Theory Of Structural Phase Transitions Research Articles

STRUCTURAL PHASE TRANSITIONS IN JAHN-TELLER CRYSTAL PLATES

The cooperative Jahn-Teller effect is considered in the crystal samples of finite size. Peculiarities of the plate sample phonon spectra and their influence on the microscopic theory of the structural phase transitions are in the focus of attention. The mutual orientation of the crystal axes and the plate plane is discussed. As an example the Lamb wave role is analyzed in detail. It is shown that the ferrodistortive ordered phase is significantly inhomogeneous. This inhomogeneity is the consequence of the space coordinate dependence of the intersite electron-electron interaction. Some new thermodynamic and dynamic effects are considered as a result of the microscopic theory of structural phase transitions in plates.

Phenomenological thermodynamics and the structure formation mechanism of the CuTi₂S₄ rhombohedral phase.

The theory of structural phase transition in CuTi2S4 is proposed. The symmetry of order parameters, thermodynamics and the mechanism of the atomic structure formation of the rhombohedral Cu-Ti-thiospinel have been studied. The critical order parameter inducing the phase transition has been found. Within the Landau theory of phase transitions, it is shown that the phase state may change from the high-symmetry cubic disordered Fd3[combining macron]m phase to the low-symmetry ordered rhombohedral R3[combining macron]m phase as a result of phase transition of the first order close to the second order. It is shown that the rhombohedral structure of CuTi2S4 is formed as a result of the displacements of all types of atoms and the ordering of Cu-atoms (1 : 1 order type in tetrahedral spinel sites), Ti-atoms (1 : 1 : 6 order type in octahedral spinel sites), and S-atoms (1 : 1 : 3 : 3 order type). The Cu- and Ti-atoms form metal nanoclusters which are named a "bunch" of dimers. The "bunch" of dimers in CuTi2S4 is a new type of self-organization of atoms in frustrated spinel-like structures. It is shown that Ti-atoms also form other types of metal nanoclusters: trimers and tetrahedra.

Theory of structural phase transition in MgTi2O4

A theory of phase transition in MgTi2O4 is proposed based on a study of the order-parameter symmetry, thermodynamics, and mechanisms of formation of the atomic and orbital structure of the low-symmetry MgTi2O4 phase. The critical order parameter (which induces a phase transition) is determined. It is shown that the calculated MgTi2O4 tetragonal structure is a result of displacements of magnesium, titanium, and oxygen atoms; ordering of oxygen atoms; and the participation of dxy, dxz, and dyz orbitals. The contribution of noncritical representations to ion displacements is proven to be insignificant. The existence of various metal clusters in the tetragonal phase has been established by calculation in correspondence with experimental data. It is shown (within the Landau theory of phase transitions) that phase states can be changed as a result of both first- and second-order phase transitions: the high-symmetry phase borders two low-symmetry phases by second-order transition lines, while the border between low-symmetry phases is a first-order transition line.

A theory for structural phase transitions in BaTiO3 single crystal and PbZrO3 -xPbTiO3 solid solution

A phenomenological theory has been proposed for the diffusionless structuralphase transitions in BaTiO3single crystal and PbZrO3 -xPbTiO3 solid solution here. It has been found that for BaTiO3single crystal, both the phase transitionsand the crystal structurescan be predicted with the crystalline anisotropy constants and strain constants that depend on the temperature. For PbZrO3 -xPbTiO3 solution, the morphotropic phase boundaries arise from the strong dependence of the crystalline anisotropy constants on the composition. The good agreement between the numerical results and experimental observations has shown that our theory is effective for the diffusionless structuralphase transitions.

Peak effect and square-to-rhombic vortex lattice transition inLa2−xSrxCuO4

A theory of structural phase transition of the vortex lattice in tetragonal superconductors is constructed based on the self consistent harmonic approximation for lattice anharmonicities, within the fourfold-symmetric generalization of the London model. Thermal fluctuations on the mesoscopic scale are strong enough to affect the location of the square to rhomb transition line in the $T\text{\ensuremath{-}}H$ plane. We find that the slope of the transition line is generally negative: thermal fluctuations favor the more symmetric square lattice. The calculated transition line is concave, and fits the experimental line deduced in LaSCO crystals from the onset of the second magnetization peak. Near the transition line the ``squash'' modulus ${C}_{\mathit{sq}}=2({C}_{11}+{C}_{12})\ensuremath{-}{C}_{66}$ is softened leading to enhancement of the critical current, born out in the experiment as a second magnetization peak.

Structural order parameter and itinerant electron magnetism in Cd 2Re 2O 7

We describe the low-temperature behaviour of the magnetic susceptibility of Cd 2Re 2O 7 in terms of a Landau theory of structural phase transitions. We calculate the zero temperature Pauli susceptibility using a tight-binding approach to reveal the mechanism of coupling between the structural order parameter and itinerant magnetism.

Independent anharmonic oscillator approximation in the theory of structural phase transitions in crystals

A new method in the microscopic theory of anharmonic crystal lattice dynamics—the independent anharmonic oscillator (IAO) approximation—is discussed. The method is compared with traditional approaches (such as the mean-field and renormalized self-consistent phonon methods) from the standpoint of the analysis of the main approximations. Different methods are applied to the description of the structural phase transition in a monoatomic anharmonic crystal, the results obtained are analyzed, and the numerical accuracy of different approximations is estimated. It is demonstrated that, for this model in the displacement-type instability range, the new method, unlike the self-consistent phonon method, adequately describes the phase transition as a second-order transition. The phase transition temperature calculated in the displacement limit monotonically tends to the exact value in contrast with the temperature obtained within the mean field approximation.

To the theory of structural phase transitions in ferronematics

The Frederiks effect and corrugations of a flat free surface of ferronematics has been studied. The characteristic time of ferroparticle reorientation relatively to nematic solvent is supposed to be very large. Our results show that the Frederiks transition may occur due to space separation of ferroparticles with different orientations of their magnetic moments in an homogeneous external magnetic field. The deformation of a free surface of such ferronematics, in contrast to the ordinary magnetic liquids, may occur even in the absence of an external field. We have calculated the critical ferronematics magnetization, corresponding to this phenomenon and estimated the equilibrium wave number of these deformations.

Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys

In this paper, a system of nonlinear partial differential equations modelling the dynamics of martensitic phase transitions in shape memory alloys is further investigated. In a previous paper published in SIAM J. Math. Anal., the global existence of a unique solution and the asymptotic behaviour of the solution as time goes to infinity have been established; in the present paper the existence of a compact maximal attractor is proved.

First-principles theory of structural phase transitions for perovskites: Competing instabilities

We extend our previous first-principles theory for perovskite ferroelectric phase transitions to treat also antiferrodistortive phase transitions. Our approach involves construction of a model Hamiltonian from a Taylor expansion, first-principles calculations to determine expansion parameters, and Monte-Carlo simulations to study the resulting system. We apply this approach to three cubic perovskite compounds, SrTiO3, CaTiO3 and NaNbO3, that are known to undergo antiferrodistortive phase transitions. We calculate their transition sequences and transition temperatures at the experimental lattice constants. For SrTiO3, we find our results agree well with experiment. For more complicated compounds like CaTiO3 and NaNbO3. which can have many different structures with very similar energy, the agreement is somewhat less satisfactory.

Infrared and Raman spectroscopy of Li2Ge7O15 single crystals: spectra of the paraelectric and aristotype phases

Polarized Raman and infrared spectra of Li2Ge7O15 single crystals were measured in the frequency range 5-1000 cm-1 at room temperature. The spectra are analysed within the framework of the Landau theory of structural phase transitions from a (hypothetical) fully disordered deficient structure (aristotype). The mechanism of the phase transition is discussed in terms of ordering and shifts of ions.

Diffuse scattering and structural phase transitions

Abstract On the basis of numerous experiments using the mono-Laue method on the diffuse scattering of X-rays and electrons we have developed the Comes-Lambert-Guinier concept of the existence of co-operative thermal vibrations in perfect crystals in which one-dimensional or two-dimensional atomic objects, i.e. chains or planes of atoms, are moving in a double-well potential with conservation of coherence. For an approximate description of such a motion we have utilized the pseudospin Ising model approach which is widely used in the theory of structural phase transitions. These ideas proved to be successful for the description of diffuse scattering patterns, and their temperature evolution in close connection with structural phase transitions. The developed theory gives the possibility through the observation of diffuse scattering at high temperatures and its analysis to predict the structural phase transition (and even the subsequent cascades of transitions) and to give the correct explanation for physica...

On the quantum finite-size scaling

We verify the finite-size scaling hypothesis in the presence of quantum fluctuations up to one-loop order in the ϵ-expansion, using the formalism of Brezin [1], Brezin and Zinn-Justin [2] and Rudnick et al. [3]. The analysis is performed within the framework of three models commonly used in the theory of structural phase transitions, superconducting phase transitions and Bose systems.

Raman spectra of Cs2CdBr4 single crystals

Polarized Raman spectra of Cs2CdBr4 single crystals were measured in the frequency range 0-350 cm-1 at 100-290 K. The spectra are analysed within the framework of the Landau theory of structural phase transitions; the analysis indicates that the transition to the triclinic phase with PI symmetry is accompanied by unit-cell volume multiplication.

On the quantum finite-size sealing

The finite-size scaling hypothesis, in the presence of quantum fluctuations, is verified by means of the ε-expansion. The analysis is performed within the framework of three models commonly used in the theory of structural phase transitions, superconducting phase transitions and Bose systems.

31P NMR study of the influence of defects on the symmetry of ferroelectric crystals of PbHPO4 above the phase transition

The width delta v of the 31P NMR in PbHPO4 is found to be larger in the paraelectric than in the ferroelectric phase. The authors interpret this increase of delta v as an unresolved splitting due to the persistence of the low temperature ferroelectric space group Pc in the high temperature paraelectric phase, where a centrosymmetric space group is expected. A comparison of delta v in a crystal grown at ambient temperature, i.e. in the ferroelectric phase, and in a crystal growth at 313 K, i.e. in the paraelectric phase, shows that delta v is smaller in the latter crystal. Annealing of this crystal resulted in a further decrease of delta v. This leads us to the conclusion that polar defects in real crystals conserve, locally, the symmetry of the ferroelectric phase above the transition temperature Tc and that a crystal free of defects should change its symmetry at Tc as required by Landau's theory of structural phase transitions.

A Phenomenological Theory of Structural Phase Transitions in Zirconia

The structural phase transitions in zirconia ZrO 2 are interpreted phenomenologically, based upon the Landau-type thermodynamic potential derived on the consideration of the change of translational as well as rotational symmetry of the unit cell. The difference between Chan's model and ours is mentioned.

Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys

Global existence of smooth solutions is proved for the system of partial differential equations governing the dynamics of martensic phase transitions in shape memory alloys. The free energy is assumed in Ginzburg-Landau form and nonconvex in the order parameter.

14N NMR study and Landau theory of phase transitions in [N(CH3)4]2ZnI4

The14N NMR spectra and spin-lattice relaxation timeT 1 of [N(CH3)4]2ZnI4 have been studied between room temperature and 200 K. Two phase transitions atT c 1=255 K and atT c 1=217 K are observed. The14N NMR lineshape andT 1 data suggest that the intermediate phase is commensurate rather than incommensurate in spite of the presence of a Lifshitz invariant in the expansion of the free energy density in powers of the order parameter. We also discuss the phenomenological theory of structural phase transitions in [N(CH3)4]2ZnI4.

Green's-function theory of ferroelectric phase transitions in hydrogen-bonded triglycine sulfate with the pseudospin-lattice coupled-mode model: A unified theory of structural phase transitions. II. Nonlinear properties.

Green's-function theory of ferroelectric phase transitions in hydrogen-bonded triglycine sulfate with the pseudospin-lattice coupled-mode model: A unified theory of structural phase transitions. II. Nonlinear properties.