### 2.2.3 Essentials to Chapter 2.2: Extrinsic Point Defects and Point Defect Agglomerates

| Besides intrinsic point defects, crystals always contain extrinsic point defects - impurity atoms on substitutional or interstitial sites. |  |
|  | The concentration cF of extrinsic point defects is pretty much constant - it cannot be in equilibrium. What is going on in a macroscopic way is given by the phase diagram of crystal plus impurity atoms |
|  | If we discuss extrinsic point defects (in contrast to alloys), we discuss small cF values. Nevertheless, cF might be much larger than cC, the equilibrium concentration of vacancies; especially at low temperatures. |
| The concentration cC of impurity atom - vacancy complexes is easy to calculate, the decisive parameters are the concentrations of the partners and their binding energy HC |  |
cC | = | z · cF · cV(T) 1 – z · cF | · exp | D SC k | · exp | HC kT
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|  | The situation is quite similar to the case of divacancies or multi-vacancies, except that cF is constant. The concentration of extrinsic-intrinsic complexes in equilibrium decreases with temperature |
| With extrinsic point defects the crystal can no longer be in global equilibrium; what we are looking now is local equilibrium - the minimum of the free enthalpy obtainable under some fixed circumstances |  |
| Fixed circumstances may include that the concentration of the intrinsic point defects is not in (global) equilibrium. There are many reasons for that: |
|  | Changing the equilibrium concentration of intrinsic point defects needs two ingredients: sources and sinks for intrinsic point defects - external or internal surfaces (= grain boundaries), dislocations - other defects. Sufficient mobility of the point defects to get away from or to the sources and sinks, respectively. |  |
| The latter condition always fails at low temperatures, as a result the formation of point defect clusters is favored. |  |
cnV | = (c1V)n · | z 2 | · exp | D SnV k | · exp | BnV kT
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cnV(T) increases with exp{BnV / kT} as soon as cV stays constant.
|  | The decisive quantity is the total diffusion length L of a point defect during the thermal history of its crystal - how far can it "go" before it is frozen into immobility |
|  | If L > average distance to a sink, we will find mostly equilibrium conditions; if L < average distance to a sink (Si case!), we will have to expect point defects complexes of n point defects at a concentration cnV. |
|  | The upper limit for n is the concentration of point defects contained in the volume L3. |

© H. Föll (Defects - Script)