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Chapter VII Reactivity at Dislocation….
Where, r is radius of cavity, a is its height, ∆ the change in free energy
during dissolution (chemical potential), the molecular volume of the crystal,
and the specific surface free energy of an atom or molecule going from the
solid surface into solution. The chemical potential is shown as,
∆ = - kT ln(C/C0)
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(7.2)
Where, C0 is the saturation concentration of the material in an etching
medium and C is the actual concentration at the dislocation site. The localized
energy per unit length at a dislocation, Ed is shown as,
Ed = A ln(r1/r0)
Here, (for edge dislocations) and (for screw
dislocations)
E d =
(7.3)
(7.4)
Equations (7.3 and 7.4) represent the elastic strain energy and dislocation
core energy, respectively, where, G is the shear modulus, b is the modulus of
Burgers vector of dislocation and is the Poisson’s ratio, r0 is the radius of the
dislocation core beyond which elasticity theory holds, r is the outer radius of the
strained region of the crystal and is a constant equal to 1.5 and 2.0 for screw
and edge dislocations, respectively. In the Cabrera’s theory [18-19] the free
energy change involved in the formation of a dislocation etch pit, ∆G*, is given as,
*
G
1
2 . ( 1 )
(7.5)
n