> > >The diffraction alone can not decide. Significantly different "physical" > >size distributions could describe equally well the peak profile > >(J.Appl.Cryst. v35 (2002) 338-346 - self citation too). > >Nicolae Popa > > Looking at your figures 6b1 and 6b2, I measure how we > differ on the sense of "significantly different". As you comment > in the text, "The curves 1 and 2 differ in the position of the > maximum by only 2 A and in height of the maximum by > 9.76%". > > I would not call that "significantly different" but "very similar". > > Armel
Yes, but the figure 6b represents the COLUMN LENGTH distribution not the CRYSTALLITE RADIUS distribution (in this case of spherical crystallites). The crystallite radius distributions are given in 6a1 and 6a2 (lognormal and gamma, respectively) and they are significantly different, what can be seen also in the table 1: the average radius and the dispersions are completely different. Nevertheless the profile of the diffraction peak is equaly well described. And the column length distribution is quite the same (as discussed in text and as you observed). But when we are speaking about the "physical model" we understand in fact the distribution of the crystallite radius (if spherical). Is that lognormal or gamma? Is the average radius 90(6) or 69(1) Angstroms, is the parameter c (determining the dispersion) 0.18 or 0.39? We can not say only from diffraction that one is more "physical" than other. On the other hand is the column length distribution a full "physical" description of the crystallites, I mean of the shape and radius (radii) distribution? I think not. You can imagine, for example, that the crystallites are even not spherical, but ellipsoidal. It is easy to understand that if the Euler angles representing the orientations of the ellipsoidal principal axes with respect to the crystal axes are UNIFORMLY distributed in their domains of definition, will be NO anisotropy effect. Then we can think the crystallite are spherical with a certain distribution of radius, when in fact they are ellipsoidal with other distributions of (three) radii. But the column length distribution (and the peak profile) is the same. What we see in diffraction is the column lengths (volume & area averaged) and the classics were not full ignoring the shape and radius (radii) distribution(s). Nicolae Popa (Mister, Messieur, Don, Dom, etc.)
