EQUATION REGISTRY

FCC neighbour moments

Twelve neighbours, four sign combinations per group; a geometric result.

Theory · CANDIDATE MODELEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-SD-020
dn∈a02{(±1,±1,0),(±1,0,±1),(0,±1,±1)},∑ndn,idn,j=2a02δij\mathbf d_n\in\tfrac{a_0}{2}\{(\pm1,\pm1,0),(\pm1,0,\pm1),(0,\pm1,\pm1)\},\quad\sum_nd_{n,i}d_{n,j}=2a_0^2\delta_{ij}

Twelve neighbours, four sign combinations per group; a geometric result.
Chapter reference: Ch. 4 (4.3)–(4.4); Ch. 5 (5.1.3)–(5.1.4) · ASD-BOOK-ddbade997b45

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Adopted source, conditions and previous versions

Ch. 4 (4.3)–(4.4); Ch. 5 (5.1.3)–(5.1.4)

Registered formula checked individually against the final manuscript; The mathematical content agrees; the existing expression and its derivation conditions are retained.

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  • Twelve neighbours, four sign combinations per group; a geometric result.

Source locators: p1306 · p1311 · p1750–1752

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

SD-51779505a476 · Ch. 4 (4.3)–(4.4); Ch. 5 (5.1.3)–(5.1.4)

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Uses of this equation

Subsequent equationExact equal-link scalar dispersionASD-WEB-SD-021DocumentOP-SD-004 · Continuum-to-Microscopic CorrespondenceDocumentThe FCC Microscopic Model: Links, Continuum Limit and Dispersion
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