On tensor phase transitions

Within the Landau theory, phase diagrams are obtained for second-order phase transitions with order parameter in the form of a symmetric traceless tensor of rank at most six that is transformed in accordance with a one-dimensional representation of a crystal group. The case of two-dimensional representation is analyzed for rank equal to three.     

On the order of itinerant antiferromagnetic phase transitions and superconducting phase transitions in an exchange field

The coefficients of the second and fourth order terms in a Landau expansion of the free energy are evaluated for an itinerant antiferromagnetic transition. The choice of spatial dependence is found to play an important role. A first order transition is obtained for a range of values of the band structure parameters. However if values appropriate to Cr are used it is found that the contribution from the shift in the Fermi level is sufficiently large to give second order transitions even when magnetostrictive effects are included. In the mathematically similar problem of a superconductor in an exchange field it is found that the transition from normal to superconducting states is first order near the triple point with an upper and possibly a lower critical point where the transition changes to second order.     

On the theory of phase transitions in magnetic fluids

Particles of magnetic fluids (ferrofluids), as is known from experiments, can condense to bulk dense phases at low temperatures (that are close to room temperature) in response to an external magnetic field. It is also known that a uniform external magnetic field increases the threshold temperature of the observed condensation, thus stimulating the condensation process. Within the framework of early theories, this phenomenon is interpreted as a classical gas-liquid phase transition in a system of individual particles involved in a dipole-dipole interaction. However, subsequent investigations have revealed that, before the onset of a bulk phase transition, particles can combine to form a chain cluster or, possibly, a topologically more complex heterogeneous cluster. In an infinitely strong magnetic field, the formation of chains apparently suppresses the onset of a gas-liquid phase transition and the condensation of magnetic particles most likely proceeds according to the scenario of a gas-solid phase transition with a wide gap between spinodal branches. This paper reports on the results of investigations into the specific features of the condensation of particles in the absence of an external magnetic field. An analysis demonstrates that, despite the formation of chains, the condensation of particles in this case can proceed according to the scenario of a gas-liquid phase transition with a critical point in the continuous binodal. Consequently, a uniform magnetic field not only can stimulate the condensation phase transition in a system of magnetic particles but also can be responsible for a qualitative change in the scenario of the phase transition. This inference raises the problem regarding a threshold magnetic field in which there occurs a change in the scenario of the phase transition.     

On the thermodynamics of phase transitions in metal hydrides

Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a particular phase transition in TiH _x , which can approximately be described as a second-order phase transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the density of H⁺ ions and of the distance between adjacent H⁺ ions. Moreover, as the system approaches the transition and the correlation radius increases, we show -with the help of statistical mechanics-that the statistical weight of modes involving a large number of H⁺ ions (‘collective modes’) increases sharply, in spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, the interaction of the H⁺ ions with collective modes makes a tiny suprathermal fraction of the H⁺ population appear. Our results hold for similar transitions in metal deuterides, too. A violation of an -insofar undisputed-upper bound on hydrogen loading follows.     

On the revealing of nonequilibrium phase transitions in water

It has been found that the jump and stabilization of the temperature observed in [L.N. Baturov et al., JETP Lett. 93, 91 (2011)] upon the heating/cooling of water near 4°C at a rate of ∼10⁻³ K/s are observed in water of any purification degree. However, we have not found the process of the formation/melting of supermolecular structures assumed by Baturov et al., which is sought in the shift of the center of the OH band of Raman scattering, e.g., at ∼150 cm⁻¹, as at the melting of hexagonal 1h ice [S.M. Pershin and A.F. Bunkin, Opt. Spectrosc. 85, 190 (1998); Patent RF No. 98, 103249 (1998)]. It has been shown that the revealed temperature features are absent in the presence of the mixing of water and artificial limitation of convection, as well as in a thin layer; this indicates that the regularity of the phenomenon is doubtful and that convection plays an important role. The visualization of convection flows by potassium permanganate made it possible to detect the reversion of their circulation over the trajectory of surface-wall-bottom-volume symmetry axis at the transition through a point of 4°C. The observed features have been interpreted as a manifestation of Archimedes’ principle.     

On the nature of the phase transition in MnO

The temperature dependence of the nuclear Bragg reflection (222) and of the magnetic Bragg reflection (111) of MnO was simultaneously measured by neutron diffraction on a powder sample. The intensity of the nuclear line exhibits a 40% drop at temperatures between 113 and 116 K. This dip was attributed to a decrease of the Bragg intensity due to structural fluctuations. If the effect of these fluctuations on the magnetic intensity is taken into account, the magnetization discontinuity is found to be greatly reduced or even to disappear, in disagreement with other authors.     

On structural phase transitions from a hypothetical phase

Examples known so far of structural phase transitions which can be treated as an instability of a hypothetical parent phase are enumerated. Physical requirements for being reasonable to consider such hypothetical phase are pointed out. The possibility of using this concept for explanation of successive structural phase transitions in Rochelle salt and langbeinites is discussed.The author thanks Dr. V.Janovec for many valuable remarks to this paper.     

On the topological characterization of two-dimensional phase transitions

It is shown that for the two-dimensional planar-rotator model the variance of the number of vortices inside a large loop is proportional to the perimeter of the loop at all temperatures. A similar result holds for the variance of the charge inside a loop in the lattice Coulomb gas model. Hence a topological distinction between the high and low temperature phases of these models (area law versus perimeter law) is not possible.     

On phase transitions in cold nuclear matter

Real conditions for the formation of cold subhadronic matter are considered with allowance for nontrivial properties of the QCD vacuum. It is shown that a steady state of this matter is attainable, if at all, only in the case where dynamical (massive) quarks exist as rather stable quasiparticles. This state may consist of both a degenerate nearly perfect gas of these particles and a degenerate gas of current quarks in the interior of some (compact) neutron stars. In the latter case, both phases should coexist, and the first phase should occupy a certain space between the second phase and (normal) hadron matter occurring at the periphery of the star.     

On the kinetics of the first order phase transitions

An attempt is made to analyse the kinetics of the first order structural phase transitions on the basis of the Landau-Ginzburg equation. Two simple solutions are proposed: One in the form of one-dimensional solitary wave which can be considered as a planar interface separating two phases and travelling along direction normal to the interface. Any direction of propagation is possible. The other solution has a form of a onedimensional kink-antikink couple which under supercooling conditions reveals properties of a critical nucleus. A short discussion of the free energy density form for one- and multidimensional order parameters, and of the symmetry of the quadratic gradient term is included.     

On the multidimensional theory of the first-order phase transitions

Multidimensional theory of first-order phase transitions in the vicinity of a one-dimensional saddle point is considered. Transformations of the variables describing new-phase nuclei are suggested; these transformations allow one to completely separate the variables in the Fokker-Planck equation and reduce the problem to a one-dimensional one. The distribution function and the nucleation rate are found for both stationary and non-stationary nucleation stages. As an illustration, the problem of boiling of a volatile liquid is considered in the case where new-phase nuclei are characterized by two parameters.     

On the possibility of double phase transitions in unsymmetric systems

The existence of double phase transitions in unsymmetric disordering systems is predicted. Conditions and temperatures at which these transitions are realised are obtained.     

On the phase transitions for the electronic excitations in semiconductors

A model Hamiltonian for a system of interacting electrons, holes and Wannier excitons is derived. This system of electronic excitations is assumed to be in a quasi-equilibrium state. With the aid of Bogolubov's variational principal the thermodynamic potential is calculated. Using the most general mean-field Hamiltonian as a trial Hamiltonian, a set of coupled integral equations is obtained for the self-energies. These equations are solved numerically for equal effective masses of the electrons and holes. Below a critical temperature ofk _B T _c0.65E _ex ^b whereE _ex ^b is the exciton binding energy, we find a first order phase transition from an exciton rich phase into a degenerate electron-hole phase. The mechanical and thermal stability of both phases is proven. Below a critical temperaturek _B T _c0.11E _ex ^b the exciton system becomes degenerate (Bose-Einstein condensation). A complete phase diagram of these three phases is given.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

On the nature of metal-semiconductor phase transition in vanadium dioxide

The method of coercive temperature distribution function is used to prove that the metal-semiconductor temperature-induced phase transition in vanadium dioxide manifests itself as a Mott electronic transition.     

On the nature of the phase transition in the KDP systems

Using the Landau theory of phase transitions it has been shown that for a second order phase transition Ω/k_BT_c ? 0.01. and its isomorphs 4Ω/J¹ ? 1 and for a first order transition Ω/k_BT_c ? 0.01.     

On the possibility of phase transitions in the geometric structure of space-time

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase transitions in its geometric structure. These transitions together with the evolution of each of the possible metric states make up the general picture of space-time manifold dynamics.     

On gas phase transitions in a 2D nanopore

A gas distribution function for a 2D nanopore was derived, making possible calculations of thermodynamic characteristics such as pressure and heat capacity. The dependence of pressure and heat capacity on the least nanopore size was considered suggesting the presence of specific phase transitions in the gas in a certain temperature range. The phase transitions are associated with size quantization which results in “effective” interaction (attraction) between gas molecules.     

On the nature of a new phase transition in α-MnS

Magnetic-susceptibility and X-ray-diffraction data of polycrystalline and oriented single crystal α-MnS reveal a new phase transition at T_tr = 131 K below the Néel temperature T_N = 148 K. The phase transition is characterized by an abrupt inversion of the rhombohedral distortion of the f.c.c. lattice along [111]. At T_tr there is a discontinuous change in the susceptibility of single crystals.     

On the theory of the central peak at structural phase transitions

A universal mechanism is proposed, which explains the appearance of the central peak by means of a transition from ergodic to nonergodic dynamical behaviour of the system at some temperatureT _g above the phase transition. A detailed investigation of the scalar lattice ⁴-model with defects is given. The relation between the nonergodic state and the appearance of precursor clusters and Raman scattering experiments is discussed.     

On the hydrodynamic theory of central peak in displacive structural phase transitions

A model involving nonlinear coupling between the overdamped phonon mode and temperature fluctuations is studied using the dynamic renormalization group method. It is shown that the behavior of the central peak in the dynamic form factor depends on the specific heat exponent α. For α < 0 and as T → T_c the central peak is found to merge with the over-damped phonon mode and the coupling goes to zero at T_c as (T ? T_c)^?α. An argument on the intensity of the central peak in the critical region in presented and it is concluded that the hydrodynamic coupling may not be the dominant mechanism of the central peak in SrTiO₃.