22.6: Dislocation in 3D
- Page ID
- 32684
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In three dimensions, the nature of a dislocation as a line defect becomes apparent. The dislocation line runs along the core of the dislocation, where the distortion with respect to the perfect lattice is greatest.
There are two types of three-dimensional dislocation. An edge dislocation has its Burgers vector perpendicular to the dislocation line. Edge dislocations are easiest to visualize as an extra half-plane of atoms. A screw dislocation is more complex - the Burgers vector is parallel to the dislocation line. Mixed dislocations also exist, where the Burgers vector is at some acute angle to the dislocation line. In a 2D model such as the bubble raft, only edge dislocations can exist.
https://www.doitpoms.ac.uk/tlplib/di...islocation.mp4
Virtual reality model of an edge dislocation
https://www.doitpoms.ac.uk/tlplib/di...islocation.mp4
Virtual reality model of a screw dislocation
When a dislocation moves under an applied shear stress:
- individual atoms move in directions parallel to the Burgers vector;
- the dislocation moves in a direction perpendicular to the dislocation line.
An edge dislocation therefore moves in the direction of the Burgers vector, whereas a screw dislocation moves in a direction perpendicular to the Burgers vector. The screw dislocation 'unzips' the lattice as it moves through it, creating a 'screw' or helical arrangement of atoms around the core.
The ease of dislocation glide is partly determined by the degree of distortion (with respect to the perfect lattice) around the dislocation core. When the distortion is spread over a large area, the dislocation is easy to move. Such dislocations are known as wide dislocations, and exist in ductile metals.
Width of a dislocation
The width of a dislocation gives a measure of the degree of disruption a dislocation creates with respect to the perfect lattice. If the dislocation is regarded as the transition between slipped and unslipped areas of a slip plane, then the width of the dislocation is a measure of the sharpness of the transition. Formally, the edge dislocation width w is defined as the distance over which the disregsitry is greater than one quarter of the magnitude of the Burgers vector, b. The disregistry is the magnitude of the displacement of the atoms from their perfect crystal positions.
Diagram showing width of a wide dislocation
At the centre of a perfect edge dislocation, the disregistry is always b/2.
When w is several atomic spacings in dimension, the dislocation is wide; if w is of the order of one or two atomic spacings, it is narrow. Dislocation glide occurs most easily in wide dislocations - these are found in simple metals with simple close-packed crystal structures, hence these materials are ductile . Ceramics, for example, tend to have narrow dislocations, and are hard and brittle as a result. A mathematical treatment of this relationship can be seen here.
Diagram showing width of a narrow dislocation