Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited
Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited
复制标题
重新审视华莱士定理的量子热力学处理
DOI：
10.1007/s00269-005-0038-x
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发表时间：
2005
影响因子：
1.4
通讯作者：
B. Jong
中科院分区：
文献类型：
--
作者：
M. Jacobs;B. Jong
华莱士（在晶体热力学，1972年）发展了一个定理，植根于刚性晶格动力学，其中包括内在的非谐效应在固体。这一定理在矿物物理学中的实际应用涉及计算，这是该定理没有得到应有重视的主要原因。由于内禀非谐性是行星地幔中极端条件下的一个重要问题，我们导出了一种方法，消除了应用该定理的计算障碍。我们扩展的定理，将声子谱的细节和测试我们的算法对镁橄榄石（Mg 2SiO 4）。使用最小二乘反演技术适用于所有可用的实验数据，我们表明，它的结果在一个准确的表示Mg 2SiO 4在其完整的压力-温度稳定范围内的热力学性质和声波速度。我们还表明，我们的结果的准确性是不显着影响使用不同的状态方程。
Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg2SiO4). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg2SiO4 in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.