# 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

With frame

2.1.1 Simple Vacancies and Interstitials

Solution to Exercise 1.3

© H. Föll (Defects - Script)