Empirical equations of state (EoSs) are developed for solids, applicable over extended temperature and pressure ranges. The EoSs are modeled as multiply broken power laws, in closed form without the use of ascending series expansions; their general analytic structure is explained and specific examples are studied. The caloric EoS is put to test with two carbon allotropes, diamond and graphite, as well as vitreous silica. To this end, least-squares fits of broken power-law densities are performed to heat capacity data covering several logarithmic decades in temperature, the high- and low-temperature regimes and especially the intermediate temperature range where the Debye theory is of limited accuracy. The analytic fits of the heat capacities are then temperature integrated to obtain the entropy and caloric EoS, i.e. the internal energy. Multiply broken power laws are also employed to model the isothermal EoSs of metals (Al, Cu, Mo, Ta, Au, W, Pt) at ambient temperature, over a pressure range up to several hundred GPa. In the case of copper, the empirical pressure range is extended into the TPa interval with data points from DFT calculations. For each metal, the parameters defining the isothermal EoS (i.e. the density–pressure relation) are inferred by nonlinear regression. The analytic pressure dependence of the compression modulus of each metal is obtained as well, over the full data range.

中文翻译：

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固体状态的热量和等温方程：具有多重破坏幂律密度的经验建模

经验状态方程 (EoS) 是为固体开发的，适用于扩展的温度和压力范围。EoS 被建模为多重破坏幂律，采用封闭形式，不使用升序展开；解释了它们的一般分析结构并研究了具体的例子。热量 EoS 用两种碳同素异形体、金刚石和石墨以及玻璃质二氧化硅进行测试。为此，对涵盖温度、高温和低温状态、尤其是德拜理论精度有限的中间温度范围的几个对数数十年的热容数据进行了破坏幂律密度的最小二乘拟合。然后对热容的解析拟合进行温度积分以获得熵和热量 EoS，即内能。还采用乘法破碎幂定律来模拟环境温度下金属（Al、Cu、Mo、Ta、Au、W、Pt）的等温 EoSs，压力范围高达数百 GPa。在铜的情况下，经验压力范围扩展到 TPa 区间，数据点来自 DFT 计算。对于每种金属，定义等温 EoS 的参数（即密度-压力关系）是通过非线性回归推断出来的。在整个数据范围内，还获得了每种金属的压缩模量的分析压力依赖性。经验压力范围扩展到 TPa 区间，数据点来自 DFT 计算。对于每种金属，定义等温 EoS 的参数（即密度-压力关系）是通过非线性回归推断出来的。在整个数据范围内，还获得了每种金属的压缩模量的分析压力依赖性。经验压力范围扩展到 TPa 区间，数据点来自 DFT 计算。对于每种金属，定义等温 EoS 的参数（即密度-压力关系）是通过非线性回归推断出来的。在整个数据范围内，还获得了每种金属的压缩模量的分析压力依赖性。