# Exercise 2.2-2

# Quick Questions to

## 2.2 Extrinsic Point Defects and Point Defect Agglomerates

### 2.2.1 Impurity Atoms and Point Defects; 2.2.2 Local and Global Equilibrium

| Here are some quick questions:
|  | The answers are sometimes (and possibly only indirectly) contained in the links.
| Let's look at combined defects - double vacancies, impurity atom - vacancy complex (and so on):
|  | Derive from the mass action law and write down the essential equations for the concentrations of Divacancies (c2V) Clusters with n vacancies (cnV). Impurity atom - vacancy complex (cC; cF = impurity atom conc.). Forget pre-exponential factors etc., if you don't remember, or make simple assumptions.
| Now let's do something important. You really should do this, it will teach you a lot!
|  | Make sketches of various concentrations in an Arrhenius plot. Try to produce intellegent and neat sketches with parameters as follows: The concentration of single vacancies at Tm is roughly cV » 10–4 Positive binding energies in all case; about 10 % - 20 % of the vacancy formation enthalpy HF(V). Always include the Arrhenius plot for the single vacany as reference.
|  | First, produce one Arrhenius diagram showing single and double vacancies.
|  | Second, produce an Arrhenius diagram for single vacancies, impurities, and impurity atom - vacancy complex
|  | Third, produce one Arrhenius diagram showing single and double vacancies but assume that the single vacancy concentration cannot decline anymore at some lower temperature.
|  | Discuss you curves (in particular the 2nd and 3rd), take into account how the temperature changes in "theory" and in "real life"
| Now a few really quick ones:
|  | If all vacancies present at thernal equilibrium near the melting point at a concentration of cV » 10–4 end up in vacancy clusters with an average of 100 vacancies, what is the concentration of these clusters? What is their average cluster distance compared to the average vacancy distance (assume a typical lattice constant around 0.3. nm)?
|  | Given a equilbrium vacancy concentration of cV, an (substitutional) impurity concentration cF, and some binding enthalpy and entropy HC and SC, the concentration cC of vacancy - (substitutional) impurity complexes should be proportional to:........?
|  | What would you expect for the case of no binding enthalpy and entropy?

With frame

2.2.1 Extrinsic Point Defects and Agglomerates

Solution to Exercise 1.1

Solution to Exercise 2.2-1

© H. Föll (Defects - Script)