Coherent Phase Transformation Research Articles

Size-dependent phase change in energy storage materials: Comparing the impact of solid-state wetting and of coherency stress.

Coherent phase transformations in interstitial solid solutions or intercalation compounds with a miscibility gap are of practical relevance for energy storage materials and specifically for metal hydride or lithium-ion compound nanoparticles. Different conclusions on the size-dependence of the transformation conditions are reached by modeling or theory focusing on the impact of either one (internal, solid-state-) critical-point wetting of the nanoparticle surface or coherency constraints from solute-saturated surface layers. We report a hybrid numerical approach, combining atomistic grand canonical Monte Carlo simulation with a continuum mechanics analysis of coherency stress and modeling simultaneously wetting and mechanical constraints. When the ratio between chemical and misfit-strain-related contributions to the solute-solute interaction energy takes values realistic for interstitial solutions-which are typical for energy storage materials-we find that the impact of solid-state wetting is weak and that of coherency stress is dominant. Specifically, mechanical interaction can act to reduce the phase transformation hysteresis at small system size, and it can make the solid more binding for solute, thereby reducing the "plateau" chemical potential at phase coexistence. We present equations for the impact of coherency stress on the size-dependence of upper consolute temperature, plateau chemical potential, and charging/discharging hysteresis.

Coherent Phase Change in Interstitial Solutions: A Hierarchy of Instabilities.

Metal hydrides or lithium ion battery electrodes can take the form of interstitial solid solutions with a miscibility gap. This work discusses theory approaches for locating, in temperature-composition space, coherent phase transformations during the charging/discharging of such systems and for identifying the associated transformation mechanisms. The focus is on the simplest scenario, where instabilities derive from the thermodynamics of the bulk phase alone, considering strain energy as the foremost consequence of coherency and admitting for stress relaxation at free surfaces. The extension of the approach to include capillarity is demonstrated by an example. The analysis rests on constrained equilibrium phase diagrams that are informed by geometry- and dimensionality-specific mechanical boundary conditions and on elastic instabilities-again geometry-specific-as implied by the theory of open-system elasticity. It is demonstrated that some scenarios afford the analysis of chemical stability to be based entirely on a linear stability analysis of the mechanical equilibrium, which provides closed-form solutions in a straightforward manner. Attention is on the impact of the system geometry (infinitely extended or of finite size) and on the chemical (closed or open system) and mechanical (incoherent or coherent) boundary conditions. Transformation mechanism maps are suggested for documenting the findings. The maps reveal a hierarchy of instabilities, which depend strongly on each of the above characteristics. Specifically, realistic, finite-sized systems differ qualitatively from idealized systems of infinite extension. Among the transformation mechanisms exposed by the analysis are a uniform switchover to the other phase when the open system reaches its chemical spinodal, practical coherent nucleation, as well as chemo-elastically coupled spontaneous buckling modes, which may take the form of either, single-phase or dual-phasestates.

Localized Soft Vibrational Modes and Coherent Structural Phase Transformations in Rutile TiO2 Nanoparticles under Negative Pressure.

We study the effect of size on the vibrational modes and frequencies of nanoparticles, by applying a newly developed, robust, and efficient first-principles-based method that we present in outline. We focus on rutile TiO2, a technologically important material whose bulk exhibits a softening of a transverse acoustic mode close to , which becomes unstable with the application of negative pressure. We demonstrate that, under these conditions, nanoparticles above a critical size exhibit unstable localized modes and we calculate their characteristic localization length and decomposition with respect to bulk phonons. We propose that such localized soft modes could initiate coherent structural phase transformations in small nanoparticles above a critical size.

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Localized soft vibrational modes and coherent structural phase transformations in rutile TiO2 nanoparticles under negative pressure

Advancing Plasmon-Induced Selectivity in Chemical Transformations with Optically Coupled Transmission Electron Microscopy

Nanoparticle photocatalysts are essential to processes ranging from chemical production and water purification to air filtration and surgical instrument sterilization. Photochemical reactions are generally mediated by the illumination of metallic and/or semiconducting nanomaterials, which provide the necessary optical absorption, electronic band structure, and surface faceting to drive molecular reactions. However, with reaction efficiency and selectivity dictated by atomic and molecular interactions, imaging and controlling photochemistry at the atomic scale are necessary to both understand reaction mechanisms and to improve nanomaterials for next-generation catalysts. Here, we describe how advances in plasmonics, combined with advances in electron microscopy, particularly optically coupled transmission electron microscopy (OTEM), can be used to image and control light-induced chemical transformations at the nanoscale. We focus on our group's research investigating the interaction between hydrogen gas and Pd nanoparticles, which presents an important model system for understanding both hydrogenation catalysis and hydrogen storage. The studies described in this Account primarily rely on an environmental transmission electron microscope, a tool capable of circumventing traditional TEM's high-vacuum requirements, outfitted with optical sources and detectors to couple light into and out of the microscope. First, we describe the H2 loading kinetics of individual Pd nanoparticles. When confined to sizes of less than ∼100 nm, single-crystalline Pd nanoparticles exhibit coherent phase transformations between the hydrogen-poor α-phase and hydrogen-rich β-phase, as revealed through monitoring the bulk plasmon resonance with electron energy loss spectroscopy. Next, we describe how contrast imaging techniques, such as phase contrast STEM and displaced-aperture dark field, can be employed as real-time techniques to image phase transformations with 100 ms temporal resolution. Studies of multiply twinned Pd nanoparticles and high aspect ratio Pd nanorods demonstrate that internal strain and grain boundaries can lead to partial hydrogenation within individual nanoparticles. Finally, we describe how OTEM can be used to locally probe nanoparticle dynamics under optical excitation and in reactive chemical environments. Under illumination, multicomponent plasmonic photocatalysts consisting of a gold nanoparticle "antenna" and a Pd "reactor" show clear α-phase nucleation in regions close to electromagnetic "hot spots" when near plasmonic antennas. Importantly, these hot spots need not correspond to the traditionally active, energetically preferred sites of catalytic nanoparticles. Nonthermal effects imparted by plasmonic nanoparticles, including electromagnetic field enhancement and plasmon-derived hot carriers, are crucial to explaining the site selectivity observed in PdHx phase transformations under illumination. This Account demonstrates how light can contribute to selective chemical phenomena in plasmonic heterostructures, en route to sustainable, solar-driven chemical production.

Coherent and para-equilibrium phase transformations in Mn-doped-LiFePO4 cathode materials: Implications for lithium ion battery performances

Abstract Due to the important similarities between olivine-LiFePO4 and olivine-LiMnPO4, manganese doping has drawn a lot of attention since it can improve the electronic and ionic conductivity of LiFePO4, hence enhance the electrochemical properties. The thermodynamic behavior of Mn-doped-LiFePO4 cathodes has been examined through the thermodynamic investigation of Li(MnyFe1-y)PO4-(MnyFe1-y)PO4 olivine joins. New sublattice thermodynamic models are proposed to describe the para-equilibrium in Li(MnyFe1-y)PO4-(MnyFe1-y)PO4 joins. Moreover, the elastic Gibbs energy approach extended in the large deformation regime is used to calculate the coherent miscibility gaps corresponding to (100) habit plane. The para-equilibrium and coherent miscibility gaps are calculated providing our prior estimated enthalpy of formation and the elastic constants of olivine compounds and enthalpy of mixing of binary sub-systems from first principles simulations based on Density Functional Theory (DFT). The experimental data on the para-equilibrium join is successfully reproduced, and the system is likely to experience the (100) coherent phase transformation. Our thermodynamic models of the Li(MnyFe1-y)PO4-(MnyFe1-y)PO4 join are able to describe most of the features of the electrochemical behavior of Li(MnyFe1-y)PO4 cathodes including the electrochemically driven phase diagram, open circuit voltage (OCV), asymmetry of charging/discharging processes, potential shift and favorable coherent phase transformation.

The variation and visualisation of elastic anisotropy in rock-forming minerals

Abstract. All minerals behave elastically; elasticity is a rheological property that controls their ability to support stress, strain, and pressure; controls the nature of acoustic wave propagation; and influences subsequent plastic (i.e. permanent non-reversible) deformation. All minerals are intrinsically anisotropic in their elastic properties – that is, they have directional variations that are related to the configuration of the crystal lattice. This means that the commonly used mechanical elastic properties that relate elastic stress to elastic strain, including Young's modulus (E), Poisson's ratio (ν), shear modulus (G) and linear compressibility (β), are dependent on crystallographic direction. In this paper, we explore the ranges of anisotropy of E, ν, G and β in 86 rock-forming minerals, using previously published data, and show that the range is much wider than commonly assumed. We also explore how these variations (the directionality and the magnitude) are important for fundamental processes in the solid earth, including deformation (mechanical) twinning, coherent phase transformations and brittle failure. We present a new open-source software package (AnisoVis, written in MATLAB), which we use to calculate and visualise directional variations in elastic properties of rock-forming minerals. Following previous work in the fields of chemistry and materials science, we demonstrate that by visualising the variations in elasticity, we discover previously unreported properties of rock-forming minerals. For example, we show previously unreported directions of negative Poisson's ratio and negative linear compressibility, and we show that the existence of these features is more widespread (i.e. present in many more minerals) than previously thought. We illustrate the consequences of intrinsic elastic anisotropy for the elastic normal and shear strains within α-quartz single crystal under different applied stress fields; the role of elastic anisotropy on Dauphiné twinning and the α–β phase transformations in quartz; and stress distributions around voids of different shapes in talc, lizardite, albite, and sanidine. In addition to our specific examples, elastic anisotropy in rock-forming minerals, to the degree that we describe, has significant consequences for seismic (acoustic) anisotropy, for the focal mechanisms of earthquakes in anisotropic source regions (e.g. subducting slabs), for a range of brittle and ductile deformation mechanisms in minerals, and for geobarometry using mineral inclusions.

A model for predicting critical size for dislocation formation in phase transforming planar particles of energy storage intercalation materials

Defect formation has been widely observed to occur in phase transforming intercalation materials of critical importance to many technological applications. In this work, relying on energy balance argument, we develop a planar particle model to investigate critical conditions for spontaneous dislocation formation in a single-crystalline phase transforming material. Dislocations self-energy is calculated assuming isotropic elasticity, and the work done by the background stress field during dislocation formation is examined based on bilayer and core-shell models of solute distribution. Considering well-known slip systems in cubic crystals, critical sizes are derived, as a function of transformation strain, below which dislocation formation is predicted to remain energetically suppressed throughout complete phase transformation, resulting in completely coherent phase transformation. Effect of the surface flux on the critical size is also examined using a moving interphase model. Minimum dislocation spacing is derived for an array of dislocations which could spontaneously form at the phase boundary when particle size exceeds the critical size. Numerical estimates of the critical size are presented for several materials systems, and the results are discussed with reference to the available experiments. Results of this work could have potentially important implications in terms of designing phase changing materials resistant against cyclic damage.

Modeling of coherent phase transformation and particle size effect in LiFePO4 cathode material and application to the charging/discharging process

The effect of coherent strains which is involved during the fast charge/discharge processes and the influence of particle size reduction which improves the electrochemical performance of the cathode material are modelled in this study. An extension of the linear isotropic approximation for elastic energy stored in the coherent boundaries of an orthorhombic system is performed for the first time to calculate the coherent miscibility gaps of the LiFePO4-FePO4 cathode join. Noticeably, this approach is applicable for any thermodynamic models used for describing the equilibrium LiFePO4-FePO4 join. The coherent miscibility gaps corresponding to various crystallographic directions, which could explain the occurrence of a metastable phase, favorable phase boundaries during lithiation (delithiation), and the formation of dislocations or cracks via cycling, are presented. (100) is considered as the softest direction for coherence to form and the existence of (110) and (010) habit planes is also possible. Moreover, it is the first time that a model of particle size effect on both equilibrium and coherent olivine join is developed. Additionally, it is the first combined coherency-size type of calculation ever reported. The difference between the surface energies of the pure LiFePO4 and FePO4 and the excess surface energy of the olivine solid solution are the two important model parameters affecting the equilibrium and the coherent miscibility gaps. As the particle size decreases, the miscibility gaps shrink favoring the intermediate phase region between the two miscibility gaps. At nanoscale, coherent phase transformation seems to be more likely.

Dynamical simulations of an electronically induced solid-solid phase transformation in tungsten

The rearrangement of a material's electron density during laser irradiation leads to modified nonthermal forces on the atoms that may lead to coherent atomic motions and structural phase transformation on very short time scales. We present ab initio molecular dynamics simulations of a martensitic solid-solid phase transformation in tungsten under conditions of strong electronic excitation. The transformation is ultrafast, taking just over a picosecond, and follows the tetragonal Bain path. To examine whether a solid-solid bcc-fcc phase transformation could occur during laser irradiation, we use two-temperature molecular dynamics (2T-MD) simulations with a specially developed potential dependent on the electronic temperature. Our simulations show that the occurrence of the solid-solid phase transformation is in competition with ultrafast nonthermally assisted melting with the strength of the electron-phonon coupling determining the lifetime of the new solid phase. In tungsten the melting transition is predicted to occur too rapidly for the fcc phase to be detectable during laser irradiation.

Coherent Phase Transformation in Next-Generation Nanoscale Olivine Cathodes

Due to its outstanding power, safety and cycle-life olivine LiFePO4 (LFP) has during the past decade become a widely used, and one of the most well-studied, lithium ion battery cathode materials. It is well-established that for LiFePO4 the storage/release of lithium is accompanied by a first-order phase transition between lithiated and delithiated states. First-order phase transition behavior persists well into the nanosize regime, although increasing mutual miscibility is observed with decreasing particle size.1-4 Consequently, there have been numerous attempt to describe the detailed mechanism of the phase transformation in nano-LFP. Recently, direct observations by oxidation-state-sensitive X-ray microscopy combined with transmission electron microscopy, have been used to show that at intermediate states of charge, nanoparticulate LFP electrodes are primarily a binary mixture of lithiated and delithiated with relative absence of two-phase particles.5 This preference has important implications for the kinetics of storage in the large arrays of nanoscale particles that comprise practical battery electrodes.However, it would be a mistake to conclude that the behavior of pure LFP is representative of all olivines, in particular the vast range of doped and mixed-metal olivines that are also of interest for their advantageous electrochemical properties.4,6 This is illustrated herein through investigation of the phase transformation in nanoscale olivine LiMn y Fe1-y PO4 (LMFP) during dynamic battery operation.LMFP may be regarded as the second generation olivine cathode, as it has both higher energy density than LFP due to higher average voltage, and lesser known, among the highest rate capabilities ever observed for olivine cathodes. It has been suggested7 that this is due to the existence of an intermediate solid solution (here denoted L x MFP) that reduces the misfit strain by breaking the single phase transition (observed for LFP) into two stages, first a transition of MFP to an intermediate phase L x MFP, then between L x MFP and LMFP. However, no clear conclusion has been drawn as to whether the transformations are two-phase first-order reactions or involve formation of solid solutions, which may be metastable. Significant discrepancies are found in the literature between the (x,y)-compositional phase diagrams for LMFP determined computationally versus experimentally (by chemical delithiation of large particle powders).8,9 We demonstrate here, by systematic screening of the electrochemical driven phase transitions in a series of LiMn y Fe1-y PO4 (y = 0.1, 0.2, 0.4, 0.6 and 0.8) powders, that this material exhibits a completely different phase transformation mode dominated by formation of metastable solid solutions for nanoscale LMFP compared to the binary lithiation states within the extremely well-studied case of LFP. The screening is conducted by operando synchrotron radiation powder X-ray diffraction (SR-PXD) during charge and discharge at different C-rates on powders with particle size of ~50, 100 and 150 nm. Through Rietveld refinement (>1000 PXD patterns have been refined for this study) the misfit strains during phase transformations are examined, revealing small elastic misfits between phases within the extended solid solution regime compared to either pure LiFePO4 or LiMnPO4. Hence, on the basis of the time- and state-of-charge dependence of the olivine structure parameters, we propose a coherent transformation mechanism. Finally, we bring evidence that the observed metastability is enabled by particle size reduction to the nanoscale. This work was supported by DOE project number DE-SC0002626. Work at APS was supported by DOE Contract No.DE-AC02-06CH11357. D.B.R. acknowledges the Carlsberg Foundation for funding.(1)Meethong et al. Electrochem. Solid-State Lett. 2007,10,A134. (2)Meethong et al. Adv. Funct. Mater. 2007,17,1115. (3)Meethong et al. Chem. Mater. 2008, 20,6189. (4)Meethong et al. Adv. Funct. Mater. 2009,19,1060 (5)Chueh et al. Nano Lett. 2013,13,866. (6)Chung et al. Nat. Mater. 2002,1,123. (7)Y.-H. Kao, Ph.D. thesis, MIT, 2011. (8)Yamada et al. J. Electrochem. Soc. 2001,148,A1153. (9)Malik et al. Phys. Rev. B 2009,79,214201.

Interface reorientation during coherent phase transformations

The universal thermodynamic driving force for coherent plane interface reorientation (IR) during first-order phase transformations (PT) in solids is derived. The relation between the rates of IR and interface propagation (IP) and the corresponding driving forces are derived for combined athermal and drag interface friction. The coupled evolution of IR and IP during cubic-tetragonal and tetragonal-orthorhombic PTs under three-dimensional loading is studied. An instability in the interface orientation is shown to have the features of a first-order PT.

Structure of stable solutions of a one-dimensional variational problem

We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double well potential function, we make use of explicit solution formulas to analyze the intricate interactions between the phase boundaries. Our analysis can provide insights for tackling the problem with general potential functions.

The effects of free surfaces on martensite microstructures: 3D phase field microelasticity simulation study

The phase field microelasticity approach to coherent phase transformations is extended to the case of a finite sample with free surfaces. The 3D simulation model is based on numerical solution of exact elasticity equation. No ad hoc assumptions on the microstructure morphology along evolution path are made. It is used to investigate the effects of free surfaces on multi-variant martensitic transformations in AuCd and FeNi alloys. The simulation shows that formation of free surfaces changes the martensite microstructures mostly in the surface layers, the thickness of these layers being commensurate with the size of martensite domains. It also shows that the free surfaces affect the microstructures of the high-symmetry FeNi more significantly than that of the low-symmetry AuCd because the latter has more orientation variants and can achieve better stress accommodation.

Coherent phase equilibria in a bending film

The theory of coherent phase diagrams is expanded to phase transformations in films. The misfit between the phases dictates their layer arrangement with an interface parallel to film surfaces. Then, the transformational self-strain leads to the film bending. The phase equilibrium analysis shows that the polymorphic transformation in a single component system proceeds with the thermodynamic hysteresis. However, the reversible change of the two-phase equilibrium with temperature is possible, if the phase fractions are maintained within a range (1/2, 2/3). The character of polymorphic phase transformations in a binary system depends on the concentration of a second component. The quasi-single component transformation takes place at small concentrations. The reversible coherent phase transformation should be observed at the concentration larger than the critical one. The irreversible transformations take place at intermediate concentrations. The irreversible transformations begin with the formation of a finite fraction of the second phase. Then, the two-phase system evaluates with temperature to the final two-phase state that transfers discontinuously to a single-phase state. The concentration diagram does not coincide with the phase diagram. The concentrations in the transforming phases change non-monotonously with temperature.

Thermodynamic approach of surface instability under irradiation

We analyze a model of deterioration of a solid material subjected to irradiation by energetic particles. In the frame of the thermodynamics of coherent phase transformations, the stability of the interface between the deteriorated layer and the undamaged substance has been investigated. Considering the linear regime of the roughness evolution, the growth rate of the surface fluctuations has been determined as a function of the relevant parameters of the problem: the shear modulus and Poisson's ratio of both phases; the thickness of the layer; and the initial stress. The wavelengths of the instabilities have been then calculated in the particular case of a metal/oxide interface of an irradiated zirconium alloy claddings used in nuclear power stations.

Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations

The first Phase Field model of evolution of a multi-dislocation system in elastically anisotropic crystal under applied stress is formulated. The model is a modification and extension of our Phase Field Microelasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations is calculated exactly and is explicitly incorporated in the Phase Field formalism. It also automatically takes into account the effects of “short-range interactions”, such as multiplication and annihilation of dislocations and a formation of various metastable microstructures involving dislocations and defects. The proposed 3-dimensional Phase Field model of dislocations does not impose a priori constraints on possible dislocation structures or their evolution paths. Examples of simulation of the FCC 3D system under applied stress are considered.

Alloys under irradiation

During the last two decades, some effort has been devoted to establishing a phenomenology for alloys under irradiation. Theoretically, the effects of the defect supersaturation, sustained defect fluxes and ballistic mixing on solid solubility under irradiation can now be formulated in a unified manner, at least for the most simple cases: coherent phase transformations and nearest-neighbor ballistic jumps. Even under such restrictive conditions, several intriguing features documented experimentally can be rationalized, sometimes in a quantitative manner and simple qualitative rules for alloy stability as a function of irradiation conditions can be formulated. A quasi-thermodynamic formalism can be proposed for alloys under irradiation. However, this point of view has limits illustrated by recent computer simulations.

Coherent structural transformations in random crystalline systems

The coherent phase transformation between two equilibrium single-phase states producing several orientation variants of the product phase is considered. The computer simulation shows that randomly distributed static defects may drastically change the thermodynamics, kinetics and morphology of the transformation and may lead to thermoelastic equilibrium. They are responsible for the appearance of two new fields in the phase diagram: (i) the two-phase field describing the tweed microstructure which consists of the retained parent phase and variants of the product phase and (ii) the single-phase field describing the tweed microstructure which consists of the variants of the product phase. These new fields can be attributed to the pre-transitional states observed in some of the displacive transformations. The microstructure evolution resulting in the formation of thermoelastic equilibrium is path dependent. This unusual behavior is expected in systems with a sharp dependence of the transition temperature on the defect concentration.