Scaling Behavior between Heat Capacity and Thermal Expansion in Solids

Abstract

We experimentally analyze the heat capacity and thermal expansion of reference solids in a wide temperature range from several Kelvin to melting temperature, and establish a universal double-linear relation between the experimental heat capacity C p and thermal expansion β, which is different from the previous models. The universal behavior between heat capacity and thermal expansion is important to predict the thermodynamic parameters at constant pressure, and is helpful for understanding the nature of thermal properties in solids.

Model of Heat Capacity in Volume Dimension

“…The parameters of K, V, and γ for Cu at room temperature are 140 GPa, 7.11 g/cm 3 , and 1.96, respectively. 18,28 The calculated value of [C 0 KV/(3γR) + E] for Cu is 499.6 kJ/mol, which is close to the fitted value 499.7 kJ/ mol reported in reference 18. Therefore, eq 4 is a universal equation to describe the experimental heat capacity C p of solids below melting temperature.…”

“…18 The experimental heat capacity C p approximately shows different linear dependencies on the β above or below 3R in the reference solid materials (as seen in Figure 2), which can be seen in the previous study. 18 The non-volume-dependent heat capacity C T below T m is calculated by the Debye model (C 0 f D, green lines shown in Figure 4). The maximum of C T is the fitting parameter C 0 in eq 2, and the Debye temperature θ is determined at half of the parameter C 0 : f D (θ/T = 4.02) = 0.5.…”

“…Above the Dulong-Petit’s value 3 R (or at high temperatures), the experimental heat capacity C p is approximately linearly dependent on the β: where C 0 and E are constants. The linear behavior is a universal thermodynamic property in a series of solid materials …”

“…At high temperature, both the temperature T and thermal expansion β are large, and the thermal expansion β can obviously affect the experimental heat capacity C p at high temperatures. The β-dependent excess (or anharmonic) heat capacity increases with increasing temperature (or volume) at constant pressure and is even up to 3 R at high temperature in solid materials. − At present, all studies about the thermal expansion effect on experimental heat capacity are based on the correlation or the calculation of models. − …”

“…In the present work, we analyzed the experimental heat capacity C p of the reference solids (Al 2 O 3 and Cu) below melting temperatures in the volume dimension. The volume-dependent heat capacity C TE and non-volume-dependent heat capacity C T is quantitatively determined by the universal correlation between the experimental heat capacity and thermal expansion . The experimental heat capacity C p of solids below melting temperature can be successfully explained by a new model: C p = C T + C TE .…”