Magnetic domain wall dynamics studied by in-situ Lorentz microscopy with aid of custom-made Hall-effect sensor holder.

We built a custom-made holder with a Hall-effect sensor to measure the single point magnetic flux density inside a transmission electron microscope (TEM, JEM-F200, JEOL). The measurement point is at the same place as the sample inside the TEM. We utilized information collected with the Hall-effect sensor holder to study magnetic domain wall (DW) dynamics by in-situ Lorentz microscopy. We generated an external magnetic field to the sample using the objective lens (OL) of the TEM. Based on our measurements with the Hall-effect sensor holder, the OL has nearly linear response, and when it is switched off, the strength of the magnetic field in the sample region is very close to 0 mT. A ferritic-pearlitic sample studied has globular and lamellar cementite (Fe3C) carbides in the ferrite matrix. Based on the in-situ Lorentz microscopy experiments, DWs in the ferritic matrix perpendicular to the lamellar carbides start to move first at ∼10 mT. At 160 mT, DWs inside the globular carbide start to disappear, and the saturation occurs at ∼210 mT. At 288 mT, the DWs parallel to the lamellar carbides still exist. Thus, these lamellar carbides are very strong pinning sites for DWs. We also run dynamical micromagnetic simulations to reproduce the DW disappearance in the globular carbide. As in the in-situ experiments, the DWs stay stable until the external field reaches the magnitude of 160 mT, and the DWs disappear before the field is 214 mT. In general, the micromagnetic simulations supported very well the interpretation of the experimental findings.

Barkhausen noise in disordered striplike ferromagnets: Experiment versus simulations.

In this work, we present a systematic comparison of the results obtained from the low-frequency Barkhausen noise recordings in nanocrystalline samples with those from the numerical simulations of the random-field Ising model systems. We performed measurements at room temperature on a field-driven metallic glass stripe made of VITROPERM 800 R, a nanocrystalline iron-based material with an excellent combination of soft and magnetic properties, making it a cutting-edge material for a wide range of applications. Given that the Barkhausen noise emissions emerging along a hysteresis curve are stochastic and depend in general on a variety of factors (such as distribution of disorder due to impurities or defects, varied size of crystal grains, type of domain structure, driving rate of the external magnetic field, sample shape and temperature, etc.), adequate theoretical modeling is essential for their interpretation and prediction. Here the Random field Ising model, specifically its athermal nonequilibrium version with the finite driving rate, stands out as an appropriate choice due to the material's nanocrystalline structure and high Curie temperature. We performed a systematic analysis of the signal properties and magnetization avalanches comparing the outcomes of the numerical model and experiments carried out in a two-decade-wide range of the external magnetic field driving rates. Our results reveal that with a suitable choice of parameters, a considerable match with the experimental results is achieved, indicating that this model can accurately describe the Barkhausen noise features in nanocrystalline samples.

Predicting elastic and plastic properties of small iron polycrystals by machine learning.

Deformation of crystalline materials is an interesting example of complex system behaviour. Small samples typically exhibit a stochastic-like, irregular response to externally applied stresses, manifested as significant sample-to-sample variation in their mechanical properties. In this work we study the predictability of the sample-dependent shear moduli and yield stresses of a large set of small cube-shaped iron polycrystals generated by Voronoi tessellation, by combining molecular dynamics simulations and machine learning. Training a convolutional neural network to infer the mapping between the initial polycrystalline structure of the samples and features of the ensuing stress-strain curves reveals that the shear modulus can be predicted better than the yield stress. We discuss our results in the context of the sensitivity of the system's response to small perturbations of its initial state.

Reversible-to-irreversible transition of colloidal polycrystals under cyclic athermal quasistatic deformation.

Cyclic loading on granular packings and amorphous media exhibits a transition from reversible elastic behavior to irreversible plasticity. The present study compares the irreversibility transition and microscopic details of colloidal polycrystals under oscillatory tensile-compressive and shear strain. Under both modes, the systems exhibit a reversible to irreversible transition. However, the strain amplitude at which the transition is observed is larger in the shear strain than in the tensile-compressive mode. The threshold strain amplitude is confirmed by analyzing the dynamical properties, such as mobility and atomic strain (von Mises shear strain and the volumetric strain). The structural changes are quantified using a hexatic order parameter. Under both modes of deformation, dislocations and grain boundaries in polycrystals disappear, and monocrystals are formed. We also recognize the dislocation motion through grains. The key difference is that strain accumulates diagonally in oscillatory tensile-compressive deformation, whereas in shear deformation, strain accumulation is along the x or y axis.

Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold.

Roughness of driven elastic interfaces in random media is typically understood to be characterized by a single roughness exponent ζ. We show that at the depinning threshold, due to symmetry breaking caused by the direction of the driving force, elastic interfaces with local, long-range, and mean-field elasticity exhibit asymmetric roughness. It is manifested as a skewed distribution of the local interface heights, and can be quantified by using detrended fluctuation analysis to compute a spectrum of local, segment-level scaling exponents. The asymmetry is observed as approximately linear dependence of the local scaling exponents on the difference of the segment height from the mean interface height.

Effect of thresholding on avalanches and their clustering for interfaces with long-range elasticity.

Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the depinning of a long-range elastic interface and applied different thresholds including a zero one on the data to see how the sizes and durations of events change and how this affects temporal avalanche clustering. Higher thresholds result in steeper size and duration distributions and cause the avalanches to cluster temporally. Using methods from seismology, the frequency of the events in the clusters was found to decrease as a power-law of time, and the size of an event in a cluster was found to help predict how many events it is followed by. The results bring closer theoretical studies of this class of models to real experiments, but also highlight how different phenomena can be obtained from the same set of data.

Depinning Exponents of Thin Film Domain Walls Depend on Disorder Strength.

Domain wall dynamics in ferromagnets is complicated by internal degrees of freedom of the domain walls. We develop a model of domain walls in disordered thin films with perpendicular magnetic anisotropy capturing such features, and use it to study the depinning transition. For weak disorder, excitations of the internal magnetization are rare, and the depinning transition takes on exponent values of the quenched Edwards-Wilkinson equation. Stronger disorder results in disorder-dependent exponents concurrently with nucleation of an increasing density of Bloch lines within the domain wall.

Dislocation avalanches from strain-controlled loading: A discrete dislocation dynamics study.

We study strain-controlled plastic deformation of crystalline solids via two-dimensional discrete dislocation dynamics simulations. To this end, we characterize the average stress-strain curves as well as the statistical properties of strain bursts and the related stress drops as a function of the imposed strain rate and the stiffness of the specimen-machine system. The dislocation system exhibits strain-rate sensitivity such that a larger imposed strain rate results in a higher average stress at a given strain. In the limit of small strain rate and driving spring stiffness, the sizes and durations of the dislocation avalanches are power law distributed up to a cutoff scale, and exhibit temporally asymmetric average shapes. We discuss the dependence of the results on the driving parameters and compare our results to those from previous simulations where quasistatic stress-controlled loading was used.

Effects of external noise on threshold-induced correlations in ferromagnetic systems.

In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent γ_{S/T} (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.

Impurity-induced nematic-isotropic transition of liquid crystals.

Complex fluids made of liquid crystals (LCs) and small molecules, surfactants, nanoparticles or 1D/2D nanomaterials show novel and interesting features, making them suitable materials for various applications starting from optoelectronics to biosensing. While these additives (impurities) introduce new features in the complex fluids, they may also alter the phase transition behaviour of LCs depending on the physiochemical properties of the added impurity. This article reports on the phase transition of 4-cyano-4'-alkylbiphenyl (nCB) LCs in the presence of an associative impurity, i.e., water and a non-associative impurity, i.e., hexane employing computational methods and experiments. In particular, all-atom (AA) simulations and coarse-grained (CG) models were designed for two complex systems, i.e., 6CB + water and 6CB + hexane and corresponding spectrophotometry experiments were performed using a homologous LC, i.e., 5CB. Results from the simulations and experiments elucidate that the phase transition of LCs depends on the mixing/demixing phenomenon of the impurity in the LC. While associative liquids like water which do not mix with LCs do not influence the nematic-to-isotropic phase transition of LCs, hexane, being a non-associative liquid, mixes well with LCs and induces a sharp impurity-induced nematic-to-isotropic phase transition. Upon application of both AA and CG simulations, we could reach the conclusion that the mixing/demixing phenomenon in an LC + impurity system influences the entropy of the system and hence the observed phase transitions are entropy-driven.

Propagating bands of plastic deformation in a metal alloy as critical avalanches.

The plastic deformation of metal alloys localizes in the Portevin-Le Chatelier effect in bands of different types, including propagating, or type "A" bands, usually characterized by their width and a typical propagation velocity. This plastic instability arises from collective dynamics of dislocations interacting with mobile solute atoms, but the resulting sensitivity to the strain rate lacks fundamental understanding. Here, we show, by using high-resolution imaging in tensile deformation experiments of an aluminum alloy, that the band velocities exhibit large fluctuations. Each band produces a velocity signal reminiscent of crackling noise bursts observed in numerous driven avalanching systems from propagating cracks in fracture to the Barkhausen effect in ferromagnets. The statistical features of these velocity bursts including their average shapes and size distributions obey predictions of a simple mean-field model of critical avalanche dynamics. Our results thus reveal a previously unknown paradigm of criticality in the localization of deformation.

Barkhausen Noise from Precessional Domain Wall Motion.

The jerky dynamics of domain walls driven by applied magnetic fields in disordered ferromagnets-the Barkhausen effect-is a paradigmatic example of crackling noise. We study Barkhausen noise in disordered Pt/Co/Pt thin films due to precessional motion of domain walls using full micromagnetic simulations, allowing for a detailed description of the domain wall internal structure. In this regime the domain walls contain topological defects known as Bloch lines which repeatedly nucleate, propagate, and annihilate within the domain wall during the Barkhausen jumps. In addition to bursts of domain wall propagation, the in-plane Bloch line dynamics within the domain wall exhibits crackling noise and constitutes the majority of the overall spin rotation activity.

Machine learning plastic deformation of crystals.

Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show, by employing machine learning techniques such as regression neural networks and support vector machines that deformation predictability evolves with strain and crystal size. Using data from discrete dislocations dynamics simulations, the machine learning models are trained to infer the mapping from features of the pre-existing dislocation configuration to the stress-strain curves. The predictability vs strain relation is non-monotonic and exhibits a system size effect: larger systems are more predictable. Stochastic deformation avalanches give rise to fundamental limits of deformation predictability for intermediate strains. However, the large-strain deformation dynamics of the samples can be predicted surprisingly well.

Nanoscale liquid crystal lubrication controlled by surface structure and film composition.

Liquid crystals have emerged as potential candidates for next-generation lubricants due to their tendency to exhibit long-range ordering. Here, we construct a full atomistic model of 4-cyano-4-hexylbiphenyl (6CB) nematic liquid crystal lubricants mixed with hexane and confined by mica surfaces. We explore the effect of the surface structure of mica, as well as lubricant composition and thickness, on the nanoscale friction in the system. Our results demonstrate the key role of the structure of the mica surfaces, specifically the positions of potassium (K+) ions, in determining the nature of sliding friction with monolayer lubricants, including the presence or absence of stick-slip dynamics. With the commensurate setup of confining surfaces, when the grooves created between the periodic K+ ions are parallel to the sliding direction we observe a lower friction force as compared to the perpendicular situation. Random positions of ions exhibit even smaller friction forces with respect to the previous two cases. For thicker lubrication layers the surface structure becomes less important and we observe a good agreement with the experimental data on bulk viscosity of 6CB and the additive hexane. In case of thicker lubrication layers, friction may still be controlled by tuning the relative concentrations of 6CB and hexane in the mixture.

Moving magnets in a micromagnetic finite-difference framework.

We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.

A surface topography analysis of the curling stone curl mechanism.

The curling motion of the curling stone on ice is well-known: if a small clockwise rotational velocity is imposed to the stone when it is released, in addition to the linear propagation velocity, the stone will curl to the right. A similar curl to the left is obtained by counter-clockwise rotation. This effect is widely used in the game to reach spots behind the already thrown stones, and the rotation also causes the stone to propagate in a more predictable fashion. Here, we report on novel experimental results which support one of the proposed theories to account for the curling motion of the stone, known as the "scratch-guiding theory". By directly scanning the ice surface with a white light interferometer before and after each slide, we observed cross-scratches caused by the leading and trailing parts of the circular contact band of the linearly moving and rotating stone. By analyzing these scratches and a typical curling stone trajectory, we show that during most of the slide, the transverse force responsible for the sideways displacement of the stone is linearly proportional to the angle between these cross-scratches.

Effects of precipitates and dislocation loops on the yield stress of irradiated iron.

Plastic deformation of crystalline materials is governed by the features of stress-driven motion of dislocations. In the case of irradiated steels subject to applied stresses, small dislocation loops as well as precipitates are known to interfere with the dislocation motion, leading to an increased yield stress as compared to pure crystals. We study the combined effect of precipitates and interstitial glissile [Formula: see text] dislocation loops on the yield stress of iron, using large-scale three-dimensional discrete dislocation dynamics simulations. Precipitates are included in the simulations using our recent multi-scale implementation [A. Lehtinen et al., Phys. Rev. E 93 (2016) 013309], where the strengths and pinning mechanisms of the precipitates are determined from molecular dynamics simulations. In the simulations we observe dislocations overcoming precipitates with an atypical Orowan mechanism which results from pencil-glide of screw segments in iron. Even if the interaction mechanisms with dislocations are quite different, our results suggest that in relative terms, precipitates and loops of similar sizes contribute equally to the yield stress in multi-slip conditions.

Threshold-induced correlations in the Random Field Ising Model.

We present a numerical study of the correlations in the occurrence times of consecutive crackling noise events in the nonequilibrium zero-temperature Random Field Ising model in three dimensions. The critical behavior of the system is portrayed by the intermittent bursts of activity known as avalanches with scale-invariant properties which are power-law distributed. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations show that the observed correlations emerge upon applying a finite threshold to the pertaining signals when defining events of interest. Such events are called subavalanches and are obtained by separation of original avalanches in the thresholding process. The correlations are evidenced by power law distributed waiting times and are present in the system even when the original avalanche triggerings are described by a random uncorrelated process.

Excitation Spectra in Crystal Plasticity.

Plastically deforming crystals exhibit scale-free fluctuations that are similar to those observed in driven disordered elastic systems close to depinning, but the nature of the yielding critical point is still debated. Here, we study the marginal stability of ensembles of dislocations and compute their excitation spectrum in two and three dimensions. Our results show the presence of a singularity in the distribution of excitation stresses, i.e., the stress needed to make a localized region unstable, that is remarkably similar to the one measured in amorphous plasticity and spin glasses. These results allow us to understand recent observations of extended criticality in bursty crystal plasticity and explain how they originate from the presence of a pseudogap in the excitation spectrum.

Mixture of Clustered Bayesian Neural Networks for Modeling Friction Processes at the Nanoscale.

Friction and wear are the source of every mechanical device failure, and lubricants are essential for the operation of the devices. These physical phenomena have a complex nature so that no model capable of accurately predicting the behavior of lubricants exists. Thus, lubricants cannot be designed from scratch but have to be screened through expensive trial-error tests. In this study we propose a machine learning (ML) method that infers the relationship between chemical composition of lubricants and their performance from a database. Because no such database of desirable size and completeness is publicly available, we compiled one from molecular dynamics (MD) simulations of toy-model fluids nanoconfined between shearing surfaces. The fluid-friction relation is modeled by a Bayesian neural network (BNN), trained to reproduce the results for a training set of fluids. Due to the inhomogeneous data distribution it was necessary to carefully pick fluids for training and validation from the database with advanced clustering algorithms, rather than using the standard random selection. Different BNNs were then trained on the data clusters and their predictions combined into a mixture of experts. The model provides a prediction of lubricants performance as well as an error bar, at a fraction of the cost of MD. Because most values agree with the actual MD simulations within the estimated error σ, we conclude that the model is satisfactory. This method addresses the challenges brought by noisy, badly distributed, high-dimensional data that are likely to appear in reality as well, and it can be extended to real fluids, if a database could be provided.