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Methods, Problems and Solutions

TOF (Time of Flight) Neutron Diffraction Resources and Code

Deriving the Lorentz Factor in TOF neutron diffraction

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From the Rietveld Mailing List

Date: Fri, 08 Sep 2000 09:47:11 +0100
To: rietveld_l@ill.fr
From: Neil Hyatt [nch696.pr.che.bham@is-fs12.bham.ac.uk]
Subject: Lorentz Factor in TOF neutron diffraction
Reply-To: rietveld_l@ill.fr

Dear all,

The Lorentz factor for TOF-neutron diffraction is given in the GSAS manual as:

L = d^4 sin(theta) (pg. 125 of the old manual; pg. 145 in the new).  

Does anyone know how this factor is derived?  I would greatly appreciate
any helpful references.

All the best,

Neil Hyatt.

**********
Neil Hyatt                           tel: +44-(0)121 414 4370
School of Chemistry                  fax: +44-(0)121 414 4442
University of Birmingham             email: n.c.hyatt@bham.ac.uk
Edgbaston                                   
Birmingham B15 2TT                   WWW: http://chemwww.bham.ac.uk/
UK


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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