Order-disorder Transition Research Articles

The impact of social noise on the majority rule model across various network topologies

We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order–disorder transition can reflect the consensus-polarization state in a social context. This study covers various network topologies, including complete graphs, two-dimensional (2-D) square lattices, three-dimensional (3-D) square lattices, and heterogeneous or complex networks such as Watts–Strogatz (W-S), Barabási-Albert (B-A), and Erdős-Rényi (E-R) networks, as well as their combinations (multilayer network). Social behavior is represented by the parameter p, which indicates the probability of agents exhibiting nonconformist behavior. Our results show that the model exhibits a continuous phase transition across all networks. Through finite-size scaling analysis and evaluation of critical exponents, our results suggest that the model falls into the same universality class as the Ising model.

A Ferroelastic Salt Cocrystal with Ultraviolet Emission.

The coexistence and coupling of photoluminescence and ferroelasticity in a single matter are vitally important for developing multifunctional materials and devices. However, the effective construction of ferroelastics with efficient photoluminescence, especially in the ultraviolet range, is a great challenge. In this work, a salt cocrystal, (DPA)(DPAH)PF6 (DPA = diphenylamine, DPAH = diphenylamine cation), with ultraviolet emission and ferroelasticity was reported by introducing the anion group PF6- in the parent DPA crystal. Besides, the thermally triggered order-disorder transition of PF6- groups leads to a ferroelastic phase transition at ∼340 K with the Aizu notation of 2/mF1̅. In addition, (DPA)(DPAH)PF6 displays a bright ultraviolet emission at 392 nm with a photoluminescence quantum yield of 49.4%. This work presents a strategy to achieve ultraviolet (UV)-emissive ferroelastic based on the luminescent organic crystal, which not only extends the luminescence of ferroelastic to the UV region but also paves a new way for the development of multifunctional ferroelastic materials and devices.

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.

The disorder-order transition of FeCuPt nanoparticles with various Cu content

The effect of adding a third-element on disorder-order transition of FePt has been demonstrated using FeCuPt alloy as a model. The introduction of Cu leads to an increase in the ordering degree, and a moderate amount of Cu enhancing the most. Density Functional Theory calculations indicate that the disorder-order transition in FePt is influenced by the ordering temperature and vacancy formation energy. FePtCu alloy with a moderate Cu content exhibits the lowest vacancy formation energy in the L10-phase, which promotes the atom diffusion during annealing and resulting in a higher ordering degree. This study summarizes the annealing temperature, time, and thermodynamic or kinetic conditions required to achieve L10-FePtX alloy with superior ordering degrees. The findings offer valuable insights for selecting suitable third-elements and annealing parameters to produce L10-FePtX alloy with enhanced ordering degrees.

Suppressing Energy Migration via Antiparallel Spin Alignment in One-Dimensional Mn2+ Halide Magnets with High Luminescence Efficiency.

Photoexcited energy migration is prone to causing luminescence quenching in Mn2+ luminescent materials, presenting a formidable challenge for optoelectronic applications. Although various strategies and mechanisms have been proposed to mitigate this issue, the role of spin alignment between adjacent Mn2+ ions has remained largely unexamined. In this study, we have elucidated the influence of spin alignment on energy migration within the one-dimensional Mn2+-metal halide compound (CH3)4NMnCl3 (TMMC) through variable-temperature photoluminescence (PL) and magnetic-optical spectroscopy. This investigation was conducted with reference to (CH6N3)2MnCl4 (GUA) with isolated [Mn3Cl12]6- trimers and Cd2+-doped TMMC. The spin order in TMMC below approximately 55 K is demonstrated by the disorder-order transition observed in the temperature-dependent magnetic susceptibility. This finding is further corroborated by the negligible shift in the temperature- and field-dependent emission peaks, a consequence of magnetic saturation. Our results indicate that the antiparallel spin alignment along the Mn2+ chain in TMMC effectively suppresses energy migration and multiphonon relaxation, thereby reducing nonradiative transitions and enhancing the photoluminescence quantum yield (PLQY). This research casts new light on the potential for developing high-performance Mn2+-doped phosphors for optoelectronic and spin-photonic applications, offering insights into the manipulation of spin and energy dynamics in these materials.

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.

Wave Function Localization Reduces the Bandgap of Disordered Double Perovskite Cs2AgBiBr6.

Double perovskite Cs2AgBiBr6 is a promising alternative to lead-based perovskites with excellent stability and attractive optoelectronic properties. However, a relatively large bandgap severely limits its performance in many applications such as solar cells and photodetectors. It has been reported that a random distribution of Ag and Bi atoms in Cs2AgBiBr6 effectively reduces its bandgap without introducing dopants or impurities, while the mechanism remains unclear. Here, using density functional theory calculations, we demonstrate that the Ag-Bi disorder in Cs2AgBiBr6 generates localized electronic states as band edges to regulate the bandgap. The disordered structures segregate Ag and Bi atoms in the lattice, and the formed homoatomic clusters lead to wave function localization. Moreover, the bandgap decrease exhibits a non-monotonic dependence on the degree of disorder. Our results are comparable with experimental observations and provide crucial insights into understanding the order-disorder transition in double perovskites.

Revealing Missing Protein–Ligand Interactions Using AlphaFold Predictions

Protein–ligand interactions represent an essential step to understand the bases of molecular recognition, an intense field of research in many scientific areas. Structural biology has played a central role in unveiling protein–ligand interactions, but current techniques are still not able to reliably describe the interactions of ligands with highly flexible regions. In this work, we explored the capacity of AlphaFold2 (AF2) to estimate the presence of interactions between ligands and residues belonging to disordered regions. As these interactions are missing in the crystallographic-derived structures, we called them “ghost interactions”. Using a set of protein structures experimentally obtained after AF2 was trained, we found that the obtained models are good predictors of regions associated with order–disorder transitions. Additionally, we found that AF2 predicts residues making ghost interactions with ligands, which are mostly buried and show differential evolutionary conservation with the rest of the residues located in the flexible region. Our findings could fuel current areas of research that consider, given their biological relevance and their involvement in diseases, intrinsically disordered proteins as potentially valuable targets for drug development.

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.

Absence of Amorphous Forms When Ice XIc Is Compressed at Low Temperature.

It is generally believed that ice crystal-to-crystal transitions do not occur below the glass-transition temperature. For instance, under compression, ice I becomes a metastable state but does not transform into other high-pressure ice crystals, and applying excessive pressure ends up causing its collapse into high-density amorphous ice (HDA). Here, we perform molecular dynamics (MD) simulations to demonstrate that a hydrogen-ordered form of cubic ice (ice Ic) transforms to a hydrogen-ordered form of ice IV without yielding HDA. Our comprehensive search for different configurations combined with density functional theory (DFT) calculations indicates that the hydrogen-ordered ice IV formed by compression would be the thermodynamically most stable hydrogen-ordered ice IV configuration. We also predict the phase boundary of hydrogen order-disorder transition of ice IV, which remains unknown in experiments. Our findings suggest that hydrogen ordering enables an immediate transition between ice polymorphs that is impossible when the hydrogens are disordered.

Construction and Sampling of Alloy Cluster Expansions—A Tutorial

Crystalline alloys and related mixed systems make up a large family of materials with high tunability that have been proposed as the solution to a large number of energy-related material design problems. Because of the presence of chemical order and disorder in these systems, neither experimental efforts nor computational methods alone are sufficient to span the inherently large configuration space. Therefore, fast and accurate models are necessary. To this end, cluster expansions have been widely and successfully used for the past few decades. Cluster expansions are generalized Ising models designed to predict the energy of any atomic configuration of a system after training on a small subset of the available configurations. Constructing and sampling a cluster expansion consists of multiple steps that have to be performed with care. In this tutorial, we provide a comprehensive guide to this process, highlighting important considerations and potential pitfalls. The tutorial consists of three parts, starting with cluster expansion construction for a relatively simple system, continuing with strategies for more challenging systems such as surfaces, and closing with examples of Monte Carlo sampling of cluster expansions to study order-disorder transitions and phase diagrams. Published by the American Physical Society 2024

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.

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.

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.

Durable Photo-Pyroelectric Detection in a Diamine-Constructed Lead-Free Hybrid Perovskite Ferroelectric.

As a subcategory of pyroelectric materials, hybrid perovskite ferroelectrics possess substantial pyroelectric properties and exceptional light absorption characteristics, demonstrating significant potential in the photo-pyroelectric (PPE) detection field. Despite the significant advantages of hybrid perovskite ferroelectric materials for PPE detection, both the lead issue and the weak stability from van der Waals interactions in monoamines have hindered their further application. Here, 1D lead-free ferroelectric (BDA)SbBr5 (1, where BDA is 1,4-butanediammonium) is fabricated to achieve PPE detection. Compound 1 exhibits significant symmetry breaking attributed to the order-disorder transition of organic cations and octahedral distortions. Specifically, compound 1 enables broad-spectrum PPE detection from UV to near-infrared (377-980nm) and further realizes switchable pyroelectric current after polarization. More importantly, the stability of the pyroelectric current is preserved without degradation over three months, attributed to the hydrogen bonding interactions of butanediamide. Further theoretical calculations of compound 1 reveal a more negative energy of formation than its monoamine homologs (BA)2SbBr5 (where BA is n-butylammonium), which is evidence of its stability. These findings highlight 1 as a promising candidate for high-stability and environmentally friendly PPE wide-spectrum detection, representing a noteworthy advancement in the ferroelectric field.

Effect of order-disorder transition and lattice distortion on the mechanical properties of W-X (X = V, Nb, Ta) solid solutions

With the prosperity of high entropy alloys, short-range ordering is getting more and more attentions and regarded as the deciding role in the hardening or softening of solid solutions. In this work, the phase stability and mechanical properties of short-range ordered and disordered body-centered cubic (BCC) structures of W-X solid solutions (X = V, Nb, and Ta) are systematically investigated through a combination of first-principles calculation, cluster expansion and quasi-harmonic Debye formula. Based on the calculated heat of formation (ΔHf), W-X solid solutions show a strong short-range ordering tendency, as those ordered structures have a lower ΔHf than the disordered ones. Generally, short-range ordering results in the decrease of the shear modulus to bulk modulus ratio (G/B) and hardness for W-V and W-Ta systems, while an increase for W-Nb system, manifesting solid-solution softening and hardening effect, respectively. The short-ranged ordered C11b W2X phase exhibits a singularity in mechanical properties characterized by a higher G/B than solid solution phases compared to other ordered phases. The lattice distortion breaks the symmetric W-W bonds and leads to partial covalency in the W2X phases. Besides the increased brittleness, this distortion also causes the increase of ideal strength and the reduction of maximum tensile elongation of W2X. The effect of short-range ordering and lattice distortion on the hardening or softening of the W-X systems disappears after the order-disorder transition. The W-V and W-Ta phases have higher order-disorder transition temperature than W-Nb phase. Nevertheless, the transition temperature is relatively low in comparison to their melting points, signifying the important role in controlling the solute concentration at lower temperature.

The deformation mechanism of low symmetric Ti–Pt intermetallic compounds containing high density of planar defects

Intermetallic compounds typically exhibit limited plastic deformation capacity due to challenges in activating dislocation slip and deformation twinning, coupled with a lack of alternative deformation mechanisms. Ti–Pt alloys are a prevalent type of intermetallic compound utilized in high-temperature shape memory alloys and as materials for energy applications in electric fields. However, they often exhibit poor deformation capability. Here, we prepared a low-symmetry intermetallic phase, Ti4Pt3, which demonstrates significant plastic deformation capability. This phase features a high density of parallel planar defects, resulting in an exceptionally large lattice periodicity perpendicular to these defects. Through in-situ scanning electron microscope compression tests, we observed substantial plastic deformation in this new phase. Analysis of the deformed Ti4Pt3 phase revealed that the dense planar defects create uniformly distributed sites of internal stress concentration, enabling a rapid increase in back stress within crystals. This phenomenon leads to notable lattice rotation and localized order-disorder transitions, both crucial mechanisms facilitating plastic deformation and enhancing deformation capacity. Our research underscores the potential of leveraging structural asymmetry to enable unconventional deformation mechanisms, thereby enhancing the plasticity of intermetallic materials.