Order-disorder Phase Transition Research Articles

Critical Role of Long-Range Strain-Induced Interactions in Stabilizing Zener Ordering

Abstract As a fundamental theory for structural transformations, the Zener ordering of interstitials in a body-centered cubic host lattice, which was established more than half a century ago, has been challenged by recent first-principles investigations. In this Letter, we rigorously prove the existence of the Zener ordering via Monte Carlo simulations with complete interstitial interactions and demonstrate the critical role of long-range indirect strain-induced interactions in stabilizing the Zener ordering. These insights improve our understanding of the self-induced collective ordering of point defects in a host lattice, and complete the fundamental physics of alloys and order-disorder phase transitions.

Cooling-Induced Order-Disorder Phase Transition in CsPbBr3 Nanocrystal Superlattices.

Perovskite nanocrystal superlattices are being actively studied after reports have emerged on collective excitonic properties at cryogenic temperatures, where energetic disorder is minimized due to the frozen lattice vibrations. However, an important issue related to structural disorder of superlattices at low temperatures has received little attention to date. In this work, it is shown that CsPbBr3 nanocrystal superlattices undergo a reversible order-disorder transition upon cooling to 90 K. The transition consists of the loss of structural coherence, that is, increased nanocrystal misalignment, and contraction of the superlattices, as revealed by temperature-dependent X-ray diffraction, and is ascribed to the solidification of ligands (on the basis of Raman spectroscopy). Introducing shorter amines on the nanocrystal surface allows to mitigate these changes, improve order, and shorten interparticle distance. It is demonstrated that the low temperature phase of the short ligand-capped nanocrystal superlattices is characterized by a strong exciton migration observable in the photoluminescence decay, which is due to the shrinkage of the inter-nanocrystal distance.

Zipper-Like Dynamic Switching of Coordination Bonds Gives a Polar Bimetallic Halide Toward Self-Driven X-Ray Detection.

Polar molecular crystals hold a promise for controlling bulk physical properties originated in their unique switchable polarity via structural transformation. However, the mechanisms for switching polarization are mainly limited to displacive and disorder-order phase transitions, which rarely involve the reconstruction of chemical bonds. Here, we have switched and tuned electric polarization in a bimetallic halide, (Neopentylammonium)4AgBiBr8 (1), as verified by light-excited pyroelectric effect. Most notably, its Ag-Br coordination bonds show a zipper-like dynamic switching behavior from the 'locked' to 'unlocked' state, namely, reconstruction of chemical bonds. Coupling with the dynamic ordering of organic cations, this bond-switching transition makes a contribution to switchable polarization of 1. As expected, its polarity creates pyroelectric effect for self-driven X-ray detection with high sensitivity (3.8×103 μC Gy-1 cm-2) and low limit of detection (4.8 nGy s-1). This work on the bond-switching mechanism provides an avenue to design polar molecular candidate for smart optoelectronic devices.

Toward On-Demand Polymorphic Transitions of Organic Crystals via Side Chain and Lattice Dynamics Engineering.

Controlling polymorphism, namely, the occurrence of multiple crystal forms for a given compound, is still an open technological challenge that needs to be addressed for the reliable manufacturing of crystalline functional materials. Here, we devised a series of 13 organic crystals engineered to embody molecular fragments undergoing specific nanoscale motion anticipated to drive cooperative order-disorder phase transitions. By combining polarized optical microscopy coupled with a heating/cooling stage, differential scanning calorimetry, X-ray diffraction, low-frequency Raman spectroscopy, and calculations (density functional theory and molecular dynamics), we proved the occurrence of cooperative transitions in all the crystalline systems, and we demonstrated how both the molecular structure and lattice dynamics play crucial roles in these peculiar solid-to-solid transformations. These results introduce an efficient strategy to design polymorphic molecular crystalline materials endowed with specific molecular-scale lattice and macroscopic dynamics.

Effect of non-additive mixing on entropic bonding strength and phase behavior of binary nanocrystal superlattices.

Non-additive mixing plays a key role in the properties of molecular fluids and solids. In this work, the potential for athermal order-disorder phase transitions is explored in non-additive binary colloidal nanoparticles that form substitutionally ordered compounds, namely, for equimolar mixtures of octahedra + spheres, which form a CsCl lattice compound, and cubes + spheres, which form a NaCl crystal. Monte Carlo simulations that target phase coexistence conditions were used to examine the effect on compound formation of varying degrees of negative non-additivity created by component size asymmetry and by size-tunable indentations in the polyhedra's facets, intended to allow the nestling of neighboring spheres. Our results indicate that the stabilization of the compound crystal requires a relatively large degree of negative non-additivity, which depends on particle geometry and the packing of the relevant phases. It is found that negative non-additivity can be achieved in mixtures of large spheres and small cubes having no indentations and lead to the athermal crystallization of the NaCl lattice. For similarly sized components, athermal congruent transitions are attainable and non-additivity can be generated through indentations, especially for the cubes + spheres system. Increasing indentation leads to lower phase coexistence free energy and pressure in the cubes + spheres system but has the opposite effect in the octahedra + spheres system. These results indicate a stronger stabilizing effect on the athermal compound phase by the cubes' indentations, where a deeper nestling of the spheres leads to a denser compound phase and a larger reduction in the associated pressure-volume free-energy term.

Tunable disorder on the S-state majority-voter model.

We investigate the nonequilibrium phase transition in the S-state majority-vote model for S=2,3, and 4. Each site, k, is characterized by a distinct noise threshold, qk, which indicates its resistance to adopting the majority state of its Nv nearest neighbors. Precisely, this noise threshold is governed by a hyperbolic distribution, P(k)∼1/k, bounded within the limits e-α/2<qk<1/2. Here, the parameter α plays a pivotal role as it determines the extent of disorder in the system through the spread of the threshold distribution. Through Monte Carlo simulations and finite-size scaling analyses on regular square lattices, we deduced that the model undergoes a continuous order-disorder phase transition at a specific α=αc. Interestingly, the critical threshold exhibits a power-law decay, αc∼Nv-δ, as the number Nv of neighboring sites increases. From the least square fits to the data sets results in δ=0.65±0.01 for S=2, δ=0.92±0.01 for S=3, and δ=0.93±0.01 for S=4. Furthermore, the critical exponents β/ν and γ/ν are consistent with those found in the S-state Potts model.

Enhanced phase transition temperature achieved by CH3/H substitution in Sn-based perovskite

Organic-inorganic hybrid phase transition materials have garnered significant attention due to their excellent properties and broad applications in energy storage, temperature control switches, and optoelectronic devices. The regulation of the phase transition temperature (Tc) is necessary as it determines the properties and applications of materials. (TMTBA)2SnBr6 (1) (TMTBA = N,N,N-trimethyl‑tert-butylammonium) was synthesized, featuring the Tc around 225 K and then (DMTBA)2SnBr6 (2) (DMTBA = N,N-dimethyl‑tert-butylaminium) was obtained. Progressively, the 2 exhibited a great enhancement of Tc at 404 K, with a ΔTc reaching up to 179 K. Single-crystal structure analysis confirmed that 1 underwent isomorphic phase transitions, with the space groups of Pnma. In contrast, 2 underwent an order-disorder phase transition, and the space group changed from the low-temperature phase of I2/c to high-temperature phase of R3¯. What's more, the semiconductor properties and optical band gap of the materials were also investigated, 2.59 eV for 1 and 2.65 eV for 2. It is believed that this work can enrich the field of phase transition materials and provide some guidance for the regulation of Tc.

Unraveling Interdiffusion Phenomena and the Role of Nanoscale Diffusion Barriers in the Copper-Gold System.

Diffusion is one of the most fundamental concepts in materials science, playing a pivotal role in materials synthesis, forming, and degradation. Of particular importance is solid state interdiffusion of metals which defines the usable parameter space for material combinations in the form of alloys. This parameter space can be explored on the macroscopic scale by using diffusion couples. However, this method reaches its limit when going to low temperatures, small scales, and when testing ultrathin diffusion barriers. Therefore, this work transfers the principle of the diffusion couples to small scales by using core-shell nanowires and in situ heating. This allows us to delve into the interdiffusion dynamics of copper and gold, revealing the interplay between diffusion and the disorder-order phase transition. Our in situ TEM experiments in combination with chemical mapping reveal the interdiffusion coefficients of Cu and Au at low temperatures and highlight the impact of ordering processes on the diffusion behavior. The formation of ordered domains within the solid-solution is examined using high-resolution imaging and nanodiffraction including strain mapping. In addition, we examine the effectiveness of ultrathin Al2O3 barrier layers to control interdiffusion of the diffusion couple. Our findings indicate that a 5 nm thick layer serves as an efficient diffusion barrier. This research provides valuable insights into the interdiffusion behavior of Cu and Au on the nanoscale, offering potential applications in the development of miniaturized integrated circuits and nanodevices.

Oxygen vacancy order–disorder transition process during topotactic filament formation in a perovskite oxide tracked by Raman microscopy and transmission electron microscopy

Vacancy-ordered perovskite oxides are attracting attention due to their diverse functions such as resistive switching, electrocatalytic activity, oxygen diffusivity, and ferroelectricity. It is important to clarify the chemical lattice strains arising from compositional changes and the associated vacancy order–disorder phase transitions at the atomic scale. Here, we elucidate the intermediate process of a topotactic phase transition in Ca-doped bismuth ferrite films consisting of alternating stacks of oxygen perovskite layers and a brownmillerite-type oxygen vacancy layer. We use Raman spectroscopy and transmission electron microscopy to closely examine the evolution of local strains exerted on the constituent sub-layers by electrochemical oxidation. A negative Raman chemical shift is observed during oxidation, which is linearly correlated with the local negative chemical expansivity of the oxygen layer. It seemingly contradicts with the general trend that oxides undergo lattice contraction upon oxidation. Oxygen vacancies initially confined in the vacancy layers can be understood to diffuse into the oxygen layers during melting of the ordered structure. The finding deepens our understanding of the electro-chemo-mechanical coupling of vacancy-ordered oxides.

Anion Reorientations and Cation Diffusion in Nanostructured Closo-Borates: NMR and Quasielastic Neutron Scattering Studies

The dynamical properties of sodium closo-borate NaCB11H12 embedded into SiO2-based nanoporous scaffolds have been studied by nuclear magnetic resonance (NMR) and quasielastic neutron scattering (QENS) over wide temperature ranges. It has been found that a confinement of the closo-borate in nanopores suppresses the order-disorder phase transition, retaining the orientationally disordered phase with high reorientational mobility of the anions and high diffusive mobility of the cations down to low temperatures. This paper is based on the presentation at the RNIKS-2023 conference.

Order-disorder phase transitions in Fe81Ga19-RE ALLOYS (RE = Dy, Er, Tb, Yb) according to neutron diffraction data

New data on the phase compositions and structural transformations in a number of Fe81Ga19 alloys doped with trace amount (≤ 0.2 at.%) of rare earth elements are presented. The data are obtained in neutron diffraction experiments performed with high resolution and in continuous temperature scanning mode when heated to 900 °C and subsequent cooling. It has been established that structural rearrangements proceed in a generally identical manner both in the original Fe81Ga19 alloy and in its doped analogues. Slow heating and subsequent cooling of the alloys (rate ±2 °C/min) leads to the formation of clusters of the D03 phase with sizes in the range (200–300) Å in the matrix of the disordered A2 phase. The sizes and volume fraction of clusters (~0.3 of the sample volume) weakly depend on the specific composition. The degree of ordering of the clusters atomic structure changes with temperature according to a second-order phase transition and is close to unity at room temperature. The search for structural ordering corresponding to the modified D03 phase, discovered in a number of electron diffraction studies, did not lead to a positive result.

Second-Harmonic-Generation Switching via Pressure-Suppressed Dynamical Disorder.

Second-harmonic-generation (SHG) switching is an emerging phenomenon with potential applications in bistable storage and optical switches while also serving as a sensitive probe for inversion-symmetry. Temperature-induced disorder-order phase transition has been proven to be a rational design strategy for achieving SHG bi-state switching; however, pressure-sensitive SHG switching via a disorder-order structural transition mechanism is rarely reported and lacks sensitivity and cyclicity as practical switching materials. Herein, we demonstrate the pressure-induced "dynamical disorder-order" phase transition as an effective strategy for triggering SHG and SHG switching in NH4Cl. The "dynamical disorder-order" phase transition of NH4Cl occurring at as low as 1 GPa is confirmed by comprehensive in situ high-pressure XRD, molecular vibrational spectra, and Brillouin scattering spectra. The pressure-induced SHG is responsive to a wide excitation wavelength region (800-1500 nm), and the "off-on" switching is reversible for up to 50 cycles, setting a record for pressure-driven switching materials. It is worth noting that when pressure is further increased to 14 GPa, NH4Cl exhibits another SHG "on-off" switching, which makes it the first triplet SHG "off-on-off" switching material. Molecular dynamics simulations reveal the key role of N-H···Cl hydrogen bonding in the pressure-induced "dynamic disorder-order" mechanism. Finally, we verified that chemical pressure and physical pressure can jointly regulate the SHG switching behavior of NH4X (X = Cl, Br). The pressure-driven "dynamic disorder-order" transition mechanism sheds light on the rational design of multistable SHG switching materials for photoswitches and information storage.

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.

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

Synthesis, crystal structure study, characterization, and DFT investigation of a new nickel(II) complex, [dihomopiperazine nickel (II)] sulfate tetrahydrate

A new nickel (II) complex [NiL2](H2O)4(SO4), where L = 1,4-diazepane, has been synthesized by interaction between nickel sulfate and 1,4-diazepane. This complex crystallizes in the Pmcn orthorhombic unit cell with parameters a = 9.173(2) Å, b = 11.691(2) Å, c = 17.015(2) Å, V = 1824.9(5) Å3, and Z = 4. It possesses a mononuclear structure in which the central NiII atom is coordinated by four N atoms from two 1,4-diazepane ligands in a distorted square-planar geometry. In the crystal, the anions [SO4]2−, the cations [NiL2]2+, and the water molecules are held together by H-bonding to form a 2D supramolecular structure. Differential scanning calorimetry (DSC) results showed that this compound undergoes a reversible order–disorder phase transition at 486 K with a hysteresis of 32 K. In addition, electrical conductivity measurements showed that the complex has a conductivity value of 4.15 10−4 Ω−1cm−1 at 390 K. The Density Functional Theory (DFT) study results qualitatively supported the experimental data obtained by X-ray diffraction and thermogravimetric analysis (TGA).

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.