Quantum effects on phase transitions in high-pressure ice

The H₂O ice phases VIII, VII, and X as well as their phase transformations are studied theoretically at 100 K as a function of pressure up to about 100 GPa. A combination of ab initio electronic structure calculations within the framework of density functional theory and the path integral representation of the nuclei is used. This allows the effects of thermal and quantum mechanical fluctuations on the properties of ice at high compression to be assessed separately and also in conjunction. Pronounced quantum effects are uncovered and different mechanisms are found to be at work at the antiferroelectric to paraelectric transition and the symmetrization transition.     

Quantum oscillations and reversible and irreversible superconducting phase transitions in indium microcylinders

Using a sensitive mutual inductance method, measurements of first- and second-order phase transitions in indium microcylinders (2.8–7.6 µm in diameter) have been made. Quantum oscillations in the supercooling field have been observed. The values of _SC (T/T _c )=₁(T/T _c ) derived fromH _SC =H _C3 have been corrected for both the temperature and the size dependence in the relationship betweenH _c2 andH _c3 . The results for ₁(T/T _c ) from the 7.6-µm sample then agree reasonably well with the temperature dependence of ₁ observed for niobium. However, for the smallest cylinders anomalously low values of _SC (T/T _c ) were obtained nearT _c . Very close to the transition temperature second-order (nonhysteretic) phase transitions have been observed and are interpreted in terms of the Ginzburg-Landau theory.     

Quantum theory of easy plane antiferromagnets in a magnetic field

The spin excitations of easy plane antiferromagnets with Dzyaloshinskii interactions in an external magnetic field of arbitrary direction are considered using the solution of the self-consistent quantum problem. The one-ion magnetization in the magnetic field is shown to be independent of the field only when S = 1/2; but when S = 1 the quantum equation for the spin configurations differs from the quasiclassical one. A theory of the interaction of different spin excitation branches is given without limitations on the parameters involved in the problem.     

Quantum coherence and phase transitions in granular superconductors with dissipation. I. Ordered arrays

We investigate the effect of dissipative currents on a superconducting phase transition in two- and three-dimensional granular arrays. We find the corresponding phase diagrams and show that, depending on dissipation, both long-range and local quantum fluctuations may be effective in destroying the global phase coherence. For large values of charging-to-Josephson coupling energy ratio and atT=0, we find the universal critical resistanceR _c only for three dimensional arrays while for two dimensional onesR _c ^–1 diverges logarithmically with increasing of the grain charging energy. For large values of a Josephson coupling energy, quantum phase slip effects play the main role and lead to the universal critical resistance in both cases. We also investigate the effect of dissipation on the critical temperature of theXY model phase transition and show that strong dissipation is extremely effective in suppressing quantum effects.     

Nonequilibrium phase transitions

A brief review is provided of the subject of nonequilibrium phase transitions occurring in various systems in different disciplines. All these systems exhibit a similar kind of ordering phenomena at a macroscopic level and can therefore be classified in terms of appropriate order parameters. Typical order parameter equations are discussed in the light of Landau’s phenomenological theory of phase transitions. The instabilities occurring in a few chemical reactions are discussed in some detail and the role of fluctuations pointed out. Mention is also made of the possibility of viewing some metallurgical phenomena as examples of nonequilibrium phase transitions.     

Quantum coherence and phase transitions in granular superconductors with dissipation. II. Effect of disorder

We study the effect of disorder on a superconducting phase transition in granular arrays with dissipation. It is shown that, for a quite weak Gaussian disorder, this effect does not lead to a qualitative change of the phase diagram. Local quantum fluctuations suppress Cooper pair tunneling for a part of Josephson junctions and thus effectively increase disorder. For strongly disordered systems, the critical resistance which corresponds to a dissipative phase transition is found to be universal for a wide range of parameters.     

Conductivity in allotropic phase transitions

A method is given for calculating the resistivity as a function of temperature in the presence of structural phase transitions in solids.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 2, pp. 329–335, August, 1979.     

Phase interface perturbations in phase transitions

The linear problem of viscous phase interface perturbations in intensive condensation/evaporation processes (at great transversal mass fluxes) is numerically solved. In limit cases, transition to the classic Helmholtz and Landau instability problems is ensured. The effects of viscosity, thermal conductivity, and surface tension are taken into account. The limit case of long-wavelength perturbations is considered using the method of matched asymptotic expansions.     

Instabilities in first order phase transitions

Majority of the metallurgical phase transformations are first-order transitions which occur by the nucleation and growth process near equilibrium conditions. In recent years, homogeneous transformation has been reported in some of these cases at conditions significantly away from those of equilibrium. In this paper some of these transformations will be discussed. In the first part of the presentation the thermodynamic and the mechanistic distinctions between first and higher order phase transformations will be discussed and a comparison made between homogeneous and heterogeneous modes of phase transformations and those of deformation. Based on Landau’s free energyvs generalised order parameter plots, an instability temperature is defined for first order phase transformations below which the transformation can occur by a continuous amplification of a concentration or a strain fluctuation. In the second part experimental evidence in support of the continuous mode of transformations in two ordering reactions are presented. These are: (i) a transition from the short range to the long range chemical order in Ni₄Mo (D1a structure) and (ii) a hybrid displacive-replacive ordering in Zr₂Al (B8₂ structure). In order to make the continuous mode operative in these first order transformations (which is possible at a high “supercooling”), radiation in the former and rapid quenching in the latter were employed. In the last part, the martensitic transformation and the shape memory effect is described in terms of Landau’s plots and the mechanical and thermodynamical consequences of the model are discussed. Only a summary is presented.     

Stress-induced phase transitions in elastic solids

This paper describes a continuum model, developed recently by R. Abeyaratne and the author, for the response of elastic solids capable of undergoing stress-induced phase transitions. Models of the kind sketched here and their generalizations are intended to apply to both quasi-static and dynamic experiments for shape memory alloys and to impact-induced phase changes in ceramics. The present discussion is confined to a purely mechanical theory, omitting thermal effects, so that the natural setting is the nonlinear theory of elasticity. The presentation below is limited to one space dimension.     

Some interesting phase transitions in solids

A few types of phase transitions in solids of interest to the author are discussed after a brief presentation of the general features of phase transitions. The different systems discussed include low-dimensional solids, polytypes, organic solids, plastic crystals, glasses and silver selenide. Spin-state transitions and dipole glasses are also briefly examined.     

Ground-state phase relationships and level ordering for frustrated quantum antiferromagnets

We present arguments in favor of the suggestion that the Marshall-Peierls phase relationships and the Lieb-Mattis level ordering survive the frustration in the squarelattice Heisenberg antiferromagnet for relatively strong frustration parameters.     

Study of electrical conductivity changes and phase transitions in TiO2 doped ZrO2

The electrical conductivity in ZrO₂ doped with various molar ratios of TiO₂ has been measured at different temperatures. Phase transitions depending on the temperature for different molar compositions were investigated by doping of the samples. The conductivity is also found to increase with rise in temperature till 200 °C and thereafter decreases due to collapse of the fluorite framework. A second rise in conductivity in the doped samples around 462 °C is observed due to phase transition of ZrO₂. X-ray powder diffraction recorded at high temperature show the effect of doping and the phase relationships of doped materials. DTA was also carried out for confirming doping effect and phase transition in samples.     

Structural phase transitions of FeTi-deuterides

Absorption and desorption isotherms of FeTiD_x (0≤x≤1.9) were measured at room temperature. They indicate isotope effects. The dependence of the crystal structure of FeTiD_x on D₂-pressure (≤153 bar) was investigated at room temperature by means of neutron diffraction on powder samples both in absorption and desorption. The results show that the distribution of the deuterium atoms in the orthorhombic β-phase change from $\text{0.88}\text{0.12}$ for the DI/DII sites at x=1.0 (1) to $\text{0.92}\text{0.45}$ at x=1.4. This can be interpreted as a transition from a β₁-phase of composition FeTiD to a β₂-phase of approximate composition (FeTi)₃D₄. For the last composition Lebsanft (2) has reported a $\text{0.70}\text{0.70}$ distribution over the two D-sites. In agreement with (3) the structure of γ-FeTiD (x>1.9) is found to be monoclinic (space group $\text{P}\text{2}\text{m}$). Associated with considerable lattice expansions deuterium atoms occupy both in β- and γ-phases octahedral sites.     

Quantum Melting of Domain Walls in 2D Incommensurate Phases

We investigate quantum fluctuations of striped and honeycomb domain walls in 2D incommensurate states at T=0 near the commensurate-incommensurate transition point. It is revealed that stripes melt due to quantum fluctuations and become a soliton liquid for a large-wall-spacing region. Zero-point energies of striped and honeycomb phases are calculated using an elastic theory. As a consequence of these results, phase diagrams for soliton-lattice and liquid phases are discussed for various domain-wall masses.     

Thermal relaxation near phase transitions

We consider a phenomenological approach to thermal relaxation processes near phase transitions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 4, pp. 639–642, April, 1985.     

Chemical reactions and phase transitions

We consider the questions of what effects the fluctuations in fluids near critical points have on the rates and extents of chemical reactions taking place in those fluids and of whether equilibrium polymerizations can be profitably viewed as phase transitions. We find that reaction rates are expected to be affected by critical points only in rare circumstances and that, indeed, there is no compelling experimental evidence for such effects. On the other hand, there is evidence for an effect of critical fluctuations on the extents of chemical reactions at equilibrium, but the effect is not (and is, in general, not expected to be) dramatic. We find that the experimental data on equilibrium polymerizations are in qualitative agreement with predictions based on the n=0 magnet model but that closer consideration and further experimental work are in order.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.