By Richard J. Borg and G. J. Dienes (Auth.)
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Extra resources for An Introduction to Solid State Diffusion
V)= V A ' . 61). Problems 1. W h a t are the contributions to the vacancy formation enthalpy in elemental crystals? What factor is responsible for reducing this en thalpy? Discuss. 2. 0 k ν Calculate the vacancy concentration at 161° Κ (triple point) and at 80°K. 3. The experimental vacancy parameters for gold are: Δ / / ° = 21620 c a l / m o l e AS = 1 Κ ΔΕ Β = 3450 c a l / m o l e = divacancy binding energy Calculate the monovacancy, u and divacancy, v , concentrations and the v /v ratios at the melting point, 1063°C, and at 1/2 T .
50) W e may in the case of an ideal solution identify kT In X /zX X with AF , the standard free energy of formation. 49) as follows Iv f v 0 r v AF ° = Δ Ε ° - Δ £ ° - Δ £ ° - Τ(ΔΞΪ f v 7 - Δ £ / - AS ) V υ V 4- kT In ζ. 51) We can put these results into a useful form by using the equilibrium 48 II Point Defects in Elemental Crystalline Substances constant for the reaction ζI + υ ^ Iv. Hence, (Iv) -jim- - K <2 52) The inclusion of the multiplicative term ζ is necessary, as in the case of divacancies, because the concentration of the reactants is actually the ζ nearest neighbor positions to both the uncomplexed ( / ) and (v).
As expected, the intersti tial atom is surrounded by a dilatational strain field, and the vacancy is characterized by an inward relaxation which provides a virtual compres sion. 1 *J y*- % Y J y * -y* ) \ γ* Simple point defects in mono-elemental substances, shown schematically. 2 Interstitial atoms in bcc structures, two atoms share the interstice with the " d u m b b e l l " axis along specific crystallographic directions. l). Typically, the recombination volume has linear dimensions of two to ten nearest neighbor distances.