High-Resolution Methods for Characterizing Mesoscale Dislocation Structures

It has become apparent through experimentation at the micro- and nanolevels that the crystalline defects known as dislocations have significant effects on a material’s properties. Accordingly, a complete material state description must include the characterization of the dislocated state. However, this characterization presents a twofold problem: resolution and representation. In general, high-resolution microscopy techniques are only useful for considering a few dislocations at a time, but automated high-speed methods are only capable of resolving dislocation densities well above the average density in a typical annealed metal. The second challenge is developing a method of representation for the dislocated state. Unlike most state quantities, dislocation lengths are not conserved and complete representation would require tracking of position, momentum, and interactions, as well as the creation and annihilation of dislocations. Such a scheme becomes unwieldy when considering the large numbers of dislocations involved in common crystal plasticity. In 1970, Kröner (“Initial Studies of a Plasticity Theory Based Upon Statistical Mechanics,” Inelastic Behaviors of Solids (Materials Sciences and Engineering), M. F. Kanninen et al., eds., McGraw-Hill, New York, pp. 137–147), a pioneer in the continuum representation of dislocations, proposed a statistical method using $n$-point correlations to classify the dislocated state in a compact form. In addition to providing a convenient form, the correlations naturally identify dipoles, multipoles, and other higher order structures, such as cells, networks, and braids. As formulated, Kröner’s method would require high-resolution microscopy techniques, which limits its utility for experimental measurements. The current work presents a modification to Kröner’s method that would allow it to be used within the currently available resolution limits of bulk microscopy. Furthermore, in this work, newly developed microscopy techniques are employed to refine those resolution limits to more significant levels. The high-resolution bulk dislocation characterization is applied to a well-annealed nickel specimen and the results including visualizations of mesoscale structures are presented.