Matthew and Others: One has to be careful with the Gaussian parameters, as they add as squares. There is a newer publication that deals with this problem: Size-Strain Line-Broadening Analysis of the Ceria Round-Robin Sample, Journal of Applied Crystallography 37 (2004) 911-924. The reprint can be downloaded from http://www.du.edu/~balzar/s-s_rr.htm.
Paragraph 3.3 gives a detailed procedure how to obtain size/strain data from Rietveld refinement of the U,V,W,X,Y parameters. Davor ***************************** Dr. Davor Balzar University of Denver 303-871-2137 www.du.edu/~balzar ***************************** ----- Original Message ----- From: [EMAIL PROTECTED] Date: Monday, June 25, 2007 6:28 pm Subject: Re: More Caglioti U V W parameters To: [email protected] > Just to add more fat to the fire.... > > Have a look at Young, R. A. & Desai, P. 1989, 'Crystallite Size and > Microstrain Indicators in Rietveld Refinement', Archiwum Nauki o > Materialach, vol. 10, no. 1-2, pp. 71-90. (I can send the PDF if needs > be) > > They talk about the Thompson, Cox and Hastings model, which explicitly > separates the gaussian and lorentzian components of a psuedo-Voight peak > shape. > > FWHM(G)^2 = U tan^2(T) + V tan(T) + W > FWHM(L) = X tan(T) + Y/cos(T) > > As Prof. Stephens pointed out (and is stated in Yound and Desai), the > coefficients can be broken into instrumental and sample (size, strain) > components. > > U = U_inst + U_strain > V = V_inst > W = W_inst > X = X_inst + X_strain > Y = Y_inst + Y_size > > You can fix the instrument components with your standard, and then > refine the difference with your sample. > > > If you want to stick with the straight UVW symbolism, Young and Desai > also state that you can use the size broadening term FHWM(G)^2 = > Z/cos^2(T), which yields: > > FWHM(G)^2 = Z/cos^2(T) + (U_inst + U_strain) tan^2(T) + V_inst tan(T) > + > W_inst > > which can be re-written as > > FWHM(G)^2 = (U_inst + U_strain + Z_size) tan^2(T) + V_inst tan(T) + > (W_inst + Z_size) > as long as you constrain the two Z_size's to be the same. > > The last equation is what Prof Stevens alludes to in his "refinement > of > U and W", all of the sample related parameters are folded up there. > > > > > > Of course, your mileage may vary... > > > > > > Cheers > > Matthew > > ________________ > Matthew Rowles > > CSIRO Minerals - Clayton > > Ph: +61 3 9545 8892 > Fax: +61 3 9562 8919 (site) > Email: [EMAIL PROTECTED] > > > > >
