A dislocation in face-centred cubic nickel ( ) has Burgers vector

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Seeing atoms: electron and scanning-probe microscopy

Problem

A dislocation in face-centred cubic nickel (a=3.524 A˚a=3.524\,\mathrm{\AA}) has Burgers vector b=a2[101ˉ]\mathbf b=\frac{a}{2}[10\bar1]. Three separate two-beam images of the same dislocation are recorded using the reflections G1=2πa(1,1,1)\mathbf G_1=\frac{2\pi}{a}(1,1,1), G2=2πa(0,0,2)\mathbf G_2=\frac{2\pi}{a}(0,0,2) and G3=2πa(1,1,1ˉ)\mathbf G_3=\frac{2\pi}{a}(1,1,\bar1). ((a)) Compute G⋅b\mathbf G\cdot\mathbf b for each of the three reflections and state, for each, whether the dislocation is expected to be invisible or visible, neglecting any faint residual contrast. ((b)) A second dislocation in the same foil is invisible only under G1\mathbf G_1 among these three reflections. Explain why this single observation does not, by itself, prove that its Burgers vector is a2[101ˉ]\frac{a}{2}[10\bar1], and state what a further observation would need to show to make the identification secure.

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