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We report the mechanical and microstructural characteristics of a medium-entropy alloy, Co17.5Cr12.5Fe55Ni10Mo5 (atomic percent, at%) at cryogenic temperatures, down to a record low temperature of 0.5 K. The alloy exhibits excellent strength and ductility combined with a high strain-hardening rate in the entire temperature range investigated. Its property profile, including the yield strength, ultimate tensile strength, strain hardening capability, and absorbed mechanical energy, is better than those of most alloys and HEAs used in cryogenics. Within the interval of extremely low temperatures considered (0.5–4.2 K), the alloy exhibits several unusual features, including anomalies of the temperature dependence of the yield strength and tensile ductility, discontinuous plastic deformation (DPF), and a change in the propensity for the deformation-induced martensitic transformation. While the occurrence of these effects in the same temperature interval may be fortuitous, we hypothesize that they are interrelated and provide a tentative explanation of the observed phenomena on this basis.

Metallic amorphous/crystalline (A/C) nanolaminates exhibit excellent ductility while retaining their high strength. However, the underlying physical mechanisms and the resultant structural changes during plastic deformation still remain unclear. In the present work, the structure-property relationship of CuZr/Cu A/C nanolaminates is established through integrated high-throughput micro-compression tests and molecular dynamics simulations together with high-resolution transmission electron microcopy. The serrated flow of nanolaminates results from the formation of hexagonal-close-packed (HCP)-type stacking faults and twins inside the face-centered-cubic (FCC) Cu nano-grains, the body-centered-cubic (BCC)-type ordering at their grain boundaries, and the crystallization of the amorphous CuZr layers. The serration behavior of CuZr/Cu A/C nanolaminates is determined by several factors, including the formation of dense dislocation networks from the multiplication of initial dislocations that formed after yielding, weak-spots-related configurational-transitions and shear-transition-zone activities, and deformation-induced devitrification. The present work provides an insight into the heterogeneous deformation mechanism of A/C nanolaminates at the atomic scale, and mechanistic base for the microstructural design of self-toughening metallic-glass (MG)-based composites and A/C nanolaminates.

Contradictory scaling behavior in experiments testing the principle of universality may be due to external oscillations. Thus, the effect of damped oscillatory external forces on slip avalanches in slowly deformed solids is simulated using a mean-field model. Akin to a resonance effect, oscillatory driving forces change the dynamics of avalanches with durations close to the oscillation period. This problem can be avoided by tuning mechanical resonance frequencies away from the range of the inverse avalanche durations. The results provide critical guidance for experimental tests for universality and a quantitative understanding of avalanche dynamics under a wide range of driving conditions.

Serration phenomena during tensile testing on certain alloys with diffusing solute atoms (i.e., Portevin–Le Chatelier effect) have been observed for a long time, but detailed mechanisms are not fully clear yet. This study is intended to find the mechanism from different approaches verified by tensile testing on a series of single-phase face-centered-cubic (FCC) pure metal and alloys: Ni, CoNi, CoFeNi, CoCrFeNi, and CoCrFeMnNi, which range from low to high configurational entropy. The results of tensile tests, at strain rates from 1 × 10−5 to 1 × 10−2/s and temperature from room temperature to 700 °C, show that serrations occur on stress-strain curves of CoFeNi, CoCrFeNi, and CoCrFeMnNi alloys in their specific temperature and strain-rate regime. A mechanism for dislocation pinning is proposed and verified with theoretical calculation for the present substitutional alloys. The proposed mechanism involves the in-situ rearrangement of substitutional solute atoms by “local dislocation-core diffusion” and might also be applied to similar substitutional alloys.

High-sensitivity detection of acoustic emission from granite under uniaxial stress, together with advanced statistical analysis, shows changing collapse mechanisms when a sample is pre-heated. Massive microstructural changes occur at temperatures >500 °C while low-temperature (<

Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ Amaxx and Amax ~ Dχ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude Amax as predicted by MFT but scales linearly S ~ Amax. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Recent experiments and simulations of amorphous solids plastically deformed by oscillatory drive have foundsurprising behavior - for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit-cycles in which plastic events repeat indefinitely under the oscillatory drive. Reaching reversible limit-cycles, can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again and are thus irreversible. Using a graph representation of the stable configurations of the system and the plastic events connecting them, we show that the notion of reversibility is more subtle. We find that reversible plastic events are abundant, and that a large portion of the plastic events encountered during the transient period are actually reversible, in the sense that they can be part of a reversible deformation path. We observe that the transition graph can be decomposed into clusters of configurations that are connected by reversible transitions. These clusters are the strongly connected components of the graph and their sizes turn out to be power-law distributed. The largest of these are grouped in regions of reversibility, which in turn are confined by regions of irreversibility whose number proliferates at larger strains. Our results provide an explanation for the irreversibility transition - the divergence of the transient period at a critical forcing amplitude. Long transients result from transition between clusters of reversibility in a search for a cluster large enough to contain a limit-cycle of a specific amplitude. For large enough amplitudes, the search time becomes very large, since sizes of the limit cycles become incompatible with the sizes of the regions of reversibility., 14 pages, 7 figures. Revised version with figures regrouped and two figures added

We have measured magnetic-field-induced avalanches in a square artificial spin ice array of interacting nanomagnets. Starting from the ground state ordered configuration, we imaged the individual nanomagnet moments after each successive application of an incrementally increasing field. The statistics of the evolution of the moment configuration show good agreement with the canonical one-dimensional random field Ising model. We extract information about the microscopic structure of the arrays from our macroscopic measurements of their collective behavior, demonstrating a process that could be applied to other systems exhibiting avalanches.

Uniaxial random field disorder induces a spontaneous transverse magnetization in the XY model. Adding a rotating driving field, we find a critical point attached to the number of driving cycles needed to complete a limit cycle, the first discovery of this phenomenon in a magnetic system. Near the critical drive, time crystal behavior emerges, in which the period of the limit cycles becomes an integer n > 1 multiple of the driving period. The period n can be engineered via specific disorder patterns. Because n generically increases with system size, the resulting period multiplication cascade is reminiscent of that occurring in amorphous solids subject to oscillatory shear near the onset of plastic deformation, and of the period bifurcation cascade near the onset of chaos in nonlinear systems, suggesting it is part of a larger class of phenomena in transitions of dynamical systems. Applications include magnets, electron nematics, and quantum gases., In the XY model, the application of a disordered uniaxial magnetic field leads to a long range magnetic order. Here, using a numerical approach, the authors find that at a critical rotating driving field, the number of driving cycles needed to complete a limit cycle diverges.

The explanation and control of phase transitions remain cornerstones of contemporary physics. Landau provided an invaluable insight into the thermodynamics of complex systems by formulating their phase transitions in terms of an order parameter. Within this formulation, continuous evolution of the order parameter away from zero classifies the phase transition as second-order, whereas a discontinuous change signals a first-order transition. Here we show that the temperature-tuned insulator–metal transition in the prototypical correlated electron system NdNiO3 defies this established binary classification. By harnessing a nanoscale optical probe of the local electronic conductivity, we reveal two physically distinct yet concurrent phase transitions in epitaxial NdNiO3 films. Whereas the sample bulk exhibits a first-order transition between metal and insulator phases, we resolve anomalous nanoscale domain walls in the insulating state that undergo a distinctly continuous insulator–metal transition, with hallmarks of second-order behaviour. We ascribe these domain walls to boundaries between antiferromagnetically ordered domains within the charge ordered bulk. The close correspondence of these observations to predictions from a Landau theory of coupled charge and magnetic orders highlights the importance of coupled order parameters in driving the complex phase transition in NdNiO3. A phase transition between metallic and insulating states is observed to simultaneously happen in two ways at once. The bulk of the sample shows an instantaneous jump in the conductivity, while 1D domain walls show a slow switching into a metallic state.

Compression experiments of the Al0.5CoCrCuFeNi high-entropy alloy (HEA) under displacement control were conducted at different temperatures ranging from 673 K to 873 K with a strain rate of 5 × 10−5/s to study its serration behavior. Samples after compression tests were investigated, using the synchrontron-diffraction technique and transmission-electron microscopy. By comparing the stress-strain curves at different temperatures, two opposite directions of serrations were observed, named the upward serration appearing at 573 K and 673 K and the downward serration at 773 K and 873 K. The different directions of serrations were discussed in terms of not only the relationships among the stress vs. strain, stress vs. time, and strain vs. time, but also the interactions among dislocations, atoms, and nanoparticles. Finally, the temperature effect on the flow serration is discussed by referring to a theoretical framework for the initiation of the serrated flow. Beyond a critical high temperature, the initiation of the serrated flow becomes swiftly difficult, and ultimately the plastic flow in the full deformation range turns smooth. The theoretical prediction of the normal behavior is essentially in qualitative agreement with the experimental observation in the present work, i.e., the critical strain to initiate the serration decreases with increasing the temperature.

Systems of interacting nanomagnets known as artificial spin ice1–4 have allowed the design, realization and study of geometrically frustrated exotic collective states5–10 that are absent in natural magnets. We have experimentally measured11,12 the thermally induced moment fluctuations in the Shakti geometry of artificial spin ice. We show that its disordered moment configuration is a topological phase described by an emergent dimer-cover model13 with excitations that can be characterized as topologically charged defects. Examination of the low-energy dynamics of the system confirms that these effective topological charges have long lifetimes associated with their topological protection, that is, they can be created and annihilated only as charge pairs with opposite sign and are kinetically constrained. This manifestation of classical topological order14–19 demonstrates that geometrical design in nanomagnetic systems can lead to emergent, topologically protected kinetics that can limit pathways to equilibration and ergodicity. Experiments on the Shakti geometry of artificial spin ice show that its low-energy excitations are topologically protected, and that an emergent classical topological order influences the ergodicity and equilibration of this nanomagnetic system.

Bulk metallic glasses (BMGs) demonstrate different deformation behavior under varying loading conditions. In the present work, a Zr57Cu20Al10Ni8Ti5 (atomic percent, at.%) BMG was subjected to a mixed-mode (I/II) loading condition by tailoring double-side notches. The findings show stable plastic-flow plateau stages in the loading-displacement curves, and this phenomenon is different from other notched BMG specimens with predominant-mode-I failure. More importantly, due to the stress concentrations between two notches, most of the slip events with large load drops occur on the fracture plane, resulting in a wide smooth region consisting of several shear steps on the fracture surface. We show that despite different deformation behavior, the specimens still display slip-size statistics of the plastic flow, which are similar to those seen in compression tests. The present findings give more insight into the deformation behavior/mechanisms of BMGs under varying loading conditions for practical structural applications.

High-entropy alloys (HEAs), as a new class of materials, are nearly equiatomic and multi-element systems, which can crystallize as a single phase or multi-phases. Most of the HEAs described in the literature contain multiple phases (secondary phases, nanoparticles, and so on), rather than a single solid-solution phase. Thus, it is essential to review the typical mechanical properties of both single-phase and multiphase HEAs thoroughly, with emphases on (1) the fundamental physical mechanisms and (2) the difference from conventional alloys. In this paper, mainly based on different mechanical properties, HEAs are classified into four types for the first time, i.e., (a) HEA alloy systems of 3d-transition metals only (Type 1), (b) HEA alloy systems of transition metals with larger atomic-radius elements (Type 2), (c) HEA alloy systems of refractory metals (Type 3), and (4) others (Type 4). Then a number of aspects of mechanical behavior are reviewed and discussed, including the elastic anisotropy, yield strength, high-temperature performance, serration behavior, fracture toughness, and fatigue responses, which may serve as a demonstrative summary for the current progress in the scientific research of HEAs. Several mechanisms that quantitatively explain the mechanical properties of single-phase and multiphase HEAs in terms of basic defects (dislocations, twinning, precipitates, etc.) are discussed. A number of future research activities are suggested, based on the emphasis on developing high-performance structural materials. The review concludes with a brief summary of major mechanical properties and insights into the deformation behavior of single-phase and multiphase HEAs. The comparison and contrast between HEAs and conventional alloys remain the most compelling motivation for future studies. With the integrated experimental and simulation investigations, a clearer picture of the fundamental deformation behavior of single-phase and multiphase HEAs could be explored.

Refractory high-entropy alloys present attractive mechanical properties, i.e., high yield strength and fracture toughness, making them potential candidates for structural applications. Understandings of atomic and electronic interactions are important to reveal the origins for the formation of high-entropy alloys and their structure−dominated mechanical properties, thus enabling the development of a predictive approach for rapidly designing advanced materials. Here, we report the atomic and electronic basis for the valence−electron-concentration-categorized principles and the observed serration behavior in high-entropy alloys and high-entropy metallic glass, including MoNbTaW, MoNbVW, MoTaVW, HfNbTiZr, and Vitreloy-1 MG (Zr41Ti14Cu12.5Ni10Be22.5). We find that the yield strengths of high-entropy alloys and high-entropy metallic glass are a power-law function of the electron-work function, which is dominated by local atomic arrangements. Further, a reliance on the bonding-charge density provides a groundbreaking insight into the nature of loosely bonded spots in materials. The presence of strongly bonded clusters and weakly bonded glue atoms imply a serrated deformation of high-entropy alloys, resulting in intermittent avalanches of defects movement. A cluster-and-glue model of atomic arrangements explains the yield strength and mechanical response of high entropy alloys. Inspired by metallic glass, a team led by William Yi Wang at China’s Northwestern Polytechnical University and collaborators in the United States of America used molecular dynamics to build different atomic arrangements of refractory high entropy alloys consisting of four or more elements. Depending on atomic size and the periodic table group of each atom, some atoms organized into clusters while others glued the clusters together. Chemical bonds broke and formed with plastic deformation as the alloys went from one atomic arrangement to another via the glue atoms, causing defect avalanches explaining the serrated mechanical response of high entropy alloys. Taking into account atomic arrangement may thus help us predict the properties of high entropy alloys.

The present work investigates the influence of Al-content and potential-scan-rate on stable/metastable pitting of Al xCoCrFeNi high-entropy alloys in a 3.5 wt.% NaCl solution. The increased Al content causes the volume fraction of the Cr-depleted phase to increase, resulting in thicker/dispersive passive films that degrade the localized corrosion resistance. The varied stable/metastable pitting behavior under different potential scan rates indicates that pit generation is influenced by the properties of passive films and the interactions between chloride ions and the active sites. Furthermore, a mean-field theory is employed to predict the scan-rate dependent, power-law distribution of current fluctuations.

The statistical and dynamic behaviors of the displacement-load curves of a high-entropy alloy, Al0.5 CoCrCuFeNi, were analyzed for the nanoindentation performed at two temperatures. Critical behavior of serrations at room temperature and chaotic flows at 200 °C were detected. These results are attributed to the interaction among a large number of slip bands. For the nanoindentation at room temperature, recurrent partial events between slip bands introduce a hierarchy of length scales, leading to a critical state. For the nanoindentation at 200 °C, there is no spatial interference between two slip bands, which is corresponding to the evolution of separated trajectory of chaotic behavior.

The flow of granular materials and metallic glasses is governed by strongly correlated, avalanche-like deformation. Recent comparisons focused on the scaling regimes of the small avalanches, where strong similarities were found in the two systems. Here, we investigate the regime of large avalanches by computing the temporal profile or “shape” of each one, i.e., the time derivative of the stress-time series during each avalanche. We then compare the experimental statistics and dynamics of these shapes in granular media and bulk metallic glasses. We complement the experiments with a mean-field model that predicts a critical size beyond which avalanches turn into large runaway events. We find that this transition is reflected in a characteristic change of the peak width of the avalanche profile from broad to narrow, and we introduce a new metric for characterizing this dynamic change. The comparison of the two systems points to the same deformation mechanism in both metallic glasses and granular materials.

The statistics and form of avalanches in a driven system reveal the nature of the underlying energy landscape and dynamics. In conventional metallic ferromagnets, eddy-current back action can dominate the dynamics. Here, we study Barkhausen noise in Li(Ho,Y)F4, an insulating Ising ferromagnet that cannot sustain eddy currents. For large avalanches at temperatures approaching the Curie point, we find a symmetric response free of drag effects. In the low temperature limit, drag effects contribute to the dynamics, which we link to enhanced pinning from local random fields that are enabled by the microscopic dipole-coupled Hamiltonian (the Ising model in transverse field)., 14 pages, 3 figures

Shear banding causes deformation to be heavily restricted in small volumes of a material, leading to catastrophic failure of materials. Yet how shear bands form is generally not known. Here, the authors follow the entire process of shear banding in the nanocrystalline ceramic (NCC) nanopillars of ZrN using $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ microscopy. The evidence obtained shows that the nanopillars deform through intermittent granular activities due to the nucleation and propagation of dislocations. The stress drops associated with these activities, however, are small as dislocation avalanches are restricted by the nanograin size. Shear band forms in NCC through localized and cooperative granular activities involving nanocrack formation.

The transition from elastic to plastic deformation in crystalline metals shares history dependence and scale-invariant avalanche signature with other non-equilibrium systems under external loading: dilute colloidal suspensions, plastically-deformed amorphous solids, granular materials, and dislocation-based simulations of crystals. These other systems exhibit transitions with clear analogies to work hardening and yield stress, with many typically undergoing purely elastic behavior only after 'training' through repeated cyclic loading; studies in these other systems show a power law scaling of the hysteresis loop extent and of the training time as the peak load approaches a so-called reversible-irreversible transition (RIT). We discover here that deformation of small crystals shares these key characteristics: yielding and hysteresis in uniaxial compression experiments of single-crystalline Cu nano- and micro-pillars decay under repeated cyclic loading. The amplitude and decay time of the yield precursor avalanches diverge as the peak stress approaches failure stress for each pillar, with a power law scaling virtually equivalent to RITs in other nonequilibrium systems., Comment: 5 pages, 3 figures

We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and sub-cycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft-spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provides new insights into the mechanisms that lead to reversible and irreversible behavior in amorphous solids., 5 pages, 4 figures. Minor changes, addition of of ancillary file providing numerical implementation details and supporting evidence

The origin of deterministic macroscopic properties often lies in microscopic stochastic motion. Magnetic fluctuations that manifest as domain avalanches and chaotic magnetization jumps exemplify such stochastic motion and have been studied in great detail. Here we report Fourier space studies of avalanches in a system exhibiting competing magnetic stripe and skyrmion phase using a soft X-ray speckle metrology technique. We demonstrate the existence of phase boundaries and underlying critical points in the stripe and skyrmion phases. We found that distinct scaling and universality classes are associated with these domain topologies. The magnitude and frequency of abrupt magnetic domain jumps observed in the stripe phase are dramatically reduced in the skyrmion phase. Our results provide an incisive way to probe and understand phase stability in systems exhibiting complex spin topologies., Switching of magnetic materials often occurs through discrete random avalanches. Singh et al. observe sharply reduced avalanches in the topologically protected skyrmion phase of a Fe/Gd heterostructure and obtain different critical behaviour in the stripe and skyrmion phases, suggesting distinct universality classes.

Deformation mechanisms of a high-entropy alloy with a single face-centered-cubic phase, Al0.1CoCrFeNi, at elevated temperatures are studied to explore the high temperature performances of high-entropy alloys. Tensile tests at a strain rate of 10−4 s−1 are performed at different temperatures ranging from 25 to 700 °C. While both yield strength and ultimate tensile strength decrease with increasing temperature, the maximum elongation to fracture occurred at 500 °C. Transmission electron microscopy characterizations reveal that, at both 25 and 500 °C, most of deformation occurs by dislocation glide on the normal face-centered-cubic slip system, {111}〈110〉. In contrast, numerous stacking faults are observed at 600 and 700 °C, accompanied by the decreasing of dislocation density, which are attributed to the motion of Shockley partials and the dissociation of dislocations, respectively. According to the Considere's criterion, it is assumed that the dissociation of dislocations and movement of Shockley partials at higher temperatures significantly decreases the work hardening during tensile tests, promoting the early onset of necking instability and decreasing the high-temperature ductility.

The origin of the deformation in metallic glasses is attributed to rearrangements of atoms in some structurally weak spots behaving as flow units, which are associated with free volumes. In the present study, Xe-ion beam is used to manipulate the free-volume fraction, and influence on the mechanical behavior of a Zr-based metallic glass. The irradiation at low dosages can change the structure by increasing the free volume, and by homogenising the distribution of free volume. The increase in the free-volume fraction is equivalent to the increase in the deformation temperature, thus resulting in the decrease in the yield strength. The analysis of stochastic strain burst size in the metallic glass irradiated at different dosages indicates that the strain burst depends on the yield strength and homogeneity of the glassy phase. The results of this study highlight the fact that the quantitative manipulation of the homogeneity and the amount of free volumes can be achieved through low-dose ion irradiation, which can modify the mechanical behavior of metallic glasses.

Until now most studies of discrete plasticity have focused on systems that are assumed to be driven by a monotonically increasing force; in many real systems, however, the driving force includes damped oscillations or oscillations induced by the propagation of discrete events or ``slip avalanches.'' In both cases, these oscillations may obscure the true dynamics. Here we effectively consider both cases by investigating the effects of damped oscillations in the external driving force on avalanche dynamics. We compare model simulations of slip avalanches under mean-field dynamics with observations in slip-avalanche experiments on slowly compressed micrometer-sized Au specimens using open-loop force control. The studies show very good agreement between simulations and experiments. We find that an oscillatory external driving force changes the average avalanche shapes only for avalanches with durations close to the period of oscillation of the external force. This effect on the avalanche shapes can be addressed in experiments by choosing suitable specimen dimensions so that the mechanical resonance does not interact with the avalanche dynamics. These results are important for the interpretation of avalanche experiments with built-in oscillators, and for the prediction and analysis of avalanche dynamics in systems with resonant vibrations.

Crystals deform by the intermittent multiplication and slip avalanches of dislocations. While dislocation multiplication is well-understood, how the avalanches form, however, is not clear, and the lack of insight in general has contributed to “a mass of details and controversy” about crystal plasticity. Here, we follow the development of dislocation avalanches in the compressed nanopillars of a high entropy alloy, Al0.1CoCrFeNi, using direct electron imaging and precise mechanical measurements. Results show that the avalanche starts with dislocation accumulations and the formation of dislocation bands. Dislocation pileups form in front of the dislocation bands, whose giveaway trigs the avalanche, like the opening of a floodgate. The size of dislocation avalanches ranges from few to 102 nm in the nanopillars, with the power-law distribution similar to earthquakes. Thus, our study identifies the dislocation interaction mechanism for large crystal slips, and provides critical insights into the deformation of high entropy alloys.

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO$_2$) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by dissipation and transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models., preprint, Main article: 7 pages, 3 figures. Supplementary material included in \anc folder: 6 pages, 3 figures

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin-Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems., submitted to Phys. Rev. B

Compression behavior of the Al0.5CoCrCuFeNi high-entropy alloy (HEA) was studied at different temperatures from 673 K to 873 K at a low strain rate of 5 × 10−5/s to investigate the temperature effect on the mechanical properties and serration behavior. The face-centered-cubic (fcc) structure is confirmed at the lower temperature of 673 K and 773 K, and a structure of mixed fcc and body-centered cubic (bcc) is identified at a higher temperature of 873 K after compression tests using high-energy synchrotron x-ray diffraction. By comparing the stress–strain curves at different temperatures, two opposite directions of serrations types were found, named upward serrations appearing at 673 K and 773 K and downward serrations at 873 K, which may be due to dynamic strain aging.

Low-cycle fatigue fracture of metallic glass nanowires was investigated using molecular dynamics simulations. The nanowires exhibit work hardening or softening, depending on the applied load. The structural origin of the hardening/softening response was identified as the decrease/increase of the tetrahedral clusters, as a result of the non-hardsphere nature of the glass model. The fatigue fracture is caused by shear banding initiated from the surface. The plastic-strain-controlled fatigue tests show that the fatigue life follows the Coffin–Manson relation. Such power-law form originates from plastic-strain-dependent microscopic damage accumulation. Lastly, the effect of a notch on low-cycle fatigue of nanowires in terms of failure mode and fatigue life was also discussed.

When an amorphous material is strained beyond the point of yielding it enters a state of continual reconfiguration via dissipative, avalanche-like slip events that relieve built-up local stress. However, how the statistics of such events depend on local interactions among the constituent units remains debated. To address this we perform experiments on granular material in which we use particle shape to vary the interactions systematically. Granular material, confined under constant pressure boundary conditions, is uniaxially compressed while stress is measured and internal rearrangements are imaged with x-rays. We introduce volatility, a quantity from economic theory, as a powerful new tool to quantify the magnitude of stress fluctuations, finding systematic, shape-dependent trends. For all 22 investigated shapes the magnitude $s$ of relaxation events is well-fit by a truncated power law distribution $P(s)\sim {s}^{-\tau} exp(-s/s^*)$, as has been proposed within the context of plasticity models. The power law exponent $\tau$ for all shapes tested clusters around $\tau=$ 1.5, within experimental uncertainty covering the range 1.3 - 1.7. The shape independence of $\tau$ and its compatibility with mean field models indicate that the granularity of the system, but not particle shape, modifies the stress redistribution after a slip event away from that of continuum elasticity. Meanwhile, the characteristic maximum event size $s^*$ changes by two orders of magnitude and tracks the shape dependence of volatility. Particle shape in granular materials is therefore a powerful new factor influencing the distance at which an amorphous system operates from scale-free criticality. These experimental results are not captured by current models and suggest a need to reexamine the mechanisms driving mesoscale plastic deformation in amorphous systems., Comment: 11 pages, 8 figures. v3 adds a new appendix and figure about event rates and changes several parts the text

Inside the metals, semiconductors, and magnets of our everyday experience, electrons are uniformly distributed throughout the material. By contrast, electrons often form clumpy patterns inside of strongly correlated electronic systems (SCES) such as colossal magnetoresistance materials and high temperature superconductors. In copper-oxide-based high temperature superconductors, scanning tunneling microscopy (STM) has detected an electron nematic on the surface of the material in which the electrons form nanoscale structures which break the rotational symmetry of the host crystal. These structures may hold the key to unlocking the mystery of high temperature superconductivity in these materials, but only if the nematic also exists throughout the entire bulk of the material. Using newly developed methods for decoding these surface structures, we find that the nematic indeed persists throughout the bulk of the material. We furthermore find that the intricate pattern formation is set by a delicate balance among disorder, interactions, and material anisotropy, leading to a fractal nature of the cluster pattern. The methods we have developed can be extended to many other surface probes and materials, enabling surface probes to determine whether surface structures are confined only to the surface or whether they extend throughout the material.

We measure and analyze the statistics of nanoindentation pop-ins in a bulk metallic glass that has been annealed after being subjected to high pressure torsion. We argue that these pop-ins are avalanches of slip events. Larger slip avalanches are observed after annealing at higher temperatures. The slip avalanche size distribution shows scaling behavior and suggests the existence of a critical annealing temperature. Results are shown to be consistent with the predictions of a simple mean field theory. This implies that the statistics of slip avalanches in nanoindentation can be used to extract information about the structure, history, density, and free volume of the material. The methods employed here are expected to be applicable to a wide range of materials.

We observe two distinct interevent time patterns in the slip avalanches of compressed bulk metallic glasses (BMGs). Small slip avalanches cluster together in time, but large slip avalanches recur roughly periodically. We compare the timing patterns of BMG slip avalanches with timing patterns of earthquakes and with the predictions of a mean-field model. The time clustering of small avalanches is similar to the known time clustering of earthquake foreshocks and aftershocks.

Localized heating during slip avalanches is relevant to the understanding of the transition from shear banding to cracking in bulk metallic glasses (BMGs). Here we focus on the released elastic energies (incorporating the influence of machine stiffness) and avalanche durations for regularly appearing large avalanches to study the maximum temperature increases of a Zr-based BMG compressed at three strain rates of 3 × 10−5, 3 × 10−4, and 3 × 10−3 s−1. The maximum released elastic energies during slip avalanches decrease with the increase of strain rates. The durations of the avalanches are on the scale of tens of milliseconds for each strain rate. As strain rate increases, the maximum temperature rises due to shear-band slips are decreased from 2.6, 2.3 to 1.9 K. Moderate heating during the large slip avalanches for three strain rate implies that thermal softening has only a small effect on the shear-banding instability.

Many materials are known to deform under shear in an intermittent way with slip avalanches detected as acoustic emission and serrations in the stress–strain curves. Similar serrations have recently been observed in a new class of materials, called high-entropy alloys (HEAs). Here, we discuss the serration behaviors of several HEAs from cryogenic to elevated temperatures. The experimental results of slow compression and tension tests are compared with the predictions of a slip-avalanche model for the deformation of a broad range of solids. The results shed light on the deformation processes in HEAs. Temperature effects on the distributions of stress drops and the decrease of the cutoff (i.e., of the largest observed slip size) for increasing temperature qualitatively agree with the model predictions. The model is used to quantify the serration characteristics of HEAs, and pertinent implications are discussed.