Diffuse Scattering Theory

Scope

This page summarizes the theory needed to use and interpret the diffuse-scattering calculator. It covers the forward calculation and visualization of I(h,k,l). It does not cover the MOSAIC inverse reconstruction, decoder training, or site-resolved inversion workflow.

Kinematic Approximation

The calculator uses the kinematic scattering approximation to evaluate reciprocal-space intensity from atomic positions in an .rmc6f configuration. This page keeps the theory deliberately compact and focuses on interpreting the displayed intensity rather than on implementation internals.

Total And Diffuse Intensity

Without subtraction (Subtract avg = OFF)

The raw displayed intensity is

I_total(Q) = |A_tot(Q)|²

This contains both coherent/Bragg-like intensity and diffuse intensity.

With subtraction (Subtract avg = ON)

The calculator subtracts the average-structure contribution:

I_diffuse(Q) = |ΔA(Q)|² = |A_tot(Q) − <A(Q)> ψ(Q)|²

In the ideal periodic limit the second term reproduces the Bragg scattering, so ΔA(Q) isolates the part of the signal associated with deviations from the average periodic structure.

Normalization Controls

The calculator exposes two normalization-related controls with different roles. Aavg N changes the denominator used inside the coherent-subtraction term, while Normalize Nq divides the final displayed intensity by the grid-point count.

Aavg N (average normalization denominator)

Aavg N controls which atom count is used in the average-subtraction term:

Setting	Meaning
N included (default)	Only atoms whose elements are currently selected in the element filter. Correct when computing partial diffuse scattering from a subset of elements.
N total	All atoms in the configuration regardless of element filter.

Normalize Nq (per-Q-point normalization)

When ON (default), the final intensity array is divided by the total number of reciprocal-space grid points:

I_out(Q) = I(Q) / N_Q

where N_Q = N_h × N_k × N_l is the grid size. This makes the intensity independent of grid density so that results at different resolutions are comparable.

When OFF, the raw summed intensity is kept. This is mainly useful for debugging or for absolute-scale comparisons where the grid size is fixed.

Display Scale

The calculator exposes log10 and linear viewer scales.

linear: preserves direct intensity contrast and is the clearest choice when you care about relative magnitude in a narrow range.
log10: compresses the dynamic range so weak diffuse features remain visible next to stronger intensity.

For broad diffuse problems, log10 is usually the more informative visualization setting.

Reciprocal-Space Conventions

h, k, l are reciprocal-lattice coordinates in reciprocal-lattice units.
Q is the reciprocal-space vector in Cartesian reciprocal units: Q = 2π B* (h, k, l)^T.
The tool computes and displays diffuse intensity as a function of reciprocal-space position, exposed in the UI as I(h,k,l).

Slice Modes

Axis mode

Inspect conventional crystallographic sections with one reciprocal coordinate fixed.

Normal plane mode

Define a custom plane normal and translate the plane through reciprocal space. This is the most flexible mode for studying diffuse manifolds and anisotropic features.

Volume average mode

Average the diffuse intensity over a finite slab centered on the current plane. The slab is divided into N parallel sample planes evenly spaced within the slab thickness:

I_slab(u,v) = (1/N) Σ_i=1^N I(u, v, t_i)

where t_i are the sample positions along the plane normal within [center − Slab±, center + Slab±] and (u, v) are in-plane coordinates.

Control	Meaning
Slab ±	Half-thickness of the averaging volume in HKL units (default 0.5).
Slab N	Number of sample planes within the slab (default 10, range 3–200).

This helps when the diffuse feature is broad or noisy, or when you want to integrate through a volume rather than sample a single infinitely thin plane.