Order-disorder Phase Transition Research Articles

Machine Learning Force Field-Aided Cluster Expansion Approach to Phase Diagram of Alloyed Materials.

First-principles approaches based on density functional theory (DFT) have played important roles in the theoretical study of multicomponent alloyed materials. Considering the highly demanding computational cost of direct DFT-based sampling of the configurational space, it is crucial to build efficient and low-cost surrogate Hamiltonian models with DFT accuracy for efficient simulation of alloyed systems with configurational disorder. Recently, the machine learning force field (MLFF) method has been proposed to tackle complicated multicomponent disordered systems. However, the importance of integrating significant physical considerations, including, in particular, convex hull preservation, which is the prerequisite for the accurate prediction of phase diagrams, into the training process of the MLFF remains rarely addressed. In this work, a workflow is proposed to train a convex-hull-preserved (CHP) MLFF for binary alloy systems, based on which the order-disorder phase boundary is predicted by using the Wang-Landau Monte Carlo (WLMC) technique. The predicted values for order-disorder phase transition temperatures agree well with the experiment. The CHP-MLFF is further used to build CE models with the same accuracy as the MLFF and higher efficiency in sampling configurational space. Using the results obtained from the MLFF-based WLMC simulation as a reference, the performances of different schemes for constructing CE models were evaluated in a transparent manner, which revealed the close correlation between the prediction accuracy of ground-state configurations and that of the order-disorder phase transition temperature. This work clearly indicates the great importance of reproducing the convex hull and energetics of ground-state configurations when constructing surrogate Hamiltonians for the statistical modeling of alloyed systems.

Effective optimization of atomic decoration in giant and superstructurally ordered crystals with machine learning.

Crystals with complicated geometry are often observed with mixed chemical occupancy among Wyckoff sites, presenting a unique challenge for accurate atomic modeling. Similar systems possessing exact occupancy on all the sites can exhibit superstructural ordering, dramatically inflating the unit cell size. In this work, a crystal graph convolutional neural network (CGCNN) is used to predict optimal atomic decorations on fixed crystalline geometries. This is achieved with a site permutation search (SPS) optimization algorithm based on Monte Carlo moves combined with simulated annealing and basin-hopping techniques. Our approach relies on the evidence that, for a given chemical composition, a CGCNN estimates the correct energetic ordering of different atomic decorations, as predicted by electronic structure calculations. This provides a suitable energy landscape that can be optimized according to site occupation, allowing the prediction of chemical decoration in crystals exhibiting mixed or disordered occupancy, or superstructural ordering. Verification of the procedure is carried out on several known compounds, including the superstructurally ordered clathrate compound Rb8Ga27Sb16 and vacancy-ordered perovskite Cs2SnI6, neither of which was previously seen during the neural network training. In addition, the critical temperature of an order-disorder phase transition in solid solution CuZn is probed with our SPS routines by sampling site configuration trajectories in the canonical ensemble. This strategy provides an accurate method for determining favorable decoration in complex crystals and analyzing site occupation at unprecedented speed and scale.

Hidden quantum criticality and entanglement in quench dynamics

Entanglement exhibits universal behavior near the ground-state critical point where correlations are long ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emergent quantum criticality to the soft mode not getting excited in spite of the quench. Moreover, the results presented here are universal to models whose low-energy or long-wavelength dynamics are well described by a free-fermionic field theory. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators. Published by the American Physical Society 2024

Dynamics of glassy state in MAPbBr3-xClx mixed lead halide perovskites

Mixed lead halide perovskites have shown remarkable performance in photovoltaic and optoelectronic applications. Pure hybrid halide perovskites undergo clear phase transitions, however, the phase transitions in mixed perovskites are less studied. We present a contrasting behavior of the phase transition dynamics of MAPbBr3-xClx (MA = CH3NH3+) mixed halide perovskites compared to the pure MAPbX3 (X = Cl, Br) counterparts, which typically exhibit order-disorder phase transitions through a series of distinct structural phases. We have employed several spectroscopic techniques including temperature-dependent PXRD, Raman, dielectric and Brillouin spectroscopy. The results demonstrate that the mixed halide perovskite MAPbBr1.5Cl1.5 does not undergo any structural phase transition typically observed in pure halide perovskites. We observed signatures of glassy behavior in mixed compositions of this system. In addition, we also explored the effects of replacing A-site cation on the phase transition behaviors. The results contribute to the understanding of phase transition mechanisms in perovskites and have implications for their stability and optoelectronic properties.

Achieving High Operating-Temperature Self-powered X-Ray Detection in Multilayered Hybrid Perovskites through Arylamine Intercalation.

Polar metal halide hybrid perovskites (PHPs) that exhibit outstanding bulk photovoltaic effect (BPVE), excellent semiconductor features, and strong radiation absorption ability, have shown prominent advantages in highly sensitive direct X-ray detection. However, it is still a challenge to explore PHPs with high BPVE temperature ranges, answering the demand of developing thermally stable passive X-ray detection. Herein, by intercalating arylamine into lead tribromide and inducing order-disorder phase transition, a 2D multilayered PHPs (BZA)2(MA)Pb2Br7 (BZPB, BZA = benzylamine, MA = methylamine) is synthesized. BZPB crystallizes in a polar space group Aea2 at a low-temperature phase and demonstrates a significant open-circuit of 0.3V deriving from BPVE under X-ray irradiation. Meanwhile, the strong X-ray absorption coefficient and outstanding carrier transport capability of the bilayered lead halide framework associated with the polar BPVE give BZPB excellent X-ray detection abilities. At 0V bias, the impressive sensitivity of BZPB is 98 µC Gy-1 cm-2. Importantly, the introduction of the rigid BZA ring increases the energy barrier of phase transition and thus dramatically enhances the X-ray detection operating temperature of BZPB up to 409 K without significant performance degradation. This work strongly reveals the great potential of rational design of metal halide hybrid perovskites for X-ray detection applications.

Order–disorder phase transitions in front of the exit during human crowd evacuations

Human crowds often exhibit collective behaviors through self-organization, such as orderly queueing and disordered congestion at exits. Understanding the dynamic mechanisms behind these behaviors is crucial for pedestrian traffic management and the handling of mass crowds. Although current models and experiments have provided profound insights into ordered and disordered pedestrian groups separately, the transition mechanism from order to disorder within pedestrian crowds in front of exits remains unclear. In this study, a pedestrian queueing evacuation experiment was presented to demonstrate the phase transition process of pedestrian movement states as urgency levels in the environment change. We discovered the migration pattern of the phase transition point under evacuation control and identified different propagation modes of pedestrian velocity waves. Furthermore, a pedestrian motion model based on experimental data and observed phenomena was established. This model not only replicates the observed phenomena and regularities from the experiments but also reveals the quantitative phase transition mechanism of pedestrian movement under the influence of a single factor (i.e., urgency level or queueing ratio). Our findings hold significant implications for various domains, including pedestrian management, traffic control, and pedestrian dynamics.

Gradient elasticity in Swift–Hohenberg and phase-field crystal models

The Swift–Hohenberg (SH) and phase-field crystal (PFC) models are minimal yet powerful approaches for studying phenomena such as pattern formation, collective order, and defects via smooth order parameters. They are based on a free-energy functional that inherently includes elasticity effects. This study addresses how gradient elasticity (GE), a theory that accounts for elasticity effects at microscopic scales by introducing additional characteristic lengths, is incorporated into SH and PFC models. After presenting the fundamentals of these theories and models, we first calculate the characteristic lengths for various lattice symmetries in an approximated setting. We then discuss numerical simulations of stress fields at dislocations and comparisons with analytic solutions within first and second strain-gradient elasticity. Effective GE characteristic lengths for the elastic fields induced by dislocations are found to depend on the free-energy parameters in the same manner as the phase correlation length, thus unveiling how they change with the quenching depth. The findings presented in this study enable a thorough discussion and analysis of small-scale elasticity effects in pattern formation and crystalline systems using SH and PFC models and, importantly, complete the elasticity analysis therein. Additionally, we provide a microscopic foundation for GE in the context of order-disorder phase transitions.

Towards accurate prediction of configurational disorder properties in materials using graph neural networks

The prediction of configurational disorder properties, such as configurational entropy and order-disorder phase transition temperature, of compound materials relies on efficient and accurate evaluations of configurational energies. Previous cluster expansion methods are not applicable to configurationally-complex material systems, including those with atomic distortions and long-range orders. In this work, we propose to leverage the versatile expressive capabilities of graph neural networks (GNNs) for efficient evaluations of configurational energies and present a workflow combining attention-based GNNs and Monte Carlo simulations to calculate the disorder properties. Using the dataset of face-centered tetragonal gold copper without and with local atomic distortions as an example, we demonstrate that the proposed data-driven framework enables the prediction of phase transition temperatures close to experimental values. We also elucidate that the variance of the energy deviations among configurations controls the prediction accuracy of disorder properties and can be used as the target loss function when training and selecting the GNN models. The work serves as a fundamental step toward a data-driven paradigm for the accelerated design of configurationally-complex functional material systems.

Colossal Reversible Barocaloric Effects in a Plastic Crystal Mediated by Lattice Vibrations and Ion Diffusion.

Solid-state methods for cooling and heating promise a sustainable alternative to current compression cycles of greenhouse gases and inefficient fuel-burning heaters. Barocaloric effects (BCE) driven by hydrostatic pressure (p) are especially encouraging in terms of large adiabatic temperature changes (|ΔT| ≈ 10K) and isothermal entropy changes (|ΔS| ≈ 100JK-1kg-1). However, BCE typically require large pressure shifts due to irreversibility issues, and sizeable |ΔT| and |ΔS| seldom are realized in a same material. Here, the existence of colossal and reversible BCE in LiCB11H12 is demonstrated near its order-disorder phase transition at ≈380K. Specifically, for Δp ≈ 0.23(0.10)GPa, |ΔSrev| = 280(200)JK-1kg-1 and |ΔTrev| = 32(10)K are measured, which individually rival with state-of-the-art BCE figures. Furthermore, pressure shifts of the order of 0.1GPa yield huge reversible barocaloric strengths of ≈2JK-1kg-1MPa-1. Molecular dynamics simulations are performed to quantify the role of lattice vibrations, molecular reorientations, and ion diffusion on the disclosed BCE. Interestingly, lattice vibrations are found to contribute the most to |ΔS| while the diffusion of lithium ions, despite adding up only slightly to the entropy change, is crucial in enabling the molecular order-disorder phase transition.

THz spectroscopy on the amino acids L-serine and L-cysteine.

We present a detailed study on the temperature-dependent THz spectra of the polycrystalline amino acids, L-serine and L-cysteine, for wavenumbers from 20 to 120cm-1 and temperatures from 4 to 300K. Even though the structure of these two amino acids is very similar, with a sulfur atom in the side chain of cysteine instead of an oxygen atom in serine, the excitation spectra are drastically different. Obviously, the vibrational dynamics strongly depend on the ability of cysteine to form sulfur-hydrogen bonds. In addition, cysteine undergoes an order-disorder type phase transition close to 80K, documented by additional specific heat experiments, with accompanying anomalies in the THz results. On increasing temperatures, well-defined vibrational excitations exhibit significant shifts in the eigenfrequencies with concomitant line-broadening yielding partly overlapping modes. Interestingly, several modes completely lose all their dipolar strength and are unobservable under ambient conditions. Comparing the recent results to the published work utilizing THz, Raman, and neutron-scattering techniques, as well as with abinitio simulations, we aim at a consistent analysis of the results ascribing certain eigenfrequencies to distinct collective lattice modes. We document that THz spectra can be used to fine-tune the parameters of model calculations and as fingerprint properties of certain amino acids. In addition, we analyzed the low-temperature heat capacity of both the compounds and detected strong excess contributions compared to the canonical Debye behavior of crystalline solids, indicating soft excitations and a strongly enhanced phonon-density of states at low frequencies.

Critical behavior of the dimerized Si(001) surface: Continuous order-disorder phase transition in the two-dimensional Ising universality class

Critical behavior of the dimerized Si(001) surface: Continuous order-disorder phase transition in the two-dimensional Ising universality class

Phase transition and universality of the majority-rule model on complex networks

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks’ nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model.

Understanding variations of thermal hysteresis in barocaloric plastic crystal neopentyl glycol using correlative microscopy and calorimetry

Plastic crystals (PCs) exhibit solid–solid order-disorder first-order phase transitions that are accompanied by large correlated thermal and volume changes. These characteristics make PCs promising barocaloric solid-state working bodies for heating and cooling applications. However, understanding the variation of transition temperatures and thermal hysteresis in PCs with cycling is critical if these materials are to replace traditional gaseous refrigerants. Here, for the archetypal barocaloric PC neopentyl glycol (NPG), we correlate microstructure obtained from scanning electron microscopy with local and total thermal changes at the phase transition from infra-red imaging and calorimetry, respectively. We outline an evolution in microstructure as NPG recrystallises during repeated thermal cycling through its solid–solid phase transition. The observed microstructural changes are correlated with spatially inhomogeneous heat transfer, yielding direct insight into the kinetics of the phase transition. Our results suggest that the interplay of these processes affects the undesirable thermal hysteresis and the nature of the kinetic steady-state microstructures that are stabilised during cycling between the ordered and disordered phases. These observations have implications for using NPG and other PCs as technologically relevant barocaloric materials and suggest ways in which the hysteresis in these types of materials may be modified.

Optical, electrical, and crystal structure study of BaZr0.01Ti0.99O3 ceramics modified with Gd3+ and Y3+ rare-earth ions

Ceramics with compositions Ba0.95Gd0.034Ti0.99Zr0.01O3 (BGdZT) and Ba0.95Y0.034Ti0.99Zr0.01O3 (BYZT) were prepared using the solid-state reaction method. The single tetragonal phase (space group P4mm) of BGdZT and BYZT ceramics is verified by analyzing X-ray spectra using the Rietveld method. The analysis of the tolerance factor (t) reveals an order-disorder phase transition in the tetragonal structure, resulting from the displacement of Ti4+/Zr4+ along the c-axis. A significant correlation is observed between the tolerance factor (t) and the phase transition temperature (Tc), as well as between the band gap of optical measurements and the degree of displacement of Ti4+/Zr4+ along the c-axis. The analysis of high-temperature electrical properties indicates that the conduction mechanism in both studied materials is a correlated barrier hopping (CBH) model, and electrical conductivity improves with increasing densification. The non-Debye behavior is confirmed by the curves of the M′′ vs.ƒ(Hz). The combination of M′′/M′′max and Z′′/Z′′max traces confirms the type of short-range charge carrier mobility.

Room-Temperature Anisotropic Actuation Driven by a Synergistic Order-Disorder and Displacive Phase Transition in a Ferroelectric Crystal.

Actuating materials convert different forms of energy into mechanical responses. To satisfy various application scenarios, they are desired to have rich categories, novel functionalities, clear structure-property relationships, fast responses, and, in particular, giant and reversible shape changes. Herein, we report a phase transition-driven ferroelectric crystal, (rac-3-HOPD)PbI3 (3-HOPD = 3-hydroxypiperidine cation), showing intriguingly large and anisotropic room-temperature actuating behaviors. The crystal consists of rigid one-dimensional [PbI3] anionic chains running along the a-axis and discrete disk-like cations loosely wrapping around the chains, leaving room for anisotropic shape changes in both the b- and c-axes. The shape change is switched by a ferroelectric phase transition occurring at around room temperature (294 K), driven by the exceptionally synergistic order-disorder and displacive phase transition. The rotation of the cations exerts internal pressure on the stacking structure to trigger an exceptionally large displacement of the inorganic chains, corresponding to a crystal lattice transformation with length changes of +24.6% and -17.5% along the b- and c-axis, respectively. Single crystal-based prototype devices of circuit switches and elevators have been fabricated by exploiting the unconventional negative temperature-dependent actuating behaviors. This work provides a new model for the development of multifunctional mechanically responsive materials.

A High Working Temperature Multiferroic Induced by Inverse Temperature Symmetry Breaking.

Molecular-based multiferroic materials that possess ferroelectric and ferroelastic orders simultaneously have attracted tremendous attention for their potential applications in multiple-state memory devices, molecular switches, and information storage systems. However, it is still a great challenge to effectively construct novel molecular-based multiferroic materials with multifunctionalities. Generally, the structure of these materials possess high symmetry at high temperatures, while processing an obvious order-disorder or displacement-type ferroelastic or ferroelectric phase transition triggered by symmetry breaking during the cooling processes. Therefore, these materials can only function below the Curie temperature (Tc), the low of which is a severe impediment to their practical application. Despite great efforts to elevate Tc, designing single-phase crystalline materials that exhibit multiferroic orders above room temperature remains a challenge. Here, an inverse temperature symmetry-breaking phenomenon was achieved in [FPM][Fe3(μ3-O)(μ-O2CH)8] (FPM stands for 3-(3-formylamino-propyl)-3,4,5,6-tetrahydropyrimidin-1-ium, which acts as the counterions and the rotor component in the network), enabling a ferroelastoelectric phase at a temperature higher than Tc (365 K). Upon heating from room temperature, two-step distinct symmetry breaking with the mm2Fm species leads to the coexistence of ferroelasticity and ferroelectricity in the temperature interval of 365-426 K. In the first step, the FPM cations undergo a conformational flip-induced inverse temperature symmetry breaking; in the second step, a typical ordered-disordered motion-induced symmetry breaking phase transition can be observed, and the abnormal inverse temperature symmetry breaking is unprecedented. Except for the multistep ferroelectric and ferroelastic switching, this complex also exhibits fascinating nonlinear optical switching properties. These discoveries not only signify an important step in designing novel molecular-based multiferroic materials with high working temperatures, but also inspire their multifunctional applications such as multistep switches.

Fe-Ni based alloys as rare-earth free gap permanent magnets

L10-ordered FeNi phase has potential as a rare-earth free permanent magnet due to its large magnetization and high Curie temperature. However, low long-range crystal ordering and weak magnetocrystalline anisotropy (Ku) impede its practical use in a technologically relevant permanent magnet. Employing density functional and Monte Carlo simulations, we demonstrate the substantial improvements on structural and thermal stability, disorder-order phase transition, and intrinsic permanent magnetic properties of Fe−Ni structures. We propose that this is achievable through the complementary elemental substitutions by metal elements (M) and interstitial doping with 2p elements. Fe1-xMxNi with simple metal (M = Ga and Al) and metalloid (M = Ge and Si) elemental substitutions at x = 0.5 are broadly known as Heusler (L21) structures with no permanent magnet characteristics. On the contrary, we find that for x = 0−0.5, L10-type structure is energetically favored over the Heusler-type structures. The predicted structures exhibit Ku values up to approximately 2.1 MJ/m3, which is roughly three times that of FeNi phase (0.68 MJ/m3), where the absolute value of Ku depends on the degree of L10 crystal ordering. Interstitial doping with B elevates Ku further up to a maximum value of 3.9 MJ/m3 (at 0 K), leading to room-temperature intrinsic permanent magnetic properties, including maximum energy density product (BH)max, anisotropy field μ0Ha, and hardness parameter κ, comparable to the widely investigated MnBi and MnAl permanent magnets. These results may serve as a guideline in designing Fe−Ni based rare-earth free gap permanent magnetic materials that were previously overlooked.

π Phase Interlayer Shift and Stacking Fault in the Kagome Superconductor CsV_{3}Sb_{5}.

The stacking degree of freedom is a crucial factor in tuning material properties and has been extensively investigated in layered materials. The kagome superconductor CsV_{3}Sb_{5} was recently discovered to exhibit a three-dimensional CDW phase below T_{CDW}∼94 K. Despite the thorough investigation of in-plane modulation, the out-of-plane modulation has remained ambiguous. Here, our polarization- and temperature-dependent Raman measurements reveal the breaking of C_{6} rotational symmetry and the presence of three distinct domains oriented at approximately 120° to each other. The observations demonstrate that the CDW phase can be naturally explained as a 2c staggered order phase with adjacent layers exhibiting a relative π phase shift. Further, we discover a first-order structural phase transition at approximately 65K and suggest that it is a stacking order-disorder phase transition due to stacking fault, supported by the thermal hysteresis behavior of a Cs-related phonon mode. Our findings highlight the significance of the stacking degree of freedom in CsV_{3}Sb_{5} and offer structural insights to comprehend the entanglement between superconductivity and CDW.

Criticality Controlling Mechanisms in Nematic Liquid Crystals

We theoretically study the generic mechanisms that could establish critical behavior in nematic liquid crystals (NLCs). The corresponding free energy density terms should exhibit linear coupling with the nematic order parameter and, via this coupling, enhance the nematic order. We consider both temperature- and pressure-driven, order–disorder phase transitions. We derive a scaled effective free energy expression that describes how qualitatively different mechanisms enforce critical behavior. Our main focus is on the impact of nanoparticles (NPs) in homogeneous NP-NLC mixtures. We illustrate that in the case of pressure-driven phase changes, lower concentrations are needed to impose critical point conditions in comparison with pure temperature variations.

Order–Disorder Phase Transitions in Fe81Ga19–RE Alloys (RE = Dy, Er, Tb, Yb) According to Neutron Diffraction Data

Order–Disorder Phase Transitions in Fe81Ga19–RE Alloys (RE = Dy, Er, Tb, Yb) According to Neutron Diffraction Data