Order-disorder Phase Transition Research Articles

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

Dynamic Shape Change of Liquid Crystal Polymer Based on An Order-Order Phase Transition.

Liquid crystal actuators conventionally undergo shape changes across an order-disorder phase transition between liquid crystal (LC) and isotropic phases. In this study, we introduce an innovative Liquid Crystal Polymer (LCP) actuator harnessing an order-order LC phase transition mechanism. The LCP film is easily stretchable within the LC phase, facilitated by the π-π stacking of phenyl groups serving as robust physical crosslinking points, and thereby transforms to a stable monodomain structure. The resultant monodomain LCP actuator shows a distinctive reversible dynamic shape change, exhibiting extension followed by contraction along the LC director on cooling. The extension is propelled by the reversible smectic C to smectic A phase transition, and the contraction is attributed to the re-entry to the smectic C phase from smectic A phase. Thermal annealing temperature determines this peculiar dynamic shape change, which occurs during both heating and cooling processes. This pivotal attribute finds manifestation in gripper and flower-shaped actuators, adeptly executing grabbing and releasing as well as blooming and closure motions within a single thermal stimulation. In essence, our study introduces an innovative approach to the realm of LCP actuators, ushering in a new avenue for the design and fabrication of versatile and dynamically responsive LCP actuators.

Directed propaganda in the majority-rule model

Advertisement and propaganda have changed continuously in the past decades, mainly due to the people’s interactions at online platforms and social networks, and operate nowadays reaching a highly specific online audience instead targeting the masses. The impacts of this new media effect, oriented directly for a specific audience, are investigated on this study, in which we focus on the opinion evolution of agents in the majority-rule model, considering the presence of directed propaganda. We introduce p as the probability of a “positive” external propaganda and q as the probability to the agents follow the external propaganda. Our results show that the usual majority-rule model stationary state is reached, with a full consensus, only for two cases, namely when the external propaganda is absent or when the media favors only one of the two opinions. However, even for a small influence of external propaganda, the final state is reached with a majority opinion dominating the population. For the case in which the propaganda influence is strong enough among the agents, we show that the consensus cannot be reached at all, and we observe the polarization of opinions. In addition, we show through analytical and numerical results that the system undergoes an order–disorder phase transition that occurs at [Formula: see text] for the case [Formula: see text].

Barocaloric Effects in Dialkylammonium Halide Salts.

Barocaloric effects─solid-state thermal changes induced by the application and removal of hydrostatic pressure─offer the potential for energy-efficient heating and cooling without relying on volatile refrigerants. Here, we report that dialkylammonium halides─organic salts featuring bilayers of alkyl chains templated through hydrogen bonds to halide anions─display large, reversible, and tunable barocaloric effects near ambient temperature. The conformational flexibility and soft nature of the weakly confined hydrocarbons give rise to order-disorder phase transitions in the solid state that are associated with substantial entropy changes (>200 J kg-1 K-1) and high sensitivity to pressure (>24 K kbar-1), the combination of which drives strong barocaloric effects at relatively low pressures. Through high-pressure calorimetry, X-ray diffraction, and Raman spectroscopy, we investigate the structural factors that influence pressure-induced phase transitions of select dialkylammonium halides and evaluate the magnitude and reversibility of their barocaloric effects. Furthermore, we characterize the cyclability of thin-film samples under aggressive conditions (heating rate of 3500 K s-1 and over 11,000 cycles) using nanocalorimetry. Taken together, these results establish dialkylammonium halides as a promising class of pressure-responsive thermal materials.

An order-disorder phase transition in alloy 783 bolts after long-term service

Ni-Co-Fe based alloy 783 is commonly employed as bolt material in power plants. Its initial state possesses a γ matrix strengthened through B2-type β phase and L12-type γ' phase. Over prolonged service, the alloy displays an observed increase in strength along with certain embrittlement. After 100 and 123 months of service at 600 °C, a pine-like phase enriched with Co and Fe occurs in the matrix, which is confirmed to be a BCC phase with a lattice parameter of 2.87 Å. These BCC precipitates also manifest within the coarse β particles and are coherent with the B2 phase, showing a cuboidal shape. Thermodynamic calculations suggest the transformation from the ordered B2 phase to the disordered BCC phase at temperatures below 670 °C. The identification of the order-disorder phase transition deepens the understanding of phase transition after long-term service in alloy 783 and the related mechanical properties evolution in addition to previous works.

Prediction and understanding of barocaloric effects in orientationally disordered materials from molecular dynamics simulations

Due to its high energy efficiency and environmental friendliness, solid-state cooling based on the barocaloric (BC) effect represents a promising alternative to traditional refrigeration technologies relying on greenhouse gases. Plastic crystals displaying orientational order-disorder solid-solid phase transitions have emerged among the most gifted materials on which to realize the full potential of BC solid-state cooling. However, a comprehensive understanding of the atomistic mechanisms on which order-disorder BC effects are sustained is still missing, and rigorous and systematic methods for quantitatively evaluating and anticipating them have not been yet established. Here, we present a computational approach for the assessment and prediction of BC effects in orientationally disordered materials that relies on atomistic molecular dynamics simulations and emulates quasi-direct calorimetric BC measurements. Remarkably, the proposed computational approach allows for a precise determination of the partial contributions to the total entropy stemming from the vibrational and molecular orientational degrees of freedom. Our BC simulation method is applied on the technologically relevant material CH3NH3PbI3 (MAPI), finding giant BC isothermal entropy changes (∣ΔSBC∣ ~ 10 J K−1 kg−1) under moderate pressure shifts of ~0.1 GPa. Intriguingly, our computational analysis of MAPI reveals that changes in the vibrational degrees of freedom of the molecular cations, not their reorientational motion, have a major influence on the entropy change that accompanies the order-disorder solid-solid phase transition.

SHINERS Study of Chloride Order-Disorder Phase Transition and Solvation of Cu(100).

Shell-isolated nanoparticle enhanced Raman spectroscopy (SHINERS) and density functional theory (DFT) are used to probe Cl- adsorption and the order-disorder phase transition associated with the c(2 × 2) Cl- adlayer on Cu(100) in acid media. A two-component ν(Cu-Cl) vibrational band centered near 260 ± 1 cm-1 is used to track the potential dependence of Cl- adsorption. The potential dependence of the dominant 260 cm-1 component tracks the coverage of the fluctional c(2 × 2) Cl- phase on terraces in good agreement with the normalized intensity of the c(2 × 2) superstructure rods in prior surface X-ray diffraction (SXRD) studies. As the c(2 × 2) Cl- coverage approaches saturation, a second ν(Cu-Cl) component mode emerges between 290 and 300 cm-1 that coincides with the onset and stiffening of step faceting where Cl- occupies the threefold hollow sites to stabilize the metal kink saturated Cu <100> step edge. The formation of the c(2 × 2) Cl- adlayer is accompanied by the strengthening of ν(O-H) stretching modes in the adjacent non-hydrogen-bonded water at 3600 cm-1 and an increase in hydronium concentration evident in the flanking H2O modes at 3100 cm-1. The polarization of the water molecules and enrichment of hydronium arise from the combination of Cl- anionic character and lateral templating provided by the c(2 × 2) adlayer, consistent with SXRD studies. At negative potentials, Cl- desorption occurs followed by development of a sulfate νs(S═O) band. Below -1.1 V vs Hg/HgSO4, a new 200 cm-1 mode emerges congruent with hydride formation and surface reconstruction reported in electrochemical scanning tunneling microscopy studies.