Structure.questions_VIII_answer

Structure.questions_VIII_answer - +NlnN -N -(N-n)ln(N-n)...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MTLE-2100 Structure of Engineering Materials, Questions VIII--Answers 1. What is the ratio of V Al ’’’ and V O •• of the Schottky defect in Al 2 O 3 ? To maintain the charge neutrality, 2 Al vacancy, 2 V Al ’’’ and three oxygen vacancy, 3V O •• , will be created. 2. Take the derivative of the following equation with respect to n and set it to equal to zero to obtain n/ NN’ = exp (-g/2kT). G = H - T S = ng - T kln{N!/[(N-n)!n!]}{N’!/[(N’-n)!n!]} By using the Stirling’s approximation, G= ng -kT{NlnN-N -(N-n)ln(N-n) +(N-n) -nln n +n
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: +NlnN -N -(N-n)ln(N-n) +(N-n) -nln n+n} G/ n = g -kT{ln(N-n) +1 -1-ln n -1+1 ln(N-n) +1 -1 -ln n -1 +1} = g -kTln{(N-n)(N-n)/n 2 } =0 (N-n)(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+ , 1-x fraction is Ti 4+ . 3x + 4(1-x) = 2 times1.95 4 -x = 3.90 x= 0.1...
View Full Document

This note was uploaded on 04/29/2008 for the course MTLE 2100 taught by Professor Tomozawa during the Spring '08 term at Rensselaer Polytechnic Institute.

Ask a homework question - tutors are online