Lattice Phase Transition Research Articles

Lattice instabilities, anharmonicity and phase transitions in PbZrO3 from first principles

An effective Hamiltonian for the antiferroelectric transition in PbZrO3 is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of “lattice Wannier functions''. The effective Hamiltonian consists of three-component vector degrees of freedom at the Pb sites and two-component vector degrees of freedom at the oxygen sites. This effective Hamiltonian allows us to analyze the structural energetics and identify the role of various physical contributions. We find that there exists a strong competition between sets of coupled unstable modes in producing low energy states. Two such groups of instabilities found from the effective Hamiltonian are seen to be relevant to the experimental ground and intermediate states.

Universality in Ising-like phase transitions of lattices of coupled chaotic maps

Critical exponents of nonequilibrium, Ising-like phase transitions in two-dimensional lattices of locally coupled chaotic maps are estimated numerically using equilibrium finite-size scaling theory. Numerical data supports the existence of a new universality class, which groups together phase transitions of synchronously updated models with Ising symmetry, irrespective of the specific microscopic evolution rule, and of the presence of stochastic noise. However, nonequilibrium, Ising-like phase transitions of asynchronously updated models belong to the Ising universality class. The new universality class differs from the equilibrium Ising universality class by the value of the correlation length exponent, \ensuremath{\nu}=0.89\ifmmode\pm\else\textpm\fi{}0.02, while exponent ratios \ensuremath{\mathrm{B}}/\ensuremath{\nu} and \ensuremath{\gamma}/\ensuremath{\nu} as well as Binder's cumulant ${\mathrm{U}}^{\mathrm{*}}$ assume their usual value.

Pinning in BSCCO above the ordinary irreversibility line

Frequency-dependent observations of magnetic flux structures are used to show that pinning plays a principal role in the whole mixed state in Bi2Sr2CaCu2O8 (BSCCO) single crystals. We speculate that the random pinning force on the moving vortices may dominate over thermal fluctuations and considerably modify the position of the vortex lattice phase transition.

Phase diagram of XY antiferromagnetic stacked triangular lattices.

The phase transition in antiferromagnetic stacked triangular lattices with classical XY spins interacting via antiferromagnetic nearest- and next-nearest-neighbor bonds, J 1 and J 2, is studied by means of extensive histogram Monte Carlo simulations. When J 250, the transition is of second order with critical exponents slightly different from those given by other authors. It is shown that in a range of J 2, the transition is of first order. The general phase diagram in the ( J 2 ,T) space (T, temperature! is shown and discussed. @S0163-1829~96!03530-8#

Antiferromagnetic stacked triangular lattices with Heisenberg spins: Phase transition and effect of next-nearest-neighbor interaction.

We study by extensive histogram Monte Carlo simulations the phase transition in the antiferromagnetic stacked triangular lattices with classical Heisenberg spins. It is shown that in a range of the antiferromagnetic next-nearest-neighbor interaction ${\mathit{J}}_{2}$, the transition is clearly of first order. We also reconsider the controversial question concerning the nature of the phase transition when ${\mathit{J}}_{2}$=0: we show that the critical exponents obtained, in agreement with previous simulations, exclude the possibility of the O(4) class predicted by a nonlinear \ensuremath{\sigma} model in a 2+\ensuremath{\varepsilon} renormalization-group calculation. The phase diagram in the (${\mathit{J}}_{2}$,T) space (T: temperature) is shown and discussed. For comparison, the phase diagram obtained by a Green-function method in the case of quantum Heisenberg spins is also shown.

Flux lines and lattices in superconductors with additional ordering

Flux-line and flux-lattice structures, interaction of flux lines in superconductors with a superconducting phase transition neighboring a nonsuperconducting one are considered. This transition may be a structural one: transition into a CDW state or into an AF state. Phase transitions corresponding to the appearance of addition ordering in single flux lines are predicted. The possibility of vortices attraction and formation of vortex molecules is shown. Phase transitions in flux lattices in a changing magnetic field are investigated. Magnetization curves become hysteretic despite of the absence of pinning centers in the specimens.

Perovskite at high P‐T conditions: An in situ synchrotron X ray diffraction study of NaMgF3 perovskite

The lattice distortion and structural phase transition of NaMgFa perovskite (Neighborite) have been studied using synchrotron X ray powder diffraction at high pressure and temperature. Changes in the unit cell dimensions of the perovskite are determined by conventional peak indexing and least squares routines. The stress field within the high‐pressure cell assembly is analyzed, and the yield strength of the NaMgF3 perovskite is determined at high P and T. The pressure‐ and temperature‐induced dimensional changes of the NaMgF3 perovskite structure are expressed empirically as a combination of compression/expansion of the [Mg‐F] bond length and tilting of the MgF6 octahedral framework. The linear thermal expansions of the NaMgF3 perovskite observed at different pressures show significant anisotropy with αa > αc > αb which reflects the decrease of structural distortion and the development of a phase transition in the perovskite with increasing temperature. The tilting angle of the MgF6 octahedral framework is observed to decrease rapidly toward zero, in a manner expected for a ferroelastic phase transition, as the temperature approaches the transition point Tc. The apparent [Mg‐F] bond lengths of the MgF6 octahedra experience drastic shrinkage with increasing temperature just prior to the transition. Despite a 12% change in volume due to compression, the experimental results on NaMgF3 perovskite show that the thermal expansivity is independent of pressure, i.e., dα/dP ≈ 0, and, compatibly, that the compressibility is independent of temperature, i.e., dβ/dT 0. However, the dominant compression mechanism is the compression of the octahedral bond length, whereas the dominant mechanism for thermal expansion is the diminishing of octahedral tilting. The Earth's mantle may be isochemical if the thermal expansion of MgSiO3 perovskite at high pressure behaves like NaMgF3, of which the Anderson‐Grüneisen parameter is near zero, i.e., δs ≈ 0. It is observed that crystal structure of the NaMgF3 perovskite transforms directly from the orthorhombic Pbnm phase to the cubic phase at all pressures. The transition temperature is observed to increase with increasing pressure with a positive slope of 45 K/GPa.

Pseudo-oriented dipole calculations of the lattice potential and phase transition interpretation in KCN

Using different lattice potential calculation models, the authors attempt to explain the phase transition process and the evolution with the temperature of the CN- molecule orientation in KCN. These calculation are made for the pseudo-cubic phase and consist of a comparison between two lattice potential models, one in which a three-body interaction is introduced to take account of the anisotropic evolution with temperature of the elastic constants, and the other-a so-called 'pseudo-oriented dipole' model-in which calculations are made with CN- elastic dipoles oriented along the principal (110), (001) and (111) cubic directions of the pseudo-cubic phase.

Studies of the stability of β-Ca 2SiO 4 doped by minor ions

The Ca 2SiO 4 (C 2S) samples doped by minor ions of Li +, K +, Na +, Sr 2+, Mn 2+, Mg 2+, Fe 3+, Al 3+, Ti 4+, Mn 4+, P 5+ and S 6+ have been sintered at 1500°C for 3 hr with a slow cooling and characterized by X-ray diffraction (XRD) and differential thermal analysis (DTA). It was found that the forming amount of the β phase depended on varieties of dopant ions and the composition stoichiometry in the samples. The results of XRD and DTA measurements indicated that the lattice parameters and phase transition temperatures of the samples also varied with the change of the variety of dopant ions and composition stoichiometry in the samples. Discussion is made on the stabilization mechanism of the doped β-C 2S on the basis of the experimental results.

Film-cooling-induced phase transitions in magnetic bubble lattices

A theoretical study of the transition taking place in magnetic bubble lattices (MBLs) on cooling the film has been performed. It is shown that, if the MBL was formed at room temperature, then, on cooling the film, spontaneous transitions occur from the initial MBL to a lattice with a larger domain period and diameter. The nature of these transitions is that of first-order phase transitions and they are accompanied by a change in the total number of domains in the specimen. The phase diagram or the MBL formed in thin bismuth-thulium garnet films is calculated; there is good agreement with experimental results.

Co implanted into al: Concentration dependence of the lattice site occupation and phase transition

Abstract The substitutional fraction, fs of Co implanted into Al single crystals depends on the substrate temperature and on the Co concentration. Implantation at 293 K reveals an anomalous increase of fs at low concentrations and reaches maximum fs values of 0.40 ± 0.04 for concentrations between 0.12 at.% and 0.4 at.% Co. At 77 K fs is 0.63 ± 0.04 for concentrations between 0.08 at.% and 1 at.% Co. The non-substitutional Co fraction, 1-fs is governed by Co-vacancy complexes which form within the collision cascade and by additional trapping of mobile vacancies at 293 K. The decrease of fs at high Co concentrations, which was observed for both the 77 K and the 293 K implants, is due to a transition into a disordered, probably amorphous phase. Implanting similar Co-concentrations, the disordered phase fraction is larger for 77 K implants.

Influence of substrate temperature on lattice strain field and phase transition in MeV oxygen ion implanted GaAs crystals

A detailed study of the influence of substrate temperature on the radiation-induced lattice strain field and crystalline-to-amorphous (c–a) phase transition in MeV oxygen ion implanted GaAs crystals has been made using channeling Rutherford backscattering spectroscopy, secondary ion mass spectrometry, and the x-ray rocking curve technique. A comparison has been made between the cases of room temperature (RT) and low temperature (LT) (about 100 K) implantation. A strong in situ dynamic annealing process is found in RT implantation at a moderate beam current, resulting in a uniform positive strain field in the implanted layer. LT implantation introduces a freeze-in effect which impedes the recombination and diffusion of initial radiation-created lattice damage and defects, and in turn drives more efficiently the c–a transition as well as strain saturation and relaxation. The results are interpreted with a spike damage model in which the defect production process is described in terms of the competition between defect generation by nuclear spikes and defect diffusion and recombination stimulated by electronic spikes. It is also suggested that the excess population of vacancies and their complexes is responsible for lattice spacing expansion in ion-implanted GaAs crystals.

Lattice Disordering, Phase Transition, and Substrate Temperature Effects in MeV-ION-Implanted III-V Compound Semiconductors

AbstractAn experimental study of lattice disordering, the crystalline-to-amorphous (c-a) phase transition, and substrate temperature effects in MeV-ion-implanted III-V compound semiconductor crystals is presented. A comparison has been made between the GaAs and InP systems, which have been implanted with 2 MeV oxygen ions at either room temperature (RT) or near liquid nitrogen temperature (LT). A strong in situ dynamic annealing has been found in the RT implanted GaAs, and the LT implanted GaAs exhibits heterogeneous (at the end-of-range of the ions) and homogeneous (at the subsurface region) c-a phase transitions. In InP crystals, in situ annealing is much less pronounced in RT implantation, and dose-dependent damage nucleation and layer-by-layer amorphization take place. LT implantation results in lattice disordering and phase transition with a critical dose at least one order lower than that for GaAs. The mechanisms and kinetics of lattice disordering by ion irradiation are also discussed.

Correlation Mechanism to Change Lattice Parameters and Phase Transitions in Compounds with Intermediate Valency

AbstractFor compounds with intermediate valency (IV) a microscopic mechanism of changing the parameters of crystal lattice depending on the impurity concentration (or pressure) and temperature is suggested. The mechanism is based on the exact account of the Coulomb correlation and hybridization between f‐ and d‐electrons. For that the “non‐Fröhlich” terms in the electron—phonon interaction proportional to the first and second derivatives of the Coulomb interactions and overlapping integrals of f‐ and d‐electrons are considered. These terms in the electron—phonon interaction contain an explicit dependence on the interatomic distance and cause additional (as compared to the termal) shifts of the lattice sites on account of the Coulomb correlations. The corresponding additions for the lattice parameter depend on the concentration of the impurities x (or pressure) and temperature T. The dependences of the lattice parameter on x and T are obtained for both, the semiconductor and metallic phase. The equation for the transition temperature into the state with IV and the existence condition of this state with concentration are obtained. A comparison of the dependences with experimental ones obtained on the basis of the correlation mechanism is made on the example of the solid solutions Sm1−xRS (R3+ is a rare earth element for instance Gd, Y etc.).

Phase Transition in Magnetic Bubble Lattices

A study is made of the temperature-induced phase transition in the magnetic bubble lattice (MBL) at which the MBL is decomposed into two coexistent phases, namely, blocks of a new lattice and stripe-domain areas. A thermodynnmic analysis of the process of formation of the stripe-domain nucleation centres is performed and the critical size of the nucleation centre is found. It is shown that if the film material characteristic length decreases with increasing tempernture the critical size of nucleation centre decreases and that at a certain temperature the MBL becomes unstable against the formation of two-phase structure. The dependence of the MBL thermal stability range on the bias field strength is obtained and the relative number of bubbles decomposed into stripes is found. A comparison with the experimcnt is made. [Russian Text Ignored].

Dynamic properties of blue-phase mixtures

Abstract The dynamics of electric-field-induced lattice distortions and phase transitions in the BPI, BPII and BPIII (fog) phases of blue-phase mixtures, which include low-molar-mass and/or polymeric components, have been studied. Several electric-field-induced effects have been observed in the blue phases, and the electro-optic characteristics of the driven and non-driven responses of each are considered. Anomalous behaviour in BPIII, where driven response times were measured to be slower than the relaxation responses, is described and considered with respect to relaxation processes previously observed in BPII. Finally, we present data for a mixture containing 40 per cent by weight of a side-chain-polymer liquid crystal. In this case only BPI was observed, and it appears that the increased viscosity had little effect on the response times of the system. These data are discussed.

Electric dipole interactions in molecular crystals

The importance of dipolar interactions is highlighted in a wide range of molecular crystal properties. Molecules respond via an effective polarizability (appropriate to the crystal phase) to a local field arising from the applied field and the fields of the surrounding induced dipoles, determined self-consistently. An exact treatment is possible for perfect crystals and crystals with localized imperfections, yielding the inverse dielectric function characterizing the crystal response. From this, results follow for the crystal linear and nonlinear dielectric response, for Coulomb exciton energies, and for the intensities of lattice vibrational spectra. A direct extension yields the polarization energy associated with the induced dipoles. This provides insight into the energetics of excess charge carriers in perfect and imperfect crystals and of charge-transfer excitons, into electronic Stark spectra, and into aspects of lattice dynamics and phase transitions.

Phase transition in Ising ferromagnetic lattices with fixed spins (abstract)

In this paper we report a study of the influence of the symmetry which characterizes the quenched defects (namely, 1/2 spins fixed either ‘‘up’’ or ‘‘down’’) distributions into the nature of the involved phase transitions. We have performed a Monte Carlo simulation involving L3 cubic lattices with L≤40 and, in order to conclude above the phase transition nature, a detailed finite size scaling analysis has been done. It is concluded that the transition remains second order with pure critical exponents for regularly spaced defects. Any small randomness in the location of the defects, however, makes the transition first order.

Laser Raman study of phase transitions in [N(CH3)4]2COCl4 single crystals

AbstractTemperature‐dependent Raman spectra of oriented single crystals of [N(CH3)4]2CoCl4 are reported. An assignment of the observed Raman bands has been made and it was found that the N(CH3)4+ and CoCl42− groups occupy sites of Cs symmetry in the lattice at room temperature. However, because of rapid reorientation, the CoCl42− groups retain an effective tetrahedral symmetry. The prototypic to incommensurate to commensurate phase transitions are associated with the orientational dynamics of the CoCl4 tetrahedra. The monoclinic to orthorhombic super lattice phase transition at 122 K in [N(CH3)4]2CoCl4 is triggered by the distortion of the N(CH3)4+ groups in the lattice.

Hydrogen in niobium-tantalum superlattices

We present x-ray scattering experiments showing that, in addition to providing a strained superlattice, H in Nb Ta superlattices can be modeled as a lattice gas in a modulated field. In addition, we find a coherent lattice gas-liquid phase transition where critical fluctuations having wavelengths shorter than the superlattice periodicity are suppressed.