# Exercise 2.1-8

# 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)

With frame

2.2.2 Local and Global Equilibrium

2.1.2 Frenkel Defects

2.1.4 Mixed Point defects

2.1.3 Schottky-Defects

Solution to Exercise 1.1

Point Defects in Ionic Crystals

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

Debye Length

Solution to Exercise 2.1-6

© H. Föll (Defects - Script)