Theory of Anharmonic Crystals. II. Linear Chain

Abstract

The properties of the monatomic linear chain with nearest neighbour interaction are considered a t fixed length and a t constant external tension applying the dynamical theory of the anharmonic lattice developed in our previous work. The vibrational frequency, the damping, the internal energy, the specific heat, the average length and tension are calculated. It is shown that in the case of constant external tension the chain becomes unstable a t sufficiently high temperature or a t sufficiently high aero-point energy. The critical parameters are obtained and the behaviour of the thermodynamical quantities in the vicinity of the critical point are investigated. Ha OcHoBe HnHaMmecHoCi Teopnn aHrapMoHmecKofi peluewn, p a 3~~~o f i B npe-~bI~yIUefi pa6o~e, IICCJIeJQIOTCfI CBOfiCTBa JIIIH&HOfi OHHOaTOMHOfi JJeIlO'IKII C B3aII-MOjJefiCTBIIeM MeWny B n~~r n a t h~~i~m COCenfXMII npIl @IIKCHpOBaHHOfi nJIHHe II (PIIK-CIIpOBaHHOM BHeLUHeM HaTHlfEeHIIII. OIIpeAeJIeHbI 9aCTOTa KO~Ie6aHLlfi JJeIIO9KII, IIX 3aTyXaHIIe, BHYTpeHRFi 3HeprIIFi, TeIlJlOeMKOCTb, CpeHHJWI AJIHHa HJIM HaTfIWe-HEl e JIMHefiHOfi qeIIO9KII. HOHa3aH0, 9 T O npll @IIKCHPOBaHHOM HaTHlfFeHIIH Qe-n09Ka HeyCTOfiqIIBa npll HOCTaT04HO BblCOHOfi TeMnepaType IIJIII AOCTaTO9HO 60nb-IlOBeZeHIIe TepMOAIIHaMH9eCKIIX BeJIIIYIIH B6JIII3&3 KpIITH9eCKOfi TO9KII . mofi a~e p r m HynesbIx KOJIe6aHIIfi. Onpenenem1 KpHTnsecme napaiveqm H

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

“…Each vertex corresponds to an atom in a lattice point and represents the momenta of a one-particle function such as Eqs. (16) and (17). The order of a moment is equal to the number of bars near the vertex.…”

“…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.…”

Intermolecular forces and equation of state for solid molecular in pseudoharmonic approximation

“…The coefficient of the Linear thermal expansion and the specific heat at constant pressure are given by the foHowing formulas [63,65]: …”

“…properties of the anharmonie linear ehain in the pseudoharmonie approximation and in the dynamie theory of the anharmonic lattiee [63,67]. Applying the expansion of Eq.…”

Pressure Influence on the Curie Temperature

“…The present paper deals with the pressure influence on the Curie temperature in ferromagnets whose effective potential of the lattice is described by the modified Morse potential U (R r − R r ) given in terms of pseudoharmonic approximations [1]. The pressure p is applied in the form of isotropic (hydrostatic) external force to the whole sample and scaled with respect to the normal (atmospheric) pressure p 0 (p 0 = 1.0135 × 10 −4 GPa).…”