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Vibrational mode analysis and heat capacity calculation of K2SiSi3O9-wadeite |
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| Authors: | Linlin Chang Xi Liu Hong Liu Hiroshi Kojitani Sicheng Wang |
| Institution: | 1. Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education of China, Beijing, 100871, China 2. School of Earth and Space Sciences, Peking University, Beijing, 100871, China 3. Institute of Earthquake Science, China Earthquake Administration, Beijing, 100036, China 4. Department of Chemistry, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo, 171-8588, Japan |
| Abstract: | The phonon dispersions and vibrational density of state (VDoS) of the K2SiSi3O9-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 ( $S_{298}^{0}$ ), yielding C P (T) = 469.4(6) ? 2.90(2) × 103 T ?0.5 ? 9.5(2) × 106 T ?2 + 1.36(3) × 109 T ?3 for the T range of 298–1,000 K and $S_{298}^{0}$ = 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) × 103 T ?0.5 – 8.8(2) × 106 T ?2 + 1.31(3) × 109 T ?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. |
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