[Discus-talk] match powder patterns from Debye equation and complete integration methods

[gambarimas87 <gam...@gm...>]

Hi,

I'm trying to match the powder patterns computed with the Debye equation
and the complete integration methods. I'm using as test case an isolated Ag
nanoparticle having N=3559 atoms and approximately 49 Amstrong diameter,
carved from a perfect (infinite) structure. When computing the pattern with
the Debye equation I realized that in order to make it equal (as it should
be) to N^2 f^2 at q=2PI h = 2pi dstar = 2pi *2 sin(theta)/lambda = 0, the
pattern must be scaled by a factor of 10^-4. This also makes the pattern
almost equal to the one computed by the software Debyer and Powdog that
make use of the Debye equation for the same purpose. So I'm wondering which
is the origin of this 10^-4 factor ?

When proceeding to compare the scaled Debye pattern with that computed by
the complete integration method, I need to further scale the latter as well
as apply some correction for its intensity, in order to match both. My
first issue here is that this new scaling factor depends upon the dh, dk
and dl steps used for the calculation of the intensity in reciprocal space
inside the 'powder' menu. I had to tune (decrease) this 'step' parameter in
order to make smother the pattern computed by the integration method. Then
the “correction” that I mention is just a division of the intensity at each
value of q by 4pi (q/2pi)^2 = 4pi h^2 = 4pi (2 sin(theta)/lambda)^2, i.e.
the area of the sphere in reciprocal space that contributes to the
diffracted intensity at h= 2 sin(theta)/lambda in a powder pattern. It
looks like Discus making the integration over that sphere but without
dividing the result by its area. Could you explain me why do I need to
perform these modifications over the pattern computed by the integration
method to match it with that from the Debye equation?

I'm attaching to this message the macro I used as well as the stru file to
build the Ag particle. For the pattern computed with the integration method
I limit the range in q to [2.3, 3.3] A^-1, to speed up the computation,
i.e. I actually compare only with the first two peaks of the powder pattern
obtained with the Debye equation.

Many thanks in advance

Camilo Perez