Hypothetical Phase Transition Research Articles

Unique atom hyper-kagome order in Na4Ir3O8 and in low-symmetry spinel modifications.

Group-theoretical and thermodynamic methods of the Landau theory of phase transitions are used to investigate the hyper-kagome atomic order in structures of ordered spinels and a spinel-like Na4Ir3O8 crystal. The formation of an atom hyper-kagome sublattice in Na4Ir3O8 is described theoretically on the basis of the archetype (hypothetical parent structure/phase) concept. The archetype structure of Na4Ir3O8 has a spinel-like structure (space group Fd\bar 3m) and composition [Na1/2Ir3/2](16d)[Na3/2](16c)O(32e)4. The critical order parameter which induces hypothetical phase transition has been stated. It is shown that the derived structure of Na4Ir3O8 is formed as a result of the displacements of Na, Ir and O atoms, and ordering of Na, Ir and O atoms, ordering dxy, dxz, dyz orbitals as well. Ordering of all atoms takes place according to the type 1:3. Ir and Na atoms form an intriguing atom order: a network of corner-shared Ir triangles called a hyper-kagome lattice. The Ir atoms form nanoclusters which are named decagons. The existence of hyper-kagome lattices in six types of ordered spinel structures is predicted theoretically. The structure mechanisms of the formation of the predicted hyper-kagome atom order in some ordered spinel phases are established. For a number of cases typical diagrams of possible crystal phase states are built in the framework of the Landau theory of phase transitions. Thermodynamical conditions of hyper-kagome order formation are discussed by means of these diagrams. The proposed theory is in accordance with experimental data.

Structures and phase transitions in (K1-xRbx)2SeO4

The phase diagram of the mixed crystal (K1-xRbx)2SeO4 was determined by means of thermal analysis and neutron scattering experiments. The hexagonal to orthorhombic phase transition line exists for any x. The normal-incommensurate phase transition temperature decreases continuously with increasing Rb content. However, the incommensurate-commensurate phase transition was not observed except for K2SeO4. According to the clear softening of the Σ2- Σ 3 phonon branches and the finite frequency at 0 K for x>0.34, an existence of the hypothetical phase transition was confirmed.

The liquid–glass transition – is it a fourth order phase transition?

The liquid–glass transition is analyzed using a theory of Brownian motion in liquids recently developed by the author. It is shown that if a liquid could be cooled in quasi-static process and still avoids crystallization it would transform into a stable non-crystalline solid, which would be a normal thermodynamic phase. This hypothetical phase transition is neither first nor second order. At equilibrium transition temperature the free energy of the system and its first, second and third derivatives are all continuous functions, but its fourth derivative with respect to temperature is discontinuous. Therefore, the equilibrium liquid to non-crystalline solid transition may be considered a fourth order phase transition. The temperature of this phase transition, T K, which coincides approximately with the Kauzmann temperature, is below the standard glass transition temperature T g. (When the temperature decreases below T g, the viscosity increases above 10 13 dPa s.) When the temperature decreases below T K, the system becomes an ideal solid because the molecular mobility becomes zero and the viscosity becomes infinite if we neglect vacancy-like mechanisms of mobility. This hypothetical quasi-static transition is physically unobservable because the real liquid–glass transition must be done at a cooling rate high enough to suppress the growth of nanocrystals, which makes the liquid–glass transformation a non-equilibrium complicated phenomenon. Understanding this ideal phase transition is a first step towards describing the real liquid–glass transition from first principles.

Steady-state convection in Mars’ mantle

The Martian geoid and topography of the Tharsis region can be understood as induced by a large underlying plume. Using a spherical harmonic representation, we compute the mantle flows induced by such a plume by solving numerically the equation of motion, the stress–strain relation, and Poisson's equation governing the potential readjustment due to mass redistribution. The uncertainties concerning the Martian interior structure are accounted for; the effects of the core size, of the core rheology, of a hypothetical phase transition spinel–perovskite at the bottom of the mantle, and of the mantle viscosity profile are investigated. The flow-induced boundary deformations are analyzed, and particular attention is paid to the core-mantle boundary topography and to its flattening because this parameter is important for the determination of the Free Core Nutation period of Mars in the case of a fluid core. Our results show that due to the large number of unknowns, it is impossible to constrain the internal parameters cited above from the observed geoid. Different combinations of these parameters allow the reconstruction of the geoid with reasonable density anomalies in the mantle. We have computed the non-hydrostatic core flattening corresponding to some of these models. The numerical results correspond to an increase of the difference between the equatorial and polar core radii in the range [ 0.7,2 km ] for models with a perovskite layer above the core-mantle boundary, and in the range [ 1,5.3 km ] for models without perovskite layer. The overlap between these ranges is mainly due to the uncertainty existing for the viscosity profile and the core radius.

Yellow InCl as a distorted rock-salt lattice

Because of the subgroup - group relationship which exists between the space group of yellow InCl and that of rock salt , a Landau expansion of the free energy in invariants of the symmetry group of higher order can be performed and a mechanism for distortion arises. The special feature of this hypothetical phase transition is that three lattice modes of different symmetry type and of almost equal force constant bring about the deformation. These three modes, which are apparently nearly degenerate, effect longitudinal displacements of rows of ions, with different amplitudes for the cations and the anions. When these are described by an order parameter, an expansion of the free energy up to the fourth power and containing third-order terms is possible. The cooperation of pseudo-degenerate modes of different symmetry is a hitherto unknown distortion mechanism. Yellow InCl is further characterized by bilinear quantities describing ferrodistortive chirality and electric `' octupoles and antiferrodistortive spiral arrangements. These bilinear quantities are related to fourth-order Landau invariants. Yellow InCl has an electric octupole lattice. In addition, on the basis of the analogy with optical rotatory power, new mechanisms of this effect are predicted.

Hypothetical phase transition, structural disorder and spontaneous polarization in ammonium sulfate crystals

EPR spectra of SeO3 − radicals in ammonium sulfate crystal were studied in the high temperature phase. Two magnetically inequivalent SeO3 − radicals exist in the crystal as a consequence of different coupling to two inequivalent ammonium groups: (NH4)1 and (NH4)11. It is estimated that the distinction between the two SeO3 − radicals would disappear at 585 K, which is interpreted as the hypothetical ferroelastic phase transition. The intensity ratio of the two SeO3 − radicals can be changed by appropriate heat treatment of the sample. It is inferred that the intensity ratio is related to the disorder of protons in the asymmetric potential minima in hydrogen bonds. The unusual temperature dependence of spontaneous polarization was studied in crystals grown from solutions with pH in the range 2.0 to 5.0 as well as in crystals after heat treatment.

Mn 2+ EPR study of phase transitions in dicalcium strontium propionate Ca 2Sr(C 2H 5COO) 6

X-band EPR of Mn 2+-doped single crystal of Ca 2Sr(C 2H 5COO) 6 has been used to study the phase transitions experienced by this crystal. Two phase transitions, a second-order transition at 278 ± 5 K and a first-order phase transition at 103 ± 10 K, have been deduced from the behaviour of overall splitting of lines and that of EPR linewidth, as functions of temperature. The angular variations of Mn 2+ EPR spectra have been studied in order to establish the orientations of the magnetic Z axes of the various Mn 2+ complexes in the unit cell. Further, from the behaviour of overall splitting of lines for the magnetic field orientations along the Z and X magnetic axes, as a function of temperature, a hypothetical phase transition to cubic symmetry has been deduced to occur at about 783 K. The room-temperature spin-Hamiltonian parameters are evaluated, using a rigorous least-squares fitting procedure. It is concluded, from the angular variation of the spectra, that the crystal structure is tetragonal below 278 K. Linewidth behaviour is studied to discuss the ordering of the ions surrounding Mn 2+.

On the dielectric constant and spontaneous polarization in LiH 3(SeO 3) 2

Studies on the dielectric constant and spontaneous polarization have been performed in LiH 3(SeO 3) 2 in order to find out some information on the character of the hypothetical phase transition in that ferroelectric. The results seem to indicate that the transition should be a 2nd order one.