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Small-angle x-ray scattering experiments conducted with compositionally asymmetric low molar mass poly(isoprene)-b-poly(lactide) diblock copolymers reveal an extraordinary thermal history dependence. The development of distinct periodic crystalline or aperiodic quasicrystalline states depends on how specimens are cooled from the disordered state to temperatures below the order-disorder transition temperature. Whereas direct cooling leads to the formation of documented morphologies, rapidly quenched samples that are then heated from low temperature form the hexagonal C14 and cubic C15 Laves phases commonly found in metal alloys. Self-consistent mean-field theory calculations show that these, and other associated Frank-Kasper phases, have nearly degenerate free energies, suggesting that processing history drives the material into long-lived metastable states defined by self-assembled particles with discrete populations of volumes and polyhedral shapes.

Developing affordable and light high-temperature materials alternative to Ni-base superalloys has significantly increased the efforts in designing advanced ferritic superalloys. However, currently developed ferritic superalloys still exhibit low high-temperature strengths, which limits their usage. Here we use a CALPHAD-based high-throughput computational method to design light, strong, and low-cost high-entropy alloys for elevated-temperature applications. Through the high-throughput screening, precipitation-strengthened lightweight high-entropy alloys are discovered from thousands of initial compositions, which exhibit enhanced strengths compared to other counterparts at room and elevated temperatures. The experimental and theoretical understanding of both successful and failed cases in their strengthening mechanisms and order-disorder transitions further improves the accuracy of the thermodynamic database of the discovered alloy system. This study shows that integrating high-throughput screening, multiscale modeling, and experimental validation proves to be efficient and useful in accelerating the discovery of advanced precipitation-strengthened structural materials tuned by the high-entropy alloy concept. Advanced screening strategies for the design of high-entropy alloys are highly desirable. Here the authors use the project-oriented design strategy and CALPHAD-based high-throughput calculation tool to rapidly screen promising Al-Cr-Fe-Mn-Ti structural HEAs for high-temperature applications.

Relaxor ferroelectrics were discovered almost 50 years ago among the complex oxides with perovskite structure. In recent years this field of research has experienced a revival of interest. In this paper we review the progress achieved. We consider the crystal structure including quenched compositional disorder and polar nanoregions (PNR), the phase transitions including compositional order-disorder transition, transition to nonergodic (probably spherical cluster glass) state and to ferroelectric phase. We discuss the lattice dynamics and the peculiar (especially dielectric) relaxation in relaxors. Modern theoretical models for the mechanisms of PNR formation and freezing into nonergodic glassy state are also presented.

Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (T ODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the T ODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μ m scale, showing control over this order-disorder transition on scales relevant for device applications. Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory describes the melting of an ordered two-dimensional phase to a disordered phase, via a quasi-ordered ‘hexatic’ phase. Magnetic skyrmions, as a phase of two-dimensional quasi-particles may be expected to exhibit a KTHNY melting process, however, observing such a phase transition is difficult. Herein, Meisenheimer et al study the formation of magnetic skyrmions in (Fe 0.5 Co 0.5 ) 5 GeTe 2 , and, via physical confinement at device scale, succeed in obtaining an ordered skrymion phase.

Plastic crystal neopentylglycol (NPG) exhibits colossal barocaloric effects (BCEs) with record-high entropy changes, offering exciting prospects for the field of solid-state cooling through the application of moderate pressures. Here, we show that the intermolecular hydrogen bond plays a key role in the orientational order of NPG molecules, while its broken due to thermal perturbation prominently weakens the activation barrier of orientational disorder. The analysis of hydrogen bond strength, rotational entropy free energy and entropy changes provides insightful understanding of BCEs in order-disorder transition. External pressure reduce the hydsrogen bond length and enhance the activation barrier of orientational disorder, which serves as a route of varying intermolecular interaction to tune the order-disorder transition. Our work provides atomic-scale insights on the orientational order-disorder transition of NPG as the prototypical plastic crystal with BCEs, which is helpful to achieve superior caloric materials by molecular designing in the near future. Colossal barocaloric effects with high entropy changes is reported in plastic crystal neopentylglycol, while microscopic mechanism needs to be further explored. Here, the authors show hydrogen bond related reorientational dynamics of neopentylglycol and provide insights in order-disorder transition.

The order-disorder transition (ODT) of A 2 B 2 O 7 compounds obtained enormous attention owing to the potential application for thermal barrier coating (TBC) design. In this work, the influence of ODT on the mechanical and thermophysical properties of dual-phase A 2 B 2 O 7 high-entropy ceramics was investigated by substituting Ce 4+ and Hf 4+ with different ionic radii on B-sites (Zr 4+ ). The X-ray diffraction (XRD), Raman, and transmission electron microscopy (TEM) results show that r A 3 + / r B 4 + = 1.47 is the critical value of ODT phase boundary with different doping B-site ion contents, and the energy dispersive spectroscopy (EDS) results further indicate the uniform distribution of elements. Interestingly, owing to the high intrinsic disorder derived from high-entropy effect, the A 2 B 2 O 7 high-entropy ceramics exhibit unreduced modulus ( E 0 ≈ 230 GPa) and enhanced mechanical properties ( HV ≈ 10 GPa, K IC ≈ 2.3 MPa·m 0.5 ). A 2 B 2 O 7 high-entropy ceramics exhibit excellent thermal stability with relatively high thermal expansion coefficients (TECs) (Hf0.25, 11.20×10 −6 K −1 , 1000 °C). Moreover, the matching calculation implied that the ODT further enhances the phonon scattering coefficient, leading to a relatively lower thermal conductivity of (La 0.25 Eu 0.25 Gd 0.25 Yb 0.25 ) 2 (Zr 0.85 Ce 0.15 ) 2 O 7 (1.48–1.51 W/(m·K), 100–500 °C) compared with other components. This present work provides a novel composition design principle for high-entropy ceramics, as well as a material selection rule for high-temperature insulation applications.

Two-dimensional organic-inorganic hybrid halide perovskites possess diverse structural polymorphs with versatile physical properties, which can be controlled by order-disorder transition of the spacer cation, making them attractive for constructing semiconductor homojunctions. Here, we demonstrate a space-cation-dopant-induced phase stabilization approach to creating a lateral homojunction composed of ordered and disordered phases within a two-dimensional perovskite. By doping a small quantity of pentylammonium into (butylammonium) 2 PbI 4 or vice versa, we effectively suppress the ordering transition of the spacer cation and the associated out-of-plane octahedral tilting in the inorganic framework, resulting in phase pining of the disordered phase when decreasing temperature or increasing pressure. This enables epitaxial growth of a two-dimensional perovskite homojunction with tunable optical properties under temperature and pressure stimuli, as well as directional exciton diffusion across the interface. Our results demonstrate a previously unexplored strategy for constructing two-dimensional perovskite heterostructures by thermodynamic tuning and spacer cation doping. Hong et al. report 2D perovskite lateral homojunction consists of ordered and disordered phases, achieved by organic cation doping induced phase pinning, built upon which they develop tuneable optical properties under external stimuli and directional exciton diffusion in the homojunctions.

Amorphous calcium carbonate (ACC) is a metastable phase often observed during low temperature inorganic synthesis and biomineralization. ACC transforms with aging or heating into a less hydrated form, and with time crystallizes to calcite or aragonite. The energetics of transformation and crystallization of synthetic and biogenic (extracted from California purple sea urchin larval spicules, Strongylocentrotus purpuratus) ACC were studied using isothermal acid solution calorimetry and differential scanning calorimetry. Transformation and crystallization of ACC can follow an energetically downhill sequence: more metastable hydrated ACC → less metastable hydrated ACC ⇒ anhydrous ACC ∼ biogenic anhydrous ACC ⇒ vaterite → aragonite → calcite. In a given reaction sequence, not all these phases need to occur. The transformations involve a series of ordering, dehydration, and crystallization processes, each lowering the enthalpy (and free energy) of the system, with crystallization of the dehydrated amorphous material lowering the enthalpy the most. ACC is much more metastable with respect to calcite than the crystalline polymorphs vaterite or aragonite. The anhydrous ACC is less metastable than the hydrated, implying that the structural reorganization during dehydration is exothermic and irreversible. Dehydrated synthetic and anhydrous biogenic ACC are similar in enthalpy. The transformation sequence observed in biomineralization could be mainly energetically driven; the first phase deposited is hydrated ACC, which then converts to anhydrous ACC, and finally crystallizes to calcite. The initial formation of ACC may be a first step in the precipitation of calcite under a wide variety of conditions, including geological CO₂ sequestration.

Interactions in active matter systems inherently involve delays due to information processing and actuation lags. We numerically investigate the impact of such delays on the phase behavior of the Vicsek model for motile active matter at a large but fixed system size. While the delayed Vicsek model retains the same three phases as the standard version-an ordered state, a liquid-gas coexistence state, and a disordered state-the presence of delay qualitatively alters the system’s dynamics. At the relatively high velocity considered in this study, the critical noise for the transition between the ordered and coexistence states exhibits a non-monotonic dependence on delay, whereas the critical noise required for the transition to the disordered state increases with delay. Consequently, the width of the noise interval in which phase separation occurs broadens with increasing delay. Short delays stabilize the ordered phase, while long delays destabilize it in favor of the coexistence phase, which is consistently stabilized compared to the disordered state. Furthermore, the number of bands observed in the coexistence state at a given noise increases, and the time required for their formation decreases with delay. This acceleration is attributed to the emergence of swirling structures whose typical radius grows with increasing delay. Our results demonstrate that time delay in the Vicsek model acts as an effective control parameter for tuning the system’s dynamic phase behavior.