Crystal and defect analysis

Using the analyses

The DXA tool extracts an independent dislocation line network with Burgers vectors and junction connectivity. Its retained CPU/Wasm topology session uses a dedicated Worker rather than the atom-range analysis pool described below. With GPU acceleration enabled, nearest-neighbor search, local crystal correspondence and tetrahedron classification can run on GPU; crystal mapping, periodic tessellation and line tracing remain on CPU, with independent fallback for GPU stages.

Load a structure and open Common neighbor analysis in the right panel. Identify structure runs adaptive CNA by default and selects Crystal structure (CNA) in Color by. No element-specific cutoff is needed in adaptive mode. Fixed cutoff CNA exposes a radius in angstroms: put it between the first and second shells for FCC/HCP or between the second and third shells for BCC.

The viewport legend lists every supported class, its atom count and fraction of the complete input frame. Each checkbox immediately shows/hides that class. Hidden atoms cannot be picked and are excluded from PNG drawing. Classification still sees the complete structure: hiding a class, slicing, changing atom size or moving the camera does not rerun or change the analysis. The filter applies when coloring by crystal structure; switching to a different color property temporarily suspends it. Checkbox preferences survive frame changes and recalculation, and reset when a different source is opened. PNG legends include counts and mark hidden classes.

Scalar analysis results use a separate legend with ten palettes: AtomEye rainbow, Viridis, Plasma, Magma, Inferno, Cividis, Turbo, Spectral, Cool–warm and Grayscale. Highlighted Auto fits the range to the current frame. Turning Auto off freezes the displayed limits; editing either limit also turns it off. Each property's fixed limits survive trajectory frame changes, reused results and switching color properties. Clicking Auto again fits the current frame and resumes automatic limits. Range, palette and outside-range filter edits do not rerun analysis, and PNG output uses the same legend settings. Processing configurations preserve the palettes and per-property range mode.

Polyhedral template matching runs the actual PTM C++ library compiled to WebAssembly inside module Workers. Click Identify to select Crystal structure (PTM). It uses the same legend/filter behavior and OVITO colors, plus these PTM classes:

The template checkboxes select candidates for identification. FCC/HCP/BCC/ICO/SC are enabled by default; diamond/hexagonal diamond/graphene require additional neighbor shells and are opt-in. The RMSD threshold defaults to 0.1; a best fit above it is Other. Setting it to 0 disables rejection. PTM also exposes best-fit RMSD and nearest-neighbor distance (Å) as scalar color properties. Rejected fits retain diagnostic RMSD but have undefined deformation/distance. The number of recognized atoms depends on the selected templates, threshold and local disorder.

With GPU acceleration enabled and supported, PTM identification, lattice estimation and fresh ideal lattice strain prepare nearest-neighbor indices and Float64 image vectors on WebGPU before CPU Wasm Voronoi ordering, topology and template fitting in the shared Worker pool. The GPU table retains strict distance/vector ordering; the CPU fitting stage uses the same PTM library and thresholds. Unavailable or unsupported GPU preparation falls back to CPU neighbor search. See PTM for preparation bounds and fallback details.

Atomic elastic strain

Under Ideal lattice reference, each input atom type has an element selector, reference crystal and editable a in Å; HCP and hexagonal diamond also expose c. Recognized source labels initialize presets for 37 elements, including common FCC/BCC/HCP metals and diamond C/Si/Ge. Numeric types and unsupported elements begin with an empty a. Estimate from structure fills missing values, and the first Calculate strain does so automatically when needed. Numeric sources keep their Type N labels and empty element selectors: no element is inferred from a numeric type ID, filename or geometric classification. Existing presets and manually entered lattice values are preserved. Element defaults resets values from the source's element labels. The approximate reference-state numbers are from ASE 3.26.0; hexagonal c is a × (c/a). They are starting values, not stress-free lattice predictions for an alloy, finite temperature or a particular potential.

Estimation requests a complete PTM geometry fit with FCC/HCP/BCC/ICO/SC/cubic diamond/hexagonal diamond candidates (flags = 127) and RMSD cutoff 0.1. CNA classification alone cannot determine a lattice length. For each numeric type, the estimator restores the absolute lengths removed by PTM normalization and takes the median of matched atoms in the dominant supported phase. Cubic a uses the cube root of the local lattice volume; hexagonal a uses the square root of the fitted basal-plane area and c uses the fitted axial length. These metrics are invariant under rigid rotation and preserve independent hexagonal a and c, including nonideal c/a.

A reference requires at least four usable matches, recognition of at least 10% of that type's atoms and a phase containing at least 80% of its recognized atoms. Phase counts include recognized unsupported environments; Other, ICO and graphene do not supply 3D strain reference values. A mixed phase population is reported as ambiguous rather than averaging unlike lattice parameters, and insufficient or unsupported fits require manual input.

The inferred constants describe the current frame's bulk geometry, including bulk strain; they are not a prediction of a stress-free material lattice. Edit them when a known reference for the composition, temperature or potential is available. Once filled, estimated values stay fixed across trajectory frames and configuration export/restore, just as manually entered references do.

Calculate strain fits PTM correspondence and computes local elastic strain relative to that ideal lattice. The selected reference phase is automatically included in the strain fit even if its PTM template checkbox is off. A previously calculated PTM result is reused when it contains the requested templates and has the same RMSD threshold. A compatible complete geometry fit from estimation is reused by strain. Editing only the lattice reference reuses its geometry fit. An explicitly restricted PTM display keeps its own selected classification.

PTM removes scale during template fitting. AlloyView restores the absolute reference lattice scale before calculating the deformation gradient F, including independent hexagonal a/c scaling. Therefore uniform lattice expansion is retained as strain. Results are dimensionless:

• Green–Lagrange tensor E = (FᵀF − I) / 2; six components use the local crystal reference axes, whose symmetry-equivalent orientation can vary by atom.
• Hydrostatic strain tr(E) / 3.
• Von Mises shear strain sqrt((dev(E) : dev(E)) / 2), using the OVITO/AtomEye shear invariant convention.
• Physical volume change det(F) − 1.

The fit scale and deformation matrix retain double precision. Tensor components and volume changes below 1e-12 in absolute magnitude are treated as numerical zero, preventing roundoff from becoming a visible strain range in ideal crystals.

GPU reference evaluation chooses each atom's element and phase, restores its absolute deformation using editable a/c, then calculates the strain fields. Raw PTM arrays retain their GPU upload across compatible reference edits; CPU preparation does not compute per-atom lattice factors. Fresh calculations can also use GPU neighbors before the CPU PTM fit. See ideal lattice strain for backend stages and limits.

The default scalar view is shear strain; choose hydrostatic strain, volume change or individual tensor components in Color by. Atoms whose best PTM phase does not match their selected reference, whose fit exceeds the cutoff or whose environment is invalid get NaN, shown gray, without an unmatched-atom count or warning. An entirely NaN frame completes normally and uses a gray NaN legend key. Strain is a least-squares local fit and includes thermal displacements; it does not measure plastic displacement or non-affine D²min. It does not use another trajectory frame as its reference. Graphene and ICO identification are available, but these do not define a supported 3D strain reference here.

Central symmetry calculates the AtomEye-style normalized parameter from 12 (FCC/HCP) or 8 (BCC) nearest-neighbor displacement vectors. The default Auto setting first identifies each atom's local structure using adaptive CNA, reusing a compatible cached classification when available. It applies 12 neighbors to FCC/HCP atoms and 8 to BCC atoms. Mixed FCC/HCP/BCC structures therefore use different neighbor counts within one calculation, without splitting the input or changing coordinates. The selected Auto option and summary report the recognized phases.

Defect atoms classified as Other inherit a neighbor setting only when supported atoms among their nearest 14 neighbors give one setting a local majority. FCC/HCP votes are combined for 12 neighbors; BCC votes select 8. A tie between 8 and 12, an unrecognized neighborhood or an ICO environment remains NaN. This permits FCC/HCP fault neighborhoods to retain the shared 12-neighbor setting without requiring agreement on the phase label. Manual settings 12 · FCC / HCP and 8 · BCC retain a single count for the complete frame; Auto/manual mode is saved in processing configurations. Older version 1 configurations containing only a neighbor count restore the manual setting.

The result is scalar-colored with the existing editable legend. Each vector is paired once, greedily choosing its most nearly opposite unused partner in nearest-neighbor order. The sum of squared vector-pair sums is divided by twice the sum of squared neighbor distances. This dimensionless value vanishes in an ideal centrosymmetric environment. Ideal HCP is not centrosymmetric and has a finite value even without defects; Auto retains that physical baseline rather than subtracting it. Values from different phases are therefore not equivalent defect thresholds. This is not the conventional CSP in Ų or OVITO's minimum-weight matching CSP. Undefined Auto environments are NaN and shown gray, including a completely unsupported frame. Manual calculations with no valid neighbor environments retain the explicit failure status.

Auto also provides Local structure (Auto symmetry) and Central symmetry neighbor count as color properties. The first retains raw CNA labels, so inferred Other sites remain Other; the second shows their selected 8/12 setting or 0 when no setting was selected.

With GPU acceleration enabled, manual and Auto central symmetry run nearest-shell selection and greedy pairing on WebGPU. Auto can reuse adaptive-CNA labels or calculate them on GPU first. The pairing shader emulates IEEE 64-bit arithmetic to preserve the CPU's strict distance/vector ordering and pair comparisons, then emits the same Float32 scalar. HCP baselines, local shell voting and NaN semantics are unchanged. See central symmetry for bounded search and fallback details.

All analyses automatically run on subsequent trajectory frames after first being enabled. Per-frame results are reused only when their method/parameters match. Changes to CNA method, fixed radius or central-symmetry mode/neighbor count replace the affected result. Older requests cannot replace a newer parameter choice or another source. Element reference edits persist by input type label across frames and reset with a new source. PTM deformation arrays are counted in the adaptive frame-cache memory budget. Results are available in Atom details and Current measurements.

Each analysis has a Cancel button beside its status. It stops that analysis's running/queued Workers and returns it to Not calculated. The button can also reset a completed analysis. Its generated properties and per-frame results are removed across the frame cache, metrics are cleared, and automatic analysis on subsequent frames stops. When the removed property was selected for coloring, the view returns to atom-type colors. Input parameters and reference constants are retained so Calculate/Identify can restart it. Imported properties that were overwritten by an analysis result are restored.

Other analyses continue independently. PTM and strain can share a geometry fit, but cancelling one does not cancel the other. A strain request waiting for a cancelled PTM job obtains its own fit; cancelled PTM display properties stay removed. Strain's internal PTM fit alone does not enable the PTM display. Shared fits are released when neither analysis needs them. Cancelled results cannot reappear through a late response or a cached frame.

Numerical implementation

src/analysis/neighbors.js implements fractional linked-cell search with cell-face-height bounds. Nearest-neighbor queries inspect a complete search sphere, expanding it until the requested neighbor count is available, before sorting. Restricted triclinic geometry, mixed PBC, and non-periodic atoms outside the nominal box are supported. Distinct periodic images, including self images, are retained; this is essential for primitive and very small crystal cells. Neighbor-neighbor bonds use the actual local displacement vectors without wrapping them a second time. Extremely thin/skewed cells that would require excessive lattice-image enumeration produce an explicit error.

CNA constructs a local neighbor bond graph and measures, for each center-neighbor pair, the number of common neighbors, the number of bonds between them and the largest connected bond-chain size. Its structure signatures are:

• FCC: twelve 421 pairs.
• HCP: six 421 and six 422 pairs.
• BCC: eight 666 and six 444 pairs (two shells, fourteen neighbors).
• ICO: twelve 555 pairs.

Adaptive CNA first tests the nearest twelve neighbors with radius mean(r₁…r₁₂) × (1 + √2) / 2. It then tests the fourteen-neighbor BCC environment with radius mean(2r₁/√3 … 2r₈/√3, r₉ … r₁₄) × (1 + √2) / 2. Fixed CNA requires exactly twelve or fourteen neighbors inside the supplied radius. Other is a classification outcome, not a separate crystal phase; surfaces, vacancies, strong thermal disorder, unsupported structures and poorly chosen fixed cutoffs can all produce Other. The result is geometric and does not distinguish chemical ordering or crystal orientation.

Parallel execution

GPU acceleration is enabled by default. With Enable GPU acceleration selected, adaptive/fixed-cutoff CNA, manual/Auto central symmetry, displacement and reference-frame strain can use WebGPU. The GPU kernels preserve the same crystal labels, central-symmetry normalization, atom correspondence, reference-neighbor convention and output fields, with CPU fallback for unsupported inputs or unavailable GPU support. PTM identification and lattice estimation can use GPU neighbor preparation followed by CPU Wasm correspondence fitting in the shared pool. Fresh ideal strain uses the same hybrid fit, then applies its reference and tensor operations on GPU. Compatible cached fits skip neighbor preparation and correspondence fitting. See CNA, central symmetry, displacement, reference-frame strain and performance for backend and precision details.

Successful Workers remain in a bounded idle pool, and PTM initializes its Wasm kernel once per Worker. Cancellation and failures terminate the affected Worker; later jobs create a replacement. Each task carries an ID, so late results or progress cannot be applied to another job. Coordinates and neighbor contexts are released after processing; only the reusable kernel remains.

Progress separates waiting for a slot, preparing inputs, initializing the kernel, constructing the neighbor search and processing atoms. PTM and strain report actual processed-atom counts, throttled to avoid flooding the UI. Non-isolated deployments copy private input arrays in 4 MiB pieces with yields to the main thread before transferring them. Shared-buffer preparation also supports cancellation. This reduces repeated startup work and keeps controls responsive during preparation; it does not remove neighbor-search or fitting cost.

Coordination, CNA, central symmetry, PTM, ideal/reference strain and displacement share AnalysisPool. Independent central atom ranges execute in module Workers; the main thread uploads results and updates controls. CNA/CSP/PTM/fresh strain use 4,096 atoms per target range; cheaper coordination, displacement and cached-fit strain target 50,000 atoms. Each PTM Worker has its own Wasm instance, avoiding pthread/shared-Wasm hosting requirements. There is one total concurrency limit across all analyses: at most six Workers and at most hardwareConcurrency - 1, with at least one Worker on small/single-core systems. Copy and scratch-memory estimates further reduce each job's range count. Different analyses may run concurrently within that budget.

On isolated local development servers, inputs use SharedArrayBuffer when available; ordinary hosting uses bounded coordinate copies. Float32/Float64 input precision is preserved. Partial structure/scalar outputs cover only their own central range; coordination retains its symmetric pair reduction. Source/frame/parameter changes terminate stale structure jobs and remove queued tasks. Closing the pool settles every pending promise and releases its Workers. The legacy coordination facade preserves its latest-request queue while using the same global scheduler.

Reference scan and further work

Reviewed snapshots (2026-10-02):

• AtomEye, A3/geo.c, especially compute_central_symm(); see the broader AtomEye inventory.
• OVITO, CNA documentation and CommonNeighborAnalysisModifier.cpp, predefined structure colors in ParticleType.cpp, PTM documentation and the separately MIT-licensed library in src/3rdparty/ptm.
• Honeycutt & Andersen, J. Phys. Chem. 91, 4950 (1987), doi:10.1021/j100303a014.
• Stukowski, Modell. Simul. Mater. Sci. Eng. 20, 045021 (2012), doi:10.1088/0965-0393/20/4/045021.

The CNA/CSP browser kernels independently implement these algorithmic definitions. No AtomEye or OVITO application source is bundled. AtomEye's reviewed tree does not contain CNA or PTM; these are separate additions inspired by OVITO's structure-identification workflow.

PTM uses the separately licensed library from the pinned OVITO snapshot, vendored unchanged in third_party/ptm/. Its modified Voro++ cell code retains the BSD notices. PTM, Voro++ and Emscripten runtime notices ship in licenses/ alongside each static build. The source pin and checksums are recorded in third_party/ptm/UPSTREAM.md and SHA256SUMS. The library uses polyhedral topology, Voronoi neighbor ordering and geometric least-squares template fits; it is not a CNA alias or a distance-only heuristic. For scientific use cite Larsen, Schmidt & Schiøtz, Modell. Simul. Mater. Sci. Eng. 24, 055007 (2016), doi:10.1088/0965-0393/24/5/055007.

wasm/ptm.cpp provides the integration ABI and neighbor callback. The generated src/analysis/ptm-kernel.mjs / .wasm are included, so ordinary development, tests and static-site builds do not require a compiler. After changing C++, run npm run build:ptm with Emscripten (validated: Debian 3.1.69 / LLVM 19), then npm test, npm run build and npm run test:browser. The prepared cloud environment also provides an isolated compiler at /workspace/.tools/wasm-sdk, which the build script detects. It verifies the vendored source checksums before compiling. Browser Workers fetch the versioned .wasm asset with relative URLs; Node scientific tests supply the same binary directly. No CDN or runtime package download is required.

Reference-frame strain, local geometric shear, radial distribution functions and bond visualization are documented in their feature guides.