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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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