Investigation of the Thermodynamic Properties of Anharmonic Crystals by the Momentum Method. III. Thermodynamic Properties of the Crystals at Various Pressures

Abstract

By the momentum method established in the preceding papers the thermodynamic properties of strongly anharmonic crystals are considered with face-centred cubic structure being under action of pressure. In the application properties as the thermal expansion coefficient, the specific heats c, and cp etc. at various pressures are calculated numerically for the inert gas solids and compared with experimental data.Mit der in friiheren Arbeiten angegebenen Momentenmethode werden die thermodynamischen Eigenschaften von stark anharmonischen Kristallen mit kubischflachenzentrierter Struktur unter Druckeinwirkung untersucht. In Anwendung werden Eigenschaften, wie thermischer Ausdehnungskoeffizient, spezifische Warmen c, und cp usw., bei verschiedenen Driicken fur Inertgasfestkorper numerisch berechnet und mit experimentellen Werten verglichen.

Systematic prediction of high-pressure melting curves of transition metals

“…In previous study of SMM theory, 15 the authors derived EOS, which describes the pressure versus volume relation of crystal lattice as…”

“…First, we applied the statistical moment method (SMM) in quantum statistical mechanics 14,15 to evaluate mean-square displacement (MSD) hu 2 i and NND r at widely used experimental melting temperature and zero pressure. Subsequently, high-pressure melting temperature of solid was determined based on this evaluated constant ratio and functions of MSD hu 2 i and NND r in SMM model.…”

Melting temperature of iron at high pressure: statistical moment method approach

“…From the SMM formalism, the authors have derived the equation of state (EOS) describing the pressure versus volume relation of crystal lattice in the form as [12] By solving this EOS we can obtain the NND , a P T at pressure P and temperature T . For numerical calculations, it is convenient to determine firstly the value of NND at zero temperature.…”

“…where 0 , y P T is the thermally induced lattice expansion which has the form as [12] 2 0 3 2γθ 3 Using the expression of the second order moment in SMM formalism we obtain the mean-square displacement (MSD) expression as [13] …”

Investigation of the Thermodynamic Properties of Anharmonic Crystals by Momentum Method. IV. The Limiting of Absolute Stability and the Melting Temperature of Crystals

“…In the case of pressure P + 0, first of all, we must determine the nearest neighbour distance at this pressure and at temperature 0 K. It can be found from (111, 1) [3] Pa3 Pa3…”