{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Structure.questions_VIII_answer

# Structure.questions_VIII_answer -...

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

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: +N’lnN’ -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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern