Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

The development of neuromorphic computing architectures based on two terminal filamentary resistance switching devices is limited in part by the high degree of variability in resistance states and switching voltages. Because of the large role filament shape plays in directing thermal and electric fields around the filament (and thus switching parameters), unambiguous knowledge of filament morphology resulting from direct characterization of filament shape is essential to solve critical ongoing challenges of device switching variability. Here, we have utilized a conductive atomic force microscopy scalpel technique to simultaneously scribe through a polycrystalline dielectric layer in formed Cu/HfO2/p+Si electrochemical metallization cell devices. Filament tomograms reveal that when conductive filaments are formed at typical bias conditions (4 V, 100 μA), a variety of filament shapes result, which deviate from the inverse conical shape predicted by the phenomenological electrochemical model. Furthermore, the observation of an increasing spectrum of damage which scales with forming voltage (associated with compliance current overshoot), and which is uncorrelated with electric field or oxide microstructure, supports the role of thermal pulses in expanding filaments, leading to irreversible dielectric breakdown structures at the extreme. Overall, these findings suggest that the original conductive filament shape can be highly varied as a result of thermally driven expansion from joule heating during the forming step, which is not explicitly accounted for in the widely accepted electrochemical model.

A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. The implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.

For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity which are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. This includes, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kroner-Nye tensor, vector density approaches which treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories which examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.