Extracting phases from anomalous scattering data

Extracting phases from anomalous scattering data 

First consider the structure factor F p+in Fig. 6.12. Applying Eq. (6.12) and solving for F + gives 

To solve this equation (see Fig. 6.13), draw the vector — AFr+ with its tail at the origin, and draw — AFj+ with its tail on the head of — AFr+. With the 

IF p + l with its center at the origin, representing the structure-factor amplitude of this same reflection in the nonanomalous scattering data set. The two points of intersection of these circles satisfy Eq. (6.13), establishing the phase of this reflection as either that of Fa or Fb. As with the SIR method, we cannot tell which of the two phases is correct. 

The Friedel partner of this reflection comes to the rescue. We can obtain a second vector equation involving F p+ by reflecting F p- and all its vector components across the real axis (Fig. 6.14a). 

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C. Extracting phases from anomalous scattering data... 

Neutron scattering methods have been used in the past primarily to explore both the structural and dynamic properties of bulk water. One example is a study in which the two phases of the water polymorphism were described, that is, the LDL and the HDL [42]. These experiments were on compressed water in a temperature regime in which the anomalous properties of water are most visible, that is, close to the ice I/ice III triple point (T = 251K, P = 209 MPa). The 00, OH, and HH partial structure factors and the site site radial distribution function between distinct atoms were extracted from the diffraction data. If we assume that the structure of water can be represented as a linear combination of the structures of the end points, that Is, the HDL and LDL structures, we obtain two values for the densities /Ohdl = L20 g cm (0.0402 molecules A ) and pldl = 0.88 g cm (0.0295 molecules/A ). These values are close to the reported densities of high-density and low-density amorphous ice [97]. 

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