forked from bai/curriculum-project-hub
feat(cph): implement nested outline manifest and batch/combined export
ADR-0029 — nested outline manifest, supersedes ADR-0008's flat [[parts]]:
- cph-model: recursive loader over manifest.toml containers / element.toml
leaves; Lesson.parts (pure elements, DFS order) + Lesson.outline (elements
interleaved with section headings at their DFS-open position); rejects
ambiguous/incomplete folders and root-vs-container table misplacement
- cph-diag: new DiagCode::ManifestMalformed for carrier-document structure
errors (discharges an existing TODO)
- cph-typst: augmented manifest now serializes the outline (element/section
entries) instead of a flat parts array
- render/lib.typ: render-lesson renders section headings at their depth
- examples/TH-141 migrated to 5 nested section containers + 3 root segments,
byte-identical element order; smoke-verified via cph check/build + pdftotext
ADR-0030 — batch & combined export, extends ADR-0009/0011:
- cph build with no --target batches every declared target (repeatable
--target for an explicit subset); any target failure => non-zero exit,
per-target ledger, independent per-target execution
- cph-model: bundle.toml loader (directory + [info]/[targets.*]/ordered
lessons with per-lesson target overrides)
- cph-typst: augmented bundle manifest (path-prefixed member outlines),
Engine::{compile_check_bundle,build_bundle_pdf}
- render/lib.typ: render-bundle assembles member lessons under per-lesson
headings, depth-shifts their own section headings, resets example/lemma
counters at each lesson boundary by default
- cph-cli: `cph bundle <path> --target <name>` subcommand, same batching
contract as `cph build`
- new bundle fixtures/tests (cph-model unit + cph-typst through-template PDF
compile), smoke-verified via a real 2-lesson merged PDF
Verification: cargo fmt/clippy/test clean across the workspace (68 tests);
real cph check/build/bundle runs against TH-141 and a bundle fixture, PDF
content inspected via pdftotext.
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kind = "lemma"
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设下半空间体相分子的数密度为 $n_v = 1 \/ d^3$。固定一个表面分子作为参考分子,对其与下半空间所有体相分子的相互作用求和。由对称性,相对参考分子距离 $r$ 在下半空间内的体积元为 $dif V = 2 pi r^2 dif r$。下限取 $r = d$,上限取 $infinity$:
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$ Delta U = 2 pi n_v integral_d^infinity u(r) thin r^2 dif r . $
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代入 $u(r)$,用 $integral r^2 dot r^(-n) dif r = r^(3 - n) \/ (3 - n)$ 化简,得
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$ Delta U tilde.op epsilon . $
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把 $Delta U$ 乘以单位面积分子数 $n_s tilde.op 1 \/ d^2$,由 @骨架公式 即得
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$ sigma tilde.op epsilon / d^2 , $
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即 @LJ标度。
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设分子间对势为 Lennard–Jones 6-12 形式
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$ u(r) = 4 epsilon [(d \/ r)^(12) - (d \/ r)^6] . $
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把一个表面分子与下半空间所有分子的相互作用积分求和,得到
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$ sigma tilde.op epsilon / d^2 . $ <LJ标度>
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此式与量纲估计 @量纲估计 同标度。
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kind = "lemma"
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在 @缺键一般式 中取 $zeta = 1\/2$,
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$ sigma_(L G) = 1/2 dot L_m thin rho^(2\/3) / (mu^(2\/3) N_A^(1\/3)) . $
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由 $d^3 = mu \/ (rho N_A)$ 得 $rho^(2\/3) \/ (mu^(2\/3) N_A^(1\/3)) = 1 \/ (d^2 N_A)$,代入即得
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$ sigma_(L G) thin d^2 approx L_m / (2 N_A) , $
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即 @Stefan估算。
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在 @缺键一般式 中取 $zeta = 1\/2$,得
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$ sigma_(L G) thin d^2 approx L_m / (2 N_A) . $ <Stefan估算>
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它是缺键模型的最简退化形式,不含任何晶格信息。
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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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kind = "lemma"
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设体相分子的最近邻数为 $Z$、每根键的能量为 $epsilon$。每根键被两个分子共享,一摩尔液体的独立键数为 $N_A Z \/ 2$,把它们全部断开所需的能量即摩尔汽化热
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$ L_m = N_A Z epsilon / 2 , quad arrow.r.double quad epsilon = (2 L_m) / (N_A Z) . $ <缺键-单键>
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表面分子的近邻数为 $zeta Z$,相比体相少 $(1 - zeta) Z$ 个近邻。按共享原则,每个缺键的能量代价为 $epsilon \/ 2$,于是每个表面分子的亏损能为
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$ Delta U = (1 - zeta) Z dot epsilon / 2 = ((1 - zeta) L_m) / N_A . $ <缺键-亏损能>
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设每个分子占体积 $d^3 = mu \/ (rho N_A)$,则单位面积分子数
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$ n_s = d^(-2) = (rho N_A / mu)^(2\/3) . $ <缺键-面密度>
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代入 @骨架公式 即得
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$ sigma_(L G) = Delta U dot n_s = (1 - zeta) thin L_m thin rho^(2\/3) / (mu^(2\/3) thin N_A^(1\/3)) , $
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即 @缺键一般式。
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设液体表面层每个分子的近邻数是体相分子近邻数的 $zeta$ 倍($0 < zeta < 1$),摩尔汽化热为 $L_m$、摩尔质量为 $mu$、质量密度为 $rho$、阿伏伽德罗常量为 $N_A$,则液气界面张力系数为
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$ sigma_(L G) = (1 - zeta) thin L_m thin rho^(2\/3) / (mu^(2\/3) thin N_A^(1\/3)) . $ <缺键一般式>
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kind = "lemma"
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设液体的单键能为 $epsilon$、分子间距为 $d$,仅由量纲组合可得液气界面张力的标度
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$ sigma tilde.op epsilon / d^2 . $ <量纲估计>
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此式不依赖具体势函数、晶格结构或相变热,是后续更精细模型的下限基准。
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