The Investigation of the Ferroelectric Phase Transition in Cluster Systems of Order–Disorder Type

The problem of the functional representation for systems containing groups of atoms with a non-compensated spin momentum (magnetic clusters) is discussed. For representation of the functional of partition function a version of the collective variables method with the "reference system" as a zero-order approximation is used. A set of all isolated clusters are choosen as a reference system. Intracluster interactions are described by exchange Heisenberg-type Hamiltonian, the form of intercluster interactions depend on the structure of the system investigated. Due to the use of the recently introduced generalized transition operators (like well-known HubbardStasyuk operators) an explicit form of the functional of partition function is found.

Section: Hamiltonian Reference Systemmentioning

confidence: 99%

Section: Thermodynamics Of the Reference Two-particle Systemmentioning

confidence: 99%

Section: Functional Of the Partition Functionmentioning

confidence: 99%

See 1 more Smart Citation

On the Functional Representation of Partition Function for Quantum Magnetic Cluster Systems

Korynevskii¹

2002

“…To put it in another way, the nonuniversal characteristics of the three-dimensional Ising model have been calculated in the critical region for the first time. This significant result stimulates investigations of phase transitions in different physical objects that can be described by the Ising-like models [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

On Collective Variables Method in the Microscopic Theory of Alloys

Gurskii¹

2000

Ab initio approach is developed for thermodynamical investigations of disordered binary alloys. It is based on utilizing the collective variables method. The explicit expression for the free energy and the equation determining the alloy components' chemical potentials are obtained within the rigid lattice approximation and for the case when atomic static displacements (ASD) are taken into consideration. An ASD drastic effect on the behaviour of the binary correlation function Fourier components in the first Brillouin zone is observed. The ASD is shown to favour the ordering tendency in alloys of Ca-Ba and K-Cs systems. An approach in which configurational and vibrational degrees of freedom are considered at the microscopic level in the grand partition sum calculation is advanced. The role of the atomic thermal vibrations in alloy forming is discussed. The condition when configurational and vibrational effects can be treated separately is formulated.

“…Taking the two-particle cluster approximation (see [11]) for short range interaction among particles and the self-consistent field approximation with the accuracy up to the second order of replica expansion for long range one we have for −βH the expression which contains the terms describing the correlation between ferroelectric and antiferroelectric subsystems…”

mentioning

confidence: 99%

Ferroelectric-antiferroelectric mixed systems. Equation of state, thermodynamic functions

Korynevskii¹,

Solovyan²

2006

The problem of equation of state for ferroelectric-antiferroelectric mixed systems in the whole region of a concentration change (0 n 1) is discussed. The main peculiarity of the presented model turns out to be the possibility for the site dipole momentum to be oriented ferroelectrically in z-direction and antiferroelectrically in x-direction. Such a situation takes place in mixed compounds of KDP type. The different phases (ferro-, antiferro-, paraelectric, dipole glass and some combinations of them) have been found and analyzed. : 75.10.Hk, 77.22.Ch, 77.84.F The present paper is a continuation of our recent investigations of ferroelectric-antiferroelectric mixed systems with hydrogen bonds [1][2][3]. There is an abundant experimental material concerning phase diagrams and the behaviour of thermodynamic functions for this mixed crystals [4][5][6][7][8]. The phase diagrams demonstrate the coexistence of pure and mixed ferro-, antiferro-, paraelectric, dipole glass phases in a wide region of temperatures and concentrations. A theoretical description of such systems is in its initial stage so far. The main approach is based on the statistic replica method for calculating the thermodynamic functions for a mixed system with non-equilibrium distribution of differently occupied sites, similar to the ones exploited in mixed ferromagnetic system investigations [9]. Key words: ferroelectrics and antiferroelectrics, mixed systems, equation of state PACSIt is well known that short range interparticle interactions play an important role in ferroelectrics (especially in hydrogen bonded ones). So, in order to adequately describe the ferroelectricantiferroelectric mixed systems we should take into account both the short and long range interactions. An effective method was proposed in [2], where the model Hamiltonian includes two subsystems of particles with dipole momenta perpendicular to each other, with short and long range interaction between them and which depend on the probability of occupying each lattice site. In the second order of replica expansion for −βH (β = (kT ) −1 , k is the Boltzmann constant and T is the absolute temperature) the free energy of the system investigated has been obtained. The equations for ferroelectric P = S z , antiferroelectric ξ = S x order parameters and dipole glass g z = S z mi S z m i , g x = S x mi S x m i parameters were found. Here · · · denotes thermal averaging for a given distribution of z-and x-oriented dipole momenta of particles whereas a bar denotes a stochastic averaging over different distributions; m, m denotes the nearest neighbours of particles in i-th size. The obtained phase diagram (the temperature of the corresponding order parameter appearing versus concentration) shows a possibility of different phases occurring: ferro-, antiferro-, paraelectric, dipole glass and some combinations of them.The purpose of the present paper is to perform a continual study of ferroelectric-antiferroelectric mixed system taking into account the interaction processes between both subsys...