In body-centred cubic iron ( )

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

In body-centred cubic iron (a=2.866 A˚a=2.866\,\mathrm{\AA}), diffraction-contrast imaging of an isolated dislocation shows it invisible under both G1=2πa(1,1ˉ,0)\mathbf G_1=\frac{2\pi}{a}(1,\bar1,0) and G2=2πa(0,1,1ˉ)\mathbf G_2=\frac{2\pi}{a}(0,1,\bar1), and visible under G3=2πa(2,0,0)\mathbf G_3=\frac{2\pi}{a}(2,0,0). An independent slip-trace measurement gives the magnitude of the Burgers vector as ∣b∣=2.48 A˚|\mathbf b|=2.48\,\mathrm{\AA}. ((a)) Using the invisibility criterion G⋅b=0\mathbf G\cdot\mathbf b=0, and neglecting any faint residual contrast, find the direction of b\mathbf b consistent with both G1\mathbf G_1 and G2\mathbf G_2. ((b)) Combine this direction with the measured magnitude to write b\mathbf b as a2[uvw]\frac{a}{2}[uvw] and give its Cartesian components in A˚\mathrm{\AA}. ((c)) Check that this b\mathbf b is consistent with the observation under G3\mathbf G_3.

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