1. PHYS208 - Lecture Wednesday 3. February 2010
Topics:
Debye Model '
Comment: THIS IS a original /preliminary / after the lecture version
EnAttendentDebye.pdf … FORGOTTEN .... ! ! ! !
PHYS spring page 1

2. PHYS spring page 2

3. PHYS spring page 3

4. PHYS spring page 4

5. PHYS spring page 5

6. PHYS spring page 6

7. PHYS spring page 7

8. PHYS spring page 8

9. PHYS spring page 9

10. PHYS spring page 10

11. PHYS spring page 11

12. PHYS spring page 12

13. % Simple treatment of Debye model x=0.01:0.01:20;
y=(x.^4.*exp(x))./(exp(x)-1).^2;
figure(1);
plot(x,y)
% Showing the integrand of Debye function; %
% evaluate the integral by simple summation formula
Iy=y*0; % Fill Iy by zeros
for k=2:max(size(y));Iy(k)=Iy(k-1)+y(k);end
% perform the summations
Iy=Iy*(x(2)-x(1)); % multiply by Delta x
% plot Debye integral function
figure(2);plot(x,Iy)
ipos=0;
for tau=0.01:0.01:2;
[val,ind]=sort(abs(x-1/tau));
ipos=ipos+1; HeatCap(ipos)=Iy(ind(1))*tau^3;
T(ipos)=tau;
end
figure(3);
plot(T,HeatCap);
PHYS spring page 13

14. % Simple treatment of Debye model % x=0.01:0.01:20;
y=(x.^4.*exp(x))./(exp(x)-1).^2;
figure(1);
plot(x,y)
% Showing the integrand
% evaluate the integral by simple summation formula
Iy=y*0; % Fill Iy by zeros
% perform the summations
for k=2:max(size(y));Iy(k)=Iy(k-1)+y(k);end
Iy=Iy*(x(2)-x(1)); % multiply by Delta x
% plot Debye integral function
figure(2);plot(x,Iy)
T=zeros(1,2); HeatCap=zeros(1,2);
kl=0;
for k=2:max(size(y))
tau=1/x(k);
if ( (tau>0.009) & (tau<2.0) )
kl=kl+1;
T(kl)=tau;
HeatCap(kl)=Iy(k)*tau^3;
end
% add the small T behaviour
for tt=1/20:(-0.01):0.01
T(kl)=tt;
HeatCap(kl)=Iy(max(size(y)))*tt^3;
figure(3);
plot(T,HeatCap);
PHYS spring page 14