NeutronSQ (Module)

Overview

NeutronSQ is responsible for taking a set of previously calculated $S(Q)$ from an SQ module and generating a new set of neutron-weighted structure factors. The total neutron-weighted structure factor, $F^{N}(Q)$, is generated through summation of the individual partial neutron-weighted $S(Q)$. Neutron-weighted partial and total radial distribution functions are also calculated.

The NeutronSQ module does not target any configurations itself - the underlying GR module, referenced by the SQ module, dictates the source configuration data.

Description

Basic Theory

The NeutronSQ module calculates the Faber-Ziman partial structure factors weighted by the coherent atomic neutron scattering lengths, such that

$$ S^{N}_{ij}(Q) = b_i b_j S_{ij}(Q) $$

where $b_i$ and $b_j$ are the bound coherent scattering lengths of the atom types $i$ and $j$ respectively. In a similar manner, the total neutron-weighted structure factor is

$$ F^{N}(Q) = \sum^N_{i,j,i \geq j} [2-\delta_{ij}] b_i b_j c_i c_j S_{ij}(Q) $$

Depending on the need, $F^{N}(Q)$ may be normalised to an appropriate constant with the Normalisation keyword.

Weighting

The module depends on the definition of suitable isotopologues for each species of interest in order to determine the correct $b$ values to use, and which are specified with the Isotopologue keyword. Furthermore, any atom types that undergo fast exchange (e.g. hydrogens attached to oxygen or nitrogen atoms) can be indicated with the Exchangeable keyword.

With isotopologues and exchangeable atoms provided, matrices of weighting factors between atom types on the same and different molecules can be constructed. The reason to distinguish between intramolecular and intermolecular weightings is perhaps not immediately apparent, but is necessary to correctly calculate weighted $S(Q)$ for isotopic mixtures. Consider a simplified example where two molecules H-X-H and D-X-D, where the hydrogen and deuterium are not exchangeable, are mixed together in a 1:1 ratio. In a dynamic system such as a liquid, from the point of view of a molecule (H-X-H or D-X-D) the time-averaged picture of the surrounding molecules is a blend of indistinguishable H-X-H and D-X-D molecules. Averaging this picture over all molecules, the resulting intermolecular weighting factor for the partial between the H/D atoms is a straightforward average of the two scattering lengths of H and D. However, locally within the molecule, an H is always next to another H, and a D is always next to another D. Thus, the intramolecular weighting factor is an average of the squares of the scattering lengths of H and D. If the H and D sites are both exchangeable then the intramolecular weighting factor becomes the same as in the intermolecular case.

Instrumental Broadening

The application of instrumental broadening is the responsibility of the source SQ module - see its QBroadening keyword.

Options

Targets

Keyword	Arguments	Default	Description
SourceSQs	Module	–	Required Source SQ module from which to take unweighted $S(Q)$.

Isotopes & Normalisation

Reference Data

Keyword	Arguments	Default	Description
Reference	Data1DFileAndFormat	–	Format and filename of reference $F(Q)$ data, to be displayed in the GUI alongside calculated data, and made available for other modules to utilise (e.g. EPSR)
ReferenceFTDeltaR	double	0.05	Spacing in $r$ to use when generating the Fourier-transform of the $F(Q)$
ReferenceFTQMax	double	–	Maximum Q value to use when Fourier-transforming the reference $F(Q)$ to its $G(r)$
ReferenceFTQMin	double	–	Minimum Q value to use when Fourier-transforming the reference $F(Q)$ to its $G(r)$
ReferenceNormalisedTo	NormalisationType	None	Normalisation which has been applied to the reference data
ReferenceWindowFunction	WindowFunction	Lorch0	Window function to apply when Fourier-transforming reference $F(Q)$ to a reference $g(r)$

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