Diffuse Scattering Examples

Recommended First-Use Order

1. LiFeO2.rmc6f — a practical first benchmark for learning diffuse manifolds, custom plane slicing, and short-range-order interpretation.
2. CaTiO3.rmc6f — a compact displacement benchmark for comparing rod-like and localized diffuse features produced by different structural mechanisms.
3. PMN_300k.rmc6f — the largest and most advanced benchmark, useful once you are already comfortable with the calculator workflow.

Download Sample Files

The following example profiles ship with this repository in the Examples/ directory.

• LiFeO2.rmc6f
• CaTiO3.rmc6f
• PMN_300k.rmc6f

Magnetic examples (see Magnetic Examples):

• magnetic/MnO_order_spins.txt, magnetic/MnO_random_spins.txt (Scatty spin files)
• magnetic/MnO.rmc6f, magnetic/MnO_spins.cfg, magnetic/MnO.dat (RMCProfile, load together)
• lammps/fe_bcc_spins.data, lammps/skyrmion_film.data (LAMMPS atom_style spin)

Modulated structures (see Modulated Structures):

• modulation/KCP_Pt_chains.rmc6f (the Pt chains of KCP, each with its own Peierls wave)
• modulation/Cr_bcc.rmc6f (bcc Cr, for the Modulation tools)

At A Glance

γ-LiFeO2 Chemical-Order Benchmark

LiFeO2.rmc6f is based on the MOSAIC manuscript benchmark for γ-LiFeO2. It is a practical first example for learning how the calculator behaves on a configuration with a clear diffuse-scattering manifold.

In the manuscript model, Li and Fe are distributed so that each oxygen is coordinated by exactly 3 Li and 3 Fe cations. That local rule creates short-range order and yields the characteristic diffuse surface approximately described by cos(πh) + cos(πk) + cos(πl) ≈ 0. On top of that, nanoscale L1_1-type ordering introduces condensation of intensity near 1/2(111)-type locations.

Why This Sample Matters

• It shows both a broad diffuse manifold and more localized superlattice-related condensation.
• It is chemically simple enough that the 3D slice plane and 2D slice map are easy to interpret.
• It is a useful sample for learning normal-plane slicing.

Inspect First

• the broad short-range-order manifold in the 3D Slice Plane
• the buildup of intensity near 1/2(111)-type locations
• how the same feature family looks in 3D context versus the 2D slice map

Suggested Workflow

1. Compute diffuse.
2. Start in Normal plane mode.
3. Move the plane through the manifold and watch how the 2D slice changes as it cuts the broad diffuse surface.
4. Then move the plane toward 1/2(111)-type regions to compare manifold scattering with condensed intensity.

Practical Notes

• This file is large enough to be meaningful but still friendly for first runs.
• If you are just learning the UI, start with a moderate grid step before refining the grid.
• Best first views: 3D Slice Plane and 2D Slice Map.

Scientific context source: MOSAIC manuscript, A Filter-Based Approach Linking Diffuse Scattering Features to Site-Resolved Real-Space Fields, LiFeO2 benchmark section.

CaTiO3 Displacement Benchmark

CaTiO3.rmc6f is based on the MOSAIC CaTiO3 displacement benchmark. It is a compact example for seeing that two different structural mechanisms can generate diffuse features with different reciprocal-space shapes.

In the manuscript benchmark, the structure contains two coexisting distortion families:

• octahedral rotations, which produce rod-like diffuse intensity
• breathing distortions, which produce more localized superlattice-related intensity around 1/2(111)

Why This Sample Matters

• It shows overlapping diffuse signatures caused by different displacement mechanisms.
• It is ideal for comparing elongated rod-like features against more localized features in the same dataset.
• It is smaller than PMN and therefore a practical second benchmark after LiFeO2.

Inspect First

• rod-like diffuse features running through (1/2,1/2,l)-type regions
• localized/spherical features near 1/2(111)
• how different slices emphasize one distortion family more strongly than the other

Suggested Workflow

1. Compute diffuse.
2. Begin with axis slices to find elongated rods.
3. Switch to normal-plane mode to compare rod-dominated cuts with cuts that isolate more localized intensity.
4. Use the 2D slice map to compare shape and anisotropy directly.

Practical Notes

• This is a strong benchmark for users who want to understand how reciprocal-space shape maps to structural mechanism.
• Best first views: 2D Slice Map for feature-shape comparison, then 3D Slice Plane for orientation.

Scientific context source: MOSAIC manuscript, A Filter-Based Approach Linking Diffuse Scattering Features to Site-Resolved Real-Space Fields, CaTiO3 benchmark section.

PMN At 300 K Relaxor Benchmark

PMN_300k.rmc6f is a 300 K PMN relaxor ferroelectric benchmark and the most advanced shipped sample. It is the right file when you want to inspect strongly anisotropic diffuse scattering and practice more demanding slice placement in reciprocal space.

PMN is a widely studied relaxor with chemically disordered B-site occupancy and pronounced polar/displacement correlations. The 2025 Nature Communications article discusses mesoscale polarization textures and chemically driven heterogeneity in PMN and related relaxor systems, while the earlier 2019 Nature Communications paper provides complementary local-order and polar-nanoregion context for classical PMN. For the purposes of this calculator, the practical point is that PMN produces broad anisotropic diffuse intensity that is often easier to interpret by combining a 3D overview with targeted 2D cuts.

Why This Sample Matters

• It is the most demanding and most structurally rich example included with the calculator.
• It is useful for exploring anisotropic diffuse scattering, broad reciprocal-space features, and careful slice placement.
• It is a demanding example for both UI workflow and computational settings because it is the largest shipped file.

Inspect First

• anisotropic diffuse features rather than only isolated compact spots
• how the 2D slice shape and contrast change as you move through different diffuse regions
• the 3D isosurface as a global view before deciding where to place more detailed slices

Suggested Workflow

1. Compute diffuse.
2. Start from the 3D Isosurface to see where the main anisotropic diffuse regions sit.
3. Then use the 2D Slice Map to inspect anisotropic regions in more detail.
4. Use custom plane slicing only after you have identified a feature family you want to follow through reciprocal space.

Practical Notes

• This is the largest shipped file: 320,000 atoms in a 40×40×40 supercell.
• It is not the recommended first-run example. Start with LiFeO2 or CaTiO3 first.
• For first exploration, begin with a coarser reciprocal-space grid than you would use for a publication-quality figure.

Scientific context references: Eremenko et al., Emergent topological polarization textures in relaxor ferroelectrics, Nature Communications 16, 7531 (2025); and Eremenko et al., Local atomic order and hierarchical polar nanoregions in a classical relaxor ferroelectric, Nature Communications 10(1), 2728 (2019).

Magnetic Examples

Six sets of spin configurations ship in Examples/magnetic and Examples/lammps. Three have buttons, under MnO spins and LAMMPS spins in the Structure card's Examples; load the others with the file picker. Each button sets the grid, and after the first compute the slice opens on the plane with the main features. Magnetic scattering is computed for neutrons. When a file carries spins and the Magnetic mode is nuclear only, the mode switches to nuclear + magnetic.

A LAMMPS data file has no unit cell, so the calculator takes the whole box as the cell, and h, k, l count reciprocal-box units. The Fe box is 10 cells wide, so bcc (1 1 0) appears at (10 10 0). The skyrmion period of 10 sites in a 60-site box puts the satellites 6 units from the origin, at (6 0 0), (0 6 0), (6 6 0) and their opposites. The box is periodic, so it scatters only at integer box units, and the examples use step 1, the default for LAMMPS data. Between integer units, a finite box shows only its size fringes. Both files are written by tools/make_lammps_examples.py, which also checks that the skyrmion texture has topological charge −1 per magnetic cell.

The MnO Scatty results are checked against J. A. M. Paddison's Scatty in the test suite.

Modulated Structures

Modulations: KCP Pt chains loads the Pt atoms of KCP, K₂Pt(CN)₄Br_0.3·3H₂O (Examples/modulation/KCP_Pt_chains.rmc6f): chains along c with Pt 2.89 Å apart, 9.87 Å from chain to chain, 17×17 chains of 40 Pt. Each chain carries a longitudinal Peierls wave with q = 2k_F = 0.85 per Pt spacing, in a phase of its own. The volume opens as a cut-away cube on a log scale.

• With no phase relation between the chains, the satellites at l = n ± 0.85 do not form spots: they spread over all h and k into diffuse sheets, as in the X-ray photographs of KCP (Comès et al., 1973).
• The sheets grow as l², the displacements being along the chains; the faint sheets between them are the second order, at l = n ± 1.7.
• The faces of the cube cut the sheets into lines; the 2D slice map shows the (0 k l) plane, where every sheet is a line.

Examples/modulation/Cr_bcc.rmc6f is a plain bcc Cr box (21×21×21 cells) for the Modulation tools: Modulations → Modulate the loaded structure applies chromium's incommensurate transverse spin-density wave, whose satellites stay sharp because the wave is in step throughout the box. The guide gives the settings and what to look for.

How To Choose The Right Example

Scope Note

These examples are included to help users learn reciprocal-space navigation and qualitative interpretation of diffuse features. The calculator is a forward diffuse-scattering and visualization tool; it does not perform the MOSAIC inverse reconstruction workflow.