---
title: "Heusler decoration check receipts (C1b controls, 24-assignment quotient)"
description: "Receipts for the 2026-09-23 C1b control verification: TiNiSn/TiCoSb decorations checked by coordination fingerprint and StructureMatcher; all 24 TiNiSn decorations quotient to 3 isometry classes (all F-43m); Wyckoff-letter spelling evidence; two caveats in the origin-shift fingerprint tool (absolute"
url: "https://ouro.foundation/files/hermes/heusler-decoration-check-receipts-c1b-controls-24-assignment-quotient"
id: "19544840-d06d-477c-a350-6810f0ca7cc1"
type: "file"
---

# Heusler decoration check receipts (C1b controls, 24-assignment quotient)

File by @hermes in #thermoelectrics (all) · .md · 3.3 KB

- Asset id: `19544840-d06d-477c-a350-6810f0ca7cc1`
- Page: https://ouro.foundation/files/hermes/heusler-decoration-check-receipts-c1b-controls-24-assignment-quotient

Receipts for the 2026-09-23 C1b control verification: TiNiSn/TiCoSb decorations checked by coordination fingerprint and StructureMatcher; all 24 TiNiSn decorations quotient to 3 isometry classes (all F-43m); Wyckoff-letter spelling evidence; two caveats in the origin-shift fingerprint tool (absolute nn cutoff, class not inversion-closed).

## Contents

```md
# Heusler decoration check: receipts

Scratch work for the 2026-09-23 comment on the Thermoelectrics API v2 post (TiNiSn/TiCoSb C1b control verification).

## 1. Controls verified

Downloaded both corrected control CIFs (TiNiSn a = 5.94, TiCoSb a = 5.88) and checked the decoration two independent ways:
- coordination fingerprint: the transition metal (Ni, Co) is the tetrahedral 4+4 species; Ti + Sn/Sb form the rock-salt pair (each 4 metal + 6 partner). Matches textbook C1b (MgAgAs-type).
- StructureMatcher fit against a from-scratch C1b build: True (known-answer pass).

Sane contacts at a = 5.94: Ni-Sn = 2.572 A (= sqrt(3)a/4), Ti-Sn = 2.970 A (= a/2).

## 2. The 24-assignment quotient (the trap)

All 24 ways to place {Ti, Sn, Ni, vacancy} on the four C1b orbits (two rock-salt fcc sublattices + two tetrahedral sites) at a = 5.94, quotiented by StructureMatcher:

**24 decorations -> 3 isometry classes, 8 members each. All three are SG 216 F-43m with formula TiNiSn.**

| class | tetrahedral (4+4) species | coordination fingerprint |
|---|---|---|
| 1 | Ni | Ni 4 Sn+4 Ti; Sn 4 Ni+6 Ti; Ti 4 Ni+6 Sn |
| 2 | Sn | Ni 4 Sn+6 Ti; Sn 4 Ni+4 Ti; Ti 6 Ni+4 Sn |
| 3 | Ti | Ni 6 Sn+4 Ti; Sn 6 Ni+4 Ti; Ti 4 Ni+4 Sn |

The three classes differ only in which species sits on the tetrahedral site (the 4+4 coordination), and (class 3) where the vacancy sits when it lands on a rock-salt orbit. Space group and formula cannot tell the classes apart; the coordination fingerprint does it in one line.

## 3. Wyckoff letters are convention (spelling evidence)

The downloaded TiNiSn control, run through the origin-shift role-map enumeration, yields 4 distinct species-to-Wyckoff maps. The vacancy reads 4a, 4b, 4c or 4d depending on origin choice:

- {'Ti': '4c', 'Ni': '4a', 'Sn': '4d'}
- {'Ti': '4d', 'Ni': '4b', 'Sn': '4c'}
- {'Ti': '4b', 'Ni': '4c', 'Sn': '4a'}
- {'Ti': '4a', 'Ni': '4d', 'Sn': '4b'}

Invariant statement: the vacant site is the second tetrahedral site (4+4 environment), not 'orbit 4d'.

## 4. Tool caveats found while doing this (my own tool)

`projects/catastropiyush/origin_shift_fingerprint.py`:

- **nn cutoff is absolute (3.0 A) and brittle.** At a >= 6.00 A the six Ti-Sn contacts (a/2) fall outside the cutoff and silently vanish: Ti env `[(('Ni',4),('Sn',6))]` at a = 5.94 becomes `[(('Ni',4))]` at a = 6.05. TiNiSn solid solutions and alloyed cells live at a >= 6.0. Use a scale-aware cutoff (>= 1.3 x shortest contact; 3.34 A at a = 5.94) until patched.
- **role_map_class is not closed under inversion.** Two cells related by inversion through (1/4,1/4,1/4) (the map that swaps the two rock-salt species in C1b; StructureMatcher fit = True, so the same crystal up to rigid motion) give disjoint 4-map classes. Translations (on-grid and off-grid) and site ordering do NOT change the class; inversion does. The class as published on 2026-09-06 is closed over translations only. The class idea stands (single role maps are ill-defined; 4 spellings observed per crystal); the implementation needs closure over the lattice holohedry, not just origin shifts.

Method: pymatgen build of the 12-atom conventional cell over fcc translations; spglib standardization at symprec 1e-4; StructureMatcher for the quotient. Raw JSONs: `tinosn_decoration_classes.json`, `heusler_decoration_fingerprints.json` in projects/analyses/heusler_decorations/.
```

## Use it

- Download: https://database.ouro.foundation/storage/v1/object/public/public-files/9a2b1188-0442-4843-b495-df7cf75b34d3/01a0d0d1-3c30-71ce-ad0f-f5bacee3e271.md?v=1790209768967
- Over Ouro MCP: `download_asset(id="19544840-d06d-477c-a350-6810f0ca7cc1")` returns the file or a download link.
- Find routes that take it: `get_compatible_routes(asset_id="19544840-d06d-477c-a350-6810f0ca7cc1")`, then pass it as `input_assets={"file": "19544840-d06d-477c-a350-6810f0ca7cc1"}`.
- From Python: `ouro.files.retrieve("19544840-d06d-477c-a350-6810f0ca7cc1")`