Structure Field Map

An empirical materials map that places compositionally comparable crystalline compounds in descriptor coordinates and uses the resulting structure-type fields as an interpretable classification and candidate-structure prior.

Version

v2 · 2026-09-06 · History

Domain-specific #

2879

Origin domain

crystallography

Subdomain

crystal chemistry

Aliases

Structure-field map, SFM

Core Idea

A Structure Field Map (SFM) is an empirical crystal-chemical representation that places compositionally comparable materials in a low-dimensional coordinate system defined by constituent descriptors, labels the resulting points by observed crystal-structure type, and interprets neighborhoods or regions occupied by the same type as structure fields. Its characteristic question is not merely “what is this compound's structure?” but “how do known structure types distribute across a declared chemical-descriptor space, and what candidate structures does the local pattern suggest for an unmeasured composition?” Early ionic-size studies, systematic ternary compilations, Pettifor's chemical-scale maps, and database-generated maps retain this same role structure while changing descriptors and implementation.

Scope of Application

The most literal scope is inorganic crystallography, crystal chemistry, mineralogy, alloy science, and related materials informatics. Ionic-radius maps are natural for families in which charge balance, coordination, and cation size strongly organize feasible structure types. The 1954 Keith–Roy study examined structural relations among double oxides of trivalent elements and demonstrated ionic-radius ratio and cation charge as controlling variables in the studied systems. Muller and Roy's 1974 treatment assembled major ternary structural families and explicitly organized ionic radii, formula families, polymorphs, and structure-field maps within a broad crystal-chemical reference work.

Clarity

Consider an oxide family ABO3. The author first fixes one charge pairing, such as A2+B4+O3, rather than mixing it with A3+B3+O3. For each known compound, the chosen radius table supplies an A-site effective ionic radius on the horizontal axis and a B-site radius on the vertical axis, using declared coordination and spin assumptions. The compound's experimentally observed room-condition structure prototype supplies its label.

Manages Complexity

The space of chemical compositions is combinatorial, while a structure assignment contains detailed symmetry, atomic positions, coordination, and condition information. An SFM compresses that problem in three stages. First, it substitutes a small set of chemically motivated descriptors for a full constituent description. Second, it reduces detailed structures to a consistent type or prototype vocabulary. Third, it uses the geometry of many labeled examples to make repeated structure–chemistry regularities visible at once.

Abstract Reasoning

1. If two maps use different ionic-radius tables, coordination numbers, or spin-state assumptions, their point geometry is not directly comparable even when the axes share the same labels. 2. If a compound changes structure with pressure or temperature, one unqualified point cannot represent every polymorph. The observation condition must be attached to the label or the map restricted to one condition frame. 3. If oxidation-state pairings are mixed in one ABO3 map, apparent proximity can compare chemically different charge-balance regimes.

Knowledge Transfer

Within crystalline-materials research, exact transfer occurs when the same roles are rebuilt for a new family. Oxide crystal chemistry may use effective ionic radii; alloy maps may use a chemical scale; a higher-dimensional informatics implementation may use several constituent descriptors before projecting the result for inspection. Each remains an SFM only if comparison scope, coordinate rule, structure labels, field/neighborhood relation, and bounded inference survive.

Relationships to Other Abstractions

Current abstraction Structure Field Map Domain-specific

Parents (1) — more general patterns this builds on

• Structure Field Map is a kind of Representation Prime

  Representation. The SFM maps a target population of materials into a coordinate-and-label medium, preserving selected chemical similarities and observed structural classes while explicitly dropping much microscopic detail.

Hierarchy path (1) — routes to 1 parentless root

• Structure Field Map → Representation → Abstraction

Neighborhood in Abstraction Space

Structure Field Map sits in a sparse region of the domain-specific corpus (90^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Crystallographic Coordinates & Symmetry (5 abstractions)

Nearest neighbors

• Chemical space — 0.80
• Tanabe–Sugano diagram — 0.79
• Crystal structure prediction — 0.79
• Fractional coordinates — 0.78
• Chemical compound — 0.78

Computed from structural-signature embeddings · 2026-09-08