A Peierls perspective on mechanisms of atomicfriction

Stick-slip behavior observed from nanoscale asperity friction experiments are often modeled by the one-degree-of-freedom Tomlinson model, which is unable to explain the effects of lattice structure and interface defects, or by molecular simulations which suffer temporal limitations in modeling the velocity- and temperature-dependent frictional behavior. A Peierls-type model developed in this work views the atomic frictional process as the initiation and gliding passage of dislocations with diffused cores on the interface. As a consequence of loss-of-ellipticity instability, the occurrence of stick-slip behavior relies on the interaction among interface slip field, contact stress fields, and existing defects. The friction stress for commensurate interface under large contact area can be approximated from the Rice model of screw-dislocation nucleation from a planar crack tip. The spatially inhomogeneous nature of rate-limiting processes and the coupling effects between contact size and interface incommensurability are successfully determined, which cannot otherwise be tackled in the Tomlinsonmodel.     

Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening

The study of micro-plastic behavior of rough surface contacts is the critical link towards a fundamental understanding of contact, friction, adhesion, and surface failures at small length scales. In the companion paper (Yu, H.H., Shrotriya, P., Gao, Y.F., Kim, K.-S., 2007. Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation. J. Mech. Phys. Solids 55, 489–516), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micro-mechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice–Thomson criterion is used to model dislocation nucleation. Dislocations nucleated from the surface step are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pileup will exert a strong back stress to prevent further dislocation nucleation and thus lead to the contact hardening behavior, the degree of which depends on the slip-plane orientation. Particularly, we find that dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named “latent softening”. A mechanistic explanation shows that the latent softening is closely related to the stress-concentration mode mixity at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes, which influences the subsequent dislocation nucleation. Our calculations show that the dislocation pileup on one slip plane can even cause the spontaneous dislocation nucleation on the other slip plane without further increase of the contact load. Furthermore, it is found that rough surface contacts at small length scale can lead to the dislocation segregation and the formation of a surface tensile sub-layer. The discrete-dislocation model presented here and in the companion paper provides novel insights in bridging the atomistic simulations and continuum plastic flow analysis of surface asperity contact.     

Statistical mechanics of a system of interacting dislocations: a self-consistent field approach

Summary The equilibrium statistical mechanics of a population ofN massless dislocations is tackled in the frame of the multivariate Fokker-Planck equation associated with the corresponding system ofN nonlinear stochastic differential equations of motion. First the diffusion coefficient is found as a function of the dislocation drag parameter and absolute temperature. Then the initial many-body problem is reduced to an effective single-particle problem by means of a mean (self-consistent) field strategy leading to a nonlinear singular integral equation for the density and the “thermodynamic potential” at temperatureT. This last equation is solved numberically and the results are shown with comparison to exact continuum deterministic distributions.

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Riassunto Il lavoro affronta la meccanica statistica di equilibrio di un sistema diN dislocazioni interagenti in un campo esterno. Le dislocazioni sono trattate come singolarità prive di massa il cui moto è governato daN equazioni differenziali stocastiche di cui si studia l'associata equazione di Fokker-Planck multivariata. Si calcola anzitutto il coefficiente di diffusione in funzione del coefficiente di dissipazione e della temperatura. Quindi il problema a molti corpi viene ridotto ad un problema efficace di particella singola per mezzo di una tecnica di campo medio autoconsistente che si esprime in un'equazione integrale singolare non lineare per la densità delle dislocazioni e l'appropriato potenziale termodinamico alla temperaturaT. Quest'ultima equazione è risolta numericamente mediante un metodo di approssimazioni successive e i risultati sono illustrati confrontandoli con quelli ottenibili da una teoria esatta ma deterministica ed affetta dall'approssimazione del continuo.

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Резюме Рассматривается равновесная статистическая механика совокупностиN безмассовых дислокаций в рамках уравнения фоккера-Планка связанного с соответствующей системойN нелинейных стохастических дифференциальных уравнений движения. Сначала получается коэффициент диффузии, как функция параметра, характеризующего сопротивление при движении дислокаций, и абсолютной температуры. Эатем исходная проблема многих тел сводится к эффективной проблеме одной частицы, используя подход самосогласованного, поля, который приводит к нелинейному сингулярному интегральному уравнению для плотности и ?термодинамического потенциала? при температуреT. Полученное уравнение решается численно. Результаты сравниваются с точными с точными непрерывными детерминистическими распределениями.

     

SiGe/Si异质结缺陷的光致发光研究

本文用光致发光(PL)光谱对Si0.87Ge0.13/Si异质结的缺陷进行了研究。对PL光谱中与SiGe外延层应变驰豫产生的失配位错相关的D-Band进行了分析,发现应变驰豫同时在SiGe层和Si衬底中诱生了位错。由于在PL光谱中观察到了D1而没有观察到D2,因此D1,D2很可能并不对应于相同的位错。通过进一步的分析,我们推测引起SiGe/Si异质结的PL光谱中D-Band的位错的微观结构很可能和Si-Si相关。     

Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys

In this paper a crystal plasticity-based crack nucleation model is developed for polycrystalline microstructures undergoing cyclic dwell loading. The fatigue crack nucleation model is developed for dual-phase titanium alloys admitting room temperature creep phenomenon. It is a non-local model that accounts for the cumulative effect of slip on multiple slip systems, and involves evolving mixed-mode stresses in the grain along with dislocation pileups in contiguous grains. Rate dependent, highly anisotropic behavior causes significant localized stress concentration that increases with loading cycles. The crystal plasticity finite element (CPFE) model uses rate and size-dependent anisotropic elasto-crystal plasticity constitutive model to account for these effects. Stress rise in the hard grain is a consequence of time-dependent load shedding in adjacent soft grains, and is the main cause of crack nucleation in the polycrystalline titanium microstructure. CPFE simulation results are post-processed to provide inputs to the crack nucleation model. The nucleation model is calibrated and satisfactorily validated using data available from acoustic microscopy experiments for monitoring crack evolution in dwell fatigue experiments.     

Investigations of pipe-diffusion-based dislocation climb by discrete dislocation dynamics

A new numerical dislocation climb model based on incorporating the pipe diffusion theory (PDT) of vacancies with 3D discrete dislocation dynamics (DDD) is developed. In this model we hold that the climb rate of dislocations is determined by the gradient of the vacancy concentration on the segment, but not by the mechanical climb force as traditionally believed. The nodal forces on discrete dislocation segments in DDD simulation are transferred to PDT to calculate the vacancy concentration gradient. This transfer establishes a bridge connecting the DDD and PDT. The model is highly efficient and accurate. As verifications, two typical climb-involved examples are predicted, e.g. the activation of a Bardeen-Herring source as well as the shrinkage and annihilation of prismatic loops. Finally, the model is applied to study the breakup process of an infinite edge dislocation dipole into prismatic loops. This coupling methodology provides us a useful tool to intensively study the evolution of dislocation microstructures at high temperatures.     

An atomistically-informed dislocation dynamics model for the plastic anisotropy and tension-compression asymmetry of BCC metals

Atomistic simulations have shown that a screw dislocation in body-centered cubic (BCC) metals has a complex non-planar atomic core structure. The configuration of this core controls their motion and is affected not only by the usual resolved shear stress on the dislocation, but also by non-driving stress components. Consequences of the latter are referred to as non-Schmid effects. These atomic and micro-scale effects are the reason slip characteristics in deforming single and polycrystalline BCC metals are extremely sensitive to the direction and sense of the applied load. In this paper, we develop a three-dimensional discrete dislocation dynamics (DD) simulation model to understand the relationship between individual dislocation glide behavior and macro-scale plastic slip behavior in single crystal BCC Ta. For the first time, it is shown that non-Schmid effects on screw dislocations of both {110} and {112} slip systems must be implemented into the DD models in order to predict the strong plastic anisotropy and tension-compression asymmetry experimentally observed in the stress-strain curves of single crystal Ta. Incorporation of fundamental atomistic information is critical for developing a physics-based, predictive meso-scale DD simulation tool that can connect length/time scales and investigate the underlying mechanisms governing the deformation of BCC metals.     

Spin-polarized scanning tunneling spectroscopy of dislocation lines in Fe films on W(1 1 0)

We have studied the spin-resolved electronic properties of dislocation lines on the Fe double-layer (DL) on W(1 1 0) by spin-polarized scanning tunneling spectroscopy. The data reveal that the dislocation lines are ferromagnetically ordered with the magnetic contrast exhibiting a pronounced bias-dependence. By comparing tunneling spectra which were measured on the pseudomorphic DL and at different lateral separation from the dislocation line, we find a pronounced shift of a peak which originally appears at positive sample bias towards the Fermi level _EF$E_{\mathrm{F}}$. In contrast, the binding energy of a peak just below _EF$E_{\mathrm{F}}$ remains constant but increases in intensity. This causes a pronounced modification of the bias voltage-dependent magnetic asymmetry.     

Chemical etching to dissolve dislocation cores in multicrystalline silicon

Multicrystalline silicon wafers are used for approximately half of all solar cells produced at present. These wafers typically have dislocation densities of up to ∼10⁶ cm⁻². Dislocations and associated impurities act as strong recombination centres for electron–hole pairs and are one of the major limiting factors in multicrystalline silicon substrate performance. In this work we have explored the possibility of using chemical methods to etch out the cores of dislocations from mc-Si wafers. We aim to maximise the aspect ratio of the depth of the etched structure to its diameter. We first investigate the Secco etch (1K₂Cr₂O₇ (0.15 M): 2HF (49%)) as a function of time and temperature. This etch removes material from dislocation cores much faster than grain boundaries or the bulk, and produces tubular holes at dislocations. Aspect ratios of up to ∼7:1 are achieved for ∼15 μm deep tubes. The aspect ratio decreases with tube depth and for ∼40 μm deep tubes is just ∼2:1, which is not suitable for use in bulk multicrystalline silicon photovoltaics. We have also investigated a range of etches based on weaker oxidising agents. An etch comprising 1I₂ (0.01 M): 2HF (49%) attacked dislocation cores, but its etching behaviour was extremely slow (<0.1 μm/h) and the pits produced had a low aspect ratio (<2:1).     

二维声子晶体异质位错结的界面传导模研究

以二维水银／四氯化碳体系正方格子声子晶体为研究对象，采用平面波法结合超元胞的方法研究了声子晶体异质位错结的能带结构及三种形式的位错对带隙内传导模影响。结果表明，对于原型异质结，在带隙中不会出现界面传导模；横、纵向及横纵向同时作用的位错效应，在界面处形成传导模，可以使处于禁带频率范围内的声波沿位错通道进行传播，从而形成声波导。