[Ifeffit] Re: relation between DW factors in uranyls

Hi Shelly, On Thu, 30 Oct 2003, Kelly, Shelly D. wrote:

Hello All,

Does anyone know of a reference that explicitly shows that sigma2 for a linear backscattering path is approximately twice a single scattering path?

I think one can show that this approximation is justfied to some extent by the large difference in masses between U and O atoms. One can always calculate any MS sigma2 as <(delta R)**2> delta R = sum_i (u_i-u_i+1)dot ^r_i,i+1 where u_i is the displacement at site i. This gives sigma2 as a sum of correlation functions with various path dependent coefficients.

My example is for a uranyl moiety (UO2). The structure of this moiety is symmetric and linear with a dumbbell shape with O1=U=O2 all in a row. I need a reference that does the calculation to show that the 4 leg path (U-O1-U-O2-U) has a sigma2 value that is twice the single scattering path (U-O1-U) from one of the oxygen atoms.

For the single scattering path (U-O1-U) this gives sigma2_(U-O)= + - 2 while for the 4 leg path the central atom doesn't contribute (for small vibrations) and one has sigma2_(U-O1-U-O2-U)= 2 - 2 Thus since ~ 1/M and 2nd neighbor correlations are small, sigma2_(U-O) approx while sigma2_(U-O1-U-O2-U) approx 2 The errors in this approximation can be estimated by using a simple spring model and calculating the correlation functions (e.g. as done by the equation of motion routines in FEFF8). John Rehr