Resources; Mineralogy; Original Paper; Perturbation theory; Specific heat; Thermodynamic properties; wadeite; First-principles simulation; Heat capacity; Kieffer’s lattice vibrational model; K; SiSi; Vibrational density of states; O
• ISSN: 0342-1791; 1432-2021
• DOI: 10.1007/s00269-013-0593-5

The phonon dispersions and vibrational density of state (VDoS) of the K 2 SiSi 3 O 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 ( ), yielding C P ( T ) = 469.4(6) − 2.90(2) × 10 3  T −0.5 − 9.5(2) × 10 6  T −2  + 1.36(3) × 10 9  T −3 for the T range of 298–1,000 K and  = 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 3  T −0.5 – 8.8(2) × 10 6  T −2  + 1.31(3) × 10 9  T −3 for the T range of 298–1,000 K and  = 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.