Halide perovskites differ from many conventional semiconductors in the extent to which their electronic properties are coupled to lattice motion. In bromide perovskites, the lead-halide octahedral framework does not act as a rigid scaffold; its response depends strongly on the A-site cation and on the soft, anharmonic character of the lattice. Light, heat, electrical bias, and mechanical strain can all perturb the structure, and those perturbations can feed directly into absorption, emission, carrier transport, and lattice stability. For this reason, the structural response of halide perovskites under operating conditions is not a secondary detail; it is part of the functional physics of the material. Much of the technological interest in halide perovskites has been built around thin-film devices, yet polycrystalline films bring grain boundaries, substrate interactions, and residual strain into the interpretation of structural change. Single crystals offer a cleaner setting for examining how the lattice itself responds to optical excitation. They remove many of the complications associated with interfaces and grain-boundary disorder, allowing the intrinsic relation between photocarriers and lattice deformation to be examined more directly. That distinction matters when the central question is not simply whether a perovskite device changes under illumination, but how the crystal framework responds when above-bandgap light generates carriers inside a soft, anharmonic lattice.

In a recent research paper published in Advanced Materials PhD candidate Mansha Dubey and Professor Marina S. Leite from University of California, Davis working together with Dr. Bekir Turedi, Dr. Andrii Kanak Professor Maksym V. Kovalenko Empa-Swiss Federal Laboratories for Materials Science and Technology developed an in situ optical-pump X-ray-probe approach for measuring photoinduced lattice distortions in halide perovskite single crystals. They applied it to MAPbBr₃, FAPbBr₃, and CsPbBr₃ to compare how organic and inorganic A-site cations control reversible out-of-equilibrium lattice deformation. The technically distinct contribution is the demonstration of hysteresis-free, power-dependent, multi-state lattice distortion under above-bandgap illumination, with full recovery in the dark. They also established experimental controls showing that the measured distortion is primarily associated with photocarrier-lattice interaction rather than ordinary heating or phase segregation.

The researchers examined three bromide perovskite single crystals that differ in their A-site cation: MA⁺, FA⁺, and Cs⁺. MAPbBr₃ and FAPbBr₃ crystals were grown by inverse-temperature crystallization, while CsPbBr₃ crystals were prepared using Bridgman growth. The use of single crystals was important because the measurements were intended to isolate lattice distortion from grain-boundary and substrate effects. Above-bandgap 532 nm laser excitation served as the optical stimulus, and X-ray diffraction provided the structural probe. By increasing and decreasing the pump power while repeatedly returning the crystal to dark conditions, the team could distinguish reversible elastic distortion from irreversible structural change.

The diffraction response revealed a clear dependence on cation chemistry. The investigators noticed under increasing laser power, the organic perovskites displayed shifts of the out-of-plane Bragg peaks toward smaller diffraction angles, consistent with an expansion of the relevant interplanar spacing. At the same time, the peak intensity decreased, especially for MAPbBr₃, and the peak shape developed multiple components. This behavior indicates more than uniform lattice expansion. It reflects a distribution of interplanar spacings and distortions in the diffracting planes, consistent with lattice deformation involving octahedral tilting and local structural rearrangement. A design choice at the A-site therefore had a direct scientific consequence: molecular cations with orientational dynamics produced stronger photoinduced lattice distortion than the inorganic cesium analogue.

The team found MAPbBr₃ gave the strongest structural response among the three materials. At high pump power, its diffraction profile showed a pronounced decrease in relative peak intensity and a broader spread in diffraction angle, with multiple peak components becoming distinguishable. FAPbBr₃ also distorted under illumination, but its main peak remained more dominant across the pump-power range, indicating a lower degree of structural disruption despite measurable lattice expansion. CsPbBr₃ behaved differently. Its diffraction peaks shifted only slightly, and their intensities remained comparatively stable, pointing to much greater resistance against photoinduced deformation.

The authors found that the organic cations introduce rotational and orientational degrees of freedom inside the lead-bromide octahedral cage, and the paper links their different dynamic character to the different distortion amplitudes observed experimentally. MA+ is associated with stronger dynamic disorder than FA+, while Cs+ lacks molecular dipoles and does not introduce the same cation reorientation. The inorganic lattice of CsPbBr₃ therefore responds with a smaller structural change. Quantitatively, the reported change in the out-of-plane lattice parameter reached approximately 0.3% for MAPbBr₃, 0.18% for FAPbBr₃, and 0.062% for CsPbBr₃. A central part of the analysis was the separation of photoinduced distortion from heating and the researchers estimated the temperature rise that would result if the laser energy were treated conservatively as heat, then compared that expectation with controlled temperature-dependent diffraction measurements. Heating produced the expected thermal expansion but did not reproduce the same intensity loss or peak-shape changes seen under illumination. Sub-bandgap excitation also did not generate the structural changes observed with above-bandgap light. These comparisons support the assignment of the distortion to photocarrier-lattice interactions rather than simple laser-induced warming.

Cyclability gave the most direct evidence that the deformation is elastic and reversible. After each illuminated measurement, the authors measured the crystals again in the dark, and the diffraction response returned to its equilibrium state. Across repeated increases and decreases in pump power, the lattice distortion recovered with about 99% reversibility. MAPbBr₃ and FAPbBr₃ also maintained stable illuminated states over the minutes-long measurement window, without progressive structural drift. When cycled between laser-on and laser-off conditions while the pump power was varied, MAPbBr₃ displayed multiple distinguishable distorted states, whereas FAPbBr₃ showed a sharper early response followed by a plateau in intensity. This power-dependent structural modulation is one of the most important observations in the paper.

The new collaborative study directly connects photoexcitation, A-site chemistry, and reversible lattice deformation in bulk halide perovskite single crystals. Rather than treating light-induced structural change as an incidental instability, the paper defines it as a controllable, recoverable response of the soft lattice. That distinction is scientifically important because it shifts attention from permanent degradation or phase change toward elastic structural modulation under optical excitation. The crystals do not simply tolerate illumination; their lattices enter reproducible out-of-equilibrium states and return to equilibrium when the stimulus is removed.

The comparison among MAPbBr₃, FAPbBr₃, and CsPbBr₃ gives the findings their interpretive strength. The same experimental strategy applied across three A-site cations shows that the magnitude and character of lattice distortion are not generic properties of bromide perovskites. They depend on how the cation interacts with the lead-bromide framework and on how strongly the resulting lattice couples to photogenerated carriers. MAPbBr₃ offers the largest and most tunable distortion, FAPbBr₃ provides a substantial but more structurally concentrated response, and CsPbBr₃ offers higher resistance to optical deformation. This cation-dependent behavior gives a concrete materials-design basis for selecting perovskites according to whether structural modulation or structural resilience is desired.

The study also demonstrates the methodological value of in situ X-ray diffraction under controlled optical excitation. By monitoring the lattice while the crystals are driven away from equilibrium, the researchers could identify reversible distortion, separate it from thermal expansion, and compare the response over many pump-power states. That capability matters for future studies of ionic semiconductors because the relevant material state during operation may not be the dark, equilibrium structure. For halide perovskites, where photocarriers and lattice motion are closely coupled, the operating lattice can carry information that conventional static measurements would miss. The implications remain properly bounded by the demonstrated systems: single-crystal bromide perovskites under above-bandgap optical excitation. Within that scope, the new  findings support the use of halide perovskites as materials for strain-driven optical and electrostrictive functionality, especially when reversible, power-dependent lattice modulation is required. The work also clarifies why A-site cation selection should be treated as a structural control parameter, not merely a compositional variable for phase stability or optoelectronic tuning.

Re-entrant honeycombs are compelling architected materials because their internal geometry gives them a deformation behavior that conventional cellular solids cannot achieve. Their negative Poisson’s ratio means that, under compression or tension, the transverse deformation can proceed in the same sense as the imposed axial deformation. For protective and energy-absorbing structures, that unusual kinematic response is attractive because it can alter load transfer, delay local collapse, and increase the capacity of the structure to dissipate mechanical work through controlled deformation. The main challenge is that the same geometry responsible for the negative Poisson’s ratio also creates a mechanical compromise. A re-entrant honeycomb requires open internal space and inclined cell walls to deform inward or outward in the desired auxetic mode. That porosity lowers strength and stiffness before densification. Strengthening the cell by adding material or constraining deformation can improve load-bearing capacity, but it may also reduce the negative Poisson’s ratio effect that gives the structure its distinctive mechanical value. The design problem is therefore not simply to make the honeycomb stronger. It is to improve crushing resistance, stiffness, deformation stability, and energy absorption while retaining the essential re-entrant deformation mechanism. In a recently published research paper in Composite Structures, Dr. Ran Gu and Dr. Wanhai Han from Guangxi University, Professor Yonghui An from Dalian University of Technology and Guangxi University, and Professor Jinping Ou from Harbin Institute of Technology (Shenzhen) developed a biomimetic arc support enhanced re-entrant honeycomb in which curved internal supports are embedded within conventional re-entrant unit cells. The technically distinct feature is the use of arc walls to provide simultaneous vertical and lateral resistance while increasing coupled plastic hinge formation during compression. They also developed a plateau-stress theoretical model based on plastic dissipation and a parameter optimization framework that identifies which geometric variables most strongly control crushing performance and energy absorption.

The research team defined the BASERH geometry through a baseline unit cell with specified height, horizontal wall length, inclined wall angle, arc angle, arc radius, inclined wall thickness, arc wall thickness, and out-of-plane width. For parameter analysis, the geometry is expressed through four dimensionless variables: the length-to-height ratio, radius-to-height ratio, width-to-height ratio, and wall thickness ratio between the inclined and arc walls. This formulation allowed the researchers to vary one geometric feature at a time while preserving a controlled reference design.

The physical specimens were manufactured from 316L stainless steel by selective laser melting. Material tensile testing supplied the elastic-plastic properties used later in simulation, including the measured modulus, yield stress, and ultimate stress. Quasi-static compression tests then provided the mechanical response of the BASERH arrays, while digital image correlation was used to determine the deformation field and Poisson’s ratio during loading. The authors calibrated the finite element model against the experimental deformation modes, stress-strain response, plateau stress, specific energy absorption, and Poisson’s ratio. Agreement between experiment and simulation gave the subsequent parameter study a firm mechanical basis.

The team divided the compression response of the baseline BASERH into four stages: an initial elastic stage, a decline stage after the first peak, a plateau stage, and a densification stage. During the plateau stage, most of the cell walls entered plastic deformation, and plastic hinges developed at joints and buckling regions. The arc support generated vertical reaction forces while also resisting inward deformation of the inclined walls. That design choice, embedding an arc inside the re-entrant cell rather than just thickening the original walls, changed the collapse mechanism by increasing coupled plastic hinge deformation and sustaining a higher plateau stress. The comparison with the conventional re-entrant honeycomb is the strongest evidence for the role of the arc support. BASERH developed an X-shaped deformation mode, whereas the traditional honeycomb followed a different re-entrant collapse pattern with lower deformation stability. The plateau stress of BASERH reached 37.4 MPa, compared with 3.6 MPa for the conventional structure. Its linear stiffness was about 4.4 times higher, and its plateau stress and specific energy absorption were reported as 10.4 times those of the traditional re-entrant honeycomb. The negative Poisson’s ratio effect was not lost; after densification, the reduction relative to the conventional structure was only 9.3 percent.

The theoretical model for plateau stress used an energy-conservation approach, treating collapse in terms of plastic dissipation at hinges in the inclined and arc walls. The model required only geometry and material parameters and predicted the baseline plateau stress with an 8.8 percent relative error against the experimental value. Across the examined configurations, the average error remained below 9 percent. The parameter study then identified the arc wall thickness as the dominant factor for strength and energy absorption, followed by the height-to-length relationship. Width had the smallest effect. Smaller structural height also suppressed global buckling and improved energy absorption stability. They extended the work from planar arrays to tubular structures made of PLA, comparing BASERH tubes with conventional tubes of identical mass and external dimensions. Under axial and radial compression, the BASERH tubes also carried higher peak loads than conventional tubes of the same mass and dimensions, with increases of 19.7 percent under axial compression and 32.9 percent under radial compression. Their specific energy absorption improved under both loading directions, although the radial response remained lower than the axial response, confirming the directional nature of the tube’s energy absorption behavior.

The engineering value of the BASERH design comes from its ability to strengthen a re-entrant honeycomb without removing the deformation mechanism that makes auxetic structures useful in the first place. By embedding arc supports into the re-entrant cells, the structure develops additional plastic hinge regions and a more stable collapse pattern, allowing mechanical energy to be absorbed through controlled deformation and a more stable collapse process. In automotive crash beams, the design could be used as an energy-absorbing core where high plateau stress and stable crushing are desirable. The reported improvement in axial and radial tube compression suggests that BASERH-based tubular members may be useful in components that must resist impact from different directions while maintaining predictable deformation. The negative Poisson’s ratio response is also important here, because inward lateral motion during compression can help concentrate deformation and reduce uncontrolled spreading or premature local failure.

For aerospace structures, the same design logic could support lightweight protective or load-bearing elements where stiffness and energy absorption must be balanced carefully. The study specifically identifies aircraft wings as a possible application area, and the relevance is clear: a cellular architecture that offers improved compressive strength and energy dissipation without a large penalty to auxetic behavior may be useful in internal cores, panels, or protective substructures subjected to complex loading. The authors’ findings also point toward civil and protective infrastructure uses. Canal gate impact panels, for example, require materials that can absorb accidental impact while preserving structural integrity under repeated or localized loading. BASERH offers a geometry-driven route to improve crushing resistance and energy dissipation in such panels. The design uses architecture to guide collapse and dissipate energy. Its practical importance extends beyond one product to structures where deformation must be controlled as carefully as load capacity.

Composite sandwich structures achieve high bending efficiency by placing strong skins on either side of a lightweight core. The outer skins carry most of the bending stresses, and the core keeps them separated and resists transverse shear which provide a combination of low weight, stiffness, and resistance to bending and makes sandwich structures useful in transport, marine, aerospace, and industrial applications. However, the performance of composite sandwich depends heavily on a reliable bond between the skins and the core and when the bond is weak, debonding, local shear, and stress concentration at the interface can control failure before the full strength of either material is reached. Material extrusion additive manufacturing provides an interesting route for producing sandwich cores because it can generate internal and surface geometries that are difficult to obtain through conventional molding or machining. A printed core need not remain a passive lightweight spacer. Its surface can be shaped to influence resin flow, contact area, and the way the skin becomes mechanically engaged with the core. Such opportunities are especially relevant for short-carbon-fiber-filled thermoplastic cores, where the deposited-bead morphology and fiber orientation can introduce microstructural features at the printed surface. Even with additive manufacturing, the mechanical response of the assembled structure remains closely dependent on resin infiltration and the quality of skin-core load transfer. A carbon-fiber-reinforced skin bonded to a printed polymer core still depends on the quality of resin infiltration and the ability of the cured interlayer to distribute stress without premature separation. Previous approaches to improving skin-core bonding have included chemical modification, surface treatment, reinforcement through inserts or perforations, and the incorporation of nanoscale additives into polymer matrices. Surface texturing can enlarge the effective bonding area and create geometrical resistance to separation. Nanofillers can influence local stress transfer, crack development, and the adhesion of resin to reinforcing fibers. Their combined use in composite-to-composite sandwich bonding, particularly where a printed core carries deliberately formed mesoscale grooves, remained insufficiently examined.

In a recently published paper in Polymer Composites, Mr. Yang Liu, Professor Zhaogui Wang, and Mr. Bohao Yi from Dalian Maritime University developed a hybrid composite sandwich structure combining a fused-deposition-modeled short-carbon-fiber/ABS core with carbon-fiber-fabric skins bonded by vacuum-assisted epoxy infusion. The resulting design couples core-surface architecture with nanoparticle-assisted resin-fiber bridging rather than relying on a conventional smooth adhesive boundary.

The researchers first established the effect of panel placement within the sandwich architecture. Carbon-fiber fabric positioned as outer skin sheets produced a more favorable bending response than fabric placed in the middle layer of the structure. Increasing the number of skin layers raised bending strength and bending modulus, confirming that the outer carbon-fiber plies carried the principal tensile and compressive stresses generated during three-point bending. The investigators noticed the printed CF-ABS cores patterned with shallow and deeper meso-grooves to create a controlled increase in surface texture without changing the basic sandwich geometry. Optical measurements confirmed that groove depth substantially increased surface roughness relative to the untreated core. This mattered because the deeper texture allowed liquid epoxy to penetrate recessed regions during vacuum-assisted curing, enlarging the resin-accessible contact area and producing a stronger geometrical connection between the carbon-fiber skins and core.

The authors performed mechanical testing and showed that both grooved configurations improved bending behavior relative to the untreated sandwich, with the deeper grooves producing the stronger response. Stiffness also increased after surface texturing. Load-deflection behavior changed as well: instead of reaching a maximum load followed by a sharp drop, the grooved specimens failed more gradually. Increasing groove depth therefore influenced not only strength and stiffness, but also the way the structure accommodated progressive damage under bending. Microscopy supplied an important interpretation of that response. The fused-deposition process produced irregular burr-like regions around the groove boundaries. These regions contained short carbon fibers and residual ABS material extending beyond the deposited-bead profile. After resin infusion and curing, epoxy penetrated the groove network and surrounded these exposed features. The result was not a smooth adhesive boundary but a mechanically interlocked region in which resin, printed polymer, protruding short fibers, and carbon-fiber fabric became locally connected. In the grooved specimens without graphene, core shear remained the dominant failure mode despite the improved interfacial connection.

The team incorporated graphene nanoplatelets into the epoxy resin used with the deeper-grooved core as their final modification. Compared with the grooved structure without graphene, the graphene-containing sandwich showed further gains in bending strength and stiffness. Its failure behavior also changed: while the meso-grooved specimens mainly failed through core shear, the graphene-modified structure showed yielding of the carbon-fiber skin sheets. This shift indicates that the reinforced interface transferred load more effectively to the external skins instead of allowing early damage to remain concentrated in the core or bonded region.

The authors conducted SEM and EDS and found that Graphene nanoplatelets were distributed through the resin-rich region near the interface, including areas adjacent to the residual fibers located at groove edges. he examined graphene-modified interfacial regions appeared continuous after bending, without prominent cracks or gaps in the observed areas. Liu and colleagues interpreted the nanoplatelets as bridges within the resin-fiber region, where they reduced stress concentration, impeded crack extension, and strengthened the connection between the epoxy matrix and carbon-fiber surfaces. The interfacial architecture therefore developed through the combined action of printed groove geometry, microscale fiber-related features, and graphene-assisted resin bridging.

The interfacial strategy developed by Professor Zhaogui Wang and colleagues is relevant wherever lightweight sandwich panels must carry bending loads without allowing the skin-core boundary to become the first location of failure. Their approach is especially suited to composite structures in which a material-extrusion-manufactured core can be combined with carbon-fiber skins through vacuum-assisted curing and instead of treating the core as a geometrically simple spacer, the study shows that its printed surface can be designed to participate directly in structural load transfer. In marine engineering, the new principle could be applied to lightweight interior panels, equipment enclosures, deck-adjacent partitions, protective covers, and non-primary structural components where reduced weight and resistance to flexural loading are both desirable. The use of a carbon-fiber-reinforced ABS core offers the practical advantage of manufacturing complex core shapes through fused deposition modeling, while the meso-grooved surface improves the connection to carbon-fiber skins. For components exposed to repeated handling, vibration, or local bending, a stronger skin-core interface could reduce the likelihood that deformation becomes concentrated at the bonded boundary.

The same concept may be useful for aerospace and transportation panels that require tailored geometry but are not easily produced through conventional core-forming routes. Material extrusion permits local modification of core surfaces, allowing grooves or related textural features to be placed only where higher interfacial stresses are expected. This could be valuable near fasteners, support locations, edges, cut-outs, or regions subjected to concentrated loading. The study indicates that deeper meso-grooves increased the effective contact area available to the infused resin and promoted mechanical interlocking, suggesting a method for locally tuning the core-skin connection without changing the entire panel architecture.

The graphene-modified resin formulation adds a second level of design control. In the reported sandwich structures, graphene nanoplatelets strengthened the resin-fiber region and shifted the observed failure mode from core shear toward yielding of the carbon-fiber skins. From an engineering standpoint, this shift is meaningful because it indicates that the interface can sustain a greater share of the applied load before damage becomes localized. Components designed for bending-dominated service may therefore benefit from an interface that transfers stress more effectively into the outer skins. The hybrid manufacturing method reported by Liu, Wang and Yi also has relevance for prototyping and low- to medium-volume production. A core can be digitally redesigned, printed, and then integrated with conventional carbon-fiber fabric and epoxy processing. This flexibility may be useful for customized structural panels, curved protective housings, marine outfitting elements, and application-specific sandwich components. Overall, the new approach combines printed core design with resin modification to improve interfacial performance under bending.

 

Thermal vacancies play an important role in the thermodynamics of metallic phases. They are structural defects, and their equilibrium population rises with temperature, affecting measurable properties including heat capacity, diffusivity, thermal conductivity, and melting behavior. Any thermodynamic description intended to represent metals at elevated temperature must therefore accommodate vacancies in a way that is consistent with both phase stability and chemical equilibrium. Within CALPHAD-based thermodynamics, the Compound Energy Formalism provides a widely used language for representing phases with one or more sublattices, while the substitutional solution model serves as its single-sublattice form. In that setting, vacancies are commonly introduced as an additional component occupying lattice sites. A vacancy endmember represents a hypothetical crystal containing only vacancies, and assigning a molar Gibbs energy to such an entity has long been problematic. When the vacancy-endmember parameter is chosen poorly, the resulting thermodynamic description can yield unstable phases or more than one equilibrium vacancy concentration. Positive values have often been introduced to maintain a unique equilibrium state, but the physical interpretation of those choices remains unsettled. The issue becomes especially important when vacancy formation energies are temperature dependent or when vacancy-related interactions are incorporated into multicomponent alloys. An earlier thermal-vacancy model treated vacancies as forming a solution with the matrix alloy and avoided some of the difficulties associated with a conventional substitutional description. That formulation, however, separates the Gibbs energy into alloy and vacancy contributions in a manner that complicates derivatives such as the chemical potentials of non-vacancy components. Such derivatives become really important when the thermodynamic model is intended for diffusion calculations or future extension to phases containing multiple sublattices.

In a recently published paper in Acta Materialia, Dr. Cheng-Hui Xia of Hangzhou City University and Professor Xiao-Gang Lu of Shanghai University developed a modified substitutional solution model for metallic phases containing thermal vacancies. The modified substitutional solution model distinguishes between the site fractions of all lattice occupants and the mole fractions of the non-vacancy components. In the conventional substitutional solution model, binary and ternary interaction terms are written in terms of site fractions, so the presence of vacancies changes the compositional variables entering every interaction contribution. The modified formulation instead writes interactions among non-vacancy species through their atomic mole fractions, while vacancy-related interactions are multiplied explicitly by the vacancy site fraction. This design choice separates the alloy thermodynamics from the vacancy population without discarding their coupling.

That distinction produces a useful expression for the vacancy chemical potential. In the modified model, the equilibrium vacancy concentration follows analytically from the condition of zero vacancy chemical potential and takes an exponential form determined by an effective vacancy formation energy. The same formulation gives a simple logarithmic relation between vacancy chemical potential and the ratio of the instantaneous vacancy concentration to its equilibrium value. Such relations are important because non-equilibrium vacancy concentrations enter diffusion simulations through chemical-potential driving forces. The conventional substitutional model does not yield an equivalent analytical expression, even for a pure metal with a vacancy interaction parameter.

The authors first examined pure BCC titanium to expose the contrasting behavior of the two models across a wide range of vacancy concentrations. When vacancy-related interaction terms were absent, the two descriptions coincided. Once positive vacancy interactions were introduced, however, the conventional model could generate multiple equilibrium vacancy concentrations unless both the vacancy-endmember energy and the vacancy interaction parameter were selected carefully. The modified model retained a single equilibrium solution and a stable phase description. Its vacancy-endmember parameter could be zero or assigned a physically meaningful value, because the effective formation energy is determined through the combined vacancy-related terms.

Dr. Cheng-Hui Xia and Professor Xiao-Gang Lu tested how the modified treatment affects temperature-dependent thermodynamic properties by performing calculations for BCC tungsten and found at near melting temperature, the two models predicted closely related equilibrium vacancy concentrations and nearly indistinguishable Gibbs energies. Their effects became more visible in quantities involving temperature derivatives of the Gibbs energy, especially heat capacity. The analysis showed that a relatively high vacancy concentration combined with a rapidly changing vacancy-related interaction parameter can increase the calculated heat capacity substantially. Enthalpy and entropy also departed from vacancy-free reference calculations at high temperature, reflecting the thermodynamic contribution of the equilibrium vacancy population.

Binary Co–Cr calculations provided a more demanding comparison because alloy composition and vacancy concentration vary simultaneously. At equilibrium, the conventional and modified models produced similar heat capacities, Gibbs energies, and chemical potentials of Co and Cr when vacancy concentrations remained low. Their vacancy chemical potentials differed more fundamentally. In the modified model, the vacancy chemical potential rose monotonically with vacancy concentration at fixed alloy composition, preserving the one-to-one relation required for a unique equilibrium concentration. The conventional model showed non-monotonic behavior over part of the concentration range, a feature associated with the possibility of multiple equilibrium solutions. Xia and Lu then examined the role of interaction parameters and found interactions among non-vacancy components affected the vacancy concentration differently in the two models: attractive mixing increased the equilibrium vacancy concentration predicted by the modified model but decreased that predicted by the conventional model. Vacancy-related binary and ternary interaction parameters, by contrast, could be adjusted in the modified model to fit equilibrium vacancy concentrations while exerting little influence on other equilibrium thermodynamic properties when vacancies were dilute. Finally, the FCC Cu–Ni system was used to evaluate composition-dependent vacancy formation energies. By incorporating Cu–Ni–vacancy interaction parameters, the model reproduced the assessed vacancy formation-energy trend and its corresponding equilibrium vacancy concentrations across composition.

The modified substitutional solution model reported by Xia and Lu offers a practical thermodynamic basis for engineering calculations in metallic systems where thermal vacancies cannot be treated as negligible background defects. In high-temperature processing and service, vacancy populations influence diffusion-related phenomena, heat capacity, chemical potentials, and the effective thermodynamic state of an alloy. A model that provides a unique equilibrium vacancy concentration is therefore useful wherever computational predictions must remain stable across changing temperature and composition. CALPHAD databases for FCC and BCC metallic phases provide one immediate setting for applying the modified model. The modified model retains the conventional substitutional description when vacancies are excluded, allowing established alloy thermodynamic parameters to remain relevant. At the same time, it separates vacancy-related parameters from the interaction terms that describe the atomic alloy. This can make it easier to refine vacancy thermodynamics without unnecessarily changing the calculated Gibbs energies, phase equilibria, or chemical potentials of the major alloying elements. For database development, that separation is valuable because vacancy formation energies and equilibrium vacancy concentrations can be fitted more directly to appropriate thermodynamic information.

The analytical vacancy-concentration expression is relevant to diffusion modeling. Vacancy-mediated transport calculations require chemical potentials that respond consistently when the vacancy concentration differs from equilibrium. The modified model supplies a direct logarithmic relation between vacancy chemical potential and the ratio of actual to equilibrium vacancy concentration. This provides a clear thermodynamic driving force for simulations involving vacancy diffusion, vacancy generation, and vacancy relaxation. It may therefore support computational descriptions of processes in which local vacancy populations change during thermal treatment or under composition gradients.

The Cu–Ni calculations also show how vacancy formation energies can vary systematically with alloy composition when vacancy-related binary and ternary interaction parameters are included. That capability is relevant to alloy design tasks in which compositional changes alter vacancy populations without strongly altering the broader equilibrium thermodynamics of the phase. Engineers can evaluate how alloy composition changes equilibrium vacancy concentrations across a composition range, without assigning a single vacancy energy based only on the pure constituents. The model is also suited to situations where heat capacity, enthalpy, and entropy must be evaluated near elevated temperatures. The tungsten calculations demonstrate that vacancies can affect these quantities through their contribution to the temperature derivatives of Gibbs energy, especially when vacancy concentrations rise rapidly. Incorporating this effect in thermodynamic calculations can improve consistency between vacancy behavior and temperature-dependent property predictions within the same modeling framework.

 

 

Carbon fiber reinforced silicon carbide (C/SiC) composites are designed for demanding thermal-structural environments where low density, resistance to ultra-high temperature, and durability must be combined with reliable mechanical performance. Their mechanical response depends on more than the intrinsic properties of the carbon fibers and silicon carbide (SiC) matrix. Fiber-bundle architecture, interphase, residual thermal stresses, matrix cracking, interface debonding, and load transfer after damage initiation all contribute to the deformation and fracture process. Minicomposites provide a useful level of observation for this problem. They retain the essential fiber, interphase, and matrix interactions of ceramic matrix composites while allowing constitutive behavior to be studied with greater mechanical clarity than in a full composite component. For C/SiC systems, previous room-temperature studies had already shown that matrix crack density changes with tensile stress, that the pyrolytic carbon (PyC) interphase affects fiber pull-out and interface debonding, and that nonlinear deformation can accompany interface-related damage. Tensile curves of PyC-containing C/SiC minicomposites may also display “sawtooth” regions, where the load drops abruptly and then recovers during continued displacement-controlled loading. Ultra-high-temperature tensile behavior presents a distinct problem for ceramic matrix minicomposites. Although these materials are intended for thermal-structural service, their constitutive response under elevated-temperature loading remains insufficiently characterized, especially once matrix cracking and interfacial debonding begin to alter the local stress field. Direct strain measurement is difficult when a very small specimen is heated to ultra-high temperature, and the strain field is not uniform once matrix cracks and debonded zones appear. A meaningful constitutive description therefore has to account for both the experimental limitations of ultra-high-temperature tensile testing and the internal mechanics of a specimen whose load-bearing state changes locally whenever a new matrix crack forms.

In a recent research paper published in Journal of the American Ceramic Society by  Mr. Siru Li, Mr. Zhiqi Ma, Ms. Jingwen Lv, and Research Fellow Tianbao Cheng from the College of Aerospace Engineering at Chongqing University developed an induction-heated tensile testing method for ceramic matrix minicomposites at temperatures up to 1800°C in argon. They also developed a constitutive model that calculates tensile stress–deformation behavior by tracking bonded zones, debonded zones, slip zones, reverse slip zones, crack history, thermal mismatch stresses, and temperature variation along the specimen. The technically distinct feature is the treatment of dynamic stress redistribution after matrix cracking, which allows the model to reproduce the nonlinear and “sawtooth” features observed experimentally. The method was applied to C/PyC/SiC minicomposite with a PyC interphase and SiC matrix infiltrated around carbon fiber bundle.

The team prepared C/PyC/SiC minicomposite by coating carbon-fiber bundle with a thin PyC interphase and then introducing the SiC matrix through chemical vapor infiltration process. They then tested the specimens in argon from room temperature to very high temperature using an induction-heating tensile system designed to maintain controlled heating while protecting the loading assembly from thermal, electromagnetic, and vibration effects. The arrangement combined a heated susceptor, thermal insulation, shielding, vibration absorber, and a compact servo-driven loading mechanism, which allowed tensile behavior to be monitored under elevated-temperature conditions. They tested multiple specimens at each temperature to examine the reproducibility of the stress–displacement response. Matrix cracking and debonded zones make deformation nonuniform, so the model incorporated loading-system compliance to relate the measured displacement-controlled response to internal cracking and load transfer.

The authors found that across the tested temperatures, the tensile curves first rose approximately linearly and then became distinctly nonlinear after the first matrix cracking. At the instant of matrix cracking, the displacement of the specimen ends remains effectively unchanged, but the new crack forces a local change in load sharing: the matrix cannot carry load at the crack, so the fiber bears the load there, and slip zones develop near the crack through interface shear transfer. That local rise in fiber stress increases the total elongation slightly; under displacement control, the applied load correspondingly drops. Reloading then continues until additional cracking occurs. Especially, when the new crack produces before the reverse slips are completely covered, multiple “slip zone-reverse slip zone-slip zone” presents in the debonded zones. The researchers developed model and noticed the minicomposite is separated into bonded and debonded zones. In bonded zones, the fiber and matrix deform according to an equal-strain assumption, with temperature-dependent moduli and thermal mismatch stresses included. In debonded regions, the model follows the stress on the fiber as it changes across slip zones, reverse slip zones, and newly formed slip zones. The history of matrix cracking is recorded because each debonded zone may have formed at a different applied stress, and adjacent debonded zones can interfere when cracks are close.

The calculated curves reproduced the main nonlinear form of the experimental stress–displacement response, including the “sawtooth” drops that are not represented when the dynamic stress evolution of debonded zones is omitted. Scanning electron microscopy of tested specimens confirmed matrix cracks roughly perpendicular to the tensile direction and distributed randomly along the minicomposites. The number of “sawtooth” features and the average crack density showed a positive correlation, supporting the interpretation that the “sawtooth” response is caused by matrix cracking.

The investigators noticed temperature altered the first matrix cracking stress in a systematic way and it increased from room temperature through intermediate elevated temperatures and then showed a slight reduction at 1800°C. The authors attributed the initial increase to the change in residual thermal stress in the matrix: tensile residual stress is largest at room temperature, decreases as temperature approaches the preparation temperature, and becomes compressive above that range because of thermal mismatch. The slight reduction at 1800°C was attributed to degradation of matrix performance. Parameter calculations further showed that increasing fiber volume fraction reduced the initial slope because the carbon fiber modulus is lower than that of the SiC matrix, promoted earlier matrix cracking through the associated change in matrix stress, and reduced the stress-drop magnitude. Higher interface shear stress shortened debonded zones and reduced the influence of those zones on the tensile response.

The findings of Research Fellow Tianbao Cheng and his graduate students are directly relevant to the engineering evaluation of C/SiC composites intended for ultra-high-temperature structural service. Components made from C/SiC systems may operate in environments where load, temperature, and damage evolution occur together rather than separately. For that reason, a constitutive description that can represent matrix cracking, interface debonding, slip-zone development, and temperature-dependent constituent properties and thermal residual stress is very valuable for interpreting how these materials carry load after the first damage event has occurred. The paper’s treatment of C/PyC/SiC minicomposites gives engineers a more detailed way to read tensile response under elevated-temperature conditions instead of relying only on final strength values or initial stiffness. One practical application is in the design and assessment of thermal structural components where local cracking does not immediately mean total loss of load-bearing capacity. The observed “sawtooth” response shows that each matrix crack changes the internal stress distribution, transfers load locally to the fibers, and then allows the specimen to continue carrying increasing load as reloading proceeds. In engineering terms, this helps distinguish crack initiation from progressive damage accumulation. That distinction matters when evaluating reliability, because a material may enter a nonlinear damage regime before final fracture, and the shape of that regime carries information about interfacial sliding, debonded-zone growth, and stress redistribution.

The results also support better use of minicomposite testing as an intermediate evaluation tool during ceramic matrix composite development. Full composite components contain more complex fiber architectures, but minicomposites expose the essential interaction between fiber, interphase, and matrix. By testing C/PyC/SiC minicomposites up to 1800°C in argon and modeling the resulting stress–displacement behavior, the study provides a route for assessing how interphase behavior and matrix cracking may influence larger composite systems. This is especially useful when comparing processing conditions, fiber volume fractions, or interface characteristics before moving to more expensive component-level testing. Indeed, the parameter analysis further indicates that fiber volume fraction and interface shear stress influence the degree of nonlinear deformation and the stress drops associated with matrix cracking, providing useful guidance for interpreting progressive damage in C/PyC/SiC minicomposites. Overall technical route for “dynamic” constitutive response of ceramic matrix minicomposites at ultra-high temperatures.

 

Ceramic cutting tools are essential in high-speed machining because they must operate where several demanding properties are required at once: hardness, thermal stability, wear resistance, and enough resistance to brittle failure to survive severe cutting conditions. Alumina-based ceramics are attractive because of their chemical inertness and cost effectiveness, and the addition of high-entropy carbides can provide more hardness and high-temperature capability through multi-principal-element design. In Al₂O₃– (HfNbTaTiZr)C ceramics, however, the same stiffness and hot hardness that make the material useful for cutting also leave it vulnerable to chipping and premature fracture. The challenge is to tune the microstructure so that strength, fracture toughness, heat transport, and wear resistance work together in a more reliable tool material. Graphene is attractive because it does not act as a simple filler added to make the ceramic stronger and its effect depends on how it sits inside the matrix and how it interacts with cracks, interfaces, heat, and sliding contact. When a crack meets graphene, the sheet can redirect the crack path, bridge the opening, branch the damage, or dissipate energy through pull-out and interfacial sliding. At the same time, graphene brings the mechanical problem closer to the cutting problem itself: its high in-plane thermal conductivity can help move heat away from the tool-chip interface, while its layered structure can contribute to lubrication under sliding. For that reason, layer number, sheet size, bonding strength, and orientation can determine how stress is transferred through the ceramic, how fracture develops, how heat is redistributed, and how wear progresses during machining.

In a recent research paper published in Ceramics International Dr. Yingqi Zheng, Professor Jialin Sun, Dr. Shurong Ning, and Dr. Jun Zhao from Shandong University together with Dr. Xiao Li from Weihai Weiying Tool Co., Ltd developed a three-dimensional finite element framework for optimizing graphene-reinforced Al₂O₃-(HfNbTaTiZr)C ceramic cutting tools. The model combines a Voronoi polycrystalline ceramic matrix, embedded graphene sheets, and cohesive zone elements for intergranular and transgranular fracture. They used it to identify an optimized graphene configuration and then linked that configuration to cutting simulations that account for graphene orientation, wear rate, temperature, and tool life.

Briefly, the researchers built a three-dimensional finite element model of graphene-reinforced Al₂O₃-(HfNbTaTiZr)C based on an Al₂O₃ matrix containing 40 vol% (HfNbTaTiZr)C, with graphene fixed at 0.5 vol%. They used a Python-generated Voronoi tessellation to represent the polycrystalline ceramic matrix, and graphene sheets were embedded as discrete reinforcement units. Cohesive zone elements were introduced along grain boundaries and within grains so that intergranular and transgranular fracture could both be represented. This modeling choice important because the response being optimized was controlled not only by the intrinsic stiffness of graphene or the ceramic matrix, but by where damage initiates, how it crosses interfaces, and whether cracks are redirected or allowed to pass through the microstructure.

The authors used finite element simulations to assess flexural strength, fracture toughness, and Vickers hardness. The layer-number analysis showed that four-layer and eight-layer graphene configurations were generally more favorable than three- and six-layer configurations, but not in the same way. Four-layer graphene gave the best combined response because it preserved strong flexural strength and hardness while maintaining adequate fracture toughness. Eight-layer graphene could improve toughness through increased crack deflection and related toughening mechanisms, however, it also introduced conditions associated with interlayer sliding, less uniform stress distribution, and lower hardness or strength in several comparisons. The interpretation is useful: increasing the number of graphene layers changes the balance between reinforcement, defect evolution, and interlayer mechanical stability. Graphene sheet size showed a similar non-monotonic pattern. Among the four-layer designs, G(4,4) provided the most useful combination of flexural strength, hardness, and fracture toughness. Smaller sheets did not provide the same crack deflection and load-transfer benefits, whereas larger sheets risked stacking, agglomeration, and weakened interfacial effectiveness. The selected graphene sheet size therefore acted as an intermediate design point where dispersion, matrix continuity, crack interaction, and load transfer were brought into a more favorable relation.

The team conducted interface analysis and found for ceramic matrix-ceramic matrix bonding, an intermediate grain-boundary-to-grain-interior strength ratio gave a strong balance among hardness, fracture toughness, and flexural strength. When the ratio was too low, load transfer was insufficient; when it became too high, toughness declined sharply. For graphene-ceramic bonding, a similar intermediate ratio was identified as optimal. A moderately bonded interface allowed crack deflection and energy dissipation without sacrificing the load-bearing contribution needed for strength and hardness. This is one of the more important conclusions of the paper: the desirable interface is not simply the strongest possible interface, but one that allows controlled interaction between reinforcement and matrix during deformation and fracture.

The authors coupled archard’s wear law with finite element simulation to calculate wear rate, tool life, and temperature for different graphene orientations. They defined orientation by the angle between the graphene sheets and the rake face. The team noted that the orientation of graphene significantly influences cutting temperature, wear rate, and tool life, but the relationship was not simply linear.

They also found the optimum orientation was not exactly parallel to the rake face and a slight negative inclination gave the longest simulated tool life, slightly exceeding the fully parallel case and outperforming the other tested orientations. Meanwhile, the optimum orientation for tool life was distinct from the orientation at which the lowest cutting temperature was achieved. This distinction is important because it shows that temperature reduction alone did not govern performance. The best orientation was determined by the coupled thermal and mechanical response: heat dissipation, lubrication, load-bearing capacity, and local stress distribution all contributed. Compared with the graphene-free Al₂O₃-(HfNbTaTiZr)C tool, the optimized graphene-reinforced tool substantially reduced wear rate, nearly doubled tool life, and lowered cutting temperature under the simulated cutting conditions.

The findings of Shandong University scientists have direct relevance for the engineering design of ceramic cutting tools intended for high-speed machining of difficult-to-machine steels. In such applications, tool performance is controlled not only by nominal hardness or fracture toughness, but by the way the tool material responds under simultaneous mechanical loading, sliding contact, heat generation, and localized wear. The study provides a practical design logic for graphene-reinforced Al₂O₃-(HfNbTaTiZr)C ceramic tools by identifying how graphene should be configured within the ceramic matrix to improve service behavior under cutting conditions. For tool manufacturers, the most useful outcome is the movement from graphene addition to graphene configuration control. The optimized four-layer graphene structure, intermediate sheet size, and controlled graphene-ceramic interface give concrete microstructural targets for designing ceramic tool materials with balanced flexural strength, hardness, and fracture toughness. A tool that is very hard but insufficiently tough may chip; a tool that dissipates fracture energy but loses hardness may wear too quickly. The configuration identified in the study offers a route to balance these properties rather than optimizing one at the expense of the others. The orientation results are especially important for tool design because they connect microstructure to the geometry of the cutting edge. By showing that graphene sheets oriented at about −3° relative to the rake face produced the best simulated tool life, the work suggests that reinforcement alignment can be treated as a design parameter in ceramic tool fabrication. This orientation improved the combined effect of interlayer shear, self-lubricating behavior, and in-plane thermal conduction near the tool-chip interface. Instead of relying only on experimental trial and error, engineers can use three-dimensional finite element modeling to screen graphene layer number, sheet size, interface strength, and orientation in relation to actual machining response. For advanced ceramic tools, this makes microstructural design more closely connected to service performance.

 

 

Thermal expansion of dielectric substrates is a major materials concern in electronic packaging, especially in dense multilayer architectures where thermal cycling can create mismatch stresses between the substrate and silicon chip while dielectric performance must be retained. Bismaleimide–triazine resin is well suited to this setting because the cured network combines attributes associated with cyanate ester and bismaleimide chemistry, including thermal stability, limited water absorption, and useful dielectric properties. When reinforced with glass-fiber cloth, however, the resulting composite still has a coefficient of thermal expansion substantially higher than that of silicon. Reducing this mismatch is not a matter of lowering the expansion coefficient of the polymer phase alone. The composite contains a resin network, woven glass reinforcement, ceramic inclusions, and a set of interfaces whose mechanical and thermal responses are coupled. Silica improves dimensional stability through its low positive thermal expansion coefficient, whereas negative-thermal-expansion ceramics can more directly offset expansion of the polymeric matrix. Negative-thermal-expansion ceramics offer a more direct route to suppressing matrix expansion, but their use introduces another practical consideration: fillers with strong negative thermal expansion may be costly to prepare and difficult to incorporate economically at high loading.

In a recently published research paper in Polymer Composites Dr. Zikang Zhou and Professor Fei Liang from Huazhong University of Science and Technology working together with Dr. Yuyao Zeng, Professor Chuntian Yang and Professor Zhongxin Wu from Wenzhou Institute of Industry & Science developed BT resin/glass-fiber composite substrates modified with mixed silica and zirconium tungsten phosphate ceramic fillers. Their distinct contribution was the use of a 3:7 silica-to-zirconium-tungsten-phosphate ratio to create a hybrid filler with an effective thermal expansion coefficient close to zero. They also developed an improved calculation route that combines the Turner model for the mixed filler with the Schapery model for the final composite. This approach linked hybrid-filler composition, bulk modulus, and composite thermal expansion in a single predictive procedure.

The researchers first optimized the BT resin matrix before they introduce ceramic fillers. They also varied the bismaleimide-to-cyanate-ester ratio which showed that a higher bismaleimide fraction generally increased both dielectric constant and dielectric loss. A balanced resin composition was therefore selected for subsequent modification, while its thermal expansion remained high enough to require filler-based control.

They also examined 2,2′-diallylbisphenol A as a modifier of the BT resin/glass-fiber system. Microscopy showed progressively better encapsulation of the glass-fiber cloth as its content increased. Dielectric performance, however, followed a non-monotonic trend: moderate addition reduced dielectric loss, whereas excessive addition promoted pore formation and stronger interfacial polarization. The selected formulation therefore provided good resin–fiber compatibility without introducing the dielectric penalties associated with excessive modifier content.

The authors subsequently incorporated individually Silica and zirconium tungsten phosphate as mixed fillers and found that each single filler lowered the coefficient of thermal expansion as its content increased, with zirconium tungsten phosphate producing a larger reduction because of its negative thermal expansion behavior. The hybrid fillers followed a different trend. As the silica fraction increased, the composite expansion coefficient first declined and then rose. The lowest value occurred at a silica-to-zirconium tungsten phosphate ratio of 3:7, where the mixed filler approached a near-zero thermal expansion response and reduced the BT resin/glass-fiber composite to 4.3 ppm/°C.

The team performed microscopy and found that the resin, glass fiber, silica, and zirconium tungsten phosphate were closely bonded, while the differing particle sizes of the two ceramic fillers allowed smaller particles to occupy spaces between larger ones. The mixed filler therefore contributed through more than the algebraic combination of positive and negative thermal expansion. Its particle-scale arrangement plausibly reduced voids and microstructural defects that could otherwise contribute to positive expansion. They also conducted thermomechanical modeling to clarify why the 3:7 mixture behaved differently from either single filler and found that for silica-filled composites, the rule of mixtures and Schapery model tracked the experimental values reasonably well, while the Turner model underestimated them. For zirconium tungsten phosphate-filled composites, the Turner model was closest to experiment, reflecting the importance of the negative-expansion filler’s relatively low bulk modulus. Neither the conventional rule of mixtures nor the Turner model adequately described the mixed-filler composites. The researchers therefore calculated the hybrid filler’s effective thermal expansion using the Turner approach and inserted that value into an adapted Schapery calculation for the BT resin/glass-fiber composite. This improved procedure yielded values close to experiment.

The mixed filler approached a near-zero calculated thermal expansion coefficient at a silica-to-zirconium-tungsten-phosphate ratio of 3:7, a condition the authors termed the zero-value effect. Across the filler contents examined, this mixture consistently reduced composite thermal expansion more effectively than either silica or zirconium tungsten phosphate alone. Dielectric measurements added an important second dimension: the mixed-filler composites retained an adjustable dielectric constant and low dielectric loss. For chip-packaging substrates, the significance of the new formulation is not only lowering thermal expansion and shows that a hybrid ceramic filler can be designed to balance the expansion response of the resin-based composite and in the same time preserve dielectric characteristics appropriate for substrate applications. The result is relevant to multilayer structures, where dimensional stability must be considered alongside the compatibility of the resin, glass-fiber reinforcement, and ceramic phases.

The practical value of the silica–zirconium tungsten phosphate combination comes from its ability to reduce thermal expansion without relying entirely on a negative-thermal-expansion ceramic. Zirconium tungsten phosphate contributed the negative expansion needed to counteract the BT resin matrix, while silica adjusted the effective filler response and introduced a lower-cost component into the formulation. The 3:7 silica-to-zirconium tungsten phosphate mixture produced the lowest measured composite CTE because the hybrid filler approached a near-zero expansion condition. This creates a useful formulation principle for substrate engineers: the objective need not be to maximize the negative-expansion filler content, but to select a hybrid composition that balances filler expansion, stiffness, particle packing, and matrix constraint. The measured dielectric behavior also supports use in high-frequency substrate design. The mixed-filler composites retained an adjustable dielectric constant together with low dielectric loss, allowing thermal expansion and dielectric performance to be tuned together rather than treated as separate material targets. Close bonding among the BT resin, glass cloth, and ceramic phases is also relevant to fabrication, since a well-integrated microstructure helps preserve continuity across the composite and avoids obvious interfacial separation. Beyond the particular BT resin system examined, the calculation approach offers a useful engineering method for hybrid-filler composites. By first estimating the thermal expansion of the mixed ceramic phase with the Turner model and then incorporating that effective phase into an improved Schapery calculation, the researchers provided a route for predicting multiphase composite behavior where standard two-phase models are insufficient. This can help guide filler-ratio selection before extensive formulation trials. For electronic substrate development, the study therefore connects thermal-expansion matching, dielectric adjustment, filler economics, and model-based materials design within one experimentally supported composite strategy.

Refractory complex concentrated alloys present a difficult solidification problem: very high melting temperatures, strong chemical interactions, and restricted atomic diffusion all influence which phases can form from the liquid state. Their solidification behavior is especially important because the phases selected from the liquid state can determine not only microstructure, but also stability and environmental resistance. To monitor directly these liquid-solid transitions is not simple because refractory liquids require extreme temperatures and are easily affected by crucible reactions and heterogeneous nucleation. Conventional processing can introduce unwanted reactions, heterogeneous nucleation, and complex thermal histories that make it harder to isolate the true competition between solid solutions and intermetallic phases. For alloys containing W, Nb, Hf, and Zr, achieving the liquid state requires extreme high temperature, and multicomponent chemistry restricts how quickly atoms can redistribute during solidification.

Laves phases are especially relevant here because they are ordered intermetallic compounds whose formation is controlled by atomic size, electronic structure, and local packing. In multicomponent refractory alloys, their formation cannot be treated simply as the low-temperature consequence of equilibrium thermodynamics. A Laves phase may be thermodynamically favored, but does not appear when the liquid-solid transition moves too quickly for the required atomic rearrangement. When the liquid is undercooled beyond a critical point, the balance changes: the ordered Laves phase can nucleate directly from the melt instead of waiting for the slower peritectic reaction to form it and the challenge is to determine when stability can actually be expressed during solidification.

In a recently published research paper in Acta Materialia, Mr. Kelun Liu, Dr. Ruilin Xiao, Mr. Bohan Sun, Professor Ying Ruan, and Professor Bingbo Wei from Northwestern Polytechnical University developed an electrostatic-levitation-based solidification approach for resolving the growth mechanism of a refractory multicomponent Laves phase in W₂₅Nb₂₅Hf₂₅Zr₂₅ alloy. They identified the Laves phase as C15-type (W,Nb)₂(Hf,Zr), with W/Nb and Hf/Zr occupying distinct crystallographic sublattices supported by atomic-resolution imaging and first-principles calculations. They established a processing-dependent phase-transition map in which near-equilibrium peritectic formation, non-equilibrium BCC phase selection, and deep-undercooling direct Laves crystallization are separated by undercooling and cooling-rate conditions. They also linked direct Laves formation and altered BCC2 boundary character to improved pitting resistance in sulfuric acid solution.

The research team showed that W₂₅Nb₂₅Hf₂₅Zr₂₅ does not follow a single solidification route and found that below a critical undercooling of about 395 K, the alloy solidified through three sequential body-centered cubic phases. The primary BCC1 phase, enriched in W and therefore associated with the highest melting temperature, formed first from the undercooled liquid. BCC2 then grew epitaxially from BCC1, maintaining a cube-on-cube orientation relationship with a very small average misorientation. A third BCC phase appeared at grain boundaries, enriched in W and Hf relative to the surrounding phases. This sequence is scientifically important because it shows that a multicomponent alloy with strong Laves-forming propensity can still avoid Laves formation when the kinetic path does not permit sufficient solute redistribution.

The authors observed once ΔT exceeded 395 K, the primary phase switched from BCC1 to a Laves phase identified as (W,Nb)₂(Hf,Zr), followed by formation of a BCC2 matrix. The growth kinetics reflected this discontinuity. The BCC1 and Laves regimes were described by different power-law relationships, with the primary Laves phase appearing only after the undercooled liquid crossed the threshold corresponding to the interval between the liquidus and peritectic transition temperature. The researchers also measured the growth velocity of BCC2 as a function of peritectic undercooling and found it to be much faster than the Laves phase growth. The design choice of independently varying undercooling and peritectic undercooling therefore separated the origin of the Laves phase from the later BCC2 growth event, making the phase-selection mechanism clearer rather than treating the final microstructure as a single solidification product. Crystallographic analysis showed no fixed orientation relationship between the Laves phase and BCC2 under these conditions, consistent with independent formation events. The final deeply undercooled microstructure contained faceted Laves particles uniformly embedded in the BCC2 matrix.

The team performed atomic-resolution characterization to determine the structural identity of the intermetallic phase and found that the Laves phase adopted a C15-type cubic structure, with W and Nb occupying the smaller-atom sublattice and Hf and Zr occupying the larger-atom sublattice. First-principles calculations supported this arrangement. The calculated formation energy of (W,Nb)₂(Hf,Zr) was far lower than those of the BCC phases and also lower than alternative atomic substitution arrangements within the Laves structure. This result is central to the paper’s logic: the Laves phase is the most stable phase considered, but its appearance depends on whether solidification conditions allow that stability to be realized.

The investigators conducted near-equilibrium levitation experiments and found at very small undercooling and low cooling rate, the Laves phase appeared wrapped around primary BCC1, consistent with a peritectic transition from liquid plus BCC1 to (W,Nb)2(Hf,Zr), followed by a eutectic reaction involving Laves and BCC2. Under faster non-equilibrium conditions below the critical undercooling, that peritectic reaction was suppressed. The authors attribute this suppression to restricted atomic diffusion in the chemically complex liquid-solid environment, especially for the larger Hf and Zr atoms. A comparison with a simpler Zr-W binary peritectic system strengthened the interpretation: in the binary alloy, the peritectic product persisted under undercooling, whereas the multicomponent W-Nb-Hf-Zr alloy could bypass it entirely. Additionally, deep undercooling studies showed that instead of allowing the usual peritectic pathway to proceed, it supplied enough thermodynamic driving force for direct nucleation of (W,Nb)₂(Hf,Zr) from the liquid.

The team showed in sulfuric acid solution, the sample solidified at higher undercooling showed a pitting potential of 2.11 VSCE, about 40 percent higher than the lower-undercooling condition. Impedance behavior indicated greater charge-transfer resistance and a more capacitive response, while surface analysis showed passive films containing ZrO2, HfO2, WO3, and Nb2O5. The higher-undercooling sample had slightly higher fractions of ZrO2 and HfO2 and a higher lattice oxygen content. Corrosion morphology also changed: pits in the lower-undercooling alloy were associated mainly with BCC3 at grain boundaries, whereas the deeply undercooled alloy showed fewer, shallower pits at Laves/BCC2 interfaces, with the Laves phase itself remaining unaffected.

The engineering importance of the findings of Northwestern Polytechnical University scientists is that solidification pathway control can be used as a practical design variable for refractory alloys. In high-temperature structural materials, especially those based on W, Nb, Hf, and Zr, processing conditions often decide whether the final alloy contains metastable BCC solid solutions, ordered intermetallic phases, or mixed microstructures with very different boundary populations and corrosion responses. By showing that deep undercooling can trigger direct crystallization of a C15-type (W,Nb)₂(Hf,Zr) Laves phase, this work provides a route for engineering microstructures through liquid-solid transitions rather than relying only on post-solidification heat treatment. One immediate application is in the development of refractory complex concentrated alloys for severe thermal and chemical environments. Components exposed to high temperature, acidic media, or aggressive service conditions require not only phase stability but also resistance to localized degradation.

The findings also have relevance for rapid solidification technologies, including containerless processing, laser-based melting andadvanced casting of reactive refractory alloys where steep thermal gradients and non-equilibrium cooling are common. In such processes, deep undercooling and rapid thermal extraction can shift phase selection away from equilibrium pathways. The study gives a mechanistic basis for exploiting that shift deliberately: a diffusion-limited peritectic reaction may be bypassed, while direct intermetallic nucleation becomes possible once the thermodynamic driving force is sufficiently high. The results position undercooling as a controllable phase-selection parameter in refractory alloy processing, especially when diffusion-limited peritectic reactions compete with direct intermetallic nucleation. For refractory alloy development, this could help guide processing windows that avoid undesirable grain-boundary phases, promote stable intermetallic dispersions, refine microstructure, and improve resistance to localized corrosion. The practical value is therefore in linking processing, phase nucleation, atomic structure, and service-relevant behavior within a single design framework.

Nano-architected metals present a demanding materials-design problem because their geometry, microstructure, and defect populations are intertwined at nearly the same length scale. In conventional architected materials, the load-bearing architecture is often much larger than the characteristic microstructural dimensions of the solid from which it is made. That separation allows one to describe the constituent material by an effective property and then analyze the lattice, shell, or cellular structure at a higher scale. At the nanoscale, that assumption becomes less secure. When beams, shells, grains, and processing-induced pores all fall within tens to hundreds of nanometers, the architecture is not simply a scaled-down version of a familiar cellular metal. Its mechanical response is shaped by a direct encounter between structural geometry and the defects embedded inside the load-bearing members. The central technical challenge is therefore twofold. First, complex three-dimensional metallic architectures must be fabricated with sufficient resolution, structural integrity, and reproducibility to make meaningful mechanical testing possible. Second, the mechanical behavior must be interpreted in a way that connects nanoscale building-block properties with architecture-level deformation and failure. Existing nanoscale additive manufacturing approaches have reached important feature-size regimes, but the paper frames a remaining gap: the need for a method that can combine three-dimensional freeform fabrication, metallic conversion, controlled geometry, and mechanically diagnostic experiments in the same platform. Without that combination, it is difficult to determine whether observed strength reflects architecture, constituent material size effects, processing defects, or some mixture of all three. In a recent research paper published in Nature Communications, Dr. Wenxin Zhang, Dr. Zhi Li, Dr. Huajian Gao, and Professor Julia Greer from California Institute of Technology, developed a two-photon-lithography-based hydrogel infusion additive manufacturing process for complex three-dimensional metallic nano-architectures with approximately 100 nm critical dimensions and tens-of-nanometers surface roughness. They produced beam-based, shell-based, periodic, and non-periodic nickel nano-architectures and coupled their fabrication with in situ nano-compression testing. They also developed a physics-informed finite-element strategy that incorporates experimentally measured building-block behavior and nodal porosity distributions to predict size-dependent strength and failure. Its technical distinction is the direct linkage of nanoscale defect statistics to architecture-level deformation in additively manufactured metals.

 The researchers used nano-HIAM to fabricate three representative classes of nickel nano-architecture: beam-based periodic octahedral nanolattices, shell-based periodic Schwarz-P nanolattices, and shell-based non-periodic spinodal-like architectures. The process began with two-photon lithography of polymeric templates, followed by infusion with nickel salt solution and thermal conversion to metallic nickel. A modified photoresist formulation increased printing speed while maintaining spatial resolution, allowing the preparation of more complex three-dimensional structures. The resulting architectures had feature dimensions in the hundreds of nanometers, surface roughness on the order of tens of nanometers, and structural relative densities of roughly 20–40%. Their nickel microstructure was nanocrystalline and nanoporous, with grain dimensions near 50 nm and uniform nanoporosity at smaller feature sizes.

The authors carried out mechanical testing by in situ nano-compression, which allowed deformation to be followed while stress–strain behavior was measured. Most specimens showed an extended linear loading regime followed by catastrophic global collapse. In the periodic lattices, short strain bursts sometimes preceded the final collapse, consistent with local events occurring before global failure. A smaller number of samples showed gradual layer-by-layer deformation associated with visible fabrication imperfections; these were distinguished from the dominant material-failure response so that the analysis could focus on the intrinsic size-dependent behavior of the nano-architectures. The strength data revealed that architecture-level compressive strength depended not only on relative density but also on feature dimension. That second dependence is central to the paper. At these sizes, the metal building blocks themselves have size-dependent strength, and the architectural structure inherits part of that behavior. The authors described the architecture strength as a product of a density-dependent term and a feature-size-dependent term. Periodic octahedral and Schwarz-P lattices showed a stronger size scaling than the non-periodic spinodal-like architectures. This difference was interpreted through the distribution and severity of defects: periodic architectures contained concentrated porosity at nodal or locally thickened regions, whereas the non-periodic structures had a more stochastic distribution of shell thickness and stress concentration.

The researchers found that in octahedral lattices, concentrated pore regions appeared preferentially at nodal junctions, where local effective feature dimensions were larger than the average beam diameter. The scientific consequence is important: the same architectural sites that carry high stress also tend to contain more severe porosity, making them likely origins for deformation and fracture. The researchers quantified nodal porosity distributions and used them as input for finite-element simulations. Their simulations first incorporated building-block stress–strain behavior and nanovoids at the unit-cell level, then introduced degraded nodal properties into full-lattice models. Failure initiated at local nodal elements and progressed toward global collapse, matching the experimental observations. Both a homogeneous nodal-degradation model and a porosity-distribution-based model captured the measured size effects in periodic nanolattices. This connection between measured nanoscale defect statistics and architecture-level prediction is one of the paper’s strongest scientific contributions.

The engineering applications of Professor Julia Greer and colleagues findings are most immediate in the design and manufacturing of mechanically reliable nanoscale metallic components. The study shows that nickel nano-architectures can be fabricated with feature dimensions of roughly 100–500 nm while retaining high structural definition, low surface roughness, and specific strengths . That combination is relevant for nanoscale manufacturing systems where small metallic architectures must carry load without losing geometric precision. Possible application areas include nanoelectromechanical systems, nanorobotic components, miniaturized load-bearing metallic parts, and small functional structures where stiffness, strength, and three-dimensional geometry must be controlled together. The practical value is not simply that the structures are small; it is that their mechanical response can be linked to fabrication-induced nanoporosity, feature size, relative density, and architecture type. For engineers, this gives a clearer route for deciding whether a beam-based lattice, shell-based lattice, or non-periodic architecture is more suitable for a given load-bearing requirement. Periodic architectures may offer higher axial load-bearing capacity, while non-periodic structures may distribute local stress and defect sensitivity differently. The paper therefore supports a more careful design logic for metallic nano-architectures: feature size, topology, nodal geometry, and porosity distribution must be treated as coupled design variables rather than independent details.

A second important application is in predictive engineering of hierarchical materials. The authors show that concentrated nanoporosity, especially at nodal junctions in periodic lattices, can control deformation initiation and architecture-level strength. This is highly relevant for any nanoscale device or micro-structure expected to undergo repeated loading, compression, vibration, or contact stresses, because failure may begin at nanoscale defect-rich regions rather than in the average material volume. By measuring porosity distributions and incorporating them into finite-element simulations, the study provides a practical computational pathway for diagnosing and predicting the strength of nano-architected metals before device integration. This could help engineers avoid overestimating performance by simply extrapolating from isolated nanopillar properties. The approach may also guide the development of more robust nano-architectures for biomedical microdevices, flexible electronics, aerospace micro-structures, and other small engineered systems where metallic components must be both lightweight and mechanically dependable. The broader manufacturing implication is equally important: nano-HIAM is described as adaptable to other metals, ceramics, and composites through infusion and thermal treatment chemistry, meaning the same fabrication-and-diagnosis strategy could be extended beyond nickel. In that sense, the work provides not just a material result, but an engineering methodology for designing, testing, and modeling complex nanoscale architectures with defect-aware mechanical reliability.

Mechanical metamaterials are increasingly expected to do more than carry load or deform in unusual ways. In many engineered systems, the same structural architecture may need to absorb mechanical energy, guide or block acoustic waves, reduce vibration, and adapt to changing operating conditions. When the same internal structure shapes stiffness, folding motion, energy absorption, and acoustic bandgaps, the material is no longer just a passive assembly of repeating cells and becomes a programmed physical system, with performance set by the precision of the link between geometry and function. The difficulty is that multifunctionality often brings unwanted coupling. A change introduced to improve one response can shift another response at the same time, because both are controlled by overlapping design parameters. Mechanical behavior depends on deformation mode, load path, local hinge or panel response, and the available folding or collapse sequence. Acoustic behavior depends on periodicity, internal pathways, symmetry, and the wave-propagation environment. A geometry selected for energy absorption may not give the desired bandgap; a geometry selected for wave attenuation may impose an unsuitable stiffness. This is why independent programmability remains a demanding problem rather than a simple matter of adding more structural features.

One possible solution is to assign different functions to different sub-units within the same material. That strategy can separate mechanical and acoustic responses to some degree, but it also increases architectural complexity and does not naturally provide post-fabrication tunability. A material whose properties are fixed once fabricated can be carefully designed, but it cannot easily respond to a new directional requirement, a different loading condition, or a changed acoustic target. The unresolved question, therefore, is whether a single structural design can support both independent programming and later reconfiguration without relying on separate functional modules. Origami-inspired metamaterials provide a disciplined way to approach this question because folding kinematics gives the deformation a predictable geometric basis, instead of leaving the response to uncontrolled structural bending or collapse. In a recent research paper published in Composites Part B: Engineering, Dr. Mengyue Li, Professor Jiayao Ma, Dr. Xiao-Lei Tang, Professor Yan-Feng Wang, and Professor Yan Chen from Tianjin University developed a new class of double-tubular origami metamaterials capable of independently programming and tuning mechanical and acoustic properties within a unified folding architecture..

The researchers designed a double-tubular origami unit built from connected parallelogram panels, producing two perpendicular tubular pathways aligned with orthogonal directions. Its motion was formulated as a single-degree-of-freedom rigid folding process, with one dihedral angle used to determine the remaining folding angles and the changing dimensions of the unit cell. By changing the geometric parameters, they identified three kinematic categories. One type is not flat-foldable along either tubular direction, another is flat-foldable along one direction, and the most special case is flat-foldable along both directions. This third configuration, referred to as C3, becomes the decisive design because it has a geometric transposition property: under paired folding states, the dimensions along the two orthogonal directions can be exchanged.

The authors performed mechanical testing and modelling then to clarify how that kinematic structure translates into compression response. They found for the non-flat-foldable and partially flat-foldable designs, compression involved a plateau associated with origami folding until self-locking or full squeezing altered the deformation mode. In the C3 metamaterial, both orthogonal compression directions retained the rigid-origami folding character and produced plateau-type force-displacement behavior. The analytical model treated the creases as elastic-plastic hinges and the panels as rigid, thereby establishing an explicit analytical relationship between folding kinematics, deformation mechanics, and energy absorption performance. Agreement between theory and experiment was close for the tested C3 prototype, with reported errors no larger than 2.5% for stiffness and 5.3% for specific energy absorption.

The analysis treated the panels as sound-hard boundaries and examined wave propagation through the periodic air domain formed by the origami architecture. Complete bandgaps appeared in geometrically symmetric cases, while an asymmetric configuration generated direction-dependent partial bandgaps. For C3 at its symmetric folding state, two complete bandgaps were identified, and the transmission-loss behavior was identical along the two orthogonal directions. The design choice of using a flat-foldable, geometrically transposable C3 unit therefore had a direct scientific consequence: it allowed symmetry, dimensional exchange, and directional acoustic behavior to be connected through the same folding variable.

The team also found that mechanical properties varied strongly with the initial folding angle and sector angle, while acoustic bandgaps followed a different, nonlinear dependence on the same parameters. Because the mapping from design parameters to properties was not one-to-one, the researchers could select configurations that preserved one property while changing another. Under constant stiffness, the frequency range of the complete bandgap changed by up to 10.4 times. In the reverse direction, stiffness changed by up to 16.9 times without altering the complete bandgap, while specific energy absorption varied by 5.4 times under the same bandgap condition. The transposed C3 pairs also showed exchanged mechanical properties between directions, indicating that geometric transposition directly controlled the functional response and was not simply a dimensional symmetry of the folded structure.

The researchers demonstrated post-fabrication tunability using thermoplastic polyurethane prototypes. They mechanically reconfigured the printed metamaterial in fixtures, applied heat treatment, cooled the constrained assembly, and repeated the process to obtain target folding states. A symmetric state gave nearly identical stiffness and transmission-loss behavior along the two directions. Reconfiguration to a general folding state created pronounced directional differences in both force response and acoustic transmission-loss peaks. Reconfiguration to the corresponding transposed state swapped the directional mechanical and acoustic behavior.

Through innovative structural design and theoretical characterization, the double-tubular origami metamaterials break the long-existing bottleneck in multifunctional metamaterials, i.e., different properties are handled by separate material layers. The engineering applications are strongest in systems where mechanical protection and acoustic control must be designed as part of the same structural architecture. A second important application for the study of Tianjin University scientists is in direction-sensitive engineering structures because the C3 design can exchange its mechanical and acoustic behavior between orthogonal directions through geometric transposition, it could be useful in components that experience different loading or noise conditions depending on orientation. For example, an internal panel, isolating block, or modular insert could be configured to provide higher stiffness in one direction while targeting acoustic attenuation in another. The directional mechanical and acoustic responses can be deliberately programmed through the folding state and, in the TPU prototypes, reconfigured after fabrication through thermomechanical treatment. Reconfiguration produced different force responses and transmission-loss peaks along the two axes, while the transposed state swapped those responses.

The findings also have clear implications for adaptive noise-control and vibration-isolation systems. The periodic geometry of the metamaterial controls how sound waves pass through the structure, producing complete or partial bandgaps and measurable transmission loss across selected frequency ranges. Since the same architecture allows mechanical stiffness and acoustic bandgaps to be adjusted with some independence, designers could target a required stiffness level without necessarily losing control over the acoustic response. The study further demonstrates post-fabrication tunability through thermomechanical reconfiguration of TPU prototypes. By reconfiguring the metamaterial into different folding states, the researchers were able to alter and even exchange the directional mechanical and acoustic responses of the same structure. This capability makes the design particularly promising for adaptive protective systems, aerospace structures, machinery components, and other engineering applications requiring multifunctional performance under changing operating conditions.

Block copolymer melts offer a clear example of how molecular architecture forms nanoscale organization in soft materials. When two chemically distinct polymer blocks are covalently joined, their tendency of phase separation is restricted by chain connectivity, producing either a disordered melt or ordered microphase-separated structures depending on composition, molecular size, and segmental incompatibility. In the classical treatment of linear AB diblock copolymers, this balance is commonly described through the volume fraction of each block, the total degree of polymerization, and the Flory–Huggins interaction parameter between the two components. For a symmetric diblock, the order–disorder transition is a sensitive measure of how strongly the two blocks repel one another relative to the entropy cost of organizing the chains. Multiblock, triblock, branched, and ring copolymers can contain the same chemical components while placing the blocks in different spatial and conformational environments. The connecting manner of the chains can alter the effective segregation strength, shift the order–disorder transition, and change the characteristic length scale of concentration fluctuations or microdomains.   Ring block copolymers are especially informative systems because they contain no free chain ends and their closed-chain architecture alters how the molecule occupies space in the melt. Unlike linear chains, which are often approximated as Gaussian coils, ring polymers are expected to adopt more compact conformations because intramolecular and intermolecular chain crossing is prohibited. This self-shrinking tendency can bring different segments within the same ring molecule closer together, potentially modifying the apparent miscibility between chemically distinct blocks. The key question is whether ring topology only changes structural dimensions, or whether it also measurably reduces the effective incompatibility between polystyrene and polyisoprene blocks in the disordered melt. Previous experimental studies had mainly examined ordered ring diblock structures rather than disordered-state miscibility. In a recent research paper published in Polymer, Dr. Yuya Doi, Mr. Naoto Sakabe, Late Professor Yoshiaki Takahashi, Professor Atsushi Takano, Professor Yushu Matsushita from Nagoya University, Yamagata University and Kyushu University developed a low-molecular-weight, compositionally symmetric ring polystyrene-block-polyisoprene (SI) copolymer and compared its melt behavior with closely matched linear SI and telechelic ISI analogues. They combined temperature-dependent small-angle X-ray scattering (SAXS), dynamic viscoelasticity, and random phase approximation (RPA)-based analysis of disordered correlation-hole scattering to quantify topology-dependent changes in χ_eff.

The researchers prepared three polystyrene/polyisoprene block copolymers with similar total molecular weights (≃ 20 kg/mol) and nearly symmetric composition: a linear SI diblock (L-SI-22), a telechelic linear ISI triblock (tele-ISI-23), and a ring SI diblock (R-SI-23). The ring sample was obtained through cyclization of a tele-ISI-23 precursor followed by size-exclusion chromatography fractionation, giving a high-purity ring diblock suitable for direct comparison. The narrow molecular weight distributions and closely matched polystyrene volume fractions were important because the study focused on topology as the variable of interest.   SAXS immediately separated the linear diblock from the other two architectures. At 120 °C, L-SI-22 displayed sharp scattering peaks assigned to a lamellar microphase-separated structure, with a domain spacing of 19.4 nm. By contrast, both R-SI-23 and tele-ISI-23 showed a broad correlation-hole peak, placing it in the disordered state under conditions where the corresponding linear diblock remained ordered. R-SI-23 showed a broader correlation-hole peak, a slightly higher peak-top scattering vector than tele-ISI-23, and a scattering intensity more than an order of magnitude lower. These differences are consistent with a shorter apparent characteristic length and reduced concentration fluctuations in the ring diblock.  The authors found the linear SI diblock show peak broadening, a modest shift to higher scattering vector, and disappearance of higher-order peaks as the temperature approached the order-disorder transition under heating. The telechelic triblock and ring diblock behaved as disordered systems across the measured range, with decreasing peak intensity and broader correlation-hole features at higher temperature. That pattern is consistent with upper critical solution temperature-type behavior for the polystyrene/polyisoprene pair: increasing temperature reduces concentration fluctuations and increases miscibility.   The storage modulus of L-SI-22 decreased gradually and then sharply near the transition region under heating, while R-SI-23 and tele-ISI-23 had much lower storage moduli and disordered-state behavior already at low temperature. R-SI-23 also showed about one order of magnitude lower storage modulus than tele-ISI-23 over the measured range, a response the authors relate to the faster global relaxation dynamics characteristic of ring polymers.

The researchers fitted the correlation-hole scattering using RPA functions that account for the connectivity of the chains based on the Gaussian distribution, allowing the ring and telechelic architectures to be compared beyond a simple visual inspection of peak shape. Because both samples contain the same polystyrene and polyisoprene components, the intrinsic segmental interaction would normally be expected to depend mainly on chemistry. In this analysis, however, deviations caused by architecture and chain statistics were incorporated into an effective interaction parameter, χ_eff.   The ring diblock consistently gave a lower χ_eff than the telechelic triblock across the measured temperature range, indicating weaker effective segregation between the S and I segments. Even a modest decrease in χ_eff had a pronounced effect on the calculated scattering intensity, supporting the interpretation that ring closure enhances miscibility by forcing the two chemically distinct blocks into closer spatial proximity.

The engineering relevance of the study by Dr. Yuya Doi and colleagues is in demonstrating that chain topology can tune melt phase behavior without changing the chemical identity of the component polymers. In practical polymer engineering, miscibility is often adjusted by changing chemical composition, molecular weight, additives, or processing temperature, but these routes can also alter mechanical response, thermal stability, or manufacturability. The ring polystyrene-block-polyisoprene system examined here shows that closing the chain into a ring can reduce the effective segregation power between otherwise incompatible blocks, producing a more miscible disordered melt than a comparable telechelic linear triblock. This new principle can be useful in designing thermoplastic elastomers, nanostructured coatings, damping materials, pressure-sensitive adhesives, and soft polymer blends where excessive microphase separation may lead to brittleness, poor optical clarity, slow relaxation, or processing difficulty. The rheological findings are also important from an engineering standpoint: the ring diblock displayed much lower storage modulus than the telechelic analogue across the measured temperature range, suggesting that ring architecture may offer a route to softer, faster-relaxing melts without simply lowering molecular weight. That distinction matters in extrusion, molding, film formation, hot-melt processing, and additive manufacturing, where viscosity, relaxation time, and phase uniformity strongly influence final material quality. The SAXS analysis adds a second practical implication: the higher-q, lower-intensity correlation-hole scattering of the ring diblock indicates shorter characteristic fluctuation lengths and weaker concentration fluctuations, which may help guide the design of more homogeneous nanoscale polymer systems. For materials design, ring closure or related topological constraints could, in principle, help shift the balance between ordering and mixing while retaining the same component polymers.

Friction is usually discussed as a mechanical response of surfaces in contact, but many sliding interfaces contain internal degrees of freedom that can store, rearrange, and dissipate energy during motion. In such systems, the frictional force is not governed only by the externally applied load or by surface roughness. It may instead depend on how the internal order of the interface responds while one body moves relative to another. Magnetic order provides a particularly clean setting for this problem because magnetic moments can interact across a gap, change orientation, and dissipate energy without requiring direct mechanical abrasion. Amontons’ law gives a familiar monotonic relation between normal load and frictional force. Its empirical usefulness is undeniable, but it does not explain what happens when the sliding process perturbs structural, electronic, or magnetic configurations at the interface. Magnetic friction has therefore become an important test case for asking whether dissipation can arise from configurational dynamics alone. Earlier work had connected magnetic ordering with friction, and scanning probe methods had measured magnetic interactions at very small scales. Yet those approaches usually involve a localized tip interacting with a surface. They are powerful for probing local forces, but they do not naturally expose the collective rearrangements that can occur between two extended, laterally aligned magnetic lattices.

In a recent research paper published in Nature Materials, Dr. Hongri Gu, Dr. Anton Lüders & Professor Clemens Bechinger from the University of Konstanz in Germany developed a two-dimensional macroscopic magnetic rotor array that allows direct measurement of sliding friction while tracking the orientation of every magnetic moment. They paired this experiment with dipole-based molecular dynamics simulations and a reduced two-sublattice model that captures the essential ferromagnetic–antiferromagnetic switching mechanism. The technically distinct element is the direct linkage between non-monotonic magnetic friction, collective rotor reorientation, and hysteretic torque cycles under commensurate sliding. The platform separates magnetic dissipation from mechanical friction and makes collective magnetic order an experimentally accessible variable during motion.

The researchers built a spatially resolved macroscopic analogue of a magnetic sliding interface. The top layer consisted of a square array of rotatable neodymium–iron–boron ring magnets, each mounted so that its magnetic moment could rotate in the xz plane. Beneath it, a commensurate substrate array of fixed cylindrical magnets provided a periodic magnetic field during lateral translation. The slider was moved forwards and backwards over seven lattice periods while the lateral force and the orientation of each rotor were recorded. This design choice mattered because it converted a normally inaccessible many-body magnetic rearrangement into an experimentally trackable rotor dynamics problem.

Changing the vertical separation between the two magnetic layers tuned the balance between the substrate field and the interactions among neighbouring rotors. At small separations, the substrate field dominated. The rotors responded collectively and remained largely ferromagnetically aligned during sliding. At large separations, the substrate influence weakened and intralayer interactions prevailed, producing antiferromagnetic ordering with only small collective angular motion. The intermediate regime was more interesting. There, the interlayer and intralayer magnetic interactions became comparable, and the rotors switched between ferromagnetic and antiferromagnetic arrangements in a discontinuous fashion.

To quantify this behaviour, the researchers used an orientation correlation parameter that distinguishes parallel from antiparallel alignment of neighbouring moments. As the layer separation increased, the average magnetic order changed gradually from ferromagnetic to antiferromagnetic. The important point is that the friction peak appeared near the separation where the average order passed through zero, meaning that no single magnetic ordering dominated over a full sliding period. The force response was therefore not simply following magnetic attraction between the layers. Although the effective magnetic load decreased monotonically with separation, the measured friction did not. It reached a maximum around the intermediate competing regime.

The force signal contained both magnetic and mechanical contributions, so the researchers separated these terms rather than treating the total force as the final observable. Mechanical friction came mainly from the brass rollers used to maintain layer spacing against magnetic attraction, with an additional small load-independent contribution. Once this mechanical part was removed, the isolated magnetic friction retained the same non-monotonic dependence on separation. In the ferromagnetic and antiferromagnetic regimes, the force oscillations were nearly symmetric around the mechanical contribution, leaving little net magnetic friction over a lattice period. In the competing regime, that symmetry was lost, and the asymmetric force cycle produced a substantial magnetic contribution.

Molecular dynamics simulations, with the magnets represented as point dipoles and with rotational degrees of freedom matching the experimental geometry, reproduced the main features of the measurements. The simulations captured the ferromagnetic and antiferromagnetic regimes especially closely and also reproduced the transition between ordering states in the competing regime. The remaining irregularity in experimental switching was attributed to small physical variations in magnets and structure dimensions, which is reasonable in a system operating near a tipping point. The agreement between measured orientations, reconstructed magnetic friction, and dipole-based simulations made the central interpretation difficult to dismiss: dissipation was tied to collective magnetic reorientation, not to a hidden mechanical artefact.

The simplified theoretical description sharpened that interpretation. Because the rotor array largely occupied ferromagnetic or antiferromagnetic configurations, the slider could be reduced to two magnetic sublattices with two angular variables. In the overdamped limit, the model related energy dissipation to the torque exerted by the substrate field and to the angular motion of the moments. At small separation, torque oscillated in a nearly symmetric way and the average magnetic dissipation remained small. At large separation, both torque and angular velocity were weak. Between these limits, asymmetric torque cycles generated hysteresis, and the area of those hysteresis loops corresponded to dissipated energy during sliding.

The work of Professor Clemens Bechinger and colleagues connects friction to a sliding-induced change in collective magnetic order. The friction maximum is not an incidental feature of stronger coupling or higher load. It occurs where competing magnetic interactions force the rotor array through repeated configurational switching. That gives the work a clean physical message: magnetic friction can be generated by internal reorientation dynamics even when direct mechanical contact is not the source of dissipation. This changes the interpretation of load dependence in magnetic sliding systems. A monotonic decrease in magnetic attraction with separation does not guarantee a monotonic decrease in friction, because the relevant dissipative channel may be strongest when the interface is neither firmly in one ordered state nor another. The competing regime is therefore not just a crossover between ferromagnetic and antiferromagnetic order. It is the condition under which sliding produces hysteretic torque cycles, and those cycles provide the route for energy loss.

The new study also gives friction a diagnostic role because the frictional anomaly appears at the point where magnetic order becomes dynamically frustrated, the lateral force can act as a sensitive readout of collective magnetic rearrangement. The macroscopic nature of the experiment is useful here, not because it imitates every microscopic detail of atomic magnets, but because it makes the internal dynamics visible while preserving scale-free governing relations. The authors’ claim is carefully bounded: the mechanism should be relevant to systems with similar energetic symmetries and competing interlayer and intralayer interactions, including low-dimensional magnets, spintronic materials, XY-type systems, patterned magnetic interfaces, and possibly ferroelectric tribology where domain polarization changes influence sliding friction. The design logic is also important and instead of controlling friction through surface chemistry, roughness, or wear-prone contact, the paper points toward interfaces whose dissipation can be tuned through internal many-body ordering. The requirement is not simply “magnetism,” but a regime where sliding can repeatedly drive the system between competing configurations. That distinction gives the study its real value for future contactless friction control and magnetic metamaterial concepts.

Angle-resolved polarized Raman (ARPR) spectroscopy is a Raman spectroscopy method in which the researchers change the polarizations direction of the incoming laser and/or the scattered Raman light while measuring how the Raman intensity changes with angle. In practice, they rotate the polarizations relative to the crystal axes and record the angular intensity pattern of each Raman mode. When the polarization angle is changed in an anisotropic layered material (ALM), the Raman signal does not behave in a clean and, stable way. The difficulty is that in these materials, the measured angular Raman pattern had already been known for years to shift with flake thickness, excitation wavelength, and even the dielectric environment beneath the flake. Once a technique behaves that way, interpretation becomes unstable. A pattern that looks like an intrinsic signature of the crystal may actually contain a large contribution from the optical path the light takes before and after the scattering event. This limitation had not been fully resolved because the usual simplified treatment applicable to isotropic layered materials assumes that the incoming and outgoing polarization vectors can be treated as fixed quantities at the sample surface. For ALMs, that assumption is too crude. Inside the flake, birefringence changes phase accumulation along different in-plane axes, linear dichroism determines how far light penetrates along those axes, and the flake together with the substrate forms a multilayer optical structure that introduces interference. Consequently, inside the ALM, neither the excitation field at the Raman scattering site nor the Raman-scattered field that propagates back out of the sample plane is identical to the polarization field that the experimenter defines outside the sample.. So the measured signal becomes depth-dependent, axis-dependent, wavelength-dependent, and substrate-dependent all at once. Earlier fits based on effective complex Raman tensor elements can phenomenologically describe specific measurements, but the fitted tensor elements vary with thickness, excitation wavelength, and substrate conditions even though a Raman tensor for a thick flake with bluk-like electronic structure should be intrinsic to the material, heavily limiting their transferability and restricting their predictive power across different structures and samples.

A further challenge arises when the anisotropic material enters the atomically thin limit. In these systems, the optical propagation effects discussed above still remain important, but the electronic structure itself also evolves with layer number. As a result, the associated optical anisotropy, electron–photon/electron–phonon couplings, and Raman tensor parameters can become layer-dependent, meaning that one cannot simply transfer a model from bulk-like crystals to few-layer systems.

In a recent research paper published in Advanced Materials, Dr. Jia-Liang Xie, Dr. Tao Liu, Professor Miao-Ling Lin, and Professor  Ping-Heng Tan from the State Key Laboratory of Semiconductor Physics and Chip Technologies,  Institute of Semiconductors at  Chinese Academy of Sciences and their collaborators developed a quantitative method that predicting the ARPR intensity in anisotropic materials across atomically-thin flakes to bulk-limits by separating the intrinsic Raman tensor of a phonon scattering event inside an ALM from the effective Raman tensor measured outside the crystal. They combined experimentally determined anisotropic complex refractive indices with transfer-matrix calculations to capture birefringence, linear dichroism, and multilayer interference in the full Raman process. They applied the new approach to thick BP and four-layer Td-WTe₂ and predicted angle-resolved polarized Raman intensities across different substrate oxide thicknesses and excitation wavelengths. The distinctive step was not another fitted angular formula, but to establish a physically grounded mapping between the intrinsic scattering response inside the material and the Raman anisotropy observed under external experimental conditions.

The research team used BP as the proving ground for thick anisotropic flakes because its orthorhombic lattice, strong in-plane anisotropy, and well-known Raman modes make the mismatch between simple tensor fitting and physical expectation hard to ignore. The investigators exfoliated BP flakes onto SiO₂/Si substrates with different oxide thicknesses, measured ARPR spectra under controlled polarization geometry, and tracked how the A¹_g and A²_g angular intensity profiles changed with flake thickness. They observed that the fitted effective tensor ratios and phase differences varied substantially with thickness, even though BP in the tens-of-nanometers regime should not undergo dramatic electronic-structure changes. That observation matters because it forced the analysis away from ad hoc fitting and toward a propagation-based description of the full Raman process.

The authors then measured polarization-resolved reflectance along the two principal in-plane axes and extracted complex refractive indices for BP using a transfer-matrix treatment of the multilayer stack. With those refractive indices in hand, they calculated depth-dependent field factors for incident and scattered light inside the crystal. The researchers showed that these internal fields oscillate with position because the substrate stack creates a cavity-like interference pattern, and that the oscillations differ along the two crystal axes because birefringence and linear dichroism act simultaneously. That combination has a direct scientific consequence: the Raman event at one depth does not carry the same optical weighting as the event at another depth, so the observed spectrum is an integral over inequivalent local scattering conditions, not a single tensor contraction performed at the sample surface.

Using the new approach, the study extracted intrinsic in-plane Raman tensor elements for the BP A¹_g and A²_g modes and found them to remain effectively thickness-invariant across thick flakes and bulk-like BP at a given excitation wavelength. The investigators also found mode-dependent differences in the intrinsic tensor ratios and phases, with the A²_g mode showing stronger anisotropy than A¹_g under the measured excitations, which they connected to its more strongly in-plane vibrational character and its more effective coupling to the armchair-direction electronic transition dipole. The researchers then derived explicit relations linking the intrinsic tensor and the optical propagation factors to the effective tensor seen in experiment. Afterward, they reproduced the thickness dependence and substrate dependence of the BP angular Raman patterns without introducing extra fitting parameters for BP with different thickness on SiO₂/Si substrates with varied oxide thickness.

The study examined few-layer Td-WTe₂ to test whether the same logic could survive in a system where layer-number-dependent electronic structures complicate the optical constants themselves. The authors used four-layer Td-WTe₂, measured Raman responses of A₁ and A₂ modes, extracted anisotropic complex refractive indices from reflectance measured across substrates with different oxide thicknesses, and fitted intrinsic tensor elements for the representative A₁ (denoted P2) mode. They then predicted how the effective tensor and the ARPR pattern changed across widely different SiO₂ thicknesses and across two excitation wavelengths, 633 and 532 nm. The researchers obtained agreement between predicted and measured angular profiles in both cases. That matters because the work is not limited to any specific symmetry class or thickness regime. By validating the framework in either thick BP or few-layer Td-WTe₂, the study demonstrates that the separation between intrinsic scattering physics and external optical propagation is broadly adaptable across ALMs.

The authors’ findings are important because allows researchers to interpret Raman anisotropy in layered materials more reliably across changes in flake thickness, excitation wavelength, and substrate structure, instead of treating each measurement as an isolated fitting problem. The importance of the authors’ findings comes from the fact that it clarifies what ARPR measurements are actually reading in ALMs. More broadly, the work clarifies that the ARPR intensity observed in ALMs is jointly determined by the intrinsic Raman tensor and by anisotropic optical propagation effects such as birefringence, linear dichroism, and multilayer interference. By validating separate but connected strategies for thick BP and few-layer Td-WTe₂, the study establishes a quantitative framework for predicting ARPR responses across different thicknesses, substrates, and excitation wavelengths. That gives the method practical value by providing a more reliable quantitative basis for interpreting ARPR measurements, including Raman-based crystal orientation identification, studies of anisotropic light–matter coupling, and for work on polarization-sensitive layered optoelectronic materials such as BP and Td-WTe₂.

 

A ferroelectric film is a thin deposited layer of a ferroelectric material that exhibits spontaneous, electrically switchable polarization and when a ferroelectric film is bonded to a rigid substrate, the lattice cannot deform freely under electric field, domain walls lose mobility, and the strain that looks accessible on paper collapses in practice. That basic mechanical penalty has haunted thin-film electromechanical materials for years. Bulk ferroelectrics and relaxor-based crystals can generate very large responses, but the same chemistries in film form usually deliver far less, even when the intrinsic structural anisotropy of the crystal would seem to permit much more. In PbTiO₃-derived systems, for example, the tetragonal distortion itself implies a large ferroelastic strain reservoir, but thin films rarely access more than a small portion of it because clamping and electrical failure intervene long before full domain reorganization can occur.

That mismatch leaves the field with a design problem and one can identify materials with strong piezoelectric or ferroelastic character, but translating those qualities into sub-100-nm architectures is not a simple matter of shrinking a bulk ceramic. Once the film is epitaxially locked to a substrate, the substrate becomes part of the electromechanical problem. It constrains lattice motion, shifts the balance among allowable domain states, and forces the material to respond through pathways that are mechanically cheaper, not necessarily those that would produce the largest vertical strain. The breakdown field then adds a second limit. Thin films often need much higher electric fields than bulk crystals to generate comparable strain, so even a promising switching pathway becomes less useful if leakage and failure appear first.

That is why mixed-domain and mixed-phase ferroelectrics remain scientifically attractive. They offer a route to large response not by relying only on small linear distortions of an already selected state, but by exploiting field-driven reorganization among ferroelastic configurations that differ more substantially in polarization direction and lattice shape. Earlier work had already shown that strain can stabilize coexisting domain arrangements in tetragonal ferroelectrics, including c/a and a1/a2 motifs, and that local interconversion among them can generate strong actuation. The unresolved point was scale. Nanoscale or highly localized switching is one thing; generating a macroscopic response across a clamped capacitor is another, because the elastic cost of collective rearrangement rises quickly once the whole film tries to participate.

In a recent research paper published in Advanced Materials, Dr. Zishen Tian, Dr. Menglin Zhu, Dr. Jaegyu Kim, Dr. Piush Behera, Dr. Michael Xu, Dr. Thomas Lee, Dr. Ching-Che Lin, Dr. Sreekeerthi Pamula, Dr. Archana Raja, Dr. Hao Pan, Dr. Jieun Kim, and led by Professor James LeBeau and Professor Lane Martin from the Rice University and Massachusetts Institute of Technology developed sub-100-nm epitaxial PbZr_0.2Ti_0.8O₃ films and PbZr_0.2Ti_0.8O₃ /PMN-PT/ PbZr_0.2Ti_0.8O₃ trilayers engineered to use field-driven conversion of a₁/a₂ superdomains into c/a superdomains as the main actuation pathway. They paired macroscopic electromechanical measurements with operando second-harmonic generation and operando STEM to identify that conversion directly. The distinct advance is the coupling of domain-state design with heterointerface-controlled breakdown management, which allowed the films to move from 1.25% strain in mixed single layers to 2.1% in trilayers while remaining below 100 nm total thickness.

The researchers grew 80 nm PbZr_0.2Ti_0.8O₃ films on DyScO₃, GdScO₃, and NdScO₃ so that epitaxial strain would steer the films into c, c/a, and mixed-domain states, respectively. That choice mattered because it converted substrate selection into a controlled way of tuning the domain-energy hierarchy. The team did not treat strain as background epitaxy; they used it as the variable that determines which domain structures remain available under field. Structural characterization showed exactly that progression, with the NdScO₃ case carrying the mixed state composed of c/a and a₁/a₂ superdomains. In those mixed films, the investigators identified tilted c and a domains inside c/a superdomains and nearly untilted a-domain variants inside a₁/a₂ regions, with a through-thickness distribution that already hinted at an elastic compromise: c/a structures favored the upper part of the film, while a1/a2 domains persisted closer to the substrate where clamping cost more.

The authors then linked domain architecture to electrical and electromechanical behavior in capacitor form. As the films evolved from c to c/a to mixed-domain configurations, the dielectric constant rose, remnant polarization fell, coercive field dropped, and the macroscopic electromechanical response climbed from 0.2% to 0.3% to 0.6% under the same drive conditions, with deff,33 increasing from 55 to 84 to 170 pm V−1. That progression is not just a catalog of numbers. It shows that mixed-domain order does more than create configurational complexity. It opens a response channel that bypasses part of the usual clamping penalty by allowing field-driven ferroelastic conversion, not just small-signal lattice distortion around a fixed domain population.

To determine what actually moved under bias, the research team combined piezoresponse mapping, operando second-harmonic generation, and operando STEM. Piezoresponse measurements after poling showed a measurable increase in the c/a fraction, which captured the irreversible portion of the conversion. The SHG experiments followed the in-plane a-domain population under applied field and found that SHG intensity dropped as field-induced strain rose, directly tying loss of a-domain volume to actuation. Operando STEM then closed the loop: the investigators watched an a₁/a₂ region convert under field into a predominantly c/a configuration. That sequence mattered because the mechanism could easily have been misassigned to ordinary polarization switching inside pre-existing c/a stripes. Instead, the paper identifies a more specific event: a₁/a₂ -to-c/a superdomain interconversion. Once that point became clear, the large response in the mixed films made physical sense.

The researchers also estimated what remained inaccessible. Using lattice parameters from microscopy and domain fractions from piezoresponse data, they argued that full conversion of mixed-domain material toward c/a and then pure c would correspond to a much larger strain ceiling, about 3.5%, while the single-layer films reached about 1.25% at 1 MV cm−1 before leakage and breakdown imposed a stop. That gap is scientifically useful. It shows the response pathway is real, but the field window in a single layer is too narrow to exploit it fully. The trilayer design addressed exactly that bottleneck.

For the multilayer stage, the authors built PbZr_0.2Ti_0.8O₃ /PMN-PT/ PbZr_0.2Ti_0.8O₃ trilayers on NdScO₃ while keeping the total thickness at 80 nm and varying the PMN-PT layer thickness. Structural studies showed that these heterostructures preserved mixed-domain character, though the real-space arrangement changed into a more layered distribution, with the top PZT layer carrying mostly c/a plus some a₁/a₂ character and the bottom layer favoring a₁/a₂. The team interpreted this asymmetry through depolarization fields and mechanical compliance: the PMN-PT layer altered polarization continuity across interfaces and partly decoupled the upper PZT layer from the substrate’s mechanical grip. Under moderate fields, thinner-PMN-PT trilayers retained electromechanical response close to the mixed single-layer film, while thicker PMN-PT reduced deff,33 because the middle layer itself remained strongly clamped in thin-film form. At high fields, though, the trilayers separated clearly from the single layer. Leakage dropped by orders of magnitude, temperature-dependent transport pointed to interface-controlled barriers consistent with band misalignment, breakdown strength rose from 1.20 MV cm⁻¹ in single-layer PZT to as high as 2.25 MV cm⁻¹ in trilayers, and Smax exceeded 2% for all trilayers, reaching 2.1% in the 37/5/37 design with little fatigue after 10⁹ cycles.

Thin-film electromechanical design often defaults to the assumption that one should search for materials with larger intrinsic coefficients, then fight clamping as a secondary engineering problem. This work turns that logic around. It treats domain accessibility and electrical survivability as the main design variables, and it uses composition, epitaxial strain, superdomain selection, and interface energetics to decide which part of the crystal’s structural anisotropy can actually be used in device form. That is a stronger way of thinking about thin-film piezoceramics, especially when the intrinsic lattice reservoir is large but ordinarily locked behind unfavorable mechanics.

There is also a useful refinement in how ferroelastic response is discussed. The large signal here does not arise from a vague mixed-phase “softness.” It comes from a specific hierarchy of domain states. The a₁/a₂ superdomains function as a latent structural reservoir; c/a superdomains provide an intermediate state that is electrically and mechanically accessible; multilayer interfaces then widen the usable field range by suppressing leakage and raising breakdown strength. Each design choice changes a different bottleneck. That division of labor matters because it offers a way to generalize the strategy. One does not need every constituent to be a high-response piezoelectric in thin-film form. One layer can stabilize the convertible domain topology, another can alter compliance or interface transport, and the final behavior can exceed what either layer would deliver alone.

If comparable domain-control and interface-control schemes can be reproduced in device-relevant geometries, one can imagine thin-film actuators, transducers, or strain-mediated heterostructures that no longer accept the usual trade-off of compactness in exchange for weak displacement. The fact that the trilayers reached 2.1% strain in sub-100-nm films places these materials in a performance range that invites serious attention for microsystems. At the same time, the paper does not erase all constraints. The theoretical limit remains higher than the measured value, thicker PMN-PT layers already show a penalty in effective response, and the balance among depolarization field, mechanical compliance, and switchable domain volume looks quite delicate. That delicacy is part of the message: high response in clamped films may depend less on finding a single “best” ferroelectric than on building a structure where incompatible requirements are distributed across layers and domain states in a controlled way. Moreover, the interface-controlled leakage behavior, linked in the paper to a band offset of about 0.7 eV, opens a route that extends beyond this specific PZT/PMN-PT pair. Once electrical failure is treated as an interfacial band-engineering problem, electromechanical design can borrow ideas usually associated with transport physics and electronic heterostructures. That is likely where the longer-term value of this study will reside. Its immediate accomplishment is a strong thin-film actuator response; its broader contribution is a disciplined framework for coupling domain thermodynamics, elastic boundary conditions, and interface electronic structure inside the same materials design problem.

FIGURE: Structuresandpropertiesofc-phase,c/a-phase,andmixed-phasePbZr0.2Ti0.8O3films. Image credit: Adv Mater. 2026 Apr;38(19):e18417. doi: 10.1002/adma.202518417.

Friction ceases to follow load in any simple way once sliding starts to reorganize the internal state of the interface itself. That is the scientific tension driving this study. Classical tribology is built around Amontons’ law, where increasing normal load is expected to increase friction monotonically. Yet that empirical relation says little about cases in which the interface carries its own evolving order parameter, and magnetic systems are a particularly sharp example because dissipation can arise from configurational rearrangement rather than from abrasion or plastic contact. The unresolved issue has not been whether magnetic order can matter for friction in principle. Theory and numerical work had already tied magnetic ordering to frictional response, and scanning-probe experiments had revealed exchange forces and even single-spin dynamics. The harder problem was experimental access to collective spin rearrangements in two laterally aligned magnetic lattices moving past one another under controlled, commensurate conditions. Tip-based geometries are highly localized by construction, so they do not naturally expose the spatially correlated reordering that extended interfaces can sustain.  In a recent research paper published in Nature Materials, Dr. Hongri Gu, Dr. Anton Lüders & Professor Clemens Bechinger from the University of Konstanz in Germany, developed a spatially resolved magnetic sliding platform made from a commensurate rotor array moving above a fixed magnetic substrate, allowing simultaneous measurement of lateral force and collective rotor orientation. They coupled that platform to molecular-dynamics simulations that retain all 7 × 7 rotational degrees of freedom. They also derived a reduced overdamped two-sublattice model with collective angles φ and ϑ that reproduces the friction peak, the order crossover, and the hysteretic dissipation mechanism. What is technically new here is the direct experimental linkage of collective ferromagnetic–antiferromagnetic switching, hysteretic torque cycles, and non-monotonic contactless friction in an extended sliding magnetic lattice.

The measurements immediately showed that the mean lateral sliding force does not decline smoothly with decreasing magnetic load. As h increased, the effective magnetic attraction between the layers fell monotonically, yet the averaged friction developed a clear maximum around h ≈ 9.0 mm. To connect that anomaly to the state of the slider, the authors introduced a displacement-dependent order parameter, Σ(Δx), based on the relative orientation of neighbouring moments along y. In that representation, Σ = +1 corresponds to ferromagnetic alignment and Σ = −1 to antiferromagnetic alignment. Averaged over integer lattice spacings, ⟨Σ⟩ evolved gradually from ferromagnetic to antiferromagnetic character as h increased, and the point where ⟨Σ⟩ passed through zero coincided with the friction maximum. That coincidence matters because it ties dissipation to a regime where ordered states compete rather than to the magnitude of magnetic attraction alone.  The dynamical picture across the three regimes is clean. At small h, the substrate field dominates, every rotor feels nearly the same driving field under commensurate sliding, and the array rotates collectively in a ferromagnetic mode. At large h, intralayer coupling takes over and the slider adopts antiferromagnetic order along y, with only slight collective wiggling during translation. The intermediate regime is different in character. There, interlayer and intralayer interactions become comparable, and the rotors switch discontinuously between ferromagnetic and antiferromagnetic arrangements during sliding. This is exactly the sort of configurational instability that a localized probe would struggle to capture. Here it can be seen directly in the tracked rotor angles and in the oscillatory evolution of the order parameter. Molecular-dynamics simulations that model the magnets as point dipoles reproduced the same regime structure and the same displacement-dependent ordering behaviour, which is important because it shows that the observed frictional anomaly follows from the magnetic interactions encoded in the system rather than from an idiosyncratic detail of the apparatus.

The force traces sharpen that interpretation. The measured lateral force contains a mechanical part from the brass rollers and a magnetic part associated with energy dissipated as the moments rotate against shaft friction under the substrate field. After separating those contributions, the authors found that the mean magnetic friction is nearly absent in the ferromagnetic and antiferromagnetic regimes. In those limits, the force oscillates roughly symmetrically around the mechanical baseline over each lattice period, so the positive and negative magnetic contributions largely cancel in the average. The competing regime breaks that symmetry. There, the lateral force no longer oscillates around the mechanical contribution in a balanced way, and a substantial mean magnetic friction emerges. That asymmetry is the central observation, because it shows that dissipation is tied to the path taken through configuration space during sliding, not merely to the existence of a magnetic coupling. Starting from the slider Hamiltonian, the authors showed that the averaged dissipation rate in steady sliding is governed by the product of substrate-induced torques and rotor angular velocities. They then reduced the full array to a two-sublattice overdamped model with two collective angles, φ and ϑ, representing the ferromagnetic or antiferromagnetic sectors of the slider. That reduction is scientifically useful because the experiments had already shown that the slider spends most of its time near those two ordered states, so the simplified description keeps the part of the dynamics that actually carries the dissipation. In the substrate-dominated regime, the summed torque varies smoothly and symmetrically over a lattice period, giving almost zero average magnetic friction. At intermediate spacing, the torque cycle becomes asymmetric, generating strong magnetic friction. At large h, both torque and angular velocity become small, so the magnetic contribution again fades. When the authors plotted torque against the angle of the slider magnetization, hysteresis loops appeared, and the loop area tracked the dissipated energy. The non-monotonic friction peak is, in that sense, a hysteretic many-body effect produced by collective switching between ferromagnetic and antiferromagnetic order during sliding.

 Professor Clemens Bechinger and colleagues demonstrated that the measured force becomes a readout of collective order reconstruction under drive. The interfacial state is not a passive background; it is the dissipative object. Once that point is established experimentally, friction can no longer be treated as a scalar output determined solely by how hard two bodies are pressed together. It becomes a dynamical observable tied to internal symmetry, competing interactions, and the route by which the interface moves through metastable configurations. That conceptual shift is already implicit in earlier theoretical discussions of friction near ordering transitions, but this study gives it direct experimental form in a spatially resolved sliding lattice.

Another important feature is the scale-free character of the framework developed here. The authors make the point that the governing equations are dimensionless in the relevant sense, which is why a millimetre-scale rotor array can still capture the same class of physics expected in atomic or nanoscale magnetic interfaces. That matters because it turns the experiment into more than a macroscopic analogy. It becomes a controllable platform for isolating how interlayer coupling, intralayer coupling, commensurability, and overdamped collective motion cooperate to generate dissipation. The two-sublattice model reinforces that generality. By reducing the full many-rotor system to a small set of collective variables without losing the friction peak or its link to hysteresis, the authors identify the minimal mechanism: competing ordered states, a sliding-induced rotating substrate field, and a dissipative path that does not retrace itself over a cycle.

The consequences extend naturally to other ordered systems discussed in the article. The authors connect their findings to low-dimensional magnets, spintronic materials, XY-type systems, layered or twisted two-dimensional magnets with competing intra- and interlayer exchange, ferroelectric tribology, and patterned non-contact magnetic films. The common requirement is not a specific material chemistry. It is a regime in which interactions within a layer can compete with interactions across an interface, allowing sliding to trigger repeated reorganization of the internal order. In such systems, friction peaks need not signal stronger contact in the ordinary sense; they can mark active switching, repeated nucleation and annihilation of domains, or related hysteretic reconfiguration. That is a useful design lesson because it shifts friction control away from roughness engineering and surface chemistry toward deliberate management of collective internal degrees of freedom. The new study establishes a clear route to wear-free, contactless friction tuning through magnetic order, plus a physically transparent mechanism for why the maximum dissipation appears at intermediate coupling rather than at the largest load. It also frames friction as a possible sensing modality for magnetic order, since the force anomaly maps directly onto the crossover from ferromagnetic to antiferromagnetic organization and onto the associated hysteresis. At larger scales, the authors point to coated sliders, patterned magnetic interfaces, and programmable friction metamaterials as settings where arranged micromagnets could encode dissipative response by design. That proposal carries weight because the experiment already demonstrates the underlying principle in an interface where friction is generated by internal reorientation alone.

 

Polymer networks stiffen, soften, densify, or fail according to how their internal domains rearrange under stress and time, yet most synthetic systems cannot keep changing that internal organization once fabrication ends. Living matter does something quite different. Its condensed phases appear, reorganize, merge, and sometimes disappear as molecular interactions shift during growth or response, and those rearrangements directly alter function.  In a recent research paper published in Advanced Materials, Dr. Cheng Liu, Dr. Chaowei He, Dr. Xiaobin Dai, Prof. Li-Tang Yan, and Prof. Huaping Xu from Tsinghua University, developed a hydrogel system in which visible-light-activated diselenide units initiate in situ polymerization of methacrylic acid from an existing PMAAm-based network, generating PMAAc dangling chains that drive a timed sequence of phase generation, separation, and fusion. They also developed a spatially addressable route for building multi-region hydrogels with different local moduli using visible-light patterning.

The scientific problem is not simply how to make a hydrogel stronger. Soft materials already offer many routes for raising modulus or toughness through extra crosslinks, chain entanglement, filler addition, or dehydration. The harder question is how to build a material whose internal compatibility keeps changing after the material has been formed, so that one mechanical state does not merely switch to another, but evolves through a sequence of structurally distinct states. That issue has remained difficult to address because ordinary polymer phases arise from fixed segmental incompatibility or fixed attractive interactions. Once the network is made, the system usually settles into a stable distribution of domains or requires continuous energy input to hold a temporary one. Static chemistry produces static phase logic.

The hydrogel platform chosen for the study makes that reasoning especially compelling. Hydrogels already contain large amounts of water, mobile segments, and mechanically important mesoscale heterogeneity, so phase behavior can reshape load transfer in a way that is easy to feel and measure. In their design, methacrylic acid monomer resides within a preformed polymethyl acrylamide-based network, while diselenide units embedded in the network generate radicals under visible light and start in situ polymerization. The key expectation is not merely that new polymethacrylic acid chains will form, but that these dangling chains will first develop their own association tendencies and later interact more strongly with the host network through evolving hydrogen-bond patterns. That makes the central challenge a question of competing kinetics and thermodynamics: local phase formation can occur quickly as new chains appear, whereas deeper chain rearrangement and interphase merging demand more time because mobility and entanglement impose a real penalty on structural reorganization.

The research team first established that the diselenide chemistry could genuinely initiate methacrylic acid polymerization under visible light. NMR, GPC, and EPR measurements all supported the formation of PMAAc and the presence of propagating radical species, while the radical signal responded directly to illumination and decayed more slowly in the dark. That controllable initiation step matters for more than chemical proof. If initiation were too fast, the material would jump through structural states before they could be separated experimentally or regulated spatially; if too slow, phase reorganization would lose practical control. The reported initiation rate supplied a usable window in which the internal state of the gel could be steered by irradiation time.

Once the authors built the hydrogel containing the PMAAm-based network, MAAc, and diselenide crosslinking points, they observed an immediate macroscopic clue that the internal structure was changing: a transparent gel gradually turned opaque during irradiation. The investigators interpreted that loss of transparency as refractive-index heterogeneity created by newly formed domains, which is a sensible reading because the chemical network remained singular while the internal composition grew less uniform. The new PMAAc existed as dangling chains covalently attached to the original network, so the system did not become a simple blend of two disconnected polymers. That detail is important. Because the new chains stayed tethered, the material could separate internally without falling apart, and later fusion of phases could still feed into a continuous load-bearing framework.

The study examined the temporal sequence of those structural changes with several complementary methods. Rheology revealed that a new phase with its own glass transition emerged after irradiation, and prolonged exposure later produced two glass-transition features consistent with a fused but compositionally uneven state. Low-field NMR tracked the increasing proportion of a mixed PMAAc-PMAAm phase in the later period, while SAXS registered rising heterogeneity during the early hours and declining heterogeneity at longer times. It generated a new PMAAc-rich phase, sharpened separation from the original PMAAm-rich environment, and then moved toward a fused state in which both polymers remained enriched in different local ratios. That later merger is especially revealing because it shows that temporal order in soft matter can emerge from a moving balance between newly created incompatibility and stronger final association.

The researchers reinforced that interpretation with coarse-grained and all-atom molecular dynamics simulations, which placed the strongest phase separation near the early stage and the fusion-dominant regime later, around 6 to 24 hours. SEM images echoed the same story in structural terms: the original freeze-dried gel looked porous and loosely packed, intermediate states displayed denser regions coexisting with looser ones, and the long-irradiated material became denser and more uniform. A denser but more even internal structure changes mechanics in a very concrete way. Stress is less likely to concentrate at sharp density boundaries when interfaces are reduced, so the material can transmit load across the body more effectively. The paper never treats morphology as decoration; morphology is the route by which chemistry becomes mechanics.

To explain why the phases appeared in that order, the authors focused on hydrogen-bond evolution among carboxylic acid and amide groups. Chemical disruption of those interactions softened and clarified the gel, linking the immiscible domains to hydrogen-bonded association. FTIR and WAXS then showed that the bonding population did not stay fixed during irradiation. Small amounts of newly formed PMAAc initially associated with PMAAm, increasing PMAAc content later favored COOH-COOH interactions and PMAAc-rich domains, and continued evolution drove the system toward the more stable COOH-CONH₂ associations that promoted fusion of PMAAc-rich and PMAAm-rich regions. Here the trade-off becomes very clear. Short-time behavior follows the pace of polymer growth, which favors local PMAAc-domain formation before large-scale rearrangement can catch up. Long-time behavior follows the search for the most stable hydrogen-bond network, which pulls the system toward interphase mixing and fusion. The sequence is ordered because chain motion is slow enough to let kinetic and thermodynamic preferences act in different windows.

Tensile modulus rose from 18.5 kPa to 44.5 MPa, compressive modulus climbed from 57.7 kPa to 22.2 MPa, and the increases in storage modulus and fracture energy were similarly dramatic. The authors also identified two pronounced jumps in stiffness during irradiation, one associated with the onset of phase generation or separation and another with the onset of phase fusion.   A single monotonic stiffening curve could be explained by growing polymer content, but step-like gains aligned with phase transitions argue that internal structural reorganization, not just added solid fraction, governs the change in load-bearing behavior. The material stiffens in qualitatively different ways at different times: early domain formation introduces new physical crosslinking and dissipation pathways, while later fusion produces a denser and more uniform route for stress distribution.

The work of Professor Huaping Xu and colleagues also widened the argument beyond bulk strengthening. Visible light penetrated the hydrogel far more uniformly than UV-based initiation, which allowed the authors to generate fairly even modulus increases through thickness and across surface regions. By using patterned irradiation, they created a “steel reinforced concrete”-like hydrogel with stiff pillars inside a softer matrix, and the resulting composite displayed staged stress response and directional mechanical behavior. The same underlying chemistry also gave the irradiated gel shape-memory capability through hydrogen-bond exchange and reformation. These demonstrations matter because they convert the study from a story about a single tough gel into a broader design principle: if phase evolution can be positioned in space as well as in time, then modulus is no longer a fixed material property but a programmable field inside one connected body which mean that internal phase history can be treated as a controllable design parameter for soft composites, adaptive structures, and locally reinforced architectures.

Cracks in conventional carbon-fiber composites tend to run once local stress concentrates, because the fiber phase is strong but anisotropic and the usual thermoset matrix has little capacity to deform, spread load, or dissipate energy before rupture. That combination has given CFRPs a familiar strength profile and, at the same time, a persistent weakness: they resist static load well, yet remain vulnerable when puncture, tearing, or sharp damage pushes the response away from ideal tensile alignment. A second problem follows from the same matrix chemistry because once a conventional cured binder locks into an irreversible network, the composite no longer melts, dissolves, or reprocesses in any useful way, so recovery of intact carbon fiber becomes difficult under mild conditions. The limitation here is not simply to make the matrix stronger but the design of a binder that can absorb and redistribute force during damage and stay stable enough for service and sufficiently dynamic for recovery at the end of use. In a recent research paper published in Composites Part A: Applied Science and Manufacturing, Dr. Shunli Wang, Dr. Yinsheng Li, and Professor Limei Tian from Jilin University and Liaoning Academy of Materials developed a family of polyurethane elastomer networks, WPIN_n, that combine woven dynamic cross-linkers with multiply hydrogen-bonded hard segments. They identified WPIN_0.5 as the most effective composition and used it as a recyclable matrix for carbon-fiber composites containing 65 wt% fiber. Its key feature is the coupling of hierarchical energy dissipation with solvent-assisted matrix removal, and that allows both high tear resistance and recovery of undamaged carbon fiber.

Briefly, the research team prepared a family of polyurethane networks, WPINn, by combining PTMG and IPDI with a woven cross-linker and isophthalic dihydrazide, while varying the woven-cross-linker fraction to generate a controlled series. The authors confirmed network formation spectroscopically and verified complete isocyanate conversion. They also examined morphology with small-angle X-ray scattering and found phase-separated domains whose spacing increased with woven-cross-linker content. That trend proved important because the strongest mechanical response did not come from simply adding more dynamic junctions. The investigators observed that WPIN_0.5 reached the highest tensile strength, 78.1 MPa, and the highest toughness, 314.2 MJ m⁻³, whereas WPIN_0.75 lost some strength. The paper links that drop to excessive phase separation and renewed stress concentration. The network benefited from dynamic architecture up to a certain point, then began to lose the balance required for efficient load redistribution.

The researchers then addressed damage resistance directly by measuring puncture resistance in a 0.5 mm sheet and recorded a force of 45 N at a displacement of 29 mm, which corresponds to a puncture energy of 0.54 J. They also tested notched specimens and found an elongation at break of 924% with a fracture energy of 223 kJ m⁻². Those values align with a response if the network continues to spend mechanical energy during crack growth instead of exhausting that capacity at the moment of crack initiation. Cyclic loading reinforced that interpretation. The study examined hysteresis over successive load-unload cycles from 100% to 900% strain and found increasing dissipation with increasing strain, with low-strain dissipation associated mainly with hydrogen-bond scission and higher-strain dissipation linked to woven-cross-link dissociation.

The authors also constructed control systems. A covalently cross-linked analogue, CPIN_0.5, lost elongation and toughness, while a PD-based material with fewer hydrogen-bonding sites showed a much lower fracture strength than WPIN_0.5. Those comparisons narrowed the mechanism considerably: the superior response did not arise from polyurethane chemistry in a broad sense, but from the pairing of reversible hydrogen-bond clusters with woven dynamic nodes. The authors supported that reading with calculations. They estimated a binding energy of −45 kcal mol⁻¹ for the multiply hydrogen-bonded hard segments and a much lower value, −27 kcal mol⁻¹, for the PD-based comparison. They also calculated a large interaction energy for the woven cross-linker, −475 kcal mol⁻¹, and argued that force-driven dissociation at those sites contributes heavily to energy consumption during deformation.

The researchers then tested whether a network designed for dissipation could remain stable under conditions that often trouble supramolecular elastomers. Stress-relaxation experiments at 120 °C showed increasing relaxation times as woven-cross-linker content increased, and WPIN_0.5 followed Arrhenius behavior with an activation energy of 76 kJ mol⁻¹ across 120–150 °C. After 24 hours in water, the investigators observed little change in the stress-strain curve, and after immersion in several solvents the material retained more than 90% mass following drying. When the team used WPIN_0.5 as a carbon-fiber binder at 65 wt% fiber content, the composite reached 442 MPa tensile strength and about 1450 kJ m⁻² tear resistance, compared with about 64.6 kJ m⁻² for epoxy-CF. They also recovered clean, chemically intact carbon fiber by solvent-assisted separation in DMF and retained high composite strength across three recycling cycles. What stands out here is how effectively the selected composition balances strength, deformability, and reversibility without allowing any one of those features to dominate at the expense of the others.

The research work of Professor Limei Tian and colleagues reports a tough elastomer and a strong composite and changes where fracture resistance in CFRPs can be engineered. Much composite design still relies on the fiber phase for mechanical authority and treats the matrix mainly as an adhesive necessity. The new paper works from a different premise and treats the matrix as a programmable zone for damage management, where the sequence of molecular events under load determines whether a crack remains local or expands into structural failure. The authors’ work also increase understanding on how combining woven cross-links with clustered hydrogen bonds. Dynamic polymers are often discussed as though reversibility alone were sufficient but the findings show for a more disciplined architecture: reversible interactions need hierarchy. Lower-energy events can absorb force early, while stronger or more topologically constrained events remain available as deformation increases. That ordering changes the mechanical outcome because the network does not spend all of its dissipation capacity in a single stage. The composite data reinforce the same point at a larger structural scale. Carbon fiber remains stiff and anisotropic, yet a matrix that can stretch, yield locally, and bridge the flanks of a developing tear changes how damage travels through the laminate. That has practical meaning beyond this single polymer system. If related architectures perform similarly under broader loading histories, designers of protective CFRP systems may have a credible route for improving puncture and tear tolerance without giving up high fiber content. Recycling is equally important here and does not appear as a secondary benefit. A matrix that can be removed under mild solvent-assisted conditions while leaving carbon fiber chemically intact changes the usual end-of-life logic for CFRPs. Solvent handling, part geometry, manufacturing scale, and contamination will still shape how far such a strategy can move into application, and the paper establishes an important point: recyclability and high fracture resistance do not have to be treated as opposing design objectives. That shift in thinking will be important in areas where sharp local loading, accidental impact, and reuse all carry real weight. Protective equipment is one obvious case, but the broader message is more general. Dynamic supramolecular matrices can be designed for both reprocessability as well as mechanical participation in structural defense and this opens a more flexible route for composite design, especially when the matrix is asked to do more than just hold the reinforcement in place.