Unformatted text preview: +N’lnN’ N’ (N’n)ln(N’n) +(N’n) nln n+n} ∂∆ G/ ∂ n = g kT{ln(Nn) +1 1ln n 1+1 ln(N’n) +1 1 ln n 1 +1} = g kTln{(Nn)(N’n)/n 2 } =0 (Nn)(N’n)/n 2 = exp (g/kT) Since N, N’ >>n NN’/n 2 = exp (g/kT) n/ √ NN’ = exp (g/2kT) 3. Consider TiO 1.95 . Or what fraction of oxygen is vacant? What fraction of titanium is in Ti 3+ state? Oxygen vacancy 0.05/2 = 0.025 Assume x fraction of Ti is Ti 3+ , 1x fraction is Ti 4+ . 3x + 4(1x) = 2 times1.95 4 x = 3.90 x= 0.1...
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 Spring '08
 Tomozawa
 Ratio, Al2O3, oxygen vacancy

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