Real Materials

Internal Boundaries

· Low angle boundaries can be formed by dislocation arrays.
· For a uniform edge dislocation spacing, d, the grain boundary angle, θ, is given by: tanθ = b/D
where b is the Burgers vector and D is the inter-dislocation spacing.
· For the tilt boundary shown, the dislocations are straight edge type. For a pure twist boundary, an array of screw dislocations is required.

From: Guy & Hren, "Elements of Physical Metallurgy," Addison Wesley (1974)

· The photomicrograph shows a tilt boundary in germanium where the dislocation locations have been revealed by chemical etching.