Universal Method for Approximating the Standard Thermodynamic Functions of Solids

Abstract

The aim of this work is to offer an universal analytical description of the standard thermodynamic functions (primarily, C P °(T), S°( T ), H°(T) – H°(T r)), of solids with accuracy corresponding to experimental measurements. The main advantage of a semiempirical method of approximation under consideration consists in nonstandard usage of a linear combination of well-known thermodynamic functions of the harmonic oscillator (Planck–Einstein functions) unadjusted to the difference between isobaric and isochoric values. The article provides a description of the method, a brief theoretical analysis relating to its justification and opportunities, and examples of specific applications. The article focuses on the problem related to the practical application of thermodynamic data, the problem of standard representation of standard thermodynamic functions themselves. If the substance under investigations does not undergo phase transformations within the temperature interval (0 to T) K and the reference temperature T r ≤ T then the S°(T) and H°(T)–H°(T r) functions are easy to calculate on the basis of the values of C P °(T) and “frozen” configuration contributions to entropy if they exist. For this reason, much attention is paid to the dependence of the heat capacity of solids on the temperature.

Method for the Estimation of Standard Entropy of Crystal Phases at 298.15 K on the Limited Temperature Range of Heat Capacity Measurements

“…Moreover, the sum of α i are close to the sum of stoichiometric indexes in the formula of compounds, which was specially emphasized by Voronin and Kutsenok. 8 The entropy calculated on "nitrogen" area of measurements (S o II ) (i.e., higher 77 K) is less for all studied substances because of the impossibility of correct estimation of the low-temperature acoustic part of a vibrational spectrum by estimation of C p (T) data higher than nitrogen boiling point. The relative inaccuracies, on the average, for uranates are equal to 4.6%, for chalcogenides −2.3%.…”

A New Description of Pure C in Developing the Third Generation of Calphad Databases

“…It should be mentioned that using multiple Einstein temperatures to fit the heat capacity data was shown by Jacobs et al [69] for different elements and compounds. Arbitrarily weighted multiple Einstein functions have also been used as a mathematical mean by Voronin and Kutsenok [70] to fit the heat capacity data at both low and high temperatures, and in their approach, the ''Einstein'' frequencies are fitting mathematic quantities that have no phyiscal meanings.…”

Calculating the effect of vacancies on the thermodynamic functions and frequencies of normal vibrations of a Lennard-Jones monoatomic crystal

“…Such proposals also continue to be made today. The authors of [18] proposed using only the sum of the Einstein contributions, the number, magnitude, and frequencies of which are empirical parameters. Such constructions can of course ensure the required accuracy of coincidence between experi mental and computed curves for any thermodynamic characteristics (particularly heat capacity), but the parameters of such constructions can differ strongly from the actual vibrational spectra.…”