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 · ∑ i ( hωi 4π · kT  +  ln ( 1 –  exp – hωi 2π · kT ) )
		Second formula:
		S  =  k · ∑ i ( – ln ( 1  –  exp  hωi 2π · kT )  +     hωi 2π · kT       exp  ( hωi 2π · kT   –  1 )    )
	Now, using the approximations referred to, derive the Final formula
		SF  = k · ∑ i   ln  ωi ω'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

To index

2.1.1 Simple Vacancies and Interstitials

Solution to Exercise 1.3

© H. Föll