Single Crystal Copper Samples Research Articles

Artificial Neural Network for the Prediction of Fatigue Life of Microscale Single-Crystal Copper

Microscale single-crystal copper is widely used in electronics, communications and other fields due to its excellent properties such as high ductility, high toughness and good conductivity. Therefore, it is particularly important to research its fatigue life. In order to explore the influence of size effect, loading frequency and shear strain on the main slip surface on the fatigue life of microscale single-crystal copper based on in situ fatigue experimental data of microscale single-crystal copper, this paper used a BP neural network algorithm to construct a single-crystal copper fatigue life prediction network model. The data set included 14 groups of training data, with 11 groups as training sets and 3 groups as testing sets. The input characteristics were length, width, height, loading frequency and shear strain of the main sliding plane of a microscale single-crystal copper sample. The output characteristic was the fatigue life of microscale single-crystal copper. After training, the mean square error (MSE) of the model was 0.03, the absolute value error (MAE) was 0.125, and the correlation coefficient (R2) was 0.93271, indicating that the BP neural network algorithm can effectively predict the fatigue life of microscale single-crystal copper and has good generalization ability. This model can not only save the experimental time of fatigue life measurement of micro-scale single-crystal copper, but also optimize the properties of the material by taking equidistant points in the range of characteristic parameters. Therefore, the current study demonstrates an applicable and efficient methodology to evaluate the fatigue life of microscale materials in industrial applications.

Oxygen plasma cleaning of copper for photocathode applications: A MEIS and XPS study

MEIS and XPS studies have been conducted for a range of oxygen plasma treated copper samples (and one treated with Ar plasma), as part of a study of the preparation of photocathode surfaces. This procedure was seen to remove hydrocarbon contamination, but left an oxide film whose thickness depended on the treatment conditions used. The film thickness was seen to increase with longer treatment time and higher RF power levels with behaviour characteristic of a diffusion limited process. Annealing led to a removal of the oxide layer by diffusion of oxygen into the bulk of the samples. This indicates that where the oxide layer is sufficiently thin, it should be possible to produce a surface with low enough oxygen content to have adequate conductivity and high enough surface escape probability to allow photoemission at UV wavelengths. Ar plasma treatment was seen to result in a very thin oxide film which could satisfy these requirements and thus might be preferable. Data from single crystal copper samples showed similar total oxygen content for all the surfaces analysed.

A comparative study of integration algorithms for finite single crystal (visco-)plasticity

Computational aspects of finite crystal plasticity have been discussed in the literature for some time, yet open challenges regarding the robustness and uniqueness of predictions for different algorithms remain. In this contribution, a careful comparison between different formulations of single crystal plasticity is therefore presented, covering both rate-dependent and rate-independent behavior in the finite deformation setting. To this end, algorithms are developed for an augmented-Lagrangian formulation and a formulation based on nonlinear complementary functions in the rate-independent case. For the rate-dependent case, algorithmic treatments are considered for two commonly employed viscoplastic formulations. The robustness of the different algorithms is assessed by means of simulations at the material point level, involving proportional fully deformation-controlled tests and non-proportional loading cycles in stress space. The augmented-Lagrangian formulation and a particular viscoplastic formulation are found to be superior in terms of robustness compared to the other algorithm considered in their respective category. It is then further observed that these algorithms of choice, which perform well for the ideally-plastic case and for Taylor-type hardening, induce a significant reduction in acceptable deformation increment size for an anisotropic, phenomenological hardening law, due to the rather complex determination of the active slip systems.Additionally, it is found from a sensitivity analysis that increasing the degree of anisotropy in the hardening law amplifies the sensitivity of the model’s response to small initial misorientations, both in the rate-dependent and the rate-independent case. A sensitivity analysis is also applied in the ideally-plastic case to demonstrate that for common choices of viscous parameters, the response of a particular rate-dependent formulation of the crystal plasticity model not necessarily possesses the same characteristic features as the response obtained by the corresponding rate-independent augmented-Lagrangian formulation. Therefore, it is recommended to apply the augmented-Lagrangian formulation to determine the rate-independent model response, rather than employing a rate-dependent formulation with limiting values of the viscous parameters due to the superior robustness of the former.The application of the augmented-Lagrangian formulation in the solution of an inhomogeneous fixed-end torsion problem by means of finite element analysis demonstrates the beneficial numerical properties of this formulation and the ability of the material model to reproduce characteristic features observed in experiments on single crystal copper samples.

The effects of initial void and dislocation on the onset of plasticity in copper single crystals

Based on molecular dynamics, the effects of void and initial dislocation structure on incipient plasticity are investigated with single crystal copper samples. By introducing a void of different sizes and shapes and dislocations of different initial structures around the void in copper single crystals, we explore their effects on yielding as well as the dominated deformation mechanism. The main findings from this study are as follows: (1) for the samples with a void of the same size, the yield stress approaches to a specific value as the initial dislocation density increases; (2) for samples with a void of varying size, the yield stress becomes independent of the void size as it reaches a certain level, due to the saturation of preexisting dislocations around the void; and (3) as the strain rate increases, the effects of voids and preexisting dislocations on the yield stress become limited due to the response inertia, for which the phase transition from face-centered cubic to an amorphous phase occurs at an extremely high strain rate.

Accessing fatigue information by means of dynamic nanoindentation

Despite its relevance, fatigue is a phenomenon hardly investigated on the micro- and nano-scale. Recent developments in nanoindentation instrumentation have opened up new opportunities to study the behavior of materials dynamically probed on a small scale. Based on the experimental work on a single crystal copper sample as well as on polycrystalline copper, we show the possibility to sample fatigue information on the nanoscale, which corresponds well with existing literature. Consequently, the method introduced here provides a unique opportunity to explore the fatigue behavior and associated phenomena of surfaces or materials available only in small volumes.

High resolution neutron Larmor diffraction using superconducting magnetic Wollaston prisms

The neutron Larmor diffraction technique has been implemented using superconducting magnetic Wollaston prisms in both single-arm and double-arm configurations. Successful measurements of the coefficient of thermal expansion of a single-crystal copper sample demonstrates that the method works as expected. The experiment involves a new method of tuning by varying the magnetic field configurations in the device and the tuning results agree well with previous measurements. The difference between single-arm and double-arm configurations has been investigated experimentally. We conclude that this measurement benchmarks the applications of magnetic Wollaston prisms in Larmor diffraction and shows in principle that the setup can be used for inelastic phonon line-width measurements. The achievable resolution for Larmor diffraction is comparable to that using Neutron Resonance Spin Echo (NRSE) coils. The use of superconducting materials in the prisms allows high neutron polarization and transmission efficiency to be achieved.

A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples

A method for in situ testing of miniaturized tension specimen was developed. The size effects of the plastic deformation behavior of copper single crystals loaded along the 〈−2 3 4〉 direction were investigated. The diameter was varied between 0.5 μm and 8 μm, and the aspect ratio, gauge length to side length, between 1:1 and 13.5:1. At high aspect ratios hardening was negligible. However, an increase of the flow stress with decreasing diameter was observed. This increase was small for diameters above 2 μm, and somewhat larger below 2 μm. These findings are explained by individual dislocation sources which govern the plastic deformation. For low aspect ratios the behavior is significantly different. A pronounced hardening and a very strong size effect was observed. Both are a result of dislocation pile-ups due to the constrained glide of the dislocations caused by the sample geometry.

Characterizing dislocation structure evolution during cyclic deformation using electron channelling contrast imaging

This paper briefly reviews development of the electron channelling contrast imaging (ECCI) technique, which uses diffraction contrast to reveal dislocation structures underlying the surface of bulk samples imaged in the scanning electron microscope. In particular, the application of ECCI to the study of evolution of dislocation structures during cyclic deformation of single crystal copper samples will be described. Quantitative measurements of the vein width, separation and volume fraction within the matrix phase were made and these parameters showed rapid changes during the initial cyclic hardening of the sample, with smaller variations continuing after stress saturation. The volume fraction of persistent slip bands (PSBs) increased continuously with cycling beyond stress saturation. Measurements of PSB widths and spacings indicated that new PSBs tend to form near existing PSBs. The ECCI technique revealed PSBs of finite length with tapered ends. Stress concentrations occurring ahead of the tapered PSBs may be the cause of preferential nucleation of new PSBs close to existing ones.

Electron channelling contrast imaging characterization of dislocation structures associated with extrusion and intrusion systems and fatigue cracks in copper single crystals

The fatigue of copper single crystals, oriented for single slip, was studied using electron channelling contrast imaging (ECCI) in a scanning electron microscope. This technique allows the detection and characterization of dislocation structures in bulk specimens. This paper presents ECCI images showing dislocation arrangements associated with intrusions, extrusions and stage I and stage II cracks in single-crystal copper samples fatigued by tension-compression along [541]. The presence of intrusions or stage I cracks on the persistent slip band (PSB) planes caused no noticeable change in the local dislocation structures in the matrix vein and PSB ladder structures. Stage II cracks deviate from the PSB planes and were associated with elongated dislocation cells inclined in the direction of the loading axis. These elongated dislocation cells are confined to within 10 μm of the crack tip.

Electron channelling contrast imaging characterization of dislocation structures associated with extrusion and intrusion systems and fatigue cracks in copper single crystals

Abstract The fatigue of copper single crystals, oriented for single slip, was studied using electron channelling contrast imaging (ECCI) in a scanning electron microscope. This technique allows the detection and characterization of dislocation structures in bulk specimens. This paper presents ECCI images showing dislocation arrangements associated with intrusions, extrusions and stage I and stage II cracks in single-crystal copper samples fatigued by tension-compression along [541]. The presence of intrusions or stage I cracks on the persistent slip band (PSB) planes caused no noticeable change in the local dislocation structures in the matrix vein and PSB ladder structures. Stage II cracks deviate from the PSB planes and were associated with elongated dislocation cells inclined in the direction of the loading axis. These elongated dislocation cells are confined to within 10 μm of the crack tip.

Channeling effects during focused-ion-beam micromachining of copper

The rapid introduction of copper metallization for semiconductor devices has prompted increased research into focused-ion-beam micromachining of copper. Studies with the aim of increasing the material removal rate of Cu by focused-ion-beam micromachining have been complicated by variable micromachining behavior apparently resulting from differing Cu film morphologies produced by the various Cu deposition procedures. This work examined the micromachining behavior of thin copper films produced by physical-vapor deposition (PVD) and electroplating, as well as single-crystal copper samples. PVD copper films were found to be preferentially textured along 〈111〉, with a columnar grain structure. Channeling effects within this type of grain structure provide a geometric enhancement of the material removal rate of 30% when the sample normal is tilted 12° from the incident ion beam, regardless of sample rotation. Single-crystal (111) copper was found to exhibit similar material removal rate enhancement (averaged over 360° rotation) when tilted 12°, verifying that the etching enhancement observed in the PVD films is directly related to their 〈111〉 texture. Compared to the PVD film, electroplated (EP) copper thin films contained a significantly more random grain orientation. Consequently, the EP films did not exhibit any appreciable variation in material removal rate beyond the expected cosine dependence when tilted with respect to the incident Ga+ beam normal. Micromachining of the electroplated films, which have larger randomly oriented grains, results in grain decoration due to preferential etching producing severe micromachining-induced topography.

Dislocation arrangements in cyclically deformed copper single crystals

Detailed transmission electron microscopy (TEM) studies of dislocation arrangements in single-crystal copper samples, fatigued at a constant plastic shear strain amplitude of 0.15%, revealed clear differences between single- and multiple-slip-oriented crystals. In single-slip-oriented samples the dislocation arrangement consisted of loop patches and persistent slip bands (PSBs) with a ladder structure but, in addition, some cell formation also appeared in the PSBs. In multiple-slip-oriented crystals the dislocation matrix arrangement consisted of channel and wall layers lying nearly perpendicular to the loading axis. Ladder-type PSBs were also observed in these crystals, but they were normally separated from the matrix by cells and, in addition, PSBs seemed to have developed through cell formation. The resistance of PSBs to deformation can also locally vary because the proportional amounts of cells and ladder-like structures were not constant. On the basis of the present findings, PSBs should be considered only as structural elements into which the deformation concentrates during fatigue, regardless of their exact dislocation arrangement, which may contain ladder-type structures, cells and other possible dislocation configurations. As the role of point defects may also be significant in the initiation and, in particular, to the propagation of fatigue cracks, TEM observations were supplemented by small-angle neutron scattering and positron annihilation measurements which gave additional information about the point defect agglomerations.

Ion polishing of copper: some observations

The change in absorptivity at 10.6 microm of copper samples, at various stages of polishing including ion polishing, is reported. The ion polishing apparatus is also described; it employs a low energy Xe ion beam incident at a glancing angle to maximize the removal rate while minimizing ion penetration and damage. The sample to be polished is rotated and the beam scanned across the surface to produce uniform removal of material. Starting with single crystal copper that had been mechanically polished and by using combinations of ion polishing and vacuum annealing, the absorptivity, determined by calorimetry, was reduced from 0.92% to 0.76%. Although optical figure and scatter were not monitored, SEM pictures show that the surface features become smoother with ion polishing. A similar experiment was performed on a single crystal copper sample that had been electropolished, and the combination of ion polishing and annealing lowered the absorptivity from 0.97% to 0.89%.

Effect of hydrostatic pressure on torsional stress-strain curves of single-crystal copper

The torsional stress-strain curves for single-crystal copper samples were determined at hydrostatic pressures from 1 bar to 15 kbar. The pressure derivative of the yield stress was found to be 3.8×10−3. At strains of about six, the pressure derivative of the flow stress increased to 1.78×10−2. Stress-strain curves for the various pressures are provided. A simple model of dislocation cell structure is presented in an attempt to explain the experimental results.

Further investigation of noncollinear surface-wave interactions

Two noncollinear surface waves of 5 and 7 MHz have been excited on the surface of single-crystal copper samples in such directions that the waves could interact via the nonlinearities of the medium to produce a third surface wave at the sum frequency of 12 MHz. Using optical techniques, the three waves involved have been detected on two crystal surfaces, the (001) and (111) planes of copper, and the amplitude of each of the waves has been measured.

Detection of Surface-Wave Three-Phonon Interaction

The resultant surface phonon generated by the interaction of two noncollinear surface phonons has been detected on the (111) face of a single-crystal copper sample. Detection was accomplished by optical probing of the two primary surface waves and the resultant phonons generated in the interaction.

MEASUREMENT OF ULTRASONIC SURFACE WAVE VELOCITY AND ABSORPTIVITY ON SINGLE-CRYSTAL COPPER

Light-ultrasound interaction techniques were employed to measure the velocity and absorptivity of surface waves in various directions on the (100) face of single-crystal copper sample. Schlieren images of beam displacement at the liquid-sample interface were used to determine crystal orientation.