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From: "Radaelli, PG (Paolo) " [P.G.Radaelli@rl.ac.uk]
To: "'rietveld_l@ill.fr'" [rietveld_l@ill.fr]
Subject: RE: Lorentz Factor in TOF neutron diffraction
Date: Fri, 8 Sep 2000 11:26:15 +0100
To answer Nail's question:
The Lorentz factor can be deduced from the expression of the integrated
intensity of a single reflection of a TOF powder pattern (in the absence of
attenuation):
I=[e(lam)*Omega]*[Vs/(32*pi*Vu^2)]*[lam^4*i(lam)]*[1/sin^3(theta)]*[Mhkl*|Fh
kl|^2]=
=[e(lam)*Omega]*[Vs/(2*pi*Vu^2)]*[i(lam)]*[Mhkl*|Fhkl|^2]*[d^4*sin(theta)]
in this formula,Omega is the detector solid angle, e(lam) its efficiency, Vs
is the sample volume, Vu is the unit cell volume, lam is the wavelength,
i(lam) the incident spectrum (neutrons/cm^2/Angstrom), theta is the Bragg
angle, Mhkl is the reflection multiplicity and Fhkl is the structure factor.
The second formula is deduced from the first, keeping in mind that
lam^4/sin^3(theta)=16d^4*sin(theta). The reference to this formula is given
in B. Buras and L. Gerward, Acta Cryst A31 (1975) p372, and also reported in
the book by R. A. Young, "The Rietveld method" IUCr-Oxford University Press
(1995) p. 214. In there, the expression for the integrated intensity over
the full Debye-Scherrer cone is given. The expression I quote is easily
deduced by noting that for such a cone
Omega=8*pi*sin(theta)*cos(theta)*Dtheta
I hope this answers your question.
Paolo
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