Copper Single Crystals Research Articles

Correlation between the breaking behavior and the initial microstructural defects of the metallic nanowires: An approach from statistical analysis

It is speculated that the initial slip in the single-crystal nanowire (NW) is dominant to the final breaking position. To reveal the correlation between the initial slip and breaking position, in this paper, up to 300 independent [111] oriented single-crystal copper NWs under uniaxial tension at a temperature of 10 K have been performed using molecular dynamics (MD) simulations. Combining with Machine Learning, the position of the initial slip is determined by the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The breaking position is calculated using the atom number ratio (ANR). The calculations illustrate that the final breaking positions follow two Gaussian distributions at two ends of the NW. Similarly, the distribution of the initial slip positions also has statistical peaks at the two ends and an additional distribution at the center of the NW within a large span. The results demonstrated that there is a clear correlation between the initial slips and the breaking positions on the basis of the distribution features. Further, four representative samples were studied systematically from the aspects of the microstructure and the stress–strain properties, showing that the final breaking position is determined at the middle and late stages of the plastic deformation. It infers that the apparent correlation between the initial slip positions and the final breaking positions of NWs exhibits statistically rather than causally. The conclusion derived from this study may contribute to promoting the fundamental research of metal nanomaterials and the optimization of the nanodevices.

Twinning during recrystallization and its correlation with the deformation microstructure

The formation of annealing twins during recrystallization in a cold-rolled copper single crystal has been studied. A new method is proposed to classify annealing twins according to their orientation relationship with the surrounding deformed matrix. A statistical analysis based on the new classification method shows that during growth of a recrystallized grain, twinning occurs more frequently on twinning planes close to one of the {111} planes of the deformation microstructure, and most frequently when the {111} plane is the dominant slip plane of the deformed matrix for the present single crystal. The differences in morphology for different types of twins are discussed based on growth selection criteria. The study highlights the importance of the local deformation microstructure on the formation of annealing twins.

Micropolar regularization of crystal plasticity with the gradient-enhanced incremental hardening law

A new model of gradient crystal plasticity is developed in which the incompatibility of plastic deformation field is simultaneously included in two different ways. The first one is well known and incorporates the gradient effect of accumulated rotation of the crystallographic lattice on the kinematic hardening in the Cosserat crystal plasticity model. The second way incorporates the effect of the current incompatibility of lattice spin on the total dislocation density rate, resulting in an additional isotropic hardening term in the gradient-enhanced hardening law. The latter effect involves a natural length scale that is fully determined in terms of standard quantities of a non-gradient hardening law and evolves during plastic deformation. The relative significance of the two effects depends on the values of material parameters, which is demonstrated by the results of calculations of 1D and 3D examples for a Cu single crystal. If the second effect is predominant, then the Cosserat formulation provides only a regularization, and then the model can be used to predict size effects. This is shown by 3D simulations of the size effect in spherical indentation of a copper single crystal. Since the gradient-enhanced hardening law does not involve any adjustable parameter, the obtained agreement of the model prediction with the experimental indentation size effect on hardness can be regarded as surprisingly good.

Enhanced plastic deformability of copper single crystals under low-frequency vibrational loading

Tensile tests on copper single crystal ([110]) foils using low-frequency vibrational loading of frequencies ranging from 0 to 50 Hz were performed at room temperature to explore the mechanisms of vibration-facilitated plastic deformation in metallic materials. It was found that the total elongation of copper single crystal foils under vibrational loading increased gradually with increasing vibration frequency, indicating enhanced plastic deformability. This behavior could be rationalized with the formation of equiaxial dislocation cells (EDC) in copper single crystal ([110]) foils under vibrational loading, which reflects the activation of multiple codirectional slip systems induced by the approximate biaxial tensile stress state during the unloading stage of vibrational loading. Additionally, the formation of Lüders bands under vibrational loading at high frequencies validates their dislocation-proliferation-mediated nucleation mechanism. This work would help to understand the vibration-lowered forming resistance in metallic materials of FCC lattice structures.

Plastic Flow Characteristics of Micro Single-Crystal Copper

In order to study the plastic flow characteristics of micro single-crystal Cu, an in-situ uniaxial loading test was carried out. The slip direction of the test is determined by the Schmidt factor, which is at 1μm~4μm. Within the micropillar size range, the sample has an obvious size effect. This is essentially due to the continuous proliferation of dislocations in the micropillar flowing out of the surface. The smaller the size, the more difficult it is to store dislocations, and the easier dislocations flow out. Therefore, the yield stress significantly increases with the increment of sample diameter. This study provides guidance for the reliability evaluation of microscale components based on the single-crystal Cu.

Atomistic determination of stress fields in samples with defects

The main goal of the study is the atomistic determination of the static stress-strain state at the crack tip in isotropic and anisotropic linearly elastic materials by the molecular dynamics method implemented in the open source LAMMPS (Large-scale Atomistic/Molecular Massively Parallel Simulator). An extensive class of computational experiments has been carried out for a single-crystal copper specimen with a central crack in the LAMMPS. The circumferential distributions of the stress tensor components obtained by molecular dynamics are compared with the angular distributions of brittle fracture continuum mechanics, i.e. with Williams’ analytical solution to the problem of an infinite plate loaded with a central crack in a linearly elastic isotropic material. The comparison of the angular distributions of the stress tensor components gained in the framework of atomistic modeling and the angular distributions obtained from the classical solution of continuum mechanics has shown that, at the nanoscale level, the stress fields are in good agreement with their macroscopic values.

Optimization and inference of bin widths for histogramming inelastic neutron scattering spectra.

A data-driven bin-width optimization for the histograms of measured data sets based on inhomogeneous Poisson processes was developed in a neurophysiology study [Shimazaki & Shinomoto (2007). Neural Comput. 19, 1503-1527], and a subsequent study [Muto, Sakamoto, Matsuura, Arima & Okada (2019). J. Phys. Soc. Jpn, 88, 044002] proposed its application to inelastic neutron scattering (INS) data. In the present study, the results of the method on experimental INS time-of-flight data collected under different measurement conditions from a copper single crystal are validated. The extrapolation of the statistics on a given data set to other data sets with different total counts precisely infers the optimal bin widths on the latter. The histograms with the optimized bin widths statistically verify two fine-spectral-feature examples in the energy and momentum transfer cross sections: (i) the existence of phonon band gaps; and (ii) the number of plural phonon branches located close to each other. This indicates that the applied method helps in the efficient and rigorous observation of spectral structures important in physics and materials science like novel forms of magnetic excitation and phonon states correlated to thermal conductivities.

Atomic simulations of tip-based nanomilling on single-crystal copper

An atomic force microscopy (AFM) tip-based scratching method was used to machine 2D/3D micro-nanostructures. However, the machining efficiency is too low for these structures to find wide used in applications. An AFM tip-based nanomilling approach is more efficient due to the associated higher material removal rate. This paper compares the material removal mechanisms of single-scratch and nanomilling processes close to the atomic scale on a single-crystal copper surface using molecular dynamics simulations. By analyzing the groove morphology, atomic flow behavior, and the variation in scratching force, the material removal mechanism is revealed. Moreover, the effects of tip trajectory and crystallographic orientation on atomic removal are studied by analyzing the relationship between the evolution of subsurface defects and material removal. This work reveals the mechanism underlying material removal in nanomilling in detail, which will greatly improve the ability of the tip-based nanomachining method.

Dislocation-dominated void nucleation in shock-spalled single crystal copper: Mechanism and anisotropy

Large-scale molecular dynamics simulations are conducted on single crystal copper along eight representative orientations to investigate dislocation-dominated void nucleation during shock loading and spall failure, including mechanisms and anisotropy. Spall strength estimated from free surface velocity decreases in the order of group I ([001]), group IV ([012] and [011]), group III ([122] and [123]) and group II ([114], [112] and [111]), respectively, in good agreement with anisotropy of spall strength in previous experiments and simulations. A lower spall strength is statistically associated with a higher void nucleation rate and a higher density of stable immobile dislocations (1/6〈110〉 and 1/3〈100〉) formed before void nucleation. Stable immobile dislocation plays a key role in void nucleation. The formation of stable immobile dislocations requires three conditions: high resolved shear stress for activating mobile dislocations, two or more main slip planes for dislocation reaction, and high angle between activated slip directions for high stability of immobile dislocations. Based on crystal elastic–plastic theory, resolved shear stress on all slip systems is calculated to analyze orientation effects on the three conditions. The three conditions can be fulfilled by group II orientations, but cannot by group I, III, and IV orientations, leading to anisotropy in void nucleation and spall strength.

Crystalline phase transitions and water-soluble complexes of copper(I) 2-hydroxyethanethiolate

The coordination polymer copper(I) 2-hydroxyethanethiolate, (CuSCH2CH2OH)n, though insoluble in all common solvents, dissolved readily in basic aqueous solutions of the thiolate anion (HOCH2CH2S–) of 2-mercaptoethanol to form a single species: the tetranuclear cluster [Cu4(µ-SCH2CH2OH)6]2–. From this solution were grown X-ray quality single crystals of copper(I) 2-hydroxyethanethiolate. This compound underwent a hitherto unknown crystal phase transition at ca. 6 °C, from point group P212121 to Pna21, with noticeable changes in the geometry of the Cu-S layer and in the orientation of the alkylthiolate side chains. When the bulky base tetrabutylammonium hydroxide was employed in the aqueous thiolate solution used to dissolve (CuSCH2CH2OH)n, the water-soluble polynuclear copper(I) complex bis(tetrabutylammonium) hexakis(µ-2-hydroxyethanethiolato) tetracuprate(I), [(C4H9)4N]2[Cu4(µ-SCH2CH2OH)6], could be isolated as X-ray quality crystals. Structural characterization of this complex revealed a tetrahedral arrangement of copper(I) centers with thiolates bridging the edges of the tetrahedra. On standing, this complex degraded to a larger polynuclear Cu(I) sulfide cluster.

Formation of dislocation structures during cyclic deformation in near-[001] multiple-slip-oriented copper single crystals

Dislocation structures in [001]-oriented copper single crystals have historically been studied at relatively low plastic shear strain amplitudes (γpl). Herein, the dislocation structure is investigated across a wide γpl range of 1.7 ∙ 10−4–1.7 ∙ 10−2. When γpl < 1.5 ∙ 10−2, the dislocation structure comprised a labyrinth with a set of parallel (100) and (001) walls. However, as γpl approached 1.5 ∙ 10−2, the dislocation structure changed to a cell structure to accommodate the higher plastic strain. The formation plane of the cell boundary depends on which slip system is activated as the primary slip system.

Deformation characteristics in micro-cutting of single crystal copper: effect of cutting tool geometry and friction

Deformation characteristics in micro-cutting of single crystal copper: effect of cutting tool geometry and friction

Molecular Dynamics Simulations of Ripple Nanostructure Formation During Nanomachining via Atomic Force Microscopy

Molecular dynamics (MD) constant force simulation mode is first used to study the formation of the ripple nanostructures on the single-crystal copper surface by combining the topography generated by machined grooves with the accumulated pile-up material on the side of these grooves via a triangular pyramid atomic force microscopy (AFM) tip. Groove morphologies, lateral forces, the evolution of subsurface defects, and atomic flow laws generated by different machining parameters are discussed. Specifically, the normal load, the feed value between grooves, and the scratching direction significantly affect groove formation. The simulated morphologies of the ripple nanostructures indicate that groove consistency and symmetry increase with increasing feed, and an optimized feed for various normal loads can be determined. The interaction between adjacent grooves produces a variation in the lateral forces with the groove number and feed. This is mainly related to the evolution of subsurface defects, the atomic flow law, and the volume of material pile-ups. The distributions of subsurface defects affect the atomic flow directions, and the atomic flow laws determine groove formation. The simulations provide important guidance for ripple nanostructure fabrication on single-crystal copper surface via AFM tips.

Machine-Learning-Based Model of Elastic—Plastic Deformation of Copper for Application to Shock Wave Problem

Molecular dynamics (MD) simulations explored the deformation behavior of copper single crystal under various axisymmetric loading paths. The obtained MD dataset was used for the development of a machine-learning-based model of elastic–plastic deformation of copper. Artificial neural networks (ANNs) approximated the elastic stress–strain relation in the form of tensor equation of state, as well as the thresholds of homogeneous nucleation of dislocations, phase transition and the beginning of spall fracture. The plastic part of the MD curves was used to calibrate the dislocation plasticity model by means of the probabilistic Bayesian algorithm. The developed constitutive model of elastic–plastic behavior can be applied to simulate the shock waves in thin copper samples under dynamic impact.

Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves

AbstractIn this study, the deformation-induced misorientations that are typically found in face-centred cubic single crystals deformed in single slip into stage II (and early stage III) of the work-hardening curve are discussed with respect to the experimentally observed broadening of X-ray rocking curves. By making use of well-established empirical relationships between characteristic features of the microstructure and the flow stress, some of the ambiguities of earlier interpretations of rocking curves could be avoided, and relationships between the half-widths of the rocking curves, the density of geometrically necessary dislocations, and the flow stress could be derived for both the tilt misorientations due to the kink bands lying perpendicular to the primary Burgers vector and the twist misorientations originating from the dislocation networks (grids, sheets) lying parallel to the primary glide plane. An evaluation of largely unpublished experimental rocking-curve data obtained on different crystallographic sections of deformed copper single crystals yielded a linear relationship between the broadening of the rocking curves and the flow stress. In terms of the predictions of the model developed, this implies that the ratio of the density of the geometrically necessary dislocations (that are responsible for the misorientations) to the total dislocation density remains constant during deformation, at least up to flow stresses of about 50 MPa. The absolute densities of the geometrically necessary dislocations are found to be a small fraction (at most ca. 5%) of the total dislocation densities. In terms of the evolution laws of deformation-induced dislocation boundaries proposed in the literature, it is concluded that both kink bands and grids/ sheets follow the characteristics of so-called geometrically necessary boundaries.

Homogeneous nucleation of dislocations in copper: Theory and approximate description based on molecular dynamics and artificial neural networks

Nucleation of dislocations in a homogeneous crystal lattice is relevant for small-scale plasticity or ultra-fast loading. Previously, we improved the dislocation nucleation theory and proposed to use artificial neural networks (ANNs) trained by molecular dynamics (MD) data to obtain a self-contained description [1]. The ANNs were used to approximate material properties, such as stress-strain relationship, shear modulus and generalized stacking fault at the elastic stage prior to the nucleation of dislocations. In the present work, we consider the case of copper single crystal in a wide range of pressures from −10 GPa to +50 GPa. At preparation of training data, we apply a polynomial extrapolation of MD data beyond the nucleation limit, which allows us to improve the precision of the trained ANNs and make the theory predictions more accurate. Also we develop an approximate approach, which requires smaller and simpler MD data for training, but gives the strain rate dependence of the nucleation threshold close to the rigorous theory of dislocation nucleation.

Numerical Analysis of Multi-Angle Precision Microcutting of a Single-Crystal Copper Surface Based on Molecular Dynamics.

The molecular dynamics method was used to study the removal mechanism of boron nitride particles by multi-angle microcutting of single-crystal copper from the microscopic point of view. The mechanical properties and energy conversion characteristics of single-crystal copper during microcutting were analyzed and the atomic displacement and dislocation formation in the microcutting process are discussed. The research results showed that during the energy transfer between atoms during the microcutting process of boron nitride particles, the crystal lattice of the single-crystal copper atom in the cutting extrusion region was deformed and displaced, the atomic temperature and thermal motion in the contact area between boron nitride particles and Newtonian layer of workpiece increased, the single-crystal copper atom lattice was defective, and the atomic arrangement structure was destroyed and recombined. The interface of different crystal structures formed a dislocation structure and produced plastic deformation. With the increase of the impact cutting angle, the dislocation density inside the crystal increased, the defect structure increased and the surface quality of the workpiece decreased. To protect the internal structure of the workpiece and improve the material removal rate, a smaller cutting angle should be selected for the abrasive flow microcutting function, which can reduce the formation of an internal defect structure and effectively improve the quality of abrasive flow precision machining. The research conclusions can provide a theoretical basis and technical support for the development of precision abrasive flow processing technology.

Generation mechanism and dual-dynamics simulation of surface patterns in single-point diamond turning of single-crystal copper

Single-crystal copper (Cu), whose atom arrangement is in the same direction and has no grain boundary, is widely used in defense technology, civil electronics and network communication. As a diamond machinable material, fan-shaped patterns are commonly generated on the machined surface in single-point diamond turning (SPDT), which affects the machined surface quality and the optical function it carries. Previous studies on the surface generation mechanism in SPDT of single-crystal copper were limited to experimental analyses, while there is a lack of fundamental understanding in the generation mechanism and suppression method of fan-shaped pattern. In the present study, the fan-shaped patterns, surface quality, cutting force and chip morphology generates during SPDT of typical crystal planes (100), (110) and (111) of single-crystal copper were studied both from theoretical and experimental analyses. A molecular dynamics (MD) simulation was conducted to present the fundamental generation mechanism of the fan-shaped patterns from atom arrangement directions and its angle changing with the primary cutting direction in micro scope, while a cutting dynamics model was established to simulate the generation of fan-shaped patterns on the machined surface in macro scope. Based on theoretical and experimental analysis, it was found that the different atom density arrangement directions of single-crystal copper and main cutting direction of SPDT caused fluctuations in the friction coefficient, which further caused the vibration of the cutting system and generated the fan-shaped patterns. The SPDT of crystal planes (100) can achieve the best surface quality. The present research provides a fundamental understanding of fan-shaped pattern formation on the machined surface, and provides a reference to obtain better surface quality in machining of single-crystal copper.

Hydroxy-Group-Functionalized Single Crystal of Copper(II)-Porphyrin Complex for Electroreduction CO2 to CH4.

Purposefully developing crystalline materials at molecular level to improve the selectivity of electroreduction CO2 to CH4 is still rarely studied. Herein, a single crystal of copper(II) complex with hydroxy groups was designed and synthesized, namely 5,10,15,20-tetrakis(3,4-dihydroxyphenyl)porphyrin copper(II) (Cu-PorOH), which could serve as a highly efficient heterogeneous electrocatalyst for electroreduction of CO2 toward CH4 . In 0.5 m KHCO3 , Cu-PorOH gave a high faradaic efficiency of 51.3 % for CH4 and drove a partial current density of 23.2 mA cm-2 at -1.5 V versus the reversible hydrogen electrode in H-cell. The high performance was greatly promoted by the hydroxy groups in Cu-PorOH, which could not only form stable three-dimensional frameworks through hydrogen-bonding interactions but also stabilize the intermediate species by hydrogen bonds, as supported by density functional theory calculations. This work provides an effective avenue in exploring crystalline catalysts for CO2 reduction at molecular level.

Mechanical response of single-crystal copper under vibration excitation based on molecular dynamics simulation

Since high-frequency vibration is usually used to assist metal processing in improving processing efficiency and quality. An in-depth understanding of the strengthening mechanism of high-frequency vibration-assisted metal processing is essential. In this paper, molecular dynamics (MD) simulation is performed for scratching under different vibration-assisted conditions, non-vibration-assisted, one-dimensional vibration-assisted, and two-dimensional vibration-assisted, to investigate the effect of high-frequency vibration on the scratching process of single-crystal copper at the atomic scale. Based on crystal defect analysis technology and dislocation theory, the influence mechanism of high-frequency vibration on the surface morphology, tangential force change, potential energy change, and dislocation defect structure evolution of single-crystal copper is studied. By analyzing the MD results, it is found that vibration-assisted scratching significantly improved the surface quality of single-crystal copper and reduced the tangential force of spherical diamond and that two-dimensional vibration-assisted scratching has the best effect. Vibration-assisted scratching experiments are also conducted to compare the experimental results with the molecular dynamics simulation results to verify the accuracy and credibility of the molecular dynamics simulation.