Aluminium is fcc with conventional cubic lattice constant and shear modulus

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

Solid State Physics, Ch Point defects, dislocations and alloys

Problem

Aluminium is fcc with conventional cubic lattice constant

a = 4.05\,\text{\AA}

and shear modulus

G = 26\,\mathrm{GPa}

. Its shortest dislocation has Burgers vector length

b = a/\sqrt2

. ((a)) Using the estimate that the line energy per unit length is of order

\tfrac12 Gb^2

, calculate the energy stored in one atomic length

b

of dislocation line, in eV. ((b)) Two straight parallel dislocations of the same sign,

100\,\mathrm{nm}

apart, interact through a force per unit length

F/L = Gb^2/(2\pi r)

, where

r

is their separation. Calculate

F/L

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