Anharmonic effect on the equation of state (EoS) for NaCl |
| |
| Authors: | Tatsuya Sumita Akira Yoneda |
| |
| Institution: | 1. Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8567, Japan
2. Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori, 682-0193, Japan
|
| |
| Abstract: | We find clear intrinsic anharmonicity in the NaCl-B1 phase by examining the equation of state (EoS) based on previous ultrasonic velocity data for pressures up to 0.8 GPa and temperatures up to 800 K. The experimental EoS for this phase shows that its specific heat at constant volume (C V ) is significantly smaller than that based on a harmonic model. Also, the sign of $\left( {{{\partial C_{V} } \mathord{\left/ {\vphantom {{\partial C_{V} } {\partial P}}} \right. \kern-0pt} {\partial P}}} \right)_{T} ,$ which is normally negative in the quasi-harmonic approximation, is unexpectedly positive. The thermodynamic Grüneisen parameter (γ), which has frequently been assumed to be a single-variable function of molar volume, shows not only volume dependence but also negative temperature dependence. To understand these features of C V and γ, we introduce a thermodynamic model including positive quartic anharmonicity. To make an anharmonic model advancing the ordinarily quasi-harmonic approximation model, we introduce two parameters: anharmonic characteristic temperature (θ a ) and its volume derivative. In the anharmonic model, the value of C V is calculated along an isochore using classical statistical mechanics and a harmonic quantum correction. At high temperatures, the decrease in C V from the Dulong-Petit limit is related to the value of T/θ a . For infinitely large θ a , the system is approximately quasi-harmonic. The temperature dependence of γ is related to C V by the thermodynamic identity $\left( {{{\partial C_{V} } \mathord{\left/ {\vphantom {{\partial C_{V} } {\partial \ln V}}} \right. \kern-0pt} {\partial \ln V}}} \right)_{T} = C_{V} \left( {{{\partial \gamma } \mathord{\left/ {\vphantom {{\partial \gamma } {\partial \ln T}}} \right. \kern-0pt} {\partial \ln T}}} \right)_{V} + \gamma \left( {{{\partial C_{V} } \mathord{\left/ {\vphantom {{\partial C_{V} } {\partial \ln T}}} \right. \kern-0pt} {\partial \ln T}}} \right)_{V}.$ Even though our modification of the quasi-harmonic approximation is simple, our anharmonic model succeeds in reproducing the experimental γ and C V simultaneously for the NaCl-B1 phase. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
