Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite
Bredigite with the composition Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub> (Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bre) has been synthesized by a solid-state reaction method at 1.2 GPa and 1373 K for 7 days, and its struc...
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MDPI AG
2020-12-01
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| Online Access: | https://www.mdpi.com/2073-4352/11/1/14 |
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| author | Xinjian Bao Mingyue He Zhigang Zhang Xi Liu |
| author_facet | Xinjian Bao Mingyue He Zhigang Zhang Xi Liu |
| author_sort | Xinjian Bao |
| collection | DOAJ |
| description | Bredigite with the composition Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub> (Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-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 Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-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 Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-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<sub>p</sub></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<sub>p</sub></i> = 8.22(2) × 10<sup>2</sup> − 3.76(6) × 10<sup>3</sup><i>T</i><sup>−0.5</sup> − 1.384(4) × 10<sup>7</sup><i>T</i><sup>−2</sup> + 1.61(8) × 10<sup>9</sup><i>T</i><sup>−3</sup> J mol<sup>−1</sup> K<sup>−1</sup> 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<sup>−1</sup> K<sup>−1</sup>. |
| first_indexed | 2024-03-10T13:45:48Z |
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| spelling | doaj.art-b7768cd673104a4fb03b1f08dad789992023-11-21T02:41:04ZengMDPI AGCrystals2073-43522020-12-011111410.3390/cryst11010014Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-BredigiteXinjian Bao0Mingyue He1Zhigang Zhang2Xi Liu3Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education of China, Beijing 100871, ChinaSchool of Gemmology, China University of Geosciences (Beijing), Beijing 100083, ChinaKey Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, ChinaKey Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education of China, Beijing 100871, ChinaBredigite with the composition Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub> (Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-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 Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-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 Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-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<sub>p</sub></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<sub>p</sub></i> = 8.22(2) × 10<sup>2</sup> − 3.76(6) × 10<sup>3</sup><i>T</i><sup>−0.5</sup> − 1.384(4) × 10<sup>7</sup><i>T</i><sup>−2</sup> + 1.61(8) × 10<sup>9</sup><i>T</i><sup>−3</sup> J mol<sup>−1</sup> K<sup>−1</sup> 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<sup>−1</sup> K<sup>−1</sup>.https://www.mdpi.com/2073-4352/11/1/14bredigitesingle-crystal XRDstructure refinementfirst-principle calculationcompressibilityheat capacity |
| spellingShingle | Xinjian Bao Mingyue He Zhigang Zhang Xi Liu Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite Crystals bredigite single-crystal XRD structure refinement first-principle calculation compressibility heat capacity |
| title | Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite |
| title_full | Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite |
| title_fullStr | Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite |
| title_full_unstemmed | Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite |
| title_short | Crystal Structure and Some Thermodynamic Properties of Ca<sub>7</sub>MgSi<sub>4</sub>O<sub>16</sub>-Bredigite |
| title_sort | crystal structure and some thermodynamic properties of ca sub 7 sub mgsi sub 4 sub o sub 16 sub bredigite |
| topic | bredigite single-crystal XRD structure refinement first-principle calculation compressibility heat capacity |
| url | https://www.mdpi.com/2073-4352/11/1/14 |
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