Crystal Structure and Some Thermodynamic Properties of Ca₇MgSi₄O₁₆-Bredigite

• Main Authors: Xinjian Bao, Mingyue He, Zhigang Zhang, Xi Liu
• Format: Article
• Language: English
• Published: MDPI AG 2021-12-01
• Series: Crystals
• Subjects: bredigite; single-crystal XRD; structure refinement; first-principle calculation; compressibility; heat capacity
• Online Access: https://www.mdpi.com/2073-4352/11/1/14

Bredigite with the composition Ca₇MgSi₄O₁₆ (Ca₇MgSi₄O₁₆-Bre) has been synthesized by a solid-state reaction method at 1.2 GPa and 1373 K for 7 days, and its structure has been determined by single-crystal X-ray diffraction data. Following a relevant genealogy analysis in the literature, we have refined the structure into two space groups, <i>Pnnm</i> and <i>Pnn</i>2, and found that Ca₇MgSi₄O₁₆-Bre belongs to the space group <i>Pnnm</i>, which can be essentially derived from the space group <i>Pnn</i>2 via an atomic coordinate transformation (with an average deviation of 0.039 Å only). Furthermore, some thermodynamic properties of the Ca₇MgSi₄O₁₆-Bre have been obtained in this study. Using first-principles simulations based on density functional theory, the isothermal bulk modulus has been determined as 90.6(4) GPa with a pressure derivative of 5.7(1). Using density functional perturbation technique, the phonon dispersions and vibrational density of the states (VDoS) have been calculated. The VDoS has been combined with a quasi-harmonic approximation to compute the isobaric heat capacity (<i>C_p</i>) and standard vibrational entropy (<inline-formula><math display="inline"><semantics><mrow><msubsup><mi>S</mi><mrow><mn>298</mn></mrow><mn>0</mn></msubsup></mrow></semantics></math></inline-formula>), yielding <i>C_p</i> = 8.22(2) × 10² − 3.76(6) × 10³<i>T</i>^−0.5 − 1.384(4) × 10⁷<i>T</i>⁻² + 1.61(8) × 10⁹<i>T</i>⁻³ J mol⁻¹ K⁻¹ for the <i>T</i> range of 298-1000 K and <inline-formula><math display="inline"><semantics><mrow><msubsup><mi>S</mi><mrow><mn>298</mn></mrow><mn>0</mn></msubsup></mrow></semantics></math></inline-formula> = 534.1 (22) J mol⁻¹ K⁻¹.