Theory of Anharmonic Crystals. III. Three‐Dimensional Lattice

Abstract

The properties of the f.c.c. lattice with central nearest neighbour interaction are investigated on the basis of the dynamical theory of the anharmonic crystal developed in [l]. It is shown that in the case of constant external pressure the lattice becomes unstable a t sufficiently high zero point energy or temperature. The behaviour of the physical quantities in the vicinity of the unstability point is investigated.Ha ocnoBe jmHaMmecKofi Teopm aHrapMoHHsecHofi pemeTm, p a 3 s~~o i i paHee [ 11, HCCJIeHymTCR CBOfiCTBa rpaHe~eHTpHpOBaHHOfi HYGHY~CKOZ~ PelueTKH C napHbIM 4eHTpanhHhIM B3aMMOAefiCTBHeM 6 n~x a i i m~x COCenefi. nOKa3aH0, YTO IIpH no-CTOHHHOM BHeUIHeM HaBJIeHMM PeIIIeTKa HeyCTOfiYHBa npH HOCTaTOYHO 60~1hmofi 3HeprllH HyJIeBbIX K0~1e6aHElfi MJIH J&OCTaTOYHO BbICOKOfi TeMnepaType. PaCCMO-TpeHO IlOBeHeHHe @H3HYeCKHX BeJIMYMH B~J I H~H OT T 0 9 K H HeYCTOfi YHBOCTM peIueTIEM.

Dynamic and thermodynamic properties of solid helium in the reduced all‐neighbours approximation of the self‐consistent phonon theory

“…In the reduced second-order SCPT the simplifying assumption is taken by Plakida, Siklós and Aksienov [12,34,35] that each atom interacts only with its NN. As mentioned in the introduction, we try here to reject this assumption incorporating further shells of neighbours in the SC equations.…”

“…(13) and (14)) and the anharmonic force constants f(T, p) and g(T, p) defined (Appendix B) respectively, as the second and third derivatives of the SC potential Φ (l). Then all the dynamic and thermodynamic properties of strongly anharmonic crystals may be expressed as functions of y, Φ (l), Φ ′′ (l) and Φ ′′′ (l) [34,35] but the respective equations must take into account the potential energy of crystals obtained in the higher approximation with respect to the number of acting neighbours [36].…”

Effect of Pressure on the Solitary Wave Propagation in One-Dimensional Lattice

“…Then, for the one-dimensional chain the effect of the external forces can be described by the external pressure Ρ which acts on the ends of the chain [4] We consider the potential energy of the crystal with anharmonicities of the third and fourth orders in the series expansion of the potential energy. Thus the expression Φ(Rn,n-1) is where Φ(α) is the depth of the potential, αn is the average distance between neighbouring atoms in the harmonic approximation at Ρ = 0 and α, β, γ are the coefficients defining the interaction of atoms.…”

An overview of the interatomic correlation moments and the mean square relative atomic displacements in anharmonic crystals

“…Since then, several other approaches have been developed to take into account the anharmonic effects, among which the most prominent is the self-consistent phonon theory [12][13][14][15][16][17][18][19][20][21]. In this theory, the harmonic force constants are averaged self-consistently over a trial set of harmonic oscillator functions.…”