Temari¶
Open, relativistic, reproducible off-diagonal ionization form factors for quantitative STEM-EDX and ALCHEMI.
Temari publishes the signed inner-shell ionization form factor \(F(s, E_0)\) that quantitative STEM-EDX and ALCHEMI need: the normalized off-diagonal shape obtained by contracting the mixed dynamic form factor over the ejected electron's energy and direction, for two Bloch waves separated by \(K = 4\pi s\,a_0\) — the off-diagonal response needed to model how an EDX map depends on crystal orientation. Dataset v7.0.0 covers 525 channels from K to M5, carries a DOI, and fixes its conventions, its golden vectors and an executable data contract. Using the published tables does not require Julia.
\(F(s, E_0)\) is a normalized shape, not an absolute cross section: the absolute \(\sigma(E_0)\) shipped beside it and the edge energies both come from the Bote–Salvat coefficient set (Bote & Salvat, 2008; Bote et al., 2009), the one third-party table this code carries. Every shape and every scattering factor is computed here.
Behind the dataset is an engine that solves an isolated atom from scratch — self-consistent field, bound orbitals, distorted continuum waves — and derives from that one atom six scattering and excitation quantities. It calls no external atomic-structure code, it does not read scattering factors from a fitted table, and it depends on nothing but the Julia standard library. The published off-diagonal form factors are the product; the shared engine is why they are reproducible and why the family can grow.
Just want the numbers?
Two datasets are already published, and neither needs Julia:
- Inner-shell ionization form factors \(F(s, E_0)\) for STEM-EDX — 525 channels (K through M5), with a DOI.
- X-ray and electron atomic scattering factors \(f_x(s)\), \(f_e(s)\) for the neutral atoms Z = 1–86 (dataset-factors v2.0.0), and for 22 Watson-sphere-stabilised anions (dataset-factors-ion 1.0.0). Both are published as computed values; no file carries a certified error bound.
See Data — and read its contract before using the numbers.
The name
Temari (手毬) is a traditional Japanese craft: a sphere divided geometrically, then wound with many threads to form a pattern. That is what this code does — it lays dozens of partial waves over a spherically symmetric atomic field. The partial-wave skeleton is the same whether the exit is an ionization form factor, a generalized oscillator strength, or an elastic phase shift.
Status
The engine is in production use: it generates the STEM-EDX ionization tables shipped with ReciPro, and it generated both published datasets. It is split into the L0–L5 layer files described under Architecture, and six exits sit on top of the same atom. The ionization tables and the scattering factors have been compared by the author against external references (Verification, Against the literature) — there is no independent third-party validation yet; the EELS, GOS, phase-shift and Mott exits are checked against analytic limits and, where one exists, an external reference — the GOS comparison against the Dirac GOS database leaves a Bethe-ridge discrepancy that the Verification page records as unexplained — and no dataset has been published from them yet.
What it computes today¶
One engine, six exits. Everything below starts from the same self-consistent atom: the three ionization exits share its relativistic bound orbitals and distorted continuum waves, the two elastic exits use its continuum solver, and the scattering-factor exit reads its density directly. The exits differ in the operator and in what is reported.
| Exit | Quantity | Command |
|---|---|---|
| Ionization form factor | \(F(s, E_0)\) for K, L1–L3 and M1–M5, plus \(\sigma(E_0)\) from the Bote–Salvat coefficients | <Z> <channel> <E0> |
| EELS core-loss edge | \(\mathrm{d}\sigma/\mathrm{d}\Delta E\) and the inner-shell contribution to the stopping power | edge |
| Generalized oscillator strength | \(\mathrm{d}f/\mathrm{d}\Delta E(Q)\), the Bethe surface — independent of \(E_0\) | gos |
| Elastic phase shifts | \(\delta_l\) in the neutral atom's static field | phase |
| Mott elastic scattering | \(\mathrm{d}\sigma/\mathrm{d}\Omega\), \(\sigma_{el}\), \(\sigma_{tr}\) and the Sherman function | mott |
| Atomic scattering factors | \(f_x(s)\) for X-rays and \(f_e(s)\) for electrons, from the SCF density — computed, not read from a fitted table | fx |
What a channel is, and what s is
A channel is one element and one subshell: Fe K is iron's 1s shell, Au L3 is gold's 2p₃/₂ shell. The ionization form factor is computed per channel and per incident energy \(E_0\); the scattering factors need only the element. Throughout the site \(s = \sin\theta/\lambda\) in Å⁻¹, the crystallographic variable — a momentum transfer of \(q = 4\pi s\), so \(s = 0.5\) Å⁻¹ is \(q = 6.28\) Å⁻¹.
ALCHEMI (Atom Location by CHannelling-Enhanced MIcroanalysis) estimates site occupancy from the way characteristic X-ray yields change with crystal orientation. Temari supplies the off-diagonal ionization shape factors that the downstream Bloch-wave simulation needs; it does not perform the occupancy refinement itself.
The form factor is normalized to \(F(0) = 1\) and carries the delocalization of the inelastic image; the absolute scale is supplied by the cross section. See The physics for the prescription and its known limits, and the command-line reference for what each exit reports.
Find by goal¶
| Goal | Start here |
|---|---|
| Use the published tables without running anything | Data |
| Run it once and see a number | Getting started |
| Every subcommand and flag | Command-line reference |
| What prescription is actually implemented | The physics |
| Where a new quantity would be plugged in | Architecture |
| How far the numbers are trusted, and why | Verification |
| How the tables compare with the literature, as curves (Si, Fe) | Against the literature |
| Why an obvious optimization was rejected | Reproducibility, Performance |
| What is planned, and what is deliberately out of scope | Roadmap |
| A long batch stopped making progress on Windows | Troubleshooting |
Why this exists¶
The physics of an isolated atom scattering a fast electron, a photon, or another electron is one calculation with several exits. The quantities an electron-microscopy workflow needs are normally split across separate tools and datasets, each exposing one exit and keeping its engine to itself:
- Ionization form factors for STEM-EDX / EELS mapping are locked inside microscopy simulators.
- The generalized oscillator strength (GOS) tables that EELS quantification still runs on date from the 1980s — Egerton's SIGMAK/SIGMAL (Egerton, 2011) and the Hartree–Slater tables of Leapman et al. (1980). One modern, open, relativistic reference now exists, the Dirac GOS database (Zhang et al., 2023); it stops at \(q = 50\) Å⁻¹ (\(s \approx 3.98\) Å⁻¹) and it is a GOS table, not an ionization form-factor table for Bloch-wave or multislice codes.
- Elastic scattering phase shifts live in separate Fortran packages.
- Atomic scattering factors are commonly consumed as fitted parameterizations rather than as something you can recompute for an arbitrary ion.
Temari puts the engine in the open and adds exits to it. Three quantities — the
EELS edge shape, the inner-shell stopping power and the elastic phase shifts —
already existed inside the call graph of the ionization exit and were discarded
before returning; exposing them (as the edge and phase subcommands) was
output plumbing, not new physics. See
Architecture.
Design commitments¶
- Zero dependencies. Julia standard library only. The sole bundled third-party data file is the Bote–Salvat cross-section coefficient set (public domain).
- Standalone. No
module, no package to install: the layer files carry a flat namespace and concatenate in include order, so it stays possible to hand the whole engine to someone as a single file. - MIT licensed code, CC-BY-4.0 data. A reference implementation should be readable and usable; the generated tables carry their own licence and their own version line.
- Fast, but reproducibility outranks speed: optimizations that change floating-point summation order are adopted only when a full table regeneration is intended, and are declared as such.
- The physics is readable in the source. Comments in the code are the authoritative statement of the prescription.
- The engine/GUI boundary is a CLI contract. Any GUI is a separate process that calls subcommands and reads JSON — never linked in-process.
What is not here¶
- No dataset inside the repository. The generated tables are large and are versioned independently of the code, so they are distributed as their own releases — the ionization form factors under their own DOI, the scattering factors as a versioned GitHub release — rather than committed here; see Data. This repository holds code, documentation and small derived index tables.
- No reference data from restricted sources. Comparison against published tables and GPL-licensed codes is part of development, but those numbers are never copied into this repository. What is published is ratios and deviations, as on the comparison page.
Credits and licensing¶
The software is MIT; the datasets are CC-BY-4.0 with an MIT loader. Copyright © 2026 Yusuke SETO.
Most of the implementation code was produced with assistance from Anthropic Claude and was reviewed and integrated by the author. The author is responsible for the physical prescription, for the tests and for the released data. AI assistance is not treated as independent validation: the reproducible checks, the external comparisons and the known unresolved discrepancies are documented under Verification.
bote_salvat.json is machine-extracted from NIST's BoteSalvatICX.jl (Unlicense,
public domain). If you publish results using the cross sections, please cite
Bote & Salvat (2008) and Bote et al. (2009) as well.
References¶
- Bote, D. & Salvat, F. (2008). Calculations of inner-shell ionization by electron impact with the distorted-wave and plane-wave Born approximations. Physical Review A 77, 042701.
- Bote, D., Salvat, F., Jablonski, A. & Powell, C. J. (2009). Cross sections for ionization of K, L and M shells of atoms by impact of electrons and positrons with energies up to 1 GeV: Analytical formulas. Atomic Data and Nuclear Data Tables 95, 871–909. Erratum: 97 (2011), 186.
- Egerton, R. F. (2011). Electron Energy-Loss Spectroscopy in the Electron Microscope, 3rd ed. Springer, New York.
- Leapman, R. D., Rez, P. & Mayers, D. F. (1980). K, L, and M shell generalized oscillator strengths and ionization cross sections for fast electron collisions. Journal of Chemical Physics 72, 1232–1243.
- Zhang, Z., Lobato, I., Jannis, D., Verbeeck, J., Van Aert, S. & Nellist, P. (2023). Generalised oscillator strength for core-shell electron excitation by fast electrons based on Dirac solutions [Data set]. Zenodo. doi:10.5281/zenodo.7729585