Suppose the energy cost of an impurity atom (or a point defect like a vacancy) is e,and the energy...

Question

Suppose the energy cost of an impurity atom (or a point defect like a vacancy) is e,and the energy cost for n of them (on a lattice of N sites) is ne. In the dilute limitof the impurity concentration, c ? 0, show that the impurity concentration c(T) attemperature T, where c = n/N is
c(T) = exp(- e/kBT).

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Robert · Accepted Answer

Question: 
Suppose the energy cost of an impurity atom (or a point defect like a vacancy) is e,and the energy cost 
for n of them (on a lattice of N sites) is ne. In the dilute limit of the impurity concentration, c ? 0, show that 
the impurity concentration c(T) at temperature T, where c = n/N is 
c(T) = exp(- e/kBT). 
Solution 
At any temperature, some of the lattice points normally occupied by metal ions are vacant giving rise to 
vacancy defects. 
The number of vacancies created is dependent upon Temperature, total number of metals atoms, 
average energy required to create a vacancy 
Thus 
),,

Suppose the energy cost of an impurity atom (or a point defect like a vacancy) is e,and the energy cost for n of them (on a lattice of N sites) is ne. In the dilute limitof the impurity concentration,...

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