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

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% 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); PHYS208 - spring 2010 - page 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 % 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); PHYS208 - spring 2010 - page 14