Dynamics and Thermodynamics of Quantum Crystals Near the Instability Point in the Self-Consistent Phonon Theory
Abstract
Formally one can distinguish between the thermodynamic stability conditions (the free energy of the lattice should have a minimum with respect to small variations mechanical or otherwise) and the dynamical ones (the phonon spectrum of the lattice should be positively defined). These last conditions are easily formulated in the self-consistent phonon theory (SCPT) based on the thermodynamic double-time Green's function method. According to it the dynamic instability temperature T(sub s) for a simple Bravais lattice defines the temperature at which the bound crystalline state of atoms vanishes that really means that the phonon frequencies become complex at sufficiently high temperatures T<-T(sub s). Using the reduced second order approximation of the SCPT the dynamics of crystal lattice and the thermodynamical properties of the quantum crystals in the vicinity of the instability point are investigated. The results of calculations of the pressure dependence of the instability temperature, melting criterion, internal and free energy, free Gibbs energy as well as selected dynamic properties obtained with the help of the generalized form of the Buckingham, the Lennard-Jones and the Morse self-consistent potentials are given and compared with experimental data of solid h.c.p. He-4 and f.c.c. Ne-20. Comparison of the theoretical and experimental results allows us to state that the limiting temperatures of the dynamical stability obtained for the above-mentioned models pair potentials always appear to be the upper estimations of the real melting temperature.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2001
- Accession Number
- ADP011891
Entities
People
- Cecylia Malinowska-adamska
- Janusz Tomaszewski
- Piotr Sloma