Modelling of a displacive transformation in two-dimensional system within four-body approximation of Continuous Displacement Cluster Variation Method

Following our previous study on distorted to non-distorted displacive phase transformation in the two-dimensional square lattice based on the continuous displacement cluster variation method (CDCVM) within the Bragg–Williams (BW) approximation, we performed a higher order approximation, four-body approximation, in the entropy term and compared the results obtained by the two approximations. The transformation temperature decreases with the higher order approximation, which shares the common feature with conventional CVM studies on replacive transformations. The present study predicts the first-order transformation, which is markedly different from the previous study based on the BW approximation. Furthermore, by employing the four-body approximation, we are able to reproduce the o-type distribution of displaced atoms around a Bravais lattice point by changing the atomic interaction energy, which was by no means possible by the BW approximation.     

Ab initio study on the formation of chemically ordered Zr2Al phase by coupled replacive–displacive transformation

We performed plane wave-based first principles calculations using the projector augmented wave (PAW) potential under the generalized gradient approximation (GGA) within the density functional theory to study the formation of ordered omega (B8₂-structured) Zr₂Al phase in β-Zr₃Al alloy. The transformation involves both replacive and displacive processes. We investigated two possible paths for the transformation where steps involving replacive (diffusive) and displacive processes occur in succession with their sequence of occurrence being different in the two paths. From this study, it was possible to show that the initial chemical ordering facilitates the displacive process leading to the transformation. It was also possible to correlate instability with respect to omega-type displacements in Zr₂Al alloy with the number of Zr–Al bonds present in the unit cell. Electronic structure analysis indicated that stronger Zr–Al bonding plays an important role in the formation of chemically ordered omega phase.     

Kinetics of monolayer growth

The kinetics of a monolayer growth is studied using the two-dimensional lattice gas model by means of the path-probability method (PPM) for nonequilibrium phenomena. Kinetic equations for the combined processes of relaxation (adsorption and desorption) and diffusion are derived analytically and solved for the first time in the square approximation of the PPM. Comparison of the square approximation with the point and pair approximations along with Monte Carlo simulation shows the effect of using a larger basic cluster than in the previous studies. When the square approximation is used, the growth rate results are much improved in both cases with and without diffusion and agree well with the Monte Carlo simulations results, except for very small values of the driving forceL=/k _b T where is the chemical potential difference between the vapor and the solid phase. In the range where the agreement is good, there exists a region where the growth rateR is proportional to exp(–c/L with a constantc. This is the feature which is characteristic of two-dimensional nucleation-limited growth.     

Oxygen-vacancy ordering in the YBa2Cu3Oz basal plane studied by the cluster variation method

The cluster variation method is used to calculate a phase diagram for a two-dimensional Ising model representing the Cu₂O plane of the high-T _c superconductor YBa₂Cu₃O_z. Both first (V ₁ and second-neighbor (V ₂) interactions are considered, withV ₂/V ₁= –1/2; At high temperatures, the transition from the disordered (tetragonal) to the ordered (orthorhombic) phase is second-order. A tricritical point is found below which phase separation occurs. Fractional site occupancy and second-neighbor pair correlations are calculated as a function of temperature. The relevance of the model to the thermodynamics of ordering in the high-T _c compound is discussed.     

Crystallographic variant selection of martensite at high stress/strain

The phenomenological theory of martensitic transformation is well understood that the displacive phase transformations are mainly influenced by the externally applied stress. Martensitic transformation occurs with 24 possible Kurdjomov-Sachs (K-S) variants, where each variant shows a distinct lattice orientation. The elegant transformation texture model of Kundu and Bhadeshia for crystallographic variant selection of martensite in metastable austenite at various stress/strain levels has been assessed in this present research. The corresponding interaction energies have also been evaluated. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed at different stress/strain levels. It has been investigated that the mechanical driving force alone is able to explain the observed martensite microtextures at all stress/strain levels under uniaxial tensile deformation of metastable austenite under low temperature at a slow strain rate. The present investigation also proves that the Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.     

Pressure-induced crossover between diffusive and displacive mechanisms of phase transitions in single-crystalline alpha-GeO2

We present the first example of the phase transition occurring via the different kinetic mechanisms, displacive or diffusive, competing with each other in quartz-like alpha-GeO2 single crystals. Upon room-pressure heating, alpha-GeO2 transforms to the rutile-type phase (the alpha-->r transition) via the diffusive mechanism. With increase of the treatment pressure the diffusive mode of the temperature-induced alpha-->r transition is substituted at approximately 4 GPa by a displacive-like mode, and then at approximately 6 GPa the transition type changes from the alpha-->r sequence to a displacive martensitic-like transition to a distorted rutile-like phase (alpha-->r'. A crossover between diffusive and displacive transition modes suggests a new way to control the meso- and nanometer-scale morphology of high-pressure phases.     

The Rhodes-Wohlfarth parameter as assessment of the displacive degree in ferroelectrics: The case of the Ф4> model

The Rhodes-Wohlfarth parameter extended to ferroelectrics by Tokunaga [J. Phys. Soc. Jap. 57, 4275 (1988)] is here analyzed within the model. It is shown that it can be directly related with the displacive degree of the transition as described by the ratio C / E ₀ , between the non-local coupling, C, driving the transition and the depth of the energy well, E₀, associated with the distorted structure. However, the Rhodes-Wohlfarth parameter becomes asymptotically constant as C / E ₀ decreases, i.e. for systems closer to the order disorder limit. Under this viewpoint, the very limited range of values observed for this experimental parameter is explained and is shown that, in general, it can only assess quantitatively the character of the transition in rather displacive cases. The argument can be generalized to more complex systems, and when applied to well known materials, a rough estimation of the displacive degree and the relevant microscopic energetic parameters in rather displacive ferroelectrics is possible. Received 23 December 1998 and Received in final form 4 May 1999     

First-order character of the displacive structural transition in BaWO4

Nearly all displacive transitions have been considered to be continuous or second order, and the rigid unit mode （RUM） provides a natural candidate for the soft mode. However, in-situ X-ray diffraction and Raman measurements show clearly the first-order evidences for the scheelite-to-fergusonite displacive transition in SaWO4： a 1.6% volume collapse, coexistence of phases, and hysteresis on release of pressure. Such first-order signatures are found to be the same as the soft modes in BaWO4, which indicates the scheelite-to-fergusonite displacive phase transition hides a deeper physical mechanism. By the refinement of atomic displacement parameters, we further show that the first-order character of this phase transition stems from a coupling of large compression of soft BaOs polyhedrons to the small displacive distortion of rigid WO4 tetrahedrons. Such a coupling will lead to a deeper physical insight in the phase transition of the common scheelite-structured compounds.     

Twin walls in anorthoclase are enriched in alkali and depleted in Ca and Al

Abstract

Composition profiles have been measured in transformation twin walls of the albite type in anorthoclase. Regions close to the walls between two twin domains are enriched in K and Na and depleted in Ca and Al. Microanalysis experiments show high mobility of alkali cations close to twin boundaries. Twin walls are generated via the displacive phase transition C2/m?C[lbar] in Al, Si disordered feldspar, and the chemical heterogeneity is a fingerprint for the subsequent diffusion of alkali and earth alkali ions during the cooling history of the sample.     

Martensitic transition in single-crystalline α-GeO2 at compression

We present a structural study of single crystalline quartz-like α-GeO₂ compressed to pressures up to 12 GPa and subsequently quenched to ambient conditions. The transition to a new crystalline phase with a distorted rutile structure, occurring in the pressure interval 8 to 12 GPa, was established. The structure of the new phase was identified from X-ray and electron diffraction data as P2₁/c monoclinic. Electron transmission and scanning microscopy provide direct evidence of the martensitic (or displacive) nature of the transition, indicating, in particular, the lamellar morphology and crystallographic orientation relation between the initial α-quartz and final new monoclinic phases. Upon heating, the new monoclinic phase transforms to the rutile-type structure with a similar (and similarly oriented) oxygen structure motif. Finally, we discuss the difference in high-pressure behavior of single-crystalline and polycrystalline samples transforming to the new crystalline and amorphous phases, respectively.     

Dynamics of a locally distorted impurity in a host crystal with displacive phase transition

We study the dynamic behaviour of a soft displacive impurity in a host crystal undergoing a displacive phase transition. The impurity-induced localized mode and the dynamic autocorrelation function of the impurity below the local freezing temperature are investigated in mean-field approximation (MFA). Furthermore, we give a physical interpretation of the MFA result of the local freezing-out, and discuss the fluctuation behaviour of various types of impurities in relation to recent experiments.     

Phase transitions and dynamic effects in crystals characterized by single-cell potentials with a multi-well excited state

A study has been made of phase transitions and phase states in crystals whose unit cell potentials have a multi-well excited state. New phase states compared to the conventional order-disorder-type phase-transition models have been revealed. A phase diagram has been constructed. The applicability criteria of the mean field approximation employed are analyzed. A region of parameter variation where the system is close to the tricritical point has been found. It is shown that microdomains of the new phase can efficiently transfer to the original phase within this region, and vice versa, by resonant tunneling. This tunneling has a relaxational nature. Interaction of such a relaxor with an oscillator (the soft mode) creates in this system an efficient mechanism of formation of the central peak. Besides, this model includes a possibility of coexistence of the order-disorder-type and displacive behavior. This coexistence manifests itself, in particular, in an induced phase transition associated with interaction of the order-disorder-type soft mode with the displacive mode for oscillations in the same potential wells. This induced phase transition may serve as a microscopic model of the improper ferroelastic phase transition in the Hg₂Cl₂ model system. This transition may produce a long-range incommensurate phase involving formation of the corresponding domain system, which is likewise in agreement with the case of Hg₂Cl₂. The model developed here can be used also in describing phase transitions in oxygen-octahedron perovskites, where the relative low-symmetry minima of the single-cell potentials can be related to the charge-transfer vibronic excitons. Fiz. Tverd. Tela (St. Petersburg) 39, 547–556 (March 1997)     

Hard mode Raman spectroscopy and its application to ferroelastic and ferroelectric phase transitions

The application of Raman spectroscopy for the investigation of phase transitions focused traditionally on the observation of soft modes in displacive systems. The present furthergoing study on displacive and order-disorder systems is based on the observation of systematic changes of the scattering profiles of hard modes during the phase transition. It reveals the temperature evolution of the order parameters, the role of order-parameter fluctuations and phonon density of states effects in model systems like improper ferroelastic Pb₃(P_1-x As _x O₄)₂, lead diluted ferroelastic (Pb_1-x Ba _x )₃(PO₄)₂, pure ferroelastic As₂O₅ and the relaxor ferroelectric Pb(Sc_0.5Ta_0.5)O₃. Allied with supplementary experimental techniques hard-mode Raman spectroscopy (HMRS) is an ideal method for the investigation of order-parameter coupling effects and the characterization of structural phase transitions.     

The behaviour of an isolated impurity near a phase transition in a spherical-like model

The behaviour of an isolated impurity in a crystal undergoing a displacive phase transition is investigated in an exactly soluble spherical-like model. We find, depending on the parameter of the impurity, either a global phase transition at the bulkT _c or a freezing-out of local order at a temperatureT _c ^loc >T _c driven by a soft local mode. We furthermore discuss the dynamic autocorrelation function of the impurity by introducing a phenomenological damping.Work Supported by The Swiss National Science Foundation     

Investigation on bainite transformation and metastable omega/orthorhombic martensite phases in as-quenched Cu-bearing ferrite steel

Abstract

The as-quenched microstructures of low-carbon Cu-bearing ferrite steel are investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It is found that the granular bainite formation in Cu-bearing ferrite steel is attributed to a mixed mode of diffusional and displacive mechanisms. Besides, the particle-like or plate-shaped ω phases, along with thin-plate martensites consist of twin, are observed in the Mn1.4Cu-bearing steel, and the orientation relationship is determined as: [2 ?1 ?10]_ω // [0 1 1]_α and (0 1 ?1 0)_ω // (2 ?1 1)_α. The ultra-fine or ellipsoidal shaped nanoscale orthorhombic martensite phases, along with laths martensites consist of a high density of dislocations, are observed in the Mn0.66Cu-bearing steel, and the orientation relationship is determined as: [0 1 ?1]o//[?1 1 1]α and (?1 1 1)o//(1 0 1) α. A model is proposed to describe the overall martensite transformation kinetics by taking into account the Mn content, heterogeneity of C content and dislocation reactions play a major role in the subsequent martensite transformation.     

Amorphous boron nitride at high pressure

The pressure-induced phase transformation in hexagonal boron nitrite and amorphous boron nitrite is studied using ab initio molecular dynamics simulations. The hexagonal-to-wurtzite phase transformation is successfully reproduced in the simulation with a transformation mechanism similar to one suggested in experiment. Amorphous boron nitrite, on the other hand, gradually transforms to a high-density amorphous phase with the application of pressure. This phase transformation is irreversible because a densified amorphous state having both sp³ and sp² bonds is recovered upon pressure release. The high-density amorphous state mainly consists of sp³ bonds and its local structure is quite similar to recently proposed intermediate boron nitrite phases, in particular tetragonal structure (P4₂/mnm), rather than the known the wurtzite or cubic boron nitrite due to the existence of four membered rings and edge sharing connectivity. On the basis of this finding we propose that amorphous boron nitrite might be best candidate as a starting structure to synthesize the intermediate phase(s) at high pressure and temperature (probably below 800 °C) conditions.     

铁冲击相变的分子动力学研究

用分子动力学方法模拟了单晶铁(Fe)在一定初始温度下冲击相变(α相→ε相)的微观过程，结果显示温度会导致冲击相变压力阈值降低.基于此微观过程，对加卸载波系的传播规律进行了相应计算和分析，结果表明在卸载过程中逆相变波(ε相→α相)相对于波前以当地纵波声速传播，而相对波后以亚声速传播，这可由卸载压力-密度曲线给出相应解释；计算了不同初态的卸载压力-密度状态曲线，并给出了逆相变带的分布，其分布规律显示了卸载过程逆相变的滞后现象. 关键词： 分子动力学 多体势 冲击波 相变     

High-purity Zirconium under Niobium ion implantation: possibility of a dynamic precipitation?

High-purity (6N purity) Zirconium was subjected to different Niobium ion (Nb⁺) fluences in a particle accelerator. Grazing incidence X-ray diffraction confirmed subsurface phase transformation. While an approximate scaling was noted between Nb⁺ fluence and quantum of phase transformation, the sample subjected to the highest ion irradiation also showed significant subsurface shear residual stresses (τ₁₃). Molecular dynamics simulations, considering momentum transfer, revealed a drop in τ₁₃ beyond a critical displacements per atom or Nb⁺ fluence. High-resolution cross-sectional transmission electron microscopy (HRXTEM) confirmed formation of bcc (body-centred cubic) β phase and also linked τ₁₃ with such transformation. HRXTEM revealed, at about 100 nm depth, presence of 10–15% β with 2–15 nm size. The β particles and the surrounding α also had significant microscopic shear strains. The dynamic nature of the Nb implantation is expected to create fluctuations in temperature, Nb concentration and relative lattice damage. Such fluctuation, on the other hand, is/was hypothesized to dynamically alter the critical nuclei size: a clear possibility of ‘dynamic precipitation’.     

Antiferroelectric and ferroelectric phase transitions of the displacive and order-disorder type in PbZrO3 and PbZr1-xTi x O3 single crystals

For PbZrO₃ and PbZr_0.99Ti_0.01O₃ single crystals the first order Raman light scattering spectra in the paraelectric phase have been analysed. In lead zirconate two kinds of crystals, with and without a transient phase, were investigated. It was found that temperature dependence of the defect-induced soft mode frequency in the paraelectric phase has a negligible contribution to the low-frequency dielectric response. From the point of view of strong dielectric relaxation in the range of 10⁶–10⁹ Hz, which originates in a disorder of the lead sites, crossover of the order-disorder and displacive type of antiferroelectric phase transition in lead zirconate is considered: the phase transition mechanism is neither purely displacive nor order-disorder. Contribution of physical phenomena responsible for the ε(ω,T) dielectric response at low frequencies of an external electric field are described.