Exercise 2.1-2

Do the Math for the Formation Entropy

Do the Math needed for going from the first to the second formula:
First formula:
F  =  – kT · lnZ  =  kT ·
å
i
æ
ç
è
hwi
4p · kT
 +  ln æ
è
1 –  exp – hwi
2p · kT
ö
ø
ö
÷
ø
  Second formula:
S  =  k ·
å
i
æ
ç
è
– ln æ
è
1  –  exp  hwi
2p · kT
ö
ø
 + 
   hwi
2p · kT
  

   exp  æ
è
hwi
2p · kT
  –  1 ö
ø
  
ö
÷
ø
Now, using the approximations referred to, derive the Final formula
SF  = k ·
å
i
  ln  wi
w'i
Discuss the quality of the approximations
(Hint: Use some real numbers or order of magnitudes for e.g. Debye temperatures, vacancy concentrations etc.)
   
 
 

Link to the Solution

 

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go to 2.1.1 Simple Vacancies and Interstitials

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© H. Föll (Defects - Script)