Order-disorder Phase Transition Research Articles

(Keynote) An Automatic Rapid Screening Tool for Fast Ionic Conductors

Identifying new materials that combine high ionic conductivity with structural and electrochemical stability so far remains a slow trial and error search process. To rationally accelerate materials design and exploit the opportunities in the materials genome a dependable rapid screening of materials is required that can pre-select structures that merit higher level computational as well as experimental characterization. Here we report on the progress of our “softBV” bond-valence site energy-based automated pathway analysis utilizing our new Bond Valence Pathway Analyzer (BVPA) – with fast bond valence site energy calculations to quickly obtain suggested candidate materials for fast ionic conduction. BVPA provides rapid and simplified visualization, in order to bridge the gap between experimentalists and simulation [1,2]. Calculation of ion transport pathways can be done extremely quickly on the order of seconds or minutes on desktop PCs providing a speedup factor of 3 to 5 orders of magnitude compared to DFT-based NEB methods. Combined with a graphical user interface our software suite (that can be downloaded from [2] and is free for academic use) should enable experimentalists to quickly identify candidate solid electrolyte materials. We also aim to integrate the pre-screening into an automated workflow for subsequent DFT characterization [3].Results will be benchmarked against both experimental and DFT NEB migration barriers. Besides the migration barriers the approach now also comprises an AI-based dopant predictor utilizing bond-valence-based crystal chemical descriptors to assist experimentalists in exploring favorable substitutional doping strategies. We will also compare the predictability of absolute room temperature conductivities from static energy landscape analysis, bond-valence based empirical MD simulations and ab initio molecular dynamics (AIMD) simulations. While for small fast-ion conductor structures at sufficiently high temperatures AIMD appears to be the gold standard, the less reliable but computationally empirical approaches have an advantage in modelling complex disordered interfaces at low temperatures over longer periods. This eliminates the hazards involved in extrapolations down to room temperature properties for the frequent cases of order-disorder phase transitions at intermediate temperatures.As an example we will discuss lithium and sodium compounds containing multiple anions, in particular the combination of thiophosphate and halide anions or various MS4 polyanions. Based on computational screening using our bond valence site approach and DFT studies several thiophosphate halides along the A3PS4-LiX (Cl, Br, I; A = Li, Na) tie line [4] and the Ax(MS4)y(M’S4)z phase space [5] have been explored and their properties discussed based on BVSE pathway models and molecular dynamics simulations in combination with experimental (X-ray and neutron) diffraction, solid state NMR and electrochemical characterisation. MD simulations e.g. show that Li5(PS4)Cl2 is found to undergo an order-disorder phase transition and thus should, contrasting to earlier predictions, not be a fast Li+ ion conductor. The newly predicted thermodynamically stable cubic solid electrolyte Li15(PS4)4Cl3 was successfully prepared and characterized. Though its conductivity does not reach a superionic level, it demonstrates that the computational approach can successfully predict a completely new classes of solid electrolytes and can predict its optimization by doping. The simplicity of the approach also facilitates the study of homogeneity ranges as exemplified for the solid solution systems Li4-xPS4Ix (0<x<0.67) and Na9+x(MS4)3-x(SnS4)x (M = P, Sb; x ≈ 2).

Perovskite Crystals: Unique Pseudo-Jahn–Teller Origin of Ferroelectricity, Multiferroicity, Permittivity, Flexoelectricity, and Polar Nanoregions

In a semi-review paper, we show that the local pseudo-Jahn–Teller effect (PJTE) in transition metal B ion center of ABO3 perovskite crystals, notably BaTiO3, is the basis of all their main properties. The vibronic coupling between the ground and excited electronic states of the local BO6 center results in dipolar distortions, leading to an eight-well adiabatic potential energy surface with local tunneling or over-the-barrier transitions between them. The intercenter interaction between these dipolar dynamic units results in the formation of the temperature-dependent three ferroelectric and one paraelectric phases with order–disorder phase transitions. The local PJTE dipolar distortion is subject to the presence of sufficiently close in energy local electronic states with opposite parity but the same spin multiplicity, thus limiting the electronic structure and spin of the B(dn) ions that can trigger ferroelectricity. This allowed us to formulate the necessary conditions for the transition metal perovskites to possess both ferroelectric and magnetic (multiferroic) properties simultaneously. It clarifies the role of spin in the spontaneous polarization. We also show that the interaction between the independently rotating dipoles in the paraelectric phase may lead to a self-assembly process resulting in polar nanoregions and relaxor properties. Exploring interactions of PJTE ferroelectrics with external perturbations, we revealed a completely novel property—orientational polarization in solids—a phenomenon first noticed by P. Debye in 1912 as a possibility, which was never found till now. The hindered rotation of the local dipole moments and their ordering along an external field is qualitatively similar to the behavior of polar molecules in liquids, thus adding a new dimension to the properties of solids—notably, the perovskite ferroelectrics. We estimated the contribution of the orientational polarization to the permittivity and flexoelectricity of perovskite crystals in different limiting conditions.

Metal-Organic Phase-Change Materials for Thermal Energy Storage.

The development of materials that reversibly store high densities of thermal energy is critical to the more efficient and sustainable utilization of energy. Herein, we investigate metal-organic compounds as a new class of solid-liquid phase-change materials (PCMs) for thermal energy storage. Specifically, we show that isostructural series of divalent metal amide complexes featuring extended hydrogen bond networks can undergo tunable, high-enthalpy melting transitions over a wide temperature range. Moreover, these coordination compounds provide a powerful platform to explore the specific factors that contribute to the energy density and entropy of metal-organic PCMs. Through a systematic analysis of the structural and thermochemical properties of these compounds, we investigated the influence of coordination bonds, hydrogen-bond networks, neutral organic ligands, and outer-sphere anions on their phase-change thermodynamics. In particular, we identify the importance of high densities of coordination bonds and hydrogen bonds to achieving a high PCM energy density, and we show how metal-dependent changes to the local coordination environment during melting impact the entropy and enthalpy of metal-organic PCMs. These results highlight the potential of manipulating order-disorder phase transitions in metal-organic materials for thermal energy storage.

Reversible order-disorder phase transition and interaction topology in 4-carboxyanilinium nitrate

A reversible order-disorder phase transition in 4-carboxyanilinium nitrate (4-CAN), a 1:1 adduct formed between p-amino benzoic acid (PABA) and nitric acid has been studied via variable temperature single crystal X-ray diffraction and differential scanning calorimetry (DSC). DSC heating scans of 4-CAN shows presence of a reversible first-order phase transition at 309.5 K. At temperatures below the phase transition temperature the crystal structure was found to be monoclinic, space group P21/c, Z = 4 and at temperatures above the phase transition temperature the crystal structure was found to be orthorhombic, space group Pbcm, Z = 4. In both high and low temperature phases of 4-CAN crystal, the 4-carboxyanilinium cations and nitrate anions are connected through a three-dimensional network of strong charge-assisted NH…O and COH…O hydrogen bonds. The intermolecular interaction topology has been quantitatively analyzed using the computational tool of energy framework analysis and very high values of interaction energies are found for the hydrogen bonded anion-cation pairs in the crystal structure of 4-CAN.

Crystal structure, oxygen content and conductivity of Sr1-xGdxCoO3-δ

Solid solutions Sr1–xGdxCoO3–δ (0.0≤x ≤ 0.4) were synthesized through a glycerol-nitrate technique. The final anneals were performed at 1100 °C in air for 120 h. All the samples were slowly cooled to room temperature at a rate of about 100 °C/h; alternatively, they were quenched to room temperature at a cooling rate of about 500°/min. The structural parameters of all the samples were refined via Rietveld analysis. All the single-phase oxides slowly cooled to room temperature in air possess a tetragonal 2ap × 2ap × 4ap superstructure (sp. gr. I4/mmm). Only Sr0.9Gd0.1CoO3–δ undergoes a complete order-disorder type phase transition: heating it up to 1100 °C in air transforms it from an ordered tetragonal 2ap × 2ap × 4ap structure to a disordered cubic structure. The super-structural lines for Sr0.9Gd0.1CoO3–δ noticeably decreased at 1100 °C, but are still present in the XRD pattern. The structure of Sr1–xGdxCoO3–δ with x = 0.3 and 0.4 at 1100 °C remains almost unchanged. The oxygen content in Sr1–xGdxCoO3–δ at room temperature ranges from δ = 2.57 in the sample with x = 0.1 to δ = 2.75 in the sample with x = 0.4. The variations in oxygen content, electrical conductivity and the Seebeck coefficient in the Sr1–xGdxCoO3–δ oxides were measured in air versus temperature. The temperature dependences of conductivity for Sr1-xGdxCoO3-δ exhibit maximum (~550 S/cm) at 300–400 °C. The conductivity values depend weakly on the Gd content in Sr1–xGdxCoO3–δ. The temperature dependences of the Seebeck coefficient (S) for all oxides are represented by smooth curves with minimum. The positive S values at room temperature (12–36 μV/K) decreased down to zero or even tiny negative values (– 3 μV/K) as the temperate rose within the range of 300–800 °C and they then rose slightly to 2–14 μV/K at 1100 °C.

Concomitant singularities of Yb-valence and magnetism at a critical lattice parameter of icosahedral quasicrystals and approximants

Non-Fermi-liquid (NFL), a significant deviation from Fermi-liquid theory, usually emerges near an order-disorder phase transition at absolute zero. Recently, a diverging susceptibility toward zero temperature was observed in a quasicrystal (QC). Since an electronic long-range ordering is normally absent in QCs, this anomalous behaviour should be a new type of NFL. Here we study high-resolution partial-fluorescence-yield x-ray absorption spectroscopy on Yb-based intermediate-valence icosahedral QCs and cubic approximant crystals (ACs), some of which are new materials, to unveil the mechanism of the NFL. We find that for both forms of QCs and ACs, there is a critical lattice parameter where Yb-valence and magnetism concomitantly exhibit singularities, suggesting a critical-valence-fluctuation-induced NFL. The present result provides an intriguing structure–property relationship of matter; size of a Tsai-type cluster (that is a common local structure to both forms) tunes the NFL whereas translational symmetry (that is present in ACs but absent in QCs) determines the nature of the NFL against the external/chemical pressure.

Effect of atomic configuration on magnetic properties and electronic state of CoVMnAl quaternary heusler alloy

Atomic configuration at the equilibrium state, magnetic property and electronic state of CoVMnAl quaternary Heusler alloy were investigated by neutron diffraction, magnetic measurements, and first-principles calculations. Saturation magnetization measured at 5 K was quite small of 0.04 μB/f.u. for the specimen annealed at 873 K, and close to the expected value from the Slater-Pauling rule as predicted by Galanakis et al. (1983) [1]. Because the intensities of the superlattice diffractions of 111 and 200 were strong in the neutron diffraction, the atomic configuration of the CoVMnAl could be accurately determined. The best fitting was obtained as the L21b-type structure, in which the Co and Mn atoms randomly occupied the 8c site in the Wyckoff position in the space group number of 225. A small ferromagnetism was occurred in the specimen which was obtained by quenching at temperature above the order-disorder phase transition. The specimen exhibited a B2-like atomic configuration, where V and Al were partially distributed. Although the total energy in the LiMgPdSn-type ordered structure was 56 meV/f.u. lower than that in the L21b-type structure, the difference was small as the L21b-type structure would be obtainable in a finite temperature.

Universality in incompressible active fluid: Effect of nonlocal shear stress.

Phase transitions in active fluids attracted significant attention within the last decades. Recent results show [L. Chen etal., New J. Phys. 17, 042002 (2015)10.1088/1367-2630/17/4/042002] that an order-disorder phase transition in incompressible active fluids belongs to a new universality class. In this work, we further investigate this type of phase transition and focus on the effect of long-range interactions. This is achieved by introducing a nonlocal shear stress into the hydrodynamic description, which leads to superdiffusion of the velocity field, and can be viewed as a result of the active particles performing Lévy walks. The universal properties in the critical region are derived by performing a perturbative renormalization group analysis of the corresponding response functional within the one-loop approximation. We show that the effect of nonlocal shear stress decreases the upper critical dimension of the model, and can lead to the irrelevance of the active fluid self-advection with the resulting model belonging to an unusual long-range Model A universality class not reported before, to our knowledge. Moreover, when the degree of nonlocality is sufficiently high all nonlinearities become irrelevant and the mean-field description is valid in any spatial dimension.

Peculiarities of ion mobility and conductivity in the (NH4)6LiHf2Zr2F23 compound

Ion mobility and electrophysical properties in (NH4)6LiHf2Zr2F23 compound have been studied by 1H, 19F NMR, and impedance spectroscopy. The types of ion motions in the fluoride and ammonium sublattices of the compound have been determined in the temperature range 150–450 ​K and their activation energy was estimated. The presence of the order-disorder phase transition in this compound in the temperature range 400–450 ​K with the formation of metastable high-temperature β–modifications, in which diffusion of fluoride and ammonium ions is the dominant type of ionic motion, is established. The value of conductivity at 450 ​K–4.5·10−3 ​S/cm indicates that the compound studied belongs to the class of superionic conductors.

Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field

The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field H = iθT∕2 with the “topological” angle θ and temperature T was investigated numerically. In order to treat such a complex-valued statistical weight, we employed the transfer-matrix method. As a probe to detect the order–disorder phase transition, we resort to an extended version of the fidelity F, which makes sense even for such a non-Hermitian transfer matrix. As a preliminary survey, for an intermediate value of θ, we investigated the phase transition via the fidelity susceptibility χF(θ). The fidelity susceptibility χF(θ) exhibits a notable signature for the criticality as compared to the ordinary quantifiers such as the magnetic susceptibility. Thereby, we analyze the end-point singularity of the order–disorder phase boundary at θ = π. We cast the χF(θ) data into the crossover-scaling formula with δθ = π − θ scaled carefully. Our result for the crossover exponent ϕ seems to differ from the mean-field and square-lattice values, suggesting that the lattice structure renders subtle influences as to the multi-criticality at θ = π.

Na+ diffusivity in carbon-substituted nido- and closo-hydroborate salts: Pulsed-field-gradient NMR studies of Na-7-CB10H13 and Na2(CB9H10)(CB11H12)

The mixed-anion solid-solution closo-carbahydroborate Na2(CB9H10)(CB11H12) shows the highest room-temperature ionic conductivity among all known solid Na-ion and Li-ion conductors, and the related nido-type carbahydroborate Na-7-CB10H13 exhibits superionic conductivity above the order-disorder phase transition temperature, ∼320 K. To study the Na-ion diffusivity that is closely related to the ionic conductivity in these compounds, we have measured the diffusion coefficients of Na+ cations in Na2(CB9H10)(CB11H12) and Na-7-CB10H13 using the pulsed-field-gradient (PFG) spin-echo technique over the temperature ranges of 298–403 K and 320–403 K, respectively. These measurements have revealed the exceptionally high Na+ diffusivities (exceeding 2 × 10−6 cm2/s) for both compounds. In the studied temperature ranges, the diffusion coefficients are found to follow the Arrhenius law with the activation energies of 118(1) meV for Na2(CB9H10)(CB11H12) and 134(3) meV for Na-7-CB10H13. For the nido-type Na-7-CB10H13, the diffusivity results are complemented by the 1H and 23Na NMR and quasielastic neutron scattering measurements of the atomic jump rates. It is found that the transition from the low-T ordered phase to the high-T disordered phase occurring near 320 K is accompanied by the abrupt acceleration of both the reorientational jump rate of the [CB10H13]− anions and the diffusive jump rate of Na+ cations. For both compounds, a comparison of the measured Na+ diffusion coefficients with the ionic conductivity results and the data on the cation and anion jump rates provides new insights into unusual dynamical properties of these superionic materials.

Dielectric ordering of water molecules arranged in a dipolar lattice

Intermolecular hydrogen bonds impede long-range (anti-)ferroelectric order of water. We confine H2O molecules in nanosized cages formed by ions of a dielectric crystal. Arranging them in channels at a distance of ~5 Å with an interchannel separation of ~10 Å prevents the formation of hydrogen networks while electric dipole-dipole interactions remain effective. Here, we present measurements of the temperature-dependent dielectric permittivity, pyrocurrent, electric polarization and specific heat that indicate an order-disorder ferroelectric phase transition at T0 ≈ 3 K in the water dipolar lattice. Ab initio molecular dynamics and classical Monte Carlo simulations reveal that at low temperatures the water molecules form ferroelectric domains in the ab-plane that order antiferroelectrically along the channel direction. This way we achieve the long-standing goal of arranging water molecules in polar order. This is not only of high relevance in various natural systems but might open an avenue towards future applications in biocompatible nanoelectronics.

A mean field approach to model levels of consciousness from EEG recordings

We introduce a mean-field model for analysing the dynamics of human consciousness. In particular, inspired by the Giulio Tononi’s Integrated Information Theory and by the Max Tegmark’s representation of consciousness, we study order–disorder phase transitions on Curie–Weiss models generated by processing EEG signals. The latter have been recorded on healthy individuals undergoing deep sedation. Then, we implement a machine learning tool for classifying mental states using, as input, the critical temperatures computed in the Curie–Weiss models. Results show that, by the proposed method, it is possible to discriminate between states of awareness and states of deep sedation. Besides, we identify a state space for representing the path between mental states, whose dimensions correspond to critical temperatures computed over different frequency bands of the EEG signal. Beyond possible theoretical implications in the study of human consciousness, resulting from our model, we deem relevant to emphasise that the proposed method could be exploited for clinical applications.

Characterization of order-disorder transition in MgAl2O4:Cr3+ spinel using photoluminescence

Photoluminescence spectroscopy of Cr3+ shows considerable potential for probing local cation arrangement in MgAl2O4 spinel while undergoing order-disorder phase transition. The PL spectrum consists of R peaks (caused by ordered PL centers) and N peaks (caused by disordered PL centers). The peak dominating in the PL spectra dramatically switched from R peaks to N peaks around 850 °C and showed rather few changes above 900 °C. We defined the percent ratio of the integrated area of N peaks to the total integrated area under all peaks as a parameter to monitor the degree of disordering. This parameter can quantitatively indicate the variation of neighboring atom arrangement around Cr3+ during the order-disorder transition. A thermodynamic model based on this spectroscopic parameter can be built, and we can model the transition with an activation energy of 254 ± 49 kJ/mol. This study also attempted to determine the ability to restore the ordering of heated spinels by annealing them at 650 °C up to 8 days. Our results clearly indicated that the spectra cannot be fully restored back to the ordered state within our experimental time span, thus makes PL spectroscopy a reliable method to distinguish natural spinel from heated ones.

Hydrogen order in hydrides of Laves phases

Abstract Many Laves phases AM 2 takes up hydrogen to form interstitial hydrides in which hydrogen atoms partially occupy A 2 M 2, AM 3, and/or M 4 tetrahedral interstices. They often exhibit temperature-driven order-disorder phase transitions, which are triggered by repulsion of hydrogen atoms occupying neighboring tetrahedral interstices. Because of the phase widths with respect to hydrogen a complete ordering, i.e., full occupation of all hydrogen positions is usually not achieved. Order-disorder transitions in Laves phase hydrides are thus phase transitions between crystal structures with different degrees of hydrogen order. Comparing the crystal structures of ordered and disordered phases reveals close symmetry relationships in all known cases. This allows new insights into the crystal chemical description of such phases and into the nature of the phase transitions. Structural relationships for over 40 hydrides of cubic and hexagonal Laves phases ZrV2, HfV2, ZrCr2, ZrCo2, LaMg2, CeMg2, PrMg2, NdMg2, SmMg2, YMn2, ErMn2, TmMn2, LuMn2, Lu0.4Y0.6Mn2 YFe2, and ErFe2 are concisely described in terms of crystallographic group-subgroup schemes (Bärnighausen trees) covering 32 different crystal structure types, 26 of which represent hydrogen-ordered crystal structures.

Nanoscale structural analysis of Bi0.5Na0.5TiO3

We investigate A-site cation ordering in the ferroelectric perovskite Bi0.5Na0.5TiO3 (BNT) by synchrotron X-ray total scattering. Although BNT has a problem of low depolarization temperature, it is a promising lead-free piezoelectric material. Since the depolarization temperature is presumed to correspond to a relaxor-like gradual order–disorder phase transition, local structural analysis is necessary to understand the structure of the disorder phase. Using this approach, we reveal the elusive connection between chemical and structural heterogeneity. The short-range order structure largely deviates from the rhombohedral average structure due to the off-center shift of Ti with large randomness. Consequently, the Ti off-center shift is averaged out beyond the unit cell and the structure becomes identical to the average structure beyond the unit cell. We further locate nanoscale regions of monoclinic distortion due to the heterogeneity of the A-site ion composition. The change in the short-range-order structure with distance can determine the BNT depolarization temperature. The results show necessary models to develop next generation novel piezoelectric materials.

Elastic, electronic and electrocaloric properties near room temperature in [formula omitted]-doped [formula omitted] from first-principles calculations

Ferroelectric materials are attractive candidates for potential solid-state refrigeration. Their useful broad applications require investigation of several properties. However, the magnitude corresponding to electrocaloric effect (ECE) is seemingly too small. Insight from a theoretical approach is needed to provide support through theoretical description, leading mainly to better understanding and prediction of the electrocaloric performance, as well as additional properties that might be useful. Here, we investigate the elastic, electronic, thermoelectric, and ferroelectric properties as well as ECE of SnTiO3 by utilizing first-principles calculations and effective Hamiltonian. From the calculations toward a higher symmetry direction, the direct band gap is obtained. In addition, we have comprehensively investigated the effect of Mn-doping on the electronic and thermoelectric properties of SnTiO3 to achieve a better understanding of this material. The polarization, pyroelectric coefficient, changes in entropy ΔS and adiabatic temperature ΔT are examined in detail as a function of temperature. This work also reveals the contribution with particular attention of the applied electric field especially on the magnitude of ECE, resulting in slightly anomalous volume expansion. Typical hysteresis loops are observed to confirm the order-disorder phase transition. An enhancement route of the ECE is elucidated, which may open the door for more discussions and practical applications.

Order–disorder transition in the Dy0.2Sr0.8CoO3-δ rare-earth cobalt oxide solid solutions: Structural and thermoelectric properties

By the example of the Dy0.2Sr0.8CoO3-δ compound undergoing an order–disorder phase transition with increasing temperature, we demonstrate a significant dependence of the kinetic properties on the morphology of the internal spatially inhomogeneous structure, which forms in the sample depending on the rate of its transition from the high-temperature disordered cubic phase to the ground tetragonal ordered phase upon cooling. The results of transmission electron microscopy visualization of the spatially inhomogeneous state in the Dy0.2Sr0.8CoO3-δ ceramic samples are presented and compared with the X-ray diffraction data.

Anion and Cation Dynamics in Polyhydroborate Salts: NMR Studies.

Polyhydroborate salts represent the important class of energy materials attracting significant recent attention. Some of these salts exhibit promising hydrogen storage properties and/or high ionic conductivities favorable for applications as solid electrolytes in batteries. Two basic types of thermally activated atomic jump motion are known to exist in these materials: the reorientational (rotational) motion of complex anions and the translational diffusion of cations or complex anions. The present paper reviews recent progress in nuclear magnetic resonance (NMR) studies of both reorientational and diffusive jump motion in polyhydroborate salts. The emphasis is put on sodium and lithium closo-borates exhibiting high ionic conductivity and on borohydride-based systems showing extremely fast reorientational motion down to low temperatures. For these systems, we discuss the effects of order–disorder phase transitions on the parameters of reorientations and diffusive jumps, as well as the mechanism of low-temperature rotational tunneling.

Crossover from Ferroelectric to Relaxor Behavior in Ba1-xCaxTiO3 (x = 0.17) System.

The dielectric properties of Ba1−xCaxTiO3 (x = 0.17) ceramics were studied in a wide frequency range of 20 Hz–53 GHz. Diffused ferroelectric phase transition was revealed close to 339 K in the dielectric properties of ceramics. The behaviour of distributions of relaxation times in vicinity of the ferroelectric phase transition temperature is also typical for order-disorder ferroelectric phase transition. However, at lower temperatures (below 200 K), the most probable relaxation increased according to the Arrhenius law. At lower temperatures the maximum of the imaginary part of dielectric permittivity versus temperature strongly shifted to higher temperatures when the frequency increased (from 125 K at 1.21 kHz to 300 K at 33 GHz). This behaviour was attributed to the dynamics of Ti ions. The origin of the crossover from ferroelectric to relaxor behaviour of Ba1−xCaxTiO3 (x = 0.17) ceramics is discussed in the paper.