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)