Is there the function of "DEBYE" in MATLAB ?

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ADNAN KIRAL 2021-1-22

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回答： Jens 2022-2-5

Hi

I need the "DEBYE model". how can I plot that in matlab ? any suggestion ?

thanks in advance

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ADNAN KIRAL 2021-1-22

在 MATLAB Online 中打开

thanks for reply, but when i run it, it did not work, it says "not enough input". I am new at this study area. I just want to see the general "DEBYE" graph first.

the code is copied from that file. Thanks in advance...

function D1 = debye1(x)
%DEBYE1 First order Debye function.
%   Y = DEBYE1(X) returns the first order Debye function, evaluated at X.
%   X is a scalar.  For positive X, this is defined as
%
%      (1/x) * integral from 0 to x of (t/(exp(t)-1)) dt
%   A proper FORTRAN implementation of this function is available in the
%   MISCFUN Package written by Alan MacLead, available as TOMS Algorithm 757
%   in ACM Transactions of Mathematical Software (1996), 22(3):288-301.
%   Written by Peter Perkins, The MathWorks, Inc.
%   Revision: 1.0  Date: 2003/09/05
%   This function is not supported by The MathWorks, Inc.
%
%   Requires MATLAB R13.
if abs(x) >= realmin
    D1 = quad(@debye1_integrand,0,abs(x))./abs(x) - (x < 0).*x./2;
else
    D1 = 1;
end
function y = debye1_integrand(t)
y = ones(size(t));
nz = (abs(t) >= realmin);
y(nz) = t(nz)./(exp(t(nz))-1);

Walter Roberson 2021-1-22

在 MATLAB Online 中打开

X = logspace(-3,2);
Y = arrayfun(@debye1, X);
semilogx(X, Y)

However, this function has no parameters such as

or W so it is not clear that it is the same model that you need.

ADNAN KIRAL 2021-1-23

many thanks. Appriciate that.

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Answer 1

Jens 2022-2-5

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Hello,

you mean the Debye-function, specific heat in 3D?

you can easily program it yourself. Either by numerical integration of the definition equatin, or a rational approximant:

R=8.314462618; % molar gas constant in J/mol/K CODATA 2018, exact.

xn=Theta./T;

I=@(x) x.^4.*exp(-x)./(exp(-x)-1).^2;

DEBYE=R*9*(1./xn).^3.*integral(I,0,xn,'reltol',1e-9,'abstol',1e-11);

or

N=[0.0279254827 -0.0358437761 1.05224663 17.2857105 64.7520511 226.68446];

D=[0.000119451046 -0.000210411972 0.00744002583 0.0346090463 0.337538084 ...

1.4272431 9.53997783 21.5840170 75.5614867]; % R. J. Goetsch+ (2011)

res1=R*polyval(N,Tn)./polyval(D,Tn);

res=reshape(res1,size(T));

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