Schottky Defects
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 45
4-9-2016
1858
Schottky Defects
N atoms from a perfect crystal of total number of atoms 
are displaced to the surface of the crystal. Let ε0 be the energy needed to displace one atom from the bulk of the crystal to the surface. Find the equilibrium number of defects N at low temperatures τ << ε0, assuming 
SOLUTION
When N atoms are displaced to the surface, they leave the same number of vacancies. Now there are N vacancies and
atoms in 
lattice points. The entropy as a function of N is
(1)
where we have used Stirling’s formula
The free energy may be written
(2)
The minimum of the free energy can be found to be
(3)
or
(4)
Since 
we have
(5)
which is what one would expect.
الاكثر قراءة في مواضيع اخرى
اخر الاخبار
اخبار العتبة العباسية المقدسة
