On the Relationship Between Physical Properties of Elementary Substances and Their Characteristic Temperature

Abstract

For a condensed state of a substance, the characteristic Debye temperature is an important notion, and this temperature may be considered as the effective parameter of a solid body [1]. It is of interest to establish a relation between the physical parameters of the solid body and its characteristic Debye temperature. In the present work, this relation has been determined with a correlation analysis and a linear regression. All the calculations were based on the Statistica.8.0 software package. The initial data for standard conditions were taken from [2]. It has been shown earlier that the critical superconductivity temperature of a body is directly proportional to its Debye temperature [3]. Also, it is well known that the Debye temperature is a function of the density of a solid body [4]. This relation can be described by a fi rst-degree polynomial. However, it is only tracked with a high correlation coeffi cient for elements of the same kind, e.g., s elements of groups I and II of the Mendeleev periodic table [5]. For the s elements of group I, Fig. 1 gives the dependence of the melting temperature on the characteristic Debye temperature, which is described well by a fi rst-degree polynomial. Table 1 gives the correlation dependences of a number of physical properties of the s elements of group I (Li, Na, K, Pb, and Cs) on the Debye temperature. The functional dependences are represented by fi rst-degree polynomial. Subdivision of the s and p elements of the groups of the Mendeleev Periodic Table into typical elements and subgroups, as far as certain physical parameters are concerned, in particular, with account taken of the special properties of their electronic structure, has an effect on the representation of correlation dependences of these elements. We give as an example the dependence of the melting heat of the s elements of group I (Fig. 2) and of the surface tension of the melt of the s elements of group II on the Debye temperature (Fig. 3). Also, it should be noted that all the s elements of group I (Li, Na, K, Pb, and Cs) and certain s elements of group II (Ca, Sr, and Ba) are characterized by a cubic crystalline structure, whereas the elements Be and Mg have a hexagonal structure. The dependence of the melting heat of the elements that are between the elements Na and Cs in Mendeleev′s table on the Debye temperature is described by the linear function with a correlation coeffi cient of 0.999. Although the fi rst-degree polynomial ensures a reliable relationship between the surface tension of the body and its Debye temperature with a correlation coeffi cient of 0.98, this relationship is better described by a second-degree polynomial. It should be noted that a number of dependences in Table 1 have been derived from the physical models of the behavior of atoms in solid bodies. For example, within the framework of the Debye model, there was derived the following relation for the specifi c heat of the elements in question at constant volume [6]: