Small-beam diffraction measurements such as micro-small angle x-ray scattering (μSAXS – [ 1]) and electron nanodiffraction (END – [ 2]) are a promising methodology to probe local structure in glasses ranging from colloidal assemblies made from microparticles to metallic glasses composed of atoms. Of particular interest are spatially-resolved measurements of local centrosymmetry and strain (dilation/contraction and anisotropy) in nearest-neighbour configurations to examine local, particle-level, structural transformations during deformation [ 1].
Crystals possess translational long-range order and deform via the creation and propagation of well-defined topological defects that are discontinuities or tears in the order. These dislocations can be readily identified by a non-zero Burgers vector, defined as b i ≡ ∮ du i where du i is a displacement and i = x, y, z are Cartesian coordinates. A non-zero Burgers vector corresponds to a region where the strain is incompatible with a single-valued displacement field [ 3]. In a perfect crystal, the reference configuration can be assumed and the Burgers vector deduced from the deformed configuration alone; it is the net number of extra rows or columns as the Burgers circuit is traversed ( Fig. 1 A).
Defects and Burgers vectors can also be defined in a continuous sense appropriate for amorphous phases [ 3, 4, 5]. In Fig. 1 B, we show a slice of a simulated model polymer glass undergoing simple shear (1 scaled unit = 1 polyhedral radius) [ 5]. Some of the particle displacements are affine (with the same magnitude and direction as the applied strain) and some are non-affine. Each local configuration undergoes a unique distortion as shown. We interpolate the non-affine displacements and zoom in to a region that seems to have an isolated plastic event 1-2 polyhedra in diameter ( Fig. 1 C).
Fig. 1
(A) Edge dislocation in a crystal where the Burgers vector can be measured from the deformed configuration alone. (B) Non-affine displacements in a simulated glass showing distortions in local polyhedra (green – before shear strain and pink – after shear strain). (C) Interpolated displacements from an isolated plastic event and (D) calculated Burgers vector showing rich, fine-scale structure. (E) Actual particle displacements overlaid on the Burgers vector direction showing that the centre of the event is a large out-of-plane displacement and that the Burgers vector direction changes every polyhedral radius.
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