You are given specimens of Al, one fully annealed with a dislocation density of

Question

You are given specimens of Al, one fully annealed with a dislocation density of about 107 cm/cm3
and the other a cold worked sample with a dislocation density of about 1012 cm/cm3. For Al the shear
elastic modulus GM = 28.4 GPa and the lattice constant a = 0.405 nm. Calculate in both cases the
following:
(a) The average distance between adjacent dislocations in both samples; and
(b) The expected driving force (energy in Joules per unit volume) for recrystallisation when
annealing the cold worked material. Assume that the elastic energy locked up in a dislocation
equals E=GMb2& per unit line length of the dislocation, where b is the Burger’s vector and
GM is the shear modulus.

Explanation / Answer

So the ? (3/107) = 0.167 cm

and average distance between adjacent dislocations for other cold worked sample = ? (3/1012) = 0.054 cm

Burger vector, b = a/(?2) = 0.405/(?2) = 0.286 nm = 0.286*10-9 m

So, driving force = ½* GM* b2* ? = ½* 28.4*109 * (0.286*10-9 )2* 10700

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