Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845, Australia.
Inorg Chem. 2013 Jun 3;52(11):6590-4. doi: 10.1021/ic400617u. Epub 2013 May 20.
Entropies of solids are obtained experimentally as integrals of measured heat capacities over the temperature range from zero to ambient. Correspondingly, the Debye phonon distribution equation for solids provides a theoretical connection between these two chemical thermodynamic measures. We examine how the widely applicable Debye equation illuminates the relation between the corresponding experimental measures using more than 250 ionic solids. Estimation of heat capacities for simple ionic solids by the Dulong-Petit heat capacity limit, by the Neumann-Kopp elemental sum, and by the ion sum method is examined in relation to the Debye equation. We note that, and explain why, the ambient temperature heat capacities and entropies of ionic solids are found to be approximately equal, and how deviations from equality may be related to the Debye temperature, ΘD, which characterizes the Debye equation. It is also demonstrated that Debye temperatures may be readily estimated from the experimental ratio of ambient heat capacity to entropy, C(p)/S(p), rather than requiring resort to elaborate theoretical or experimental procedures for their determination. Correspondingly, ambient mineral entropies and heat capacities are linearly correlated and may thus be readily estimated from one another.
固体的熵可以通过实验获得，方法是将测量得到的热容积分在从 0 到环境温度的范围内。相应地，固体的德拜声子分布方程为这两个化学热力学量之间提供了理论联系。我们使用超过 250 种离子固体来研究广泛适用的德拜方程如何阐明这两个对应实验量之间的关系。我们考察了通过杜隆-珀替热容量极限、纽曼-科朴元素总和以及离子总和方法对简单离子固体的热容进行估计与德拜方程的关系。我们注意到，并且解释了为什么离子固体的环境温度热容和熵大致相等，以及偏离这种相等性的原因可能与德拜温度有关，ΘD 是德拜方程的特征参数。还证明了可以通过实验测定的环境热容与熵之比 C(p)/S(p) 来方便地估计德拜温度，而无需采用繁琐的理论或实验程序来确定德拜温度。相应地，环境矿物的熵和热容呈线性相关，因此可以方便地相互估计。
