diff --git a/CHANGELOG.md b/CHANGELOG.md index 94779a71..81eb30e3 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -372,6 +372,11 @@ one version). ### Changed +- `Lattice::gallium_nitride()` now uses the measured bulk-crystal cell + `a = 3.1890 Å`, `c = 5.18500 Å` at 300 K (Melnik et al. 1997) instead of + `3.189 Å`, `5.178 Å`; its placeholder `u` follows from the new `a`, `c`. + `GAN_DENSITY_G_CM3` is now the measured 6.1 g/cm³ (Juza and Hahn 1938), + replacing 6.15 (#179). - **Electron results change for every run that uses the `mermin-melf` inelastic model** (#342). A Mermin table row at energy `T` now draws its losses from `(1e-8 T, T]`, the window its rate integral already used, diff --git a/docs/crystal-orientation.md b/docs/crystal-orientation.md index 4d6d9399..fb11795a 100644 --- a/docs/crystal-orientation.md +++ b/docs/crystal-orientation.md @@ -164,7 +164,7 @@ accepted: the orthohexagonal search cell has `4n` sites and | Preset | `a` | `c` | Internal parameters | Temperature | Source | |---|---|---|---|---|---| -| `Lattice::gallium_nitride()` | 3.189 Å | 5.178 Å | `u = 1/4 + a²/(3c²)` (**placeholder**, equal bond lengths) | 300 K | Ioffe NSM archive, citing Qian et al. (1996); primary not opened | +| `Lattice::gallium_nitride()` | 3.1890 Å | 5.18500 Å | `u = 1/4 + a²/(3c²)` (**placeholder**, equal bond lengths) | 300 K | Melnik et al., MRS Internet J. Nitride Semicond. Res. 2, 39 (1997), Table 1 (annealed bulk crystal) | | `Lattice::silicon_carbide_4h()` | 3.08051 Å | 10.0848 Å | `z = 0, 0.18784, 0.24982, 0.43671` | not stated | Bauer et al., Acta Cryst. A 57, 60 (2001), via Mehl et al. (2017), pp. 423, 733 | | `Lattice::silicon_carbide_6h()` | 3.08129 Å | 15.11976 Å | `z = 0, 0.1254, 0.16675, 0.29215, 0.8335, −0.0415` | not stated | Bauer et al. (2001), via Mehl et al. (2017), pp. 427, 734 | diff --git a/docs/data-provenance.md b/docs/data-provenance.md index 28114225..613942a0 100644 --- a/docs/data-provenance.md +++ b/docs/data-provenance.md @@ -251,7 +251,7 @@ issuing institution is not a third-party scan and may be linked as the source. | Diamond and zincblende structures: fcc primitive vectors `a1 = (0, a/2, a/2)`, `a2 = (a/2, 0, a/2)`, `a3 = (a/2, a/2, 0)`; diamond basis `(1/8, 1/8, 1/8)`, `(7/8, 7/8, 7/8)`; zincblende basis `(0, 0, 0)` (4a), `(1/4, 1/4, 1/4)` (4c); reciprocal vectors `b_i = 2π (a_j × a_k)/V` | `lindhard/src/ion/crystal/lattice.rs` | Published crystallographic description | M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. Hart and S. Curtarolo, "The AFLOW Library of Crystallographic Prototypes: Part 1", Comput. Mater. Sci. 136, S1 (2017), doi:10.1016/j.commatsci.2017.01.017, read as arXiv:1607.02532v1 (SHA-256 `cca7a9bf7925526fdcc887afbf738eadd95d7094990f00d25cf6e1f4032c2733`): diamond A4 `A_cF8_227_a`, p. 616; zincblende B3 `AB_cF8_216_c_a`, p. 543; eqs. (6), (8)-(10), pp. 7-8. Read 2026-10-07 (#19). The Miller-index normal `g = h b1 + k b2 + l b3` follows the Wikipedia article "Miller index" (revision 1378193236, 2026-10-03), which cites Ashcroft and Mermin (1976); the book was not opened | Structure facts and formulas, cited | 2026-10-07 | | Beam-orientation convention (tilt, twist from an explicit in-plane reference direction, wafer rotation) and its channel example | `lindhard/src/ion/crystal/orientation.rs`, `docs/crystal-orientation.md`, `docs/img/crystal-orientation.svg` (our own figure) | Convention, cited | K. Nordlund, F. Djurabekova and G. Hobler, "Large fraction of crystal directions leads to ion channeling", Phys. Rev. B 94, 214109 (2016), doi:10.1103/PhysRevB.94.214109 (open access; SHA-256 of the PDF read `df2e46ff0a7920dc5be456e5c3700b89bb709c897576e53887bcf557c9a80776`), Sec. II B, p. 214109-3: tilt θ and twist ϕ on a [001] surface, `[011]` at θ = 45°, ϕ = 0° and `[111]` at θ = 54.73°, ϕ = 45°. Read 2026-10-07 (#19). The sense of ϕ and the lab axes are our own choice, stated in the module docs | Convention, cited | 2026-10-07 | | Divergence sampling laws (Rayleigh polar angle for a Gaussian divergence, solid-angle-uniform cone) and the KS acceptance test | `lindhard/src/ion/crystal/divergence.rs`, `lindhard/tests/crystal.rs` | Computed from published formulas / derived | The two CDFs are derived in the module docs (polar coordinates of the bivariate normal density; the solid-angle element). KS statistic: NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.16 (); limiting distribution: G. Marsaglia, W. W. Tsang and J. Wang, "Evaluating Kolmogorov's Distribution", J. Stat. Softw. 8(18) (2003), doi:10.18637/jss.v008.i18, section 3 (SHA-256 of the PDF read `5a519336f38db5495726fe8cdc1313df20c2fdca22276012759527e3d81913f2`). Test parameters (σ = 0.5°, cone half-angle 2°, 20 000 samples, seeds 101 and 202) are round numbers, not data. Read 2026-10-07 (#19) | Formulas, cited | 2026-10-07 | -| Hexagonal lattice parameters: wurtzite GaN `a` = 3.189 Å, `c` = 5.178 Å (300 K) and the GaN density printed with them, 6.15 g/cm³ (300 K); 4H-SiC `a` = 3.08051 Å, `c` = 10.0848 Å and Wyckoff `z1..z4` = 0, 0.18784, 0.24982, 0.43671; 6H-SiC `a` = 3.08129 Å, `c` = 15.11976 Å and `z1..z6` = 0, 0.1254, 0.16675, 0.29215, 0.8335, −0.0415 (temperature of both not stated); 4H and 6H densities 3.211 and 3.21 g/cm³ (300 K) | `lindhard/src/ion/crystal/lattice.rs` (`GAN_LATTICE_CONSTANTS`, `GAN_DENSITY_G_CM3`, `SIC_4H_LATTICE_CONSTANTS`, `SIC_4H_Z`, `SIC_6H_LATTICE_CONSTANTS`, `SIC_6H_Z`, `SIC_4H_DENSITY_G_CM3`, `SIC_6H_DENSITY_G_CM3`) | Experimental measurement, read from secondary compilations | **Read 2026-10-08 (#179).** GaN: **secondary compilation only**: Ioffe Institute "New Semiconductor Materials" archive, "Basic Parameters of Gallium Nitride (GaN)", section "Basic Parameters for Wurtzite crystal structure" (; SHA-256 of the copy read `aac8aca341b29ac09b14a6412f0a81d72e4fd3aa2dac4af818294e61cd70e6e9`, a dynamic page): "Lattice constant, a: 3.189 A, 300 K" and "Lattice constant, c: 5.178 A, 300 K", both credited to Qian et al. (1996), which the archive's reference page (`.../GaN/reference.html`, SHA-256 `1a34d25ad066a2fc71ee5e5dc089dda7d58dc62371d6ffc69f9a8ce32f7ec2de`) gives as W. Qian, M. Skowronski and G. R. Rohrer, "Structural defects and their relationship to nucleation of GaN thin films", in *III-Nitride, SiC, and Diamond Materials for Electronic Devices*, Materials Research Society Symposium Proceedings 423 (1996), 475-486; **not opened**. Both values are from that one row so that `a` and `c` belong together; the same page also lists `c` = 5.186 Å (300 K, Bougrov et al. 2001, a handbook) and ranges 3.160-3.190 Å and 5.125-5.190 Å (Lagerstedt and Monemar 1979). "Density 6.15 g cm-3, 300 K" on the same page has no reference. No measured GaN `u` was found on any page read: see Open questions. 4H and 6H: A. Bauer, P. Reischauer, J. Kräusslich, N. Schell, W. Matz and K. Goetz, Acta Cryst. A 57, 60 (2001), doi:10.1107/S0108767300012915 (closed access per Unpaywall, publisher page behind a bot wall; **not opened**), as reproduced in M. J. Mehl et al., "The AFLOW Library of Crystallographic Prototypes: Part 1", Comput. Mater. Sci. 136, S1 (2017), read as arXiv:1607.02532v1 (SHA-256 `cca7a9bf7925526fdcc887afbf738eadd95d7094990f00d25cf6e1f4032c2733`, the file of the cubic row above): "Moissanite-4H SiC (B5)" `AB_hP8_186_ab_ab`, pp. 423-424, CIF p. 733 (`_aflow_params_values '3.08051, 3.27374363336, 0.0, 0.18784, 0.24982, 0.43671'`, `_cell_length_a 3.08051`, `_cell_length_c 10.08480`); "Moissanite-6H SiC (B6)" `AB_hP12_186_ab_a2b`, pp. 427-428, CIF p. 734 (`'3.08129, 4.90695780014, 0.0, 0.1254, 0.16675, 0.29215, 0.8335, -0.0415'`, `_cell_length_c 15.11976`). The record gives no temperature, so the presets carry none. SiC densities: Ioffe archive "Basic Parameters of Silicon Carbide (SiC)" (, SHA-256 of the copy read `91f54d7b39076ae9690127357aa74d77d0a373ee0a9a3e2a01077dad82d62eea`), row "Density": 4H-SiC 3.211 g cm⁻³, 300 K, Gomes de Mesquita (1967) (Acta Crystallogr. 23, 610, per the reference page, SHA-256 `e9fe448ba061f33b86ab0bdbcd12bae08942f458e191af25b7c0ac3091838c2c`); 6H-SiC 3.21 g cm⁻³, 300 K, Harris et al. (1995b); neither primary opened. The same page's 4H and 6H lattice-constant rows were not used: both print `a = 3.0730 A, b = 10.053` (a 4H-like `c` for 6H too), which looks like a transcription error. Number-density test (`lindhard/tests/crystal_hex.rs`): 6H agrees within the printed precision (+1.05e-3 against a tolerance of 1.7e-3); 4H (+7.52e-4, printed precision 1.6e-4) and GaN (−8.52e-3, printed precision 8e-4) do **not**, and the differences are pinned in the test, see Open questions. Uses: `Lattice::gallium_nitride()`, `silicon_carbide_4h()`, `silicon_carbide_6h()` | Facts, cited | 2026-10-08 | +| Hexagonal lattice parameters: wurtzite GaN `a` = 3.1890 Å, `c` = 5.18500 Å (300 K) and the measured GaN density 6.1 g/cm³ (temperature not stated); 4H-SiC `a` = 3.08051 Å, `c` = 10.0848 Å and Wyckoff `z1..z4` = 0, 0.18784, 0.24982, 0.43671; 6H-SiC `a` = 3.08129 Å, `c` = 15.11976 Å and `z1..z6` = 0, 0.1254, 0.16675, 0.29215, 0.8335, −0.0415 (temperature of both not stated); 4H and 6H densities 3.211 and 3.21 g/cm³ (300 K) | `lindhard/src/ion/crystal/lattice.rs` (`GAN_LATTICE_CONSTANTS`, `GAN_DENSITY_G_CM3`, `SIC_4H_LATTICE_CONSTANTS`, `SIC_4H_Z`, `SIC_6H_LATTICE_CONSTANTS`, `SIC_6H_Z`, `SIC_4H_DENSITY_G_CM3`, `SIC_6H_DENSITY_G_CM3`) | Experimental measurement, read from secondary compilations | **Read 2026-10-08 (#179); GaN replaced 2026-10-10 (#179).** GaN cell: Yu. V. Melnik, K. V. Vassilevski, I. P. Nikitina, A. I. Babanin, V. Yu. Davydov and V. A. Dmitriev, "Physical Properties of Bulk GaN Crystals Grown by HVPE", MRS Internet J. Nitride Semicond. Res. 2, 39 (1997), doi:10.1557/S1092578300001654 (open access; read from Cambridge Core, SHA-256 of the PDF `ccae2c25991ac11a01c9486177976ca479a6e50387773a842b57e607a7424e05`): section 3.2 (PDF p. 3), triple-crystal Bond method on (0004) and (11-24), "measurement accuracy was 0.00005 Å for a lattice constant and 0.00002 Å for c lattice constant"; after an anneal at 1100 K for 40 min in N2 that removed the residual strain, "c = 5.18500 Å, a = 3.1890 Å" on both faces; Table 1 (PDF p. 5), "GaN a and c lattice parameters measured at 300 K (Å)", row "Annealed bulk GaN crystal grown by HVPE". A primary measurement on a free-standing bulk crystal, replacing the earlier Ioffe NSM values (`a` = 3.189 Å, `c` = 5.178 Å, credited there to a thin-film conference paper, Qian et al. 1996, not opened). GaN density: R. Juza and H. Hahn, Z. Anorg. Allg. Chem. 239, 282 (1938), doi:10.1002/zaac.19382390307 (closed per OpenAlex; **not opened**), as recorded in the Crystallography Open Database entry 1010168 (public domain; read from the COD mirror , SHA-256 `3344d12eac3f296d1af4b89794b5da9956527fe024fa6ee2dfb9bd8f87f2ef23`): `_exptl_crystal_density_meas 6.1`, with the paper's cell `a` = 3.180(4) Å, `c` = 5.166(5) Å; no temperature in the record. The earlier Ioffe density 6.15 g/cm³ (no reference on that page) was dropped: it equals, to its printed figures, the X-ray density of the 1938 cell, 6.146 (COD 9008868, the same cell via Wyckoff, *Crystal Structures* Vol. 1, 2nd ed. (1963), `_exptl_crystal_density_diffrn 6.146`; SHA-256 `7606ee5ce54581b88bc8d89f151f36a7abe9f9b09b127dd8c8ac1a32286f52b4`), which is why it disagreed with every modern cell; that it was derived this way is our inference. No measured GaN `u` was found on any page read: see Open questions. 4H and 6H: A. Bauer, P. Reischauer, J. Kräusslich, N. Schell, W. Matz and K. Goetz, Acta Cryst. A 57, 60 (2001), doi:10.1107/S0108767300012915 (closed access per Unpaywall, publisher page behind a bot wall; **not opened**), as reproduced in M. J. Mehl et al., "The AFLOW Library of Crystallographic Prototypes: Part 1", Comput. Mater. Sci. 136, S1 (2017), read as arXiv:1607.02532v1 (SHA-256 `cca7a9bf7925526fdcc887afbf738eadd95d7094990f00d25cf6e1f4032c2733`, the file of the cubic row above): "Moissanite-4H SiC (B5)" `AB_hP8_186_ab_ab`, pp. 423-424, CIF p. 733 (`_aflow_params_values '3.08051, 3.27374363336, 0.0, 0.18784, 0.24982, 0.43671'`, `_cell_length_a 3.08051`, `_cell_length_c 10.08480`); "Moissanite-6H SiC (B6)" `AB_hP12_186_ab_a2b`, pp. 427-428, CIF p. 734 (`'3.08129, 4.90695780014, 0.0, 0.1254, 0.16675, 0.29215, 0.8335, -0.0415'`, `_cell_length_c 15.11976`). The record gives no temperature, so the presets carry none. SiC densities: Ioffe archive "Basic Parameters of Silicon Carbide (SiC)" (, SHA-256 of the copy read `91f54d7b39076ae9690127357aa74d77d0a373ee0a9a3e2a01077dad82d62eea`), row "Density": 4H-SiC 3.211 g cm⁻³, 300 K, Gomes de Mesquita (1967) (Acta Crystallogr. 23, 610, per the reference page, SHA-256 `e9fe448ba061f33b86ab0bdbcd12bae08942f458e191af25b7c0ac3091838c2c`); 6H-SiC 3.21 g cm⁻³, 300 K, Harris et al. (1995b); neither primary opened. The same page's 4H and 6H lattice-constant rows were not used: both print `a = 3.0730 A, b = 10.053` (a 4H-like `c` for 6H too), which looks like a transcription error. The 4H and 6H lattice-constant rows of that page, `a = 3.0730 A, b = 10.053`, match the type III (4H) cell of N. W. Thibault, "Morphological and structural crystallography and optical properties of silicon carbide (SiC), Part II", Am. Mineral. 29, 327 (1944) (open, , SHA-256 `353fb75c07248dcbc11984baa82323c0f0cf151cdd5643c22afb4f78a81b295d`): pp. 327-328 and Table 25, p. 342, `a0` = 3.073 Å for all α types, `c0` = 10.053 Å (type III, 4H: 4 formula weights per hexagonal cell in Table 25) and 15.07₉ Å (type II, 6H: 6), "Calculated density of all α-SiC types: 3.217; observed density, type II: 3.218" (Table 25: type III calculated 3.217, observed "—"); p. 341, the type II density "d at 30°/4° C. = 3.218, using a 5 cc. pycnometer and xylene as the displacing liquid" (30 °C, referred to water at 4 °C) on chemically analysed material (0.28 % Al, Fe, Ca, Mg by mass), and pp. 341-342 state that the x-ray densities used Siegbahn's wavelengths, 1940 atomic weights and 1/N = 1.6503e-24. Thibault gives **no measured 4H density**, so it does not close the 4H gap; it is recorded here because it is open and primary. Against its 6H value 3.218 the Bauer 6H cell (3.2134) is −1.44e-3, outside that figure's last digit; the test keeps the Ioffe 3.21 for 6H, and this is noted under Open questions. Number-density test (`lindhard/tests/crystal_hex.rs`): 6H agrees within the printed precision (+1.05e-3 against a tolerance of 1.7e-3); GaN agrees within the printed precision of the 1938 density (−1.74e-3 against a tolerance of 8.3e-3: half a unit of 6.1 is 8.20e-3, the Melnik cell accuracy adds 3.5e-5); with the earlier Ioffe cell it would have been −3.9e-4, so the change of cell is not what makes the test pass. 4H (+7.52e-4, printed precision 1.6e-4) does **not** agree, and the difference is pinned in the test, see Open questions. Uses: `Lattice::gallium_nitride()`, `silicon_carbide_4h()`, `silicon_carbide_6h()` | Facts, cited | 2026-10-08, GaN 2026-10-10 | | Hexagonal structures and conventions: P6₃mc primitive vectors `a1 = (a/2, −√3a/2, 0)`, `a2 = (a/2, √3a/2, 0)`, `a3 = (0, 0, c)`; Wyckoff 2a/2b sites of wurtzite, 4H and 6H; the A/B/C stacking letters; the definition of `u`; four-index (Miller-Bravais) planes and directions; the equal-bond `u`, the orthohexagonal search cell and the ideal polytype construction | `lindhard/src/ion/crystal/lattice.rs`, `lindhard/src/ion/crystal/orientation.rs`, `lindhard/src/ion/crystal/search.rs`, `docs/crystal-orientation.md` | Published crystallographic description / derived | Mehl et al. (2017) (row above, same file): wurtzite B4 `AB_hP4_186_b_b`, p. 425 (Zn on 2b at `z1 = 0`, S on 2b at `z2`; the example CIF on p. 734 has `z2 = 0.3748`, but the page's text says the ideal structure has "z2 = 1/8", which does not agree with its own sites and was not used); 4H, p. 423 ("one possible stacking (ABAC) ... Compare this to Zincblende (ABCABC), Wurtzite (ABABAB), 6H (ABCACB) ... The 4H refers to the fact that there are 4 CSi dimers in a hexagonal unit cell"); 6H, p. 427. `u` as "the anion-cation bond length along the (0001) axis in units of c": F. Bernardini, V. Fiorentini and D. Vanderbilt, Phys. Rev. B 56, R10024 (1997), doi:10.1103/PhysRevB.56.R10024, p. 1, read as arXiv:cond-mat/9705105v1 (SHA-256 `6004a89f7c5ba7e5d31a1e3d7b7279e49f54ecaf295731ecd3873c8e9f08d6c5`). Four-index planes `(hkil)` with `h + k + i = 0` and the third basal axis along `[-1-10]`: Wikipedia "Miller index", revision 1378193236 (2026-10-03), section "Hexagonal and rhombohedral structures" (the revision of the cubic row above). The direction rule `[uvtw] = u a1 + v a2 + t a3' + w c` with `u + v + t = 0` and its conversion `[u − t, v − t, w]`, the equal-bond `u = 1/4 + a²/(3c²)`, the orthohexagonal cell and the bilayer construction of `Lattice::polytype` are derived in the module docs; F. C. Frank, "On Miller-Bravais indices and four-dimensional vectors", Acta Cryst. 18, 862 (1965), doi:10.1107/S0365110X65002116 (metadata from Crossref), the usual citation for the four-index direction symbol, was not opened (publisher bot wall). Read 2026-10-08 (#179) | Structure facts and formulas, cited / derived | 2026-10-08 | ## Validation reference data @@ -543,27 +543,30 @@ energies. Level 3 keeps the untuned comparison as the primary result. temperature against the original (or another open primary measurement) before relying on `Lattice::silicon_carbide_3c()` beyond four figures. - Hexagonal lattices (#179): - - GaN `a`, `c`: read from the Ioffe NSM archive (secondary), credited to - Qian et al. (1996), a conference paper on thin films that was not - opened. The open-access candidates found on 2026-10-08 either give the - values only in a figure (Teisseyre et al., Acta Phys. Pol. A 87, 403 - (1995), doi:10.12693/APhysPolA.87.403) or sit behind a publisher bot - wall (Leszczynski et al., J. Phys. D 28, A149 (1995), - doi:10.1088/0022-3727/28/4A/029; Moram and Vickers, Rep. Prog. Phys. 72, - 036502 (2009), doi:10.1088/0034-4885/72/3/036502); Leszczynski et al., - Appl. Phys. Lett. 69, 73 (1996), doi:10.1063/1.118123, and Schulz and - Thiemann, Solid State Commun. 23, 815 (1977), - doi:10.1016/0038-1098(77)90959-0, are closed access (metadata checked on - Crossref). Replace with a bulk-crystal measurement with its temperature. + - GaN `a`, `c`: **resolved 2026-10-10.** Now the annealed, strain-free + bulk crystal of Melnik et al. (1997), measured at 300 K with a stated + accuracy (row above), which replaced the Ioffe NSM values (credited to + Qian et al. 1996, a thin-film conference paper, not opened). Still not + opened: Leszczynski et al., J. Phys. D 28, A149 (1995), + doi:10.1088/0022-3727/28/4A/029, and Moram and Vickers, Rep. Prog. Phys. + 72, 036502 (2009), doi:10.1088/0034-4885/72/3/036502 (publisher bot + wall again on 2026-10-10); Schulz and Thiemann, Solid State Commun. 23, + 815 (1977), doi:10.1016/0038-1098(77)90959-0 (closed). - GaN `u`: **no measured value opened**. `Lattice::gallium_nitride()` uses - the geometric equal-bond value `1/4 + a²/(3c²)` (about 0.3764 for the + the geometric equal-bond value `1/4 + a²/(3c²)` (about 0.3761 for the cited `a`, `c`) as a documented placeholder. Needs a measured `u` (for example Schulz and Thiemann (1977), closed) before any result is sensitive to the N sublattice position. - - GaN density: the archive's 6.15 g/cm³ (and its 8.9e22 atoms/cm³) is - 0.85 % (1.4 %) above what its own `a`, `c` give; the source of the - density is not stated. The test pins −8.52e-3 rather than claiming - agreement. + - GaN density: now the measured 6.1 g/cm³ of Juza and Hahn (1938), read + from COD entry 1010168 (the primary is closed and was not opened; no + temperature in the record). It agrees with the Melnik cell within its + printed precision (−1.74e-3 against 8.2e-3), so the criterion is met for + GaN, but only at two figures: this is the one open measured GaN bulk + density found (OpenAlex searches 2026-10-10; the 1997 HVPE paper gives + no density). A measured density to three or more figures, with its + temperature, would tighten the check. The earlier Ioffe 6.15 g/cm³ was + the X-ray density of the 1938 cell (our inference, row above), not a + bulk measurement, and is no longer used. - 4H and 6H: cell and sites of Bauer et al. (2001) via the AFLOW library (open), primary closed; the measurement temperature is therefore unknown and the presets carry none. The 4H cell is 7.5e-4 denser than @@ -573,14 +576,18 @@ energies. Level 3 keeps the untuned comparison as the primary result. 610-617 (1967) is titled "Refinement of the crystal structure of SiC type 6H", so the archive's attribution of a **4H** density to it is doubtful; the paper is closed access (OpenAlex, no repository copy; the - publisher page is behind a bot wall) and was not opened. No open - measurement of the 4H or GaN bulk density together with lattice - parameters and a temperature was found on 2026-10-10 (OpenAlex and - Europe PMC searches; the Moram and Vickers review, the bulk-GaN HVPE - paper, the ammonothermal GaN paper and the IntechOpen SiC chapter all - returned a bot wall or contained no values; COD was unreachable). The - density criterion of #179 therefore stays **met for 6H-SiC only**; - the 4H-SiC and GaN presets remain provisional with respect to density, + publisher page is behind a bot wall) and was not opened. The open + primary Thibault (1944) (row above) gives a 4H cell and a *calculated* + density only; its one measured density (3.218, pycnometer, 30 °C) is of + 6H, and is 1.44e-3 above the density of the Bauer 6H cell, more than + its last printed digit (the 6H test uses the Ioffe 3.21, which agrees). + Not found or not opened on 2026-10-10: a measured 4H bulk density + (OpenAlex searches for pycnometric, hydrostatic and Brillouin-scattering + work on 4H-SiC); M. Stockmeier et al., J. Appl. Phys. 105, 033511 (2009), + doi:10.1063/1.3074301 (closed) and Stockmeier's dissertation (FAU + Erlangen, 2008; the repository serves a bot-check page). The density + criterion of #179 is therefore **met for 6H-SiC and GaN, not for + 4H-SiC**; the 4H-SiC preset stays provisional with respect to density, and the approved criterion has not been reinterpreted. - Electron band parameters (work function, Fermi energy, electron affinity, band gap, valence band width) for built-in material defaults: no open diff --git a/lindhard/src/ion/crystal/lattice.rs b/lindhard/src/ion/crystal/lattice.rs index 29880fef..04e504d3 100644 --- a/lindhard/src/ion/crystal/lattice.rs +++ b/lindhard/src/ion/crystal/lattice.rs @@ -236,36 +236,38 @@ pub const SIC_3C_LATTICE_CONSTANT: LatticeConstant = LatticeConstant { primary not opened", }; -/// Wurtzite gallium nitride: `a = 3.189 Å`, `c = 5.178 Å` at 300 K. +/// Wurtzite gallium nitride: `a = 3.1890 Å`, `c = 5.18500 Å` at 300 K. /// -/// Read from the Ioffe Institute "New Semiconductor Materials" archive, -/// "Basic Parameters of Gallium Nitride (GaN)", section "Basic Parameters for -/// Wurtzite crystal structure" -/// (, read 2026-10-08): -/// "Lattice constant, a: 3.189 A, 300 K" and "Lattice constant, c: -/// 5.178 A, 300 K", both credited to Qian et al. (1996) (W. Qian, -/// M. Skowronski and G. R. Rohrer, in *III-Nitride, SiC, and Diamond -/// Materials for Electronic Devices*, Materials Research Society Symposium -/// Proceedings 423 (1996), 475-486, per the archive's reference list). Both values are taken from that one row so -/// that `a` and `c` belong to the same measurement; the page also lists -/// `c = 5.186 A` at 300 K from a handbook (Bougrov et al. 2001). This is a -/// secondary compilation and the primary was **not** opened; the archive's -/// GaN density and atom count do not match these parameters, see -/// `docs/data-provenance.md` (open questions). +/// Yu. V. Melnik, K. V. Vassilevski, I. P. Nikitina, A. I. Babanin, +/// V. Yu. Davydov and V. A. Dmitriev, "Physical Properties of Bulk GaN +/// Crystals Grown by HVPE", MRS Internet J. Nitride Semicond. Res. 2, 39 +/// (1997), doi:10.1557/S1092578300001654 (open access), section 3.2 +/// (PDF p. 3) and Table 1 (PDF p. 5, "GaN a and c lattice parameters +/// measured at 300 K"): the free-standing bulk crystal after an anneal at +/// 1100 K that removed the residual strain, "c = 5.18500 Å, a = 3.1890 Å" +/// on both the N face and the Ga face, measured by the triple-crystal Bond +/// method on the (0004) and (11-24) reflections with a stated accuracy of +/// 0.00005 Å for `a` and 0.00002 Å for `c`. pub const GAN_LATTICE_CONSTANTS: HexagonalConstants = HexagonalConstants { material: "GaN (wurtzite)", - a_m: 3.189 * M_PER_ANGSTROM, - c_m: 5.178 * M_PER_ANGSTROM, + a_m: 3.1890 * M_PER_ANGSTROM, + c_m: 5.18500 * M_PER_ANGSTROM, temperature_k: Some(300.0), - source: "Ioffe NSM archive (citing Qian et al. 1996), at 300 K; primary not opened", + source: "Melnik et al., MRS Internet J. Nitride Semicond. Res. 2, 39 (1997), \ + Table 1, annealed bulk HVPE crystal, at 300 K", }; -/// The wurtzite GaN density printed on the same Ioffe page as -/// [`GAN_LATTICE_CONSTANTS`], "Density 6.15 g cm-3, 300 K" (no reference -/// given). It is **not** consistent with the archive's own `a` and `c` -/// (about 0.85 % higher than `4 M(GaN) / 2 / (N_A V)`); the test pins the -/// difference and the gap is recorded in `docs/data-provenance.md`. -pub const GAN_DENSITY_G_CM3: f64 = 6.15; +/// Measured (not X-ray) density of wurtzite GaN, `6.1 g/cm³`, temperature +/// not stated. +/// +/// R. Juza and H. Hahn, "Über die Kristallstrukturen von Cu3N, GaN und InN", +/// Z. Anorg. Allg. Chem. 239, 282 (1938), doi:10.1002/zaac.19382390307 +/// (closed access, **not opened**), as recorded in the Crystallography Open +/// Database entry 1010168 (public domain): `_exptl_crystal_density_meas 6.1`, +/// with that paper's cell `a = 3.180(4) Å`, `c = 5.166(5) Å`. Printed to two +/// figures, so half a unit in the last place is 8.2e-3 relative; this is the +/// tolerance of the number-density test against [`GAN_LATTICE_CONSTANTS`]. +pub const GAN_DENSITY_G_CM3: f64 = 6.1; /// 4H silicon carbide: `a = 3.08051 Å`, `c = 10.0848 Å`; temperature not /// stated in the record read. @@ -321,6 +323,13 @@ pub const SIC_6H_Z: [f64; 6] = [0.0, 0.1254, 0.16675, 0.29215, 0.8335, -0.0415]; /// (1967) is titled "Refinement of the crystal structure of SiC type 6H" /// (Crossref), so the attribution to 4H is doubtful. Used in the /// number-density test, which records the 4H disagreement as a gap. +/// +/// No measured 4H bulk density could be opened (checked 2026-10-10). The +/// one open primary found, N. W. Thibault, Am. Mineral. 29, 327 (1944), +/// pp. 327-328 and Table 25 on p. 342, gives for α-SiC type III (4H) +/// only a cell (`a = 3.073 Å`, `c = 10.053 Å`) and a **calculated** density +/// of 3.217; its one measured (pycnometric) density, `d` at 30°/4° C = +/// 3.218 (p. 341), is of type II (6H). See `docs/data-provenance.md`. pub const SIC_4H_DENSITY_G_CM3: f64 = 3.211; /// 6H-SiC density, "3.21 g cm-3, 300 K", credited to Harris et al. (1995b) @@ -1017,8 +1026,8 @@ mod tests { let gan = Lattice::gallium_nitride(); assert_eq!(gan.structure(), Structure::Wurtzite); - assert_eq!(gan.lattice_constant(), 3.189 * M_PER_ANGSTROM); - assert_eq!(gan.lattice_constant_c(), 5.178 * M_PER_ANGSTROM); + assert_eq!(gan.lattice_constant(), 3.1890 * M_PER_ANGSTROM); + assert_eq!(gan.lattice_constant_c(), 5.18500 * M_PER_ANGSTROM); assert_eq!(gan.temperature_k(), Some(300.0)); let z: Vec = gan.basis().iter().map(|s| s.z).collect(); assert_eq!(z, [31, 31, 7, 7]); diff --git a/lindhard/tests/crystal_hex.rs b/lindhard/tests/crystal_hex.rs index 0ecc49bd..0653376a 100644 --- a/lindhard/tests/crystal_hex.rs +++ b/lindhard/tests/crystal_hex.rs @@ -170,7 +170,7 @@ struct DensityCase { rho_g_cm3: f64, /// Elements of the compound. z: [u8; 2], - /// Printed density and its temperature, as read from the archive. + /// Printed density and its temperature, as read from the source. density_source: &'static str, /// Cell source and its temperature (or that none is stated). cell_source: &'static str, @@ -204,9 +204,11 @@ fn density_cases() -> [DensityCase; 3] { lattice: Lattice::gallium_nitride(), rho_g_cm3: GAN_DENSITY_G_CM3, z: [31, 7], - density_source: "Ioffe NSM 6.15 g/cm3, 300 K, no reference printed", - cell_source: "Ioffe NSM (Qian 1996): a=3.189, c=5.178 A, 300 K", - printed_precision: 0.005 / 6.15, + density_source: "Juza & Hahn 1938 via COD 1010168: measured 6.1 g/cm3, \ + temperature not stated", + cell_source: "Melnik 1997 Table 1, annealed bulk: a=3.1890 A (+-0.00005), \ + c=5.18500 A (+-0.00002), 300 K", + printed_precision: 0.05 / 6.1, }, ] } @@ -279,12 +281,20 @@ fn number_density_report_states_the_sources() { /// cell parameters (`a = 3.08129 Å`, `c = 15.11976 Å`) add under 2e-6 and /// the Si and C standard-weight intervals about 5e-5. Tolerance 1.7e-3. /// Found: +1.05e-3. +/// * GaN: the measured density 6.1 g/cm³ of Juza and Hahn (1938, via COD +/// 1010168; temperature not stated) is printed to two figures, half a unit +/// in the last place is 8.20e-3 relative. The cell of Melnik et al. (1997) +/// at 300 K adds 3.5e-5 (its stated accuracy, 0.00005 Å on `a` twice and +/// 0.00002 Å on `c`) and the Ga and N standard-weight intervals under 1e-4. +/// Tolerance 8.3e-3. Found: −1.74e-3. The density is the only open +/// measured GaN bulk density found, and its two figures make this a coarse +/// check; see `docs/data-provenance.md`. /// -/// Issue #179 asks for agreement within the cited precision. Only 6H meets -/// it with the sources that could be opened; 4H and GaN are in +/// Issue #179 asks for agreement within the cited precision. 6H and GaN meet +/// it with the sources that could be opened; 4H is in /// [`number_density_discrepancies_are_recorded_gaps`], which does not claim it. #[test] -fn number_density_agrees_with_the_material_module_6h() { +fn number_density_agrees_with_the_material_module() { for rel in density_differences( &Lattice::silicon_carbide_6h(), SIC_6H_DENSITY_G_CM3, @@ -292,23 +302,23 @@ fn number_density_agrees_with_the_material_module_6h() { ) { assert!(rel.abs() < 1.7e-3, "6H relative difference {rel:e}"); } + for rel in density_differences(&Lattice::gallium_nitride(), GAN_DENSITY_G_CM3, [31, 7]) { + assert!(rel.abs() < 8.3e-3, "GaN relative difference {rel:e}"); + } } -/// **Not an agreement test.** Regression pins on two known, unresolved -/// disagreements between sources, so that a change to a cell or a density is -/// noticed. The acceptance criterion of #179 (density within the cited -/// precision) is **not met** for these presets, and the test must not be read -/// as meeting it. Neither constant was adjusted to hide the offset; both are +/// **Not an agreement test.** Regression pin on a known, unresolved +/// disagreement between sources, so that a change to the cell or the density +/// is noticed. The acceptance criterion of #179 (density within the cited +/// precision) is **not met** for 4H-SiC, and the test must not be read as +/// meeting it. Neither constant was adjusted to hide the offset; the gap is /// listed under Open questions in `docs/data-provenance.md`. /// /// * 4H-SiC: against the archive's 3.211 g/cm³ (half a unit: 1.6e-4) the /// lattice is +7.52e-4 denser, outside the printed precision. The two /// numbers are different measurements (Bauer et al. 2001 cell, Gomes de /// Mesquita 1967 density, per the archive) and the cell's temperature is -/// not stated. -/// * GaN: the archive's 6.15 g/cm³ is 0.85 % above the X-ray density of the -/// archive's own `a` and `c` (lattice/material - 1 = -8.52e-3), far outside -/// its printed precision (8e-4). +/// not stated. No measured 4H bulk density could be opened. #[test] fn number_density_discrepancies_are_recorded_gaps() { for rel in density_differences( @@ -318,12 +328,6 @@ fn number_density_discrepancies_are_recorded_gaps() { ) { assert!((rel - 7.52e-4).abs() < 5e-6, "4H pinned difference {rel:e}"); } - for rel in density_differences(&Lattice::gallium_nitride(), GAN_DENSITY_G_CM3, [31, 7]) { - assert!( - (rel + 8.52e-3).abs() < 5e-6, - "GaN pinned difference {rel:e}" - ); - } } /// The close-packed column (A, B or C) of lattice coordinates `(f1, f2)`.