Aluminium has shear modulus and lattice parameter (face-centred cubic)

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Dislocations and the onset of plastic flow

Problem

Aluminium has shear modulus

G = 26\,\mathrm{GPa}

and lattice parameter

a = 0.405\,\mathrm{nm}

(face-centred cubic), so its Burgers vector is

b = a/\sqrt2

. Take the outer cut-off of a screw dislocation's stress field as the typical spacing between dislocations,

R = 1\,\mathrm{\mu m}

, and the inner (core) cut-off as

r_0 = b

. ((a)) Find the line energy per unit length,

U/L = (Gb^2/4\pi)\ln(R/r_0)

. ((b)) Convert this to the energy stored per atomic length

b

of the line, in electronvolts, and compare it with

k_BT

at room temperature (

k_BT = 0.026\,\mathrm{eV}

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