Model Of Structural Phase Transitions Research Articles

Theoretical Model of Structural Phase Transitions in Al-Cu Solid Solutions under Dynamic Loading Using Machine Learning

Theoretical Model of Structural Phase Transitions in Al-Cu Solid Solutions under Dynamic Loading Using Machine Learning

On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

The critical specific heat capacity c of a d-dimensional model describing structural phase transitions in an anharmonic crystal with a long-range interaction (decreasing at large distances r as r −d−σ , 0 < σ ≤ 2) is studied near the classical critical point Tc . At temperatures T > Tc and for dimensions σ < d < 2σ (σ and 2σ are the lower and the upper critical dimensions, respectively) the critical specific heat capacity is obtained in the form c ≈ 1 − Dεαs , where D > 0 and αs < 0 depend only on the ratio d/σ, and ε = T/Tc −1 is a measure of the deviation from the critical point. For three fixed values of the ratio d/σ the dependence c ≈ c(ε) is graphically presented. It is shown that at all temperatures T ≤ Tc the specific heat capacity retains its maximum value, c max = 1. The critical exponent αs , obtained here, coincides with that of the known mean spherical model, while c max is different for the two models.

Probabilistic model of structural phase transition in perovskites

In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.

Влияние структурных свойств на электросопротивление тонких пленок Al/Ag в процессе твердофазной реакции

Based on the study of a solid-state reaction process in Al/Ag thin films (the atomic ratio being Al:Ag=1:3) carried out by in situ electron diffraction method and electrical resistivity measurements, the reaction initiation temperature has been determined and a model of structural phase transitions occurring during the solid-state reaction has been proposed. The solid-state reaction begins at 70°C with the formation of an Al-Ag solid solution at the interface of aluminum and silver nanolayers. It has been found that in the reaction process intermetallic compounds γ-Ag2Al =&gt; µ-Ag3Al are successively formed. It has been established that for the formation of the µ-Ag3Al phase in thin films (up to 100 nm) the following is necessary: first, significant excess of silver over aluminum in the atomic composition, second, the formation of the µ-Ag3Al phase begins only after all the FCC aluminum has reacted. The work was supported by the Russian Science Foundation (grant #18-13-00080).

Reply to comment on Couzi et al. (2018): a phenomenological model for structural phase transitions in incommensurate alkane/urea inclusion compounds.

In a recent paper (Couzi et al. 2018 R. Soc. open sci. 5, 180058. (doi:10.1098/rsos.180058)), we proposed a new phenomenological model to account for the I↔II↔“III” phase sequence in incommensurate n-alkane/urea inclusion compounds, which represents an alternative interpretation to that proposed in work of Toudic et al. In a Comment (Toudic et al. 2019 R. Soc. open sci. 6, 182073. (doi:10.1098/rsos.182073)), Toudic et al. have questioned our assignment of the superspace group of phase II of n-nonadecane/urea, which they have previously assigned, based on a (3 + 2)-dimensional superspace, as C2221(00γ)(10δ). In this Reply, we present new results from a comprehensive synchrotron single-crystal X-ray diffraction study of n-nonadecane/urea, involving measurements as a detailed function of temperature across the I↔II↔“III” phase transition sequence. Our results demonstrate conclusively that “main reflections” (h, k, l, 0) with h+k odd are observed in phase II of n-nonadecane/urea (including temperatures in phase II that are just below the transition from phase I to phase II), in full support of our assignment of the (3+1)-dimensional superspace group P212121(00γ) to phase II. As our phenomenological model is based on phase II and phase “III” of this incommensurate material having the same (3+1)-dimensional superspace group P212121(00γ), it follows that the new X-ray diffraction results are in full support of our phenomenological model.

A phenomenological model for structural phase transitions in incommensurate alkane/urea inclusion compounds

n-Alkane/urea inclusion compounds are crystalline materials in which n-alkane ‘guest’ molecules are located within parallel one-dimensional ‘host’ tunnels formed by a helical hydrogen-bonded arrangement of urea molecules. The periodic repeat distance of the guest molecules along the host tunnels is incommensurate with the periodic repeat distance of the host substructure. The structural properties of the high-temperature phase of these materials (phase I), which exist at ambient temperature, are described by a (3 + 1)-dimensional superspace. Recent publications have suggested that, in the prototypical incommensurate composite systems, n-nonadecane/urea and n-hexadecane/urea, two low-temperature phases II and ‘III’ exist and that one or both of these phases are described by a (3 + 2)-dimensional superspace. We present a phenomenological model based on symmetry considerations and developed in the frame of a pseudo-spin–phonon coupling mechanism, which accounts for the mechanisms responsible for the I ↔ II ↔ ‘III’ phase sequence. With reference to published experimental data, we demonstrate that, in all phases of these incommensurate materials, the structural properties are described by (3 + 1)-dimensional superspace groups. Around the temperature of the II ↔ ‘III’ transition, the macroscopic properties of the material are not actually associated with a phase transition, but instead represent a ‘crossover’ between two regimes involving different couplings between relevant order parameters.

A Phenomenological Model of Structural Phase Transitions in RbDy(Wo4)2

A phenomenological model of structural phase transitions in double rubidium–dysprosium tungstate is proposed. The model is constructed by equivariant catastrophe theory methods. The temperature dependence of the heat capacity near the phase transitions at temperatures T1 = 9 K and T2 = 4.9 K was calculated. Comparison with the experimental data shows a satisfactory qualitative agreement. In terms of the proposed model, the low-temperature phase transition can be interpreted as isomorphic.

On the quantum critical behaviour of a model of structural phase transitions with long-range interaction

The pure quantum limit of an exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction is considered. At the upper quantum critical dimension the free energy density at T = 0 in the neighbourhood of the quantum critical point is exactly calculated in terms of the Lambert W-function. For the three real physical dimensions, the exact results, obtained here, and the asymptotic ones are compared. It is pointed out that the Lambert W-function turns out to be a very effective tool for an exact computation of non-universal characteristics in the upper critical dimensions, especially in a broader neighbourhood of the critical region.

Magnetic and structural transitions in crystals with a structure of the NaCl type

A model of simultaneous magnetic and structural first-order transitions in antiferromagnets with a strong cubic magnetic anisotropy has been constructed on the basis of a synthesis of magnetic modified 6-state and 8-state Potts models and the theoretical model of structural phase transitions in cubic crystals. A revised scheme has been suggested for the derivation of possible magnetic structures in the fcc lattice with allowance for competing interactions between the nearest and next-nearest neighbors. A calculation of the temperature evolution of high-temperature diffuse magnetic scattering of neutrons has been carried out to show that the mechanism of a magnetic transition at the Neel point is caused by the transformation of diffuse magnetic scattering into magnetic Bragg peaks.

Intermediate States at Structural Phase Transition: Model with a One-Component Order Parameter Coupled to Strains

We study a Ginzburg–Landau model of structural phase transition in two dimensions, in which a single order parameter is coupled to the tetragonal and dilational strains. Such elastic coupling terms in the free energy much affect the phase transition behavior particularly near the tricriticality. A characteristic feature is appearance of intermediate states, where the ordered and disordered regions coexist on mesoscopic scales in nearly steady states in a temperature window. The window width increases with increasing the strength of the dilational coupling. It arises from freezing of phase ordering in inhomogeneous strains. No impurity mechanism is involved. We present a simple theory of the intermediate states to produce phase diagrams consistent with simulation results.

Transformation to soluble model for structural phase transition from (4 × 1) to (8 × “2”) of In-adsorbed Si(1 1 1) surface

The Ising model proposed previously for the structural phase transition from (4 × 1) to (8 × “2”) of In-adsorbed Si(1 1 1) surface, Hamiltonian of which is consisting of a two-spin interaction as well as a four-spin interaction is shown to be equivalent in thermodynamic properties to a soluble Ising model with two-spin interactions. Temperature dependence of the long range order and the transition temperature can now be determined from the exact formulae. Comparison between the simulation results and those from the exact formulae is made to see accuracy of the simulation.

Phase transitions in antiferromagnets with a NaCl structure

A revised derivation scheme of possible magnetic structures in an FCC lattice with the nearest- and next-nearest-neighbor interactions taken into account is proposed. A model of simultaneous magnetic and structural phase transitions of the first order is developed for antiferromagnets with a NaCl structure and with a strong cubic magnetic anisotropy on the base of synthesis of magnetic modified 6-state Potts model and theoretical models of structural phase transitions in cubic crystals. It is shown that the high-temperature diffuse magnetic scattering of neutrons transforms into magnetic Bragg reflections below Néel point.

Critical Properties of Weak Ferroelectric LGO Crystals Doped with Cr3+ Ions

Angular diagrams of Cr 3+ EPR spectra in Li 2 Ge 7 O 15 (LGO) crystals confirm that magnetic ions substitute for Ge 4+ and together with interstitial lithium ions form Cr 3+ −Li + paired centers. On approaching ferroelectric phase transition point EPR lines of Cr 3+ broaden and split below T C = 283.4 K. Temperature dependence of the local order parameter η(T) determined from EPR lines splitting, shows power like behavior with critical exponent β = 0.31 of three-dimensional Izing model. Results of previous investigations evidence that on going away from T C the crossover from fluctuation regime to classical mean field one is characteristic for macroscopic and local LGO properties. For dependence η(T) in LGO:Cr such crossover is not detected. Absence of the crossover to classical mean field behavior is attributed to the defect nature of Cr 3+ −Li + centers which weaken the order parameter correlations. Influence of Cr 3+ −Li + centers on LGO properties is discussed on the basis of microscopic model of structural phase transitions.

The influence of chromium impurity centers on the critical properties of a weakly polar ferroelectric Li2Ge7O15

The Cr3+ EPR spectra of Li2Ge7O15 (LGO) crystals are analyzed in the temperature range of the ferroelectric phase transition. The temperature dependence of the local order parameter is determined from the measured splittings of the EPR lines in the polar phase. The experimental critical exponent of the order parameter β=0.31 in the range from the phase transition temperature TC to (TC-T) ∼ 40 K corresponds to the critical exponent of the three-dimensional Ising model. Analysis of the available data demonstrates that, away from the phase transition temperature TC, the macroscopic and local properties of LGO crystals are characterized by a crossover from the fluctuation behavior to the classical behavior described in terms of the mean-field theory. The temperature dependence of the local order parameter for LGO: Cr crystals does not exhibit a crossover from the Ising behavior (β=0.31) to the classical behavior (β=0.5). This is explained by the defect nature of Cr3+ impurity centers, which weaken the spatial correlations in the LGO host crystal. The specific features of the critical properties of LGO: Cr3+ crystals are discussed within a microscopic model of structural phase transitions.

Percolation model for structural phase transitions inLi1−xHxIO3mixed crystals

A percolation model is proposed to explain the structural phase transitions found in Li$_{1-x}$H$_x$IO$_3$ mixed crystals as a function of the concentration parameter $x$. The percolation thresholds are obtained from Monte Carlo simulations on the specific lattices occupied by lithium atoms and hydrogen bonds. The theoretical results strongly suggest that percolating lithium vacancies and hydrogen bonds are indeed responsible for the solid solution observed in the experimental range $0.22 < x < 0.36$.

Long-time behavior for the full one-dimensional Frémond model for shape memory alloys

This note deals with a well-posed one-dimensional initial-boundary value problem related to the Fremond thermomechanical model of structural phase transitions in shape memory materials. The long-time behavior is investigated and it is proved that the omega-limit set in a suitable topology only contains stationary states.

A mean-field model for structural phase transitions based on ab initio band calculations

Abstract We study a microscopic model of the structural phase transition in ordered systems. Our model is based on the idea that, in anharmonic potentials, smali harmonie displacements can trigger first-order phase transitions. This model is in contrast with the older conjectures of phonon softening, since a complete softening of a phonon branch is no longer necessary. In order to model the smali harmonie displacements we introduce thermally induced fluctuations of the geometrical order parameters describing the respective transition. It is shown that such a fluctuation model justifies the original ad hoc assumption of a weakly temperature-dependent phonon frequency. To demonstrate the applicability of our model, we use total energy data derived from quantum-mechanical band-structure calculations for the bcc ↔ hcp transition in sodium. It is shown that our model successfully leads to a first-order phase transition without complete phonon softening.

A mean-field model for structural phase transitions based on ab initio band calculations

A mean-field model for structural phase transitions based on ab initio band calculations

The liquid-glass transition: a mode-coupling perspective

We review the dynamics of supercooled liquids approaching the liquid-glass transition, starting with the conventional generalized hydrodynamics formulation. Empirical models for the memory function are discussed, as are empirical models for the self-energy function for phonons in crystals. Two examples of microscopic analyses based on non-linear interactions are then described, the anharmonic lattice dynamics model for structural phase transitions, and Kawasaki's mode-mode-coupling approach for critical dynamics. We then review the mode-coupling theory of the liquid-glass transition, emphasizing its relation to generalized hydrodynamics with the memory function derived from a microscopic theory of non-linear interactions. We discuss the major predictions of this theory, particularly the asymptotic expansion results, which provide specific formulae for analysing experimental data.

Global solution to the full one‐dimensional Frémond model for shape memory alloys

AbstractIn this paper, we prove the existence and uniqueness of the solution to the one‐dimensional initial‐boundary value problem resulting from the Frémond thermomechanical model of structural phase transitions in shape memory materials. In this model, the free energy is assumed to depend on temperature, macroscopic deformation and phase fractions. The resulting equilibrium equations are the balance laws of (linear) momentum and energy, coupled with an evolution variational inequality for the phase fractions. Fourth‐order regularizing terms in the quasi‐stationary momentum balance equation are not necessary, and, as far as we know for the first time, all the non‐linear terms of the energy balance equation are taken into account.