Leonid, The lognormal distribution for particle size is not my modeling (unfortunately), but if you insist, let see once again your equations.
<D> = Da + 0.25(DaDv)^0.5 and sigma<D> = <D>(Dv/Da - 1/2)/2 For lognormal distribution first equation becomes: 2=(4/3)(1+c)**2+(1/4)sqrt[2*(1+c)**5] For c=0.05 we obtain: 2=1.87, for c=0.4, 2=3.43 The second equation becomes: sqrt(c)=[(9/8)(1+c)-1/2] For c=0.05, 0.22=0.68, for c=0.4, 0.63=1.75 Well, taking account that the world is not ideal I'm ready to accept that, then I think is time to close our discussion. Best wishes, Nicolae ----- Original Message ----- From: "Leonid Solovyov" <[EMAIL PROTECTED]> To: <rietveld_l@ill.fr> Sent: Sunday, April 17, 2005 2:58 PM > Dear Nicolae, > > I will comment only upon your last statement because the limitations of > your modeling are clear. > > > Well, I don't know where from you taken these formulae > > but I observe that for spheres of equal radius, then zero dispersion, > > you have: > > sigma(D)=5<D>/4, different from zero! > > First of all, for spheres of equal radius and IDEAL definition > of Dv and Da: > sigma<D> = <D>(Dv/Da - 1/2)/2 = <D>(9/8 - 1/2)/2 = 5<D>/16 > Yes it is not zero, but the expressions I derived work only for > 0.05 < c < 0.4 and I derived them not for IDEAL Dv and Da. If you > perform WEIGHTED least-squares fitting of TCH p-V function to a profile > simulated for spherical crystal and added by ~10% background level (to > be closer to real Rietveld refinement) you will obtain the ratio of > Dv/Da~3/4 not 9/8! This ratio is wrong but this is what we have from > WEIGHTED least-squares fitting of TCH p-V to simulated data. In this > case > sigma<D> = <D>(Dv/Da - 1/2)/2 = <D>(3/4 - 1/2)/2 = <D>/8, > different from zero again, sorry, this world is not IDEAL. > > Best wishes, > Leonid > > > > > __________________________________ > Do you Yahoo!? > Plan great trips with Yahoo! Travel: Now over 17,000 guides! > http://travel.yahoo.com/p-travelguide >
