forked from bai/curriculum-project-hub
feat(examples): migrate TH-141 sample to declarative layout (WU-6)
Real-content fixture for the end-to-end pipeline. TH-141 (39 parts: 22 segment, 15 lemma, 2 example) migrated from the prototype's typst `#let parts` manifest to ADR-0008: declarative manifest.toml (project+info+ordered parts+targets) + per-element element.toml (kind + scalars; examples carry `source`). Content .typ files copied byte-identical (no math corruption); per-element main.typ + meta.toml dropped (wiring is now generated). Part order matches source exactly; 5 lemmas have no proof.typ (optional); no cross-file imports / paralearn refs / figs. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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kind = "lemma"
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数缺键以几何方式进行。
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简单立方中每个体相原子的 6 个最近邻分布在上下左右前后六个方向。(100) 面上的表面原子失去上方那 1 个邻居,故 $Z_s = 5$、$zeta = 5\/6$。
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面心立方中每个体相原子的 12 个最近邻分布在该原子周围三个 (111) 面上。(111) 面是最密堆积,表面原子失去上方一层的 3 个邻居,$Z_s = 9$、$zeta = 3\/4$。(100) 面失去 4 个上方邻居,$Z_s = 8$、$zeta = 2\/3$。(110) 面失去的近邻更多,$zeta$ 进一步减小。
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通过对几何晶格直接数缺键数,可以把 @缺键一般式 中的 $zeta$ 落到具体数字:
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- 简单立方 (100) 面:$Z = 6$、$Z_s = 5$,$zeta = 5\/6$。
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- 面心立方 (111) 面:$Z = 12$、$Z_s = 9$,$zeta = 3\/4$。
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- 面心立方 (100) 面:$Z_s = 8$,$zeta = 2\/3$。
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- 面心立方 (110) 面:$zeta < 2\/3$。
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后续讨论以 FCC (111) 面为代表,因其密度最大、$gamma$ 最低、平衡形貌中最易出现。
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