# Quick Questions to

## 2.1 Intrinsic Point Defects and Equilibrium

### 2.1.2 Frenkel Defects; 2.1.3 Schottky Defects; 2.1.4 Mixed Point Defects

Here are some quick questions:
The answers are sometimes (and possibly only indirectly) contained in the links.

2.1.2 Frenkel Defects
Why do we need "Frenkel" and "Schottky" defects besides vacancies, self-interstitials and their agglomerates?
Draw a schematic picture of a crystal with "Frenkel" and "Schottky" defects. What kind of "conservation laws" do you have to consider, and why does that lead to a fundamental difference between the two defect kinds?
What kind of charge would "the" vacancy carry in a NaCl crystal? (Consider only the realistic case).
Give some crystals where Frenkel disorder prevails.
Give an (approximate) equation for the concentration of Frenkel defects an discuss the important terms

2.1.3 Schottky Defects and 2.1.4. Mixed Defects
What, quite generally, is the Debye length?
How does the Debye length come into consideration when discussion Schottky defects (and Frenkel defects)?
If the formation enthalpies of two defect kinds differs by roughly ...???...eV, one defect type will be dominating and the other one can be neglected.
Why do we usually consider either Schottky or Frenkel defects in ionic crystals but not mixed defects? For the answer check this exercise.
Can you predict for a given ionic crystal which kind of defect type (Schottky or Frenkel) will be prevalent?
Discuss the details in the following set of equations:
NaNa + Vi  Û  Nai + VNa

ß
[NaNa] · [Vi]
[Nai] · [VNa]
=  const  =  exp   GReaction
kT

ß
cV(C) · ci(C)  =  N'
N
· exp – HFP
kT

ß
cV(C)  = ci(C)
Derive in an equivalent way the final relation for Schottky defects:
cV(A) · cV(C)  = exp – HS
kT

cV(A)  = cV(C)

2.2.2 Local and Global Equilibrium

2.1.2 Frenkel Defects

2.1.4 Mixed Point defects

2.1.3 Schottky-Defects

Exercise 2.1-6: Enthalpy difference for the limiting cases of Schottky or Frenkel Defects

Solution to Exercise 2.1-6

Point Defects in Ionic Crystals

Debye Length

© H. Föll (Defects - Script)