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Research Papers

# High-Resolution Methods for Characterizing Mesoscale Dislocation Structures

[+] Author and Article Information
C. D. Landon, B. L. Adams, J. Kacher

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602

J. Eng. Mater. Technol 130(2), 021004 (Mar 12, 2008) (5 pages) doi:10.1115/1.2840961 History: Received July 18, 2007; Revised November 28, 2007; Published March 12, 2008

## Abstract

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.

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## Figures

Figure 1

Assuming Burger’s vector of 0.25nm, the data points represent the total dislocation density estimate in a region of the well-annealed nickel specimen. As the size of the measurement voxel decreases, more SSDs are resolved into GNDs and the estimate of total dislocation density should become more accurate, but there is a competing effect in the resolution limits. Since the step size is in the denominator of the resolution limit (calculated from 0.005deg over the step size), finer spatial resolution negatively impacts dislocation density resolution. Nevertheless, even at the smallest step size of 40×10−9m, the measured density is above the resolution limit and can be expected to be a measurement of a real density increase instead of just increased error.

Figure 2

The density of type α32 fictitious edge dislocations is shown for a well-annealed nickel sample assuming typical Burger’s vector length. The brightest regions represent larger dislocation densities with positive net Burger’s vectors and the darker regions (values less than zero) indicate larger dislocation densities with negative net Burger’s vectors.

Figure 3

A correlation from Eq. 8, α3232, is shown for the well-annealed nickel sample. The correlation is defined to identify the distribution of pairs of dislocation densities α32 and α32. The bright value in the center is the average α32 dislocation density at a point in the sample. Values less than zero indicate the presence of opposite directions of the same type of dislocation, and values greater than zero indicate the same direction. The bands show the position relative to each other of pairs of opposite and same sense dislocations. The regular spacing of pairs of dislocations tends to indicate dislocation networks and cell walls.

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