Powder Diffraction - Spallation Neutron Source
Powder Diffraction - Spallation Neutron Source
Powder Diffraction - Spallation Neutron Source
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Lorentz (Cauchy) and Gaussian Broadening<br />
Functions<br />
Most instrument & sample broadening contributions are Lorentzian or<br />
Gaussian<br />
G(<br />
DT,<br />
G<br />
Normalized Gaussian<br />
G<br />
L(<br />
DT,<br />
g<br />
) =<br />
L<br />
)<br />
4ln<br />
p G<br />
2<br />
2<br />
G<br />
2<br />
=<br />
pg<br />
é-<br />
4ln<br />
2(<br />
DT<br />
)<br />
expê<br />
2<br />
êë<br />
GG<br />
Normalized Lorentzian<br />
L<br />
1<br />
æ 2DT<br />
1+<br />
ç<br />
è g L<br />
ö<br />
÷<br />
ø<br />
Note that peak widths vary so<br />
G and L are both functions of<br />
Q<br />
2<br />
2<br />
ù<br />
ú<br />
úû<br />
Gaussian & Lorentzian functions compared.<br />
Both curves have same FWHM & area, but<br />
note the much longer tails for the Lorentzian.<br />
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