


Now we look at the limiting cases of pure Schottky
or pure Frenkel disorder. 


For pure Frenkel disorder we must have
h_{FP} << h_{S}, and
c_{V}(A) = 0. 


For pure Schottky disorder we must have
h_{FP} >> h_{S}, and
c_{i}(C) = 0. 

For the first case  pure Frenkel
disorder  just look at the expression 


æ
ç
è 
1 + 
N
N' 
· exp 
h_{S} – h_{FP}
kT 
ö
÷
ø 
1/2 




For h_{S} >>
h_{FP}, the exponential in this case is positive which means



N
N' 
· exp 
h_{S} – h_{FP}
kT 
>> 1 




So you may neglect the 1 in the above expression and
replace the whole square root by 


N
N' 
· exp 
h_{S} – h_{FP}
2kT 




This gives for c_{i}(C) 


c_{i}(C) 
= 
N
N' 
· 
æ
ç
è 
exp 
h_{S} – 2h_{FP}
kT 
ö
÷
ø 
1/2 
æ
ç
è 
exp 
h_{S} – h_{FP}
kT 
ö
÷
ø 
1/2 

= 
N
N' 
· exp – 
h_{FP}
kT 




This is the result as as it should be. 

With this we immediately obtain 


c_{V}(C) 
= 
N
N' 
· exp – 
h_{FP}
2kT 





c_{V}(A) 
= 
0 




This is so because 


N
N' 
· exp 
h_{S} – h_{FP}
kT_{ } 
>> 
1 



Contrariwise, if
h_{S} << h_{FP}, 1 + N/N'
· exp[(h_{S} – h_{FP})/kT]
» 1 obtains. 


Because h_{S} –
2h_{FP} is a large negative number we get 


c_{i}(C) 
= 
N
N' 
· exp 
h_{S} – 2h_{FP}
2kT_{ } 
» 
0 




The expressions for c_{V}(C) and
c_{V}(A) immediately reduce to the proper equation 


c_{V}(C) 
= c_{V}(A) = exp – 
h_{S}
2kT_{ } 




