Nonequivalent Sublattices Research Articles

Phase transitions in two sublattice Ising systems

A two sublattice spin- 1 2 Ising systemis ionvestigated by the mean field (MF) and the renormalization group (RG) methods. The properties of the phases and the phase transitions are considered in details for the general case of nonequivalent sublattices. The MF analysis is performed by an expansion in powers of a suitable small parameter. The RG is used to establish the possibility for a fluctuation change of the order of the phase transitions to ferro- and antiferromagnetic states in systems with equivalent sublattices. It is shown that such systems exhibit fluctuation-induced weakly-first-order phase transitions. The RG investigation of systems with nonequivalent sublattices is also presented.

Succession of the low temperature phase transitions in TlInS 2 crystals

Two additional incommensurate phase transitions (PT's) at T i = 206 K and T tr = 79 K were observed in TlInS 2 crystals. Peculiarities of the temperature behaviour of the dielectric susceptibility and the dielectric loops allowed to consider the PT's at T c1 = 204 K and T c2 = 201 K as incomplete lock-in transitions and the PT at T≈195 K as a temperature range of the final lock-in transition. The PT at T tr = 79 K was considered as an isomorphous transition. The experimental results of the second harmonic generation signal at low temperature are also in favour of such a conclusion. Peculiarities of the temperature behaviour of the dielectric properties at low temperature are qualitatively explained by means of the theory of two non-equivalent sublattices.

Phase transitions in the three-state antiferromagnetic Potts model.

The three-state antiferromagnetic Potts model on the simple cubic lattice is studied by the Monte Carlo method using a new order parameter and employing the histogram technique. It is shown that apart from the low-temperature broken-sublattice-symmetry phase with nonequivalent sublattices, another type of ordering with equivalent sublattices does exist in the model between the broken-sublattice-symmetry and disordered phases. The temperature of the transition between the ordered phases is estimated from the histogram of the order parameter. The value obtained is in good agreement with that obtained from cluster variation circulations.

Domain wall dynamics in ferrites in an external oscillating magnetic field

Domain-wall drift motion in ferrimagnets with two non-equivalent sublattices induced by an external oscillating magnetic field has been studied. The dependences of the drift velocity on the amplitude, frequency and polarization of the field have been obtained. The possibility of the drift of a stripe domain structure is considered.

Ferrielectric behaviors in Li2Ge7O15crystals

Abstract Temperature dependence of spontaneous polarization P5 (T) in ferroelectric Li2Ge7O15 crystals has been measured in a wide range of temperature from 300 K to 15 K by a pyroelectric charge method. Temperature dependence of dielectric constant e (T) has precisely been measured in the paraelectric phase. It is shown that the experimental results can be explained by a ferrielectric model, in which two kinds of nonequivalent antiparallel sublattice polarizations are induced by a soft phonon mode having negligibly small oscillator strength.

Local electronic density of states in two-component penrose lattices

The electronic structure of two-component Penrose models of quasicrystals is studied by using a tight-binding model. The Penrose lattice is subdivided in non-equivalent sublattices and the local density of states are calculated at a site surrounded by clusters of distinct sizes. The strong dependence of the density of states on the cluster size and the local neighborhood is evidenced. In particular, the electronic structure of a decoration proposed to model the T-phase of AlFe, is calculated. An asymmetric density of states with no self-similar behaviour is obtained.

Landau theory of the ferrielectric phase transition with two order parameters

In order to explain ferrielectric behaviour, a phenomenological model given in terms of the polarisations of two non-equivalent sublattices is proposed. The free energy for a second-order phase transition is G=1/2f1P12+1/2f2P22+gP1P2+1/ 4h(P14+P24) (G>0, h>0), where f1-(T-T1)/C1 and f2=(T-T2)/C2; this is the same form as that for the antiferroelectrics given by Kittel (1951) other than for the temperature dependences of f1 and f2. The dielectric susceptibility shows a crossover from that of an antiferroelectric at high temperatures to that of a ferroelectric with decreasing temperature down to Tc. The calculated results for the small spontaneous polarisation, the reduction of the Curie-Weiss constant and the unusual E-P curves are discussed in connection with experimental data on ammonium sulphate.

Structural Vacancies in Nonstoichiometric Compounds at High Pressure. Thermodynamic Model

A thermodynamic model is proposed which describes the effect of high pressure on the equilibrium structural vacancy concentration of nonstoichiometric compounds possessing wide regions of homogeneity. The implicit pressure and temperature dependence of the equilibrium structural vacancy concentration is found in general form for any nonequivalent crystal sublattice of a compound. [Russian Text Ignored].

Solitons in a ferrimagnet

Exact N-soliton solutions of nonlinear Landau-Lifschitz equations are obtained by means of the modified form of the inverse scattering method (“dressing method”) for the case of an isotropic ferrimagnet with two non-equivalent sublattices.

Ferrielectric dielectric behaviour and the nature of phase transition of ammonium sulphate

Phenomenological treatments of ferrielectrics are made in terms of two non-equivalent sublattice polarizations in the paraelectric phase. Unlike the Curie-Weiss behaviour of usual proper ferro- and antiferro-electrics, the dielectric susceptibility does not depend linearly on temperature. Particularly in the case of a first order phase transition, the Curie-Weiss constant seems to be unusually small. As an example, the dielectric properties of (NH4)2SO4, which was known to be a peculiar ferroelectric, is discussed from the ferrielectric point of view. The true Curie-Weiss constant is of a comparable order of magnitude to that of the order-disorder ferroelectric.

A monte carlo study of sodium diffusion in β-alumina

Abstract The calculation by SaAo and Kikuchi (1971) of the sodium tracer diffusion coefficient in β-alumina using the path probability method is assessed using a Monte Carlo method. Two interpenetrating non-equivalent triangular sub-lattices make up the honeycomb lattice on which sodium ions are distributed subject to nearest neighbour repulsion. The Monte Carlo results for the vacancy availability factor and the effective jump frequency factor are in excellent agreement with the calculations of Sato and Kikuchi (1971). Results for the tracer correlation factor differ significantly because of the limitations of the pair-approximation to the path probability method.

Two-Sublattice Model of Ferroelectric Phase Transitions

Dielectric properties of two nonequivalent sublattice polarizations are studied. Assuming a strong coupling favoring an antiparallel alignment of polarizations, the model reveals some new features of a ferroelectric transition with no multiple change of the unit cell volume. The Curie-Weiss constant is unusually small and this fact directly accounts for a possible sign change of the spontaneous polarization by only a slight variation of model parameters with temperature. The model also can describe a para-ferroelectric phase transition followed by an isomorphous phase transition between two ferroelectric phase with no change of symmetry. Temperature dependence of susceptibility is derived with the emphasis on the critical region in which the applied pressure or electric field smears out the difference between two isomorphous phases. The model can explain some properties of ammonium sulfate, dicalcium strontium and lead propionate.

Magnetic interactions in pseudobinary rare earth-3d intermetallics

Magnetic measurements on pseudobinary intermetallic compounds of the series R(Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> ) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (R = Y, Gd, Er) R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</inf> (Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> ) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">23</inf> (R = Y, Gd, Tb, Dy, Ho, Er, Tm) R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Co <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> ) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</inf> (R = Y, Gd, Dy) R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ni <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> ) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</inf> (R = Y, Gd) are reported. Magnetization and susceptibility measurements have been performed at temperatures from 4 K to 1500 K. The magnetic interactions between Mn and Fe are discussed in terms of a localized-moment model. In the case of the R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> ) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</inf> (M = Co, Ni) compounds, a band model seems to be more appropriate. Mössbauer Fe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">57</sup> spectra obtained on the R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (Fe,Co) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</inf> series can be explained by a superposition of four different six-line patterns corresponding to the four crystallographically nonequivalent 3d sublattices.

Cation Diffusion and Conductivity in Solid Electrolytes. I

The characteristics of cation diffusion and ionic conductivity in solid electrolytes are discussed using β- and β″-alumina as examples. The problem is characterized by a cation migration by the vacancy mechanism in a “cation-disordered phase,” a system in which the number of available vacant sites is of the same order of magnitude as the number of diffusing cations. The path probability method is used to derive both the tracer diffusion and the ionic conductivity; this method avoids the difficulties connected with the application of the ordinary random walk approach to such systems. β″-Alumina is regarded as an example of the “cation-disordered phases” in which all available cation sites are equivalent, while β-alumina represents those in which available cation sites are divided into several nonequivalent sublattice sites. When the derived diffusion coefficient is interpreted using the language of the conventional random walk approach, the jump frequency of cations is found to include two factors, the vacancy availability factor V and the effective jump frequency factor W, both of which take into account the effect of surroundings of the migrating ion and characterize the cooperative mode of the cation motion. Both of these factors, as well as the correlation factor f, depend strongly on composition of cations and on temperature. The Nernst–Einstein relation which relates the tracer diffusion and the charge diffusion is found to include characteristic correlation factors. Even in ionic conductivity, a correlation factor fI is found to appear in the β-alumina-type electrolytes. Although both f and fI vary drastically depending on the cation concentration, the ratio of the two remains within limits determined by the geometry of the crystal lattice. The value of the ratio indicates the predominant mechanism of diffusion.

Mössbauer Study of Some 2–17 Lanthanide-Iron Compounds

We have studied the iron-rich, rare-earth-iron intermetallic compounds R2Fe17 (R = Pr, Gd, Tm, Lu), using the Mössbauer effect in 57Fe. The measured average hyperfine field H(T/Tc) acting on the 57Fe nuclei is a unique, monotonically decreasing function of T/Tc, with no observed irregularity at temperatures corresponding to a suspected ferromagnetic-antiferromagnetic phase transition in these compounds. The onset of paramagnetism occurs at temperatures close to the upper transition points measured by Strnat et al., namely at Tc = 282°, 472°, 271°, and 263°K for Pr2Fe17, Gd2Fe17, Tm2Fe17, and Lu2Fe17, respectively. Low-temperature (≃90°K) spectra indicate the presence of at least four magnetically nonequivalent Fe sublattices, while for T&amp;gt;Tc broadened 2-line absorption spectra typical of 57Fe at noncubic sites in paramagnetic material are observed.

Unit cell dimensions of some synthetic orthopyroxene group solid solutions

Three series of solid solutions of orthopyroxene structure, (Fe, Mg )SiO3, (Co, Mg)SiO3 and (Ni, Mg)SiO3, were synthesized, using high pressure sintering technique. Unit cell parameters of the synthesized pyroxenes were determined at room temperature. The deviation from Vegard's law is remarkable for both iron and nickel pyroxene series, whereas almost absent for cobalt one. It is suggested that the dominant factors which determine the distribution of ions among nonequivalent sublattice sites are 1) the difference in effective sizes of both ions (for the case of (Fe, Mg )SiO3) and 2) the crystal field stabilization energy (for the case of (Ni, Mg )SiO3). The nearly ideal behavior of (Co, Mg )SiO3 is a result of the compensation between these two competing factors.

Temperature dependence of the sublattice magnetization in the stable magnetic phase and the one-third-power law

It is shown that the temperature dependence of sublattice magnetizations in various ferro-, antiferro- and ferrimagnets fits a simple power law (1− T T c ) β in a range of about 0.5 T c < T < 0.99T c. Though the temperature exponent in general deviates slightly from one-third, in ferrimagnets different values are obtained for the two non-equivalent iron sublattices.

Intrasublattice antiferromagnetism in Ca 2[Fe](Fe)O 5

Ca 2[Fe](Fe)O 5 remains antiferromagnetic even upon preferential substitution of diamagnetic (Sc 3+ or Ga 3+) for Fe 3+ ions implying that the two crystallographically nonequivalent sublattices (octahedral and tetrahedral coordination) must each be antiferromagnetic. It is speculated that the intersublattice interactions are also antiferromagnetic.

Fluctuations d'aimantation et opalescence critique

This paper deals with fluctuations in magnetization in substances in which several types of magnetic ions are present simultaneously. First, by means of a localized form of the molecular field approximation, the intensity of fluctuations corresponding to each wave vector is studied. It is shown, in particular, that the results obtained below the transition temperature agree exactly at low temperatures with the rigorous formulae deduced from the theory of spin waves. Next, the relaxation of fluctuations in the paramagnetic range is considered, particularly the phenomena of “slow relaxation”. Critical opalescence phenomena are found, but they show important differences in behavior from what is known from the simple situations considered up to now. Some of these anomalies may be observed in neutron-scattering experiments. These effects are worked out numerically for magnetite, where six non-equivalent sublattices have to be considered. It is also shown that for antiferromagnets the relaxation of the critical fluctuations is slow, and, that their frequency spectrum is of the Lorentz type. This is a thermodynamic effect and is distinct from the spin diffusion effect familiar in ferromagnets.