Diffusionless Phase Transitions Research Articles

Active learning-based automated construction of Hamiltonian for structural phase transitions: A case study on BaTiO3.

The effective Hamiltonians have been widely applied to simulate the phase transitions in polarizable materials, with coefficients obtained by fitting to accurate first-principles calculations. However, it is tedious to generate distorted structures with symmetry constraints, in particular when high-ordered terms are considered. In this work, we implement and apply a Bayesian optimization-based approach to sample the potential energy surface, automating the Hamiltonian construction by selecting&#xD;distorted structures via active learning. Taking BaTiO3 (BTO) as an example, we demonstrate that the Hamiltonian can be obtained using fewer than 30 distorted structures. Follow-up Monte Carlo simulations can reproduce the structural phase&#xD;transition temperatures of BTO, comparable to experimental values with an error < 10%. Our approach can be straightforwardly applied on other polarizable materials and paves the way for quantitative atomistic modelling of diffusionless phase transitions.

Multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts

The problem of constructing the multilevel physical model of inelastic deformation in steels allowing to take into consideration diffusionless solid-state phase (martensitic) transitions is considered. The model structure includes three scale levels with the closed system of equations offered for them. Explicit internal variables reflecting the evolution of the material structure (both the defect structure and the grain one) are introduced at the lower scale levels of the model. The distinctive feature of the developed model is consideration of the lower scale level in such a way that a homogeneous element of this level completely turns into a new phase at a high speed (relative to the kinematic quasi-static loading), that is close to the speed of sound in the crystal medium. Based on the principles of classical thermodynamics the phase transformation criterion is written. According to this criterion, the choice of a transformational system under the martensitic transition is made. The algorithm of the model is developed and its realization features are described in connection with the high-rate restructuring of the face-centered cubic lattice to the body-centered tetragonal one. The result of this restructuring is a severe change in the physic-mechanical properties of the material.

A new high-pressure form of Mg2SiO4 highlighting diffusionless phase transitions of olivine

High-pressure polymorphism of olivine (α-phase of Mg2SiO4) is of particular interest for geophysicists aiming to understand the structure and dynamics of the Earth’s interior because of olivine’s prominent abundance in the upper mantle. Therefore, natural and synthetic olivine polymorphs have been actively studied in the past half century. Here, we report a new high-pressure polymorph, the ε*-phase, which was discovered in a heavily shocked meteorite. It occurs as nanoscale lamellae and has a topotaxial relationship with the host ringwoodite (γ-phase of Mg2SiO4). Olivine in the host rock entrapped in a shock-induced melt vein initially transformed into polycrystalline ringwoodite through a nucleation and growth mechanism. The ringwoodite grains then coherently converted into the ε*-phase by shear transformation during subsequent pressure release. This intermediate metastable phase can be formed by all Mg2SiO4 polymorphs via a shear transformation mechanism. Here, we propose high-pressure transformations of olivine that are enhanced by diffusionless processes, not only in shocked meteorites but also in thick and cold lithosphere subducting into the deep Earth.

Shape-driven solid–solid transitions in colloids

Solid-solid phase transitions are the most ubiquitous in nature, and many technologies rely on them. However, studying them in detail is difficult because of the extreme conditions (high pressure/temperature) under which many such transitions occur and the high-resolution equipment needed to capture the intermediate states of the transformations. These difficulties mean that basic questions remain unanswered, such as whether so-called diffusionless solid-solid transitions, which have only local particle rearrangement, require thermal activation. Here, we introduce a family of minimal model systems that exhibits solid-solid phase transitions that are driven by changes in the shape of colloidal particles. By using particle shape as the control variable, we entropically reshape the coordination polyhedra of the particles in the system, a change that occurs indirectly in atomic solid-solid phase transitions via changes in temperature, pressure, or density. We carry out a detailed investigation of the thermodynamics of a series of isochoric, diffusionless solid-solid phase transitions within a single shape family and find both transitions that require thermal activation or are "discontinuous" and transitions that occur without thermal activation or are "continuous." In the discontinuous case, we find that sufficiently large shape changes can drive reconfiguration on timescales comparable with those for self-assembly and without an intermediate fluid phase, and in the continuous case, solid-solid reconfiguration happens on shorter timescales than self-assembly, providing guidance for developing means of generating reconfigurable colloidal materials.

Toward Design Principles for Diffusionless Transformations: The Frustrated Formation of Co-Co Bonds in a Low-Temperature Polymorph of GdCoSi2.

Diffusionless (or displacive) phase transitions allow inorganic materials to show exquisite responsiveness to external stimuli, as is illustrated vividly by the superelasticity, shape memory, and magnetocaloric effects exhibited by martensitic materials. In this Article, we present a new diffusionless transition in the compound GdCoSi2, whose origin in frustrated bonding points toward generalizable design principles for these transformations. We first describe the synthesis of GdCoSi2 and the determination of its structure using single crystal X-ray diffraction. While previous studies based on powder X-ray diffraction assigned this compound to the simple CeNi1-xSi2 structure type (space group Cmcm), our structure solution reveals a superstructure variant (space group Pbcm) in which the Co sublattice is distorted to create zigzag chains of Co atoms. DFT-calibrated Hückel calculations, coupled with a reversed approximation Molecular Orbital (raMO) analysis, trace this superstructure to the use of Co-Co isolobal bonds to complete filled 18 electron configurations on the Co atoms, in accordance with the 18-n rule. The formation of these Co-Co bonds is partially impeded, however, by a small degree of electron transfer from Si-based electronic states to those with Co-Co σ* character. The incomplete success of Co-Co bond creation suggests that these interactions are relatively weak, opening the possibility of them being overcome by thermal energy at elevated temperatures. In fact, high-temperature powder and single crystal X-ray diffraction data, as well as differential scanning calorimetry, indicate that a reversible Pbcm to Cmcm transition occurs at about 380 K. This transition is diffusionless, and the available data point toward it being first-order. We expect that similar cases of frustrated interactions could be staged in other rare earth-transition metal-main group phases, providing a potentially rich source of compounds exhibiting diffusionless transformations and the unique properties these transitions mediate.

Phase Transition at High Heating Rate and Strain Rate During Maraging Steel C250 Grinding

In this study, maraging steel kinetics of both diffusion-controlled and diffusionless phase transitions under thermo-mechanical conditions was predicted using a physics-based model via the investigation of heating rate, stain rate, and contact zone temperature during grinding. It was assumed that high heating rate and high strain rate will affect phase transition. The theory of phase transition nucleation was combined with analysis of heating rate, stain rate, and contact zone temperature to predict phase transition during the grinding. The effects of heating rate and strain rate on phase transition were verified through maraging steel grinding experiments, X-ray diffractometry, and regression analyses. The results of post-grinding phase volume fractions of martensite and ferrite were compared with the results predicted from the neural network model, and models without consideration of heating rate or strain rate. Validation tests proved that the proposed physics-based model successfully predicted the occurrence and extent of phase transition associated with heating rate and strain rate. This physics-based model can be used to reduce phase transition during grinding of maraging steel, or to cause a predefined phase transition by controlling the thermo-mechanical loading.

Incommensurateness in nanotwinning models of modulated martensites

Martensites, which are the product of diffusionless phase transitions, can form phases with small periodic modulations of crystalline atomic lattice positions. Experiments have shown both that the modulation function is smooth and that when more than one modulation is present they can be incommensurate. These observations have appeared to be inconsistent with nanotwinning models. Here the authors show theoretically that in the case of the ferromagnetic shape memory alloy NiMnGa, the presence of two competing mechanisms favoring different commensurate periodic structures, a result of the interaction between different minima in the energy landscape, can lead to effective smooth incommensurate modulations consistent with nanotwinning models.

The Finite Difference Method for Two Models of Phase Transitions Driven by Configurational Force

In this paper, we study the finite difference solutions for two new models of phase transitions driven by configurational force. These models are recently proposed by Alber and Zhu in [2]. The first model describes the diffusionless phase transitions of solid materials, e.g., Steel. The second model describes phase transitions due to interface motion by interface diffusion, e.g., Sintering. We consider both the order-parameter-conserved case and the non-conserved one, under suitable assumptions. Also we compare the results of these two models with the corresponding ones for the Allen-Cahn and Cahn-Hilliard equations. Finally, some results about tending to zero are given.

Structural phase transitions during high-energy ball milling of BaTiO3

Microstructural characterization of ball milled perovskite BaTiO3 powders has been done by the modeling of X-ray diffraction profiles. The study reveals that on size reduction, BaTiO3 powders undergo a continuous, displacive, and diffusionless dynamic phase transitions involving tetragonal (T), monoclinic (M), and orthorhombic (O) symmetry via the second-order type [T → (T + M) → (M + O) → O] when stimulated by a high-power pulse of pressure in a planetary mill. The order parameter, a phenomenological quantity to describe the general behavior of a system going through phase transitions has been estimated using spontaneous strain calculated from lattice parameters or physical distortions derived from atomic coordinates or both. At room temperature, BaTiO3 nanoparticle achieved an orthorhombic phase when a critical size (<15 nm) has been reached at later stage of milling (≥70 h). Raman's study reveals similar structural phase transitions sequence on size reduction and TEM study reveals the corresponding particle diameter.

Exact Traveling Wave Solutions to a Model for Solid-Solid Phase Transitions Driven by Configurational Forces

This paper studies the exact traveling wave solutions to a model for solid-solid phase transitions driven by configurational forces. The model consists of the partial differential equations of linear elasticity coupled to a quasilinear nonuniformly parabolic equation of second order, which describes the diffusionless phase transitions of solid materials. By using the hyperbolic tangent function expansion method and homogeneous balance method, some exact traveling wave solutions, including solitary wave solutions are obtained for the phase transitions model in one space dimension.

Modulated martensite: why it forms and why it deforms easily

Diffusionless phase transitions are at the core of the multifunctionality of (magnetic) shape memory alloys, ferroelectrics and multiferroics. Giant strain effects under external fields are obtained in low symmetric modulated martensitic phases. We outline the origin of modulated phases, their connection with tetragonal martensite and consequences owing to their functional properties by analysing the martensitic microstructure of epitaxial Ni–Mn–Ga films from the atomic to the macroscale. Geometrical constraints at an austenite–martensite phase boundary act down to the atomic scale. Hence, a martensitic microstructure of nanotwinned tetragonal martensite can form. Coarsening of twin variants can reduce twin boundary energy, a process we could observe from the atomic to the millimetre scale. Coarsening is a fractal process, proceeding in discrete steps by doubling twin periodicity. The collective defect energy results in a substantial hysteresis, which allows the retention of modulated martensite as a metastable phase at room temperature. In this metastable state, elastic energy is released by the formation of a ‘twins within twins’ microstructure that can be observed from the nanometre to the millimetre scale. This hierarchical twinning results in mesoscopic twin boundaries. Our analysis indicates that mesoscopic boundaries are broad and diffuse, in contrast to the common atomically sharp twin boundaries of tetragonal martensite. We suggest that the observed extraordinarily high mobility of such mesoscopic twin boundaries originates from their diffuse nature that renders pinning by atomistic point defects ineffective.

Simulation of structural phase transitions in NiTi

By means of molecular-dynamics simulations, temperature driven diffusionless structural phase transitions in equi- and nearly equiatomic ordered nickel-titanium alloys were investigated. For this purpose, a model potential from the literature was adopted [W.S. Lai and B.X. Liu, J. Phys. Condens. Matter 12, L53 (2000)], which is based on the tight-binding model in second moment approximation. The model predicts a stable B19' phase at low temperatures and a nearly cubic B2 phase at high temperatures. After an analysis of crystallography and energetics of the emerging structures, the experimentally known strong dependence of transition temperatures on composition is confirmed and related to lattice instability. Free energy calculations finally give insight into the driving forces of the phase transitions, and reveal free energy barriers inhibiting them below the transition temperatures.

Traveling waves for models of phase transitions of solids driven by configurational forces

This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transitions of solid materials, e.g., Steel, and phase transitions due to interface motion by interface diffusion, e.g., Sintering. These models were proposed by Alber and Zhu in [3]. We consider both the order-parameter-conserved case and the non-conserved one, under suitable assumptions. Also we compare our results with the corresponding ones for the Allen-Cahn and the Cahn-Hilliard equations coupled with linear elasticity, which are models for diffusion-dominated phase transitions in elastic solids.

A General Method of Solution for the Cluster Variation Method in Ionic Solids, with Application to Diffusionless Transitions in Yttria-Stabilized Zirconia

A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.

Non-entropic and reversible long-range deformation of an encapsulating bioelastomer

Encapsulation is a widespread biological process particularly in the formation of protective egg cases of oviparous animals. The egg capsule wall of the channelled whelk Busycon canaliculum is an effective shock absorber with high reversible extensibility and a stiffness that changes significantly during extension. Here we show that post-stretch recovery in egg capsules is not driven by entropic forces as it is in rubber. Indeed, at fixed strain, force decreases linearly with increasing temperature, whereas in rubber elasticity the force increases. Instead, capsule wall recovery is associated with the internal energy arising from the facile and reversible structural alpha-helix <--> beta-sheet transition of egg capsule proteins during extension. This behaviour is extraordinary in the magnitude of energy dissipated and speed of recovery and is reminiscent of strain-induced crystallization in some polymeric fibres and of superelastic deformations associated with diffusionless phase transitions in shape-memory alloys.

On Landau theory and symmetric energy landscapes for phase transitions

The aim of this presentation is the development of a general approach for modelling the global complex energy landscapes of phase transitions. For the sake of clarity and brevity the exposition is restricted to martensitic phase transition (i.e., diffusionless phase transitions in crystalline solids). The methods, however, are more broadly applicable. Explicit energy functions are derived for the cubic-to-tetragonal phase transition, where data are fitted for InTl. Another example is given for the cubic-to-monoclinic transition in CuZnAl. The resulting energies are defined globally, in a piecewise manner. We use splines that are twice continuously differentiable to ensure sufficient smoothness. The modular (piecewise) technique advocated here allows for modelling elastic moduli, energy barriers and other characteristics independent of each other.

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

A constitutive model for diffusionless phase transitions in elastoplastic materials undergoing large deformations is developed. The model takes basic thermodynamic relations as its starting point and the phase transition is treated through an internal variable (the phase fractions) approach. The usual yield potential is used together with a transformation potential to describe the evolution of the new phase. A numerical implementation of the model is presented, along with the derivation of a consistent algorithmic tangent modulus. Simulations based on the presented model are shown to agree well with experimental findings. The proposed model provides a robust tool suitable for large-scale simulations of phase transformations in austenitic steels undergoing extensive deformations, as is demonstrated in simulations of the necking of a bar under tensile loading and also in simulations of a cup deep-drawing process.

The neutron structural analysis in studies of diffusionless phase transitions in shape memory alloys

The characteristics of alloys with the shape memory effect are presented. The physical nature of the process of a change in the shape is examined. The structure of the high-manganese alloys of Mn-Cu system with shape memory is described. The role of neutron analysis in studies of structural transformations in Mn-Cu alloys is shown. On the basis of the results of measuring the temperature dependences of internal friction in the magnetic fields of different magnetizing force, the presence of the magnetic contribution to the pretransition anomalies in Mn-Cu alloys is assumed. The prospects of applying the neutron analysis in studies of alloys with the shape memory generally and, in particularly, in the Mn-Cu alloys are shown.

The crystal structure of disordered (Zr,Ti)O2 solid solution including srilankite: evolution towards tetragonal ZrO2 with increasing Zr

Crystal structure data are presented for seven synthetic samples of disordered zirconium-titanate solid solution (Zr,Ti)O2, ranging in composition from x Ti=0.43 to 0.67, thus covering compounds such as ZrTiO4, Zr5Ti7O24, and ZrTi2O6 (srilankite). The compounds, synthesized at high temperatures and various pressures in their respective stability fields, are well crystallized and of homogeneous composition. The resulting structure data are less scattered compared to previous studies that were based on compounds synthesized metastably at low temperatures and room pressure. The compounds have the structure of scrutinyite (α-PbO2) with space group Pbcn, Z=4, unit cell parameters a=4.8495(3) A, b=5.4635(3) A, c=5.0462(3) A at x Ti=0.425 to a=4.7112(2) A, b=5.4944(1) A, c=4.9962(1) A at x Ti=0.666. The first structure refinement of pure, synthetic srilankite is presented, which is in good agreement with that of the natural counterpart. Structural trends observed in disordered zirconium-titanate solid solution along the binary join ZrO2–TiO2 are relatively smooth and continuous, except for rapid lengthening of an unshared octahedral edge which is anomalously short in scrutinyite-structure TiO2. The shortness of this edge may explain the observed instability of this structure with the relatively small Ti as the dominant cation. With increasing Zr content, the average cation position moves off-centre inside the octahedron, away from two shared edges, which permits the 12 closest cation–cation distances in the structure to become more equal. The shortening of the b dimension with increasing amount of the larger cation Zr decreases the distance between octahedral Zr and two additional oxygens in an adjacent chain of edge-sharing octahedra, implying that the Zr environment is evolving towards eightfold coordination. If the two additional oxygens are considered as part of the Zr coordination polyhedron, the bonding topology of tetragonal zirconia is obtained. The compositional evolution of the cell parameters, Zr atomic coordinates and Zr coordination environment is consistent with the idea that the structure is evolving towards that of tetragonal ZrO2. Group-theoretical relationships between scrutinyite, tetragonal zirconia, baddeleyite and fluorite structures show that the sequence of structures fluorite > tetragonal zirconia > scrutinyite > baddeleyite are all related by potentially diffusionless phase transitions driven by wavelike displacements of the oxygen substructure. The scrutinyite and tetragonal structures can act outside their stability fields as “transition states” between the structures on either side.

Dynamics and statics of interphase and domain boundaries at diffusionless phase transitions

We consider the interface dynamics of diffusionless first-order phase transitions in the case of an arbitrary dimension. We examine the generalized dynamics of interphase boundaries in the presence of mechanical stress. The displacement patterns due to interphase and domain boundaries are calculated in the case of martensitic phase transitions.