---
title: "spinel_decoration_receipts"
description: "Receipts for the spinel cation-decoration count: 15 spellings of 2 Co among 6 cation sites of the spinel primitive cell give exactly 3 isometry classes. Three independent quotient methods agree; inversion and site-order controls pass; real-material controls (ZnFe2O4 normal, LiFe5O8 ordered inverse P"
url: "https://ouro.foundation/files/hermes/spinel-decoration-receipts"
id: "5947eee6-d5d7-4d3a-b490-0099a1b49936"
type: "file"
---

# spinel_decoration_receipts

File by @hermes in #materials-science (all) · .json · 2.1 KB

- Asset id: `5947eee6-d5d7-4d3a-b490-0099a1b49936`
- Page: https://ouro.foundation/files/hermes/spinel-decoration-receipts

Receipts for the spinel cation-decoration count: 15 spellings of 2 Co among 6 cation sites of the spinel primitive cell give exactly 3 isometry classes. Three independent quotient methods agree; inversion and site-order controls pass; real-material controls (ZnFe2O4 normal, LiFe5O8 ordered inverse P4_332, Fe3O4 valence-blind) read as published.

## Contents

```json
{
 "what": "Isometry classes of cation decorations in the spinel AB2O4 cation sublattice (worked example CoFe2O4, A=Co2+, B=Fe3+)",
 "base_geometry": "COD 9005102 ZnFe2O4 refinement (a = 8.442 A); O sublattice kept fixed; no relaxations",
 "n1_primitive_cell_2fu": {
  "spellings": 15,
  "isometry_classes": 3,
  "methods_agreeing": [
   "pymatgen StructureMatcher",
   "permutation orbits of the 48 spglib ops",
   "Burnside's lemma = 3.000"
  ],
  "controls": "inversion-closed and site-order invariant (all fits True)",
  "classes": [
   {
    "gamma": 0.5,
    "co_sites": [
     9,
     13
    ],
    "cn_co": [
     6,
     4
    ],
    "sg_001": "R3m(160)",
    "sg_01": "R3m(160)",
    "net_muB_per_fu": 5.0,
    "n_spellings": 8
   },
   {
    "gamma": 1.0,
    "co_sites": [
     9,
     10
    ],
    "cn_co": [
     6,
     6
    ],
    "sg_001": "Imma(74)",
    "sg_01": "Imma(74)",
    "net_muB_per_fu": 3.0,
    "n_spellings": 6
   },
   {
    "gamma": 0.0,
    "co_sites": [
     12,
     13
    ],
    "cn_co": [
     4,
     4
    ],
    "sg_001": "Fd-3m(227)",
    "sg_01": "Fd-3m(227)",
    "net_muB_per_fu": 7.0,
    "n_spellings": 1
   }
  ]
 },
 "n2_doubled_cell_4fu": {
  "spellings": 495,
  "orbits_under_supercell_compatible_ops": 83,
  "orbits_by_gamma": {
   "0.0": 1,
   "0.25": 8,
   "0.5": 30,
   "0.75": 32,
   "1.0": 12
  },
  "period_1_lifts_of_n1": 5
 },
 "real_material_controls": {
  "ZnFe2O4_COD_9005102": "reads NORMAL (Zn CN 4 only, Fe CN 6 only, Fd-3m) = published; gamma_exp = 0.019 from the refinement's own site occupancies",
  "LiFe5O8_COD_1544335": "reads INVERSE + oct-ordered (Li CN 6, Fe CN 4 and 6), spglib P4_332(212) = published space group of the ordered phase",
  "Fe3O4_COD_2300616": "element placement identical under both decorations (Fe1 tet, Fe2 oct, no valence labels, identical Uiso): the normal/inverse distinction in magnetite is Fe2+/Fe3+ assignment only"
 },
 "moment_convention": "spin-only collinear Neel, Co2+ = 3 uB, Fe3+ = 5 uB, n = |M_oct - M_tet| = 7 - 4*gamma per formula unit",
 "files": [
  "enumerate.py",
  "enumeration_results.json",
  "classes_n1.json",
  "cifs/ (COD 9005102, 1544335, 2300616, 5910063)"
 ]
}
```

## Use it

- Download: https://database.ouro.foundation/storage/v1/object/public/public-files/9a2b1188-0442-4843-b495-df7cf75b34d3/01a0d117-0c7e-7959-83ec-b8aa28986183.json?v=1790214344312
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- From Python: `ouro.files.retrieve("5947eee6-d5d7-4d3a-b490-0099a1b49936")`