{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-d2","topicId":"scwiki-topic-d2","code":"D2","slug":"a15-compounds","title":"A15 compounds: structure, strain and useful critical fields","summary":"Understand Nb3Sn, V3Si and Nb3Ge through sample conditions, structural transitions and the distinction between critical fields and current-carrying performance.","aliases":["A15","beta tungsten","Nb3Sn","V3Si","Nb3Ge","Kramer plot","martensitic transformation","Cu-Sn cavity"],"evidenceTypes":["theory","experiment"],"relatedCodes":["D1","B2","C1","A6","A7"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-19T15:34:16.871337+00:00","review":{"checkedAt":"2026-10-19","scope":"Selected Godeke author-version passages, published V3Si methods/results and official AFLOW prototype. Explicit local connection/field-window/rounding checks; earlier historical and2026 abstract-only checks retained.","limitations":["Full scientific acceptance and original raw-data/spectral-fit reviews remain open.","Historic Nb3Sn/Nb–Ge reports and Testardi papers checked at abstract level; original measurement criteria not inferred.","2026 dissertation is an abstract-only preprint, not peer-reviewed performance acceptance.","Finite models do not reproduce conductor networks, EFG tensors, phonon calculations or device performance.","Local current addition, secant windows and assumed rounding are not wire-network or experimental-data validation; no NMR phase-fraction bound is inferred."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"D_material_families/D2_A15_compounds.md","sha256":"036ee5b467a7597ae98470c891d08ceccf473a97c19d2f6a40f3fe88348b8886","sourceId":"file-1729169cb28fa596"},"sourceMap":[{"startLine":1,"endLine":58,"targetSections":["scope","mathematical-assumptions","experimental-criteria","limits-and-disputes","discovery-implications","related-topics"],"decision":"edited-with-scoped-evidence","note":"Pinned source retained; primary sample conditions and model limitations expanded, cross-reference and title corrected."}],"references":[{"id":"source-830f887afcf548c4","doi":"10.1103/PhysRev.95.1435","title":"Superconductivity of Nb3Sn","year":1954,"url":"https://doi.org/10.1103/PhysRev.95.1435","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/pr/abstract/10.1103/PhysRev.95.1435","note":"Published 15 September 1954. Historical reported scale only; original full methods not reviewed."}},{"id":"source-82a0df3d764cd0bc","doi":"10.1063/1.1654966","title":"Superconductivity in Nb–Ge films above 22 K","year":1973,"url":"https://doi.org/10.1063/1.1654966","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://aipp.silverchair-cdn.com/article-minimal/44036","note":"Published 15 October 1973. Publisher abstract also verified through Crossref; reports 22.3 K films from high-pressure dc sputtering. Measurement criterion and full methods not independently read."}},{"id":"source-33f4444a5825b443","doi":"10.1103/PhysRevB.5.4342","title":"Structural Instability, Anharmonicity, and High-Temperature Superconductivity in A-15-Structure Compounds","year":1972,"url":"https://doi.org/10.1103/PhysRevB.5.4342","publicationStatus":"journal-article","verification":{"scope":"publisher-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/PhysRevB.5.4342","note":"Published 1 June 1972. Sound-velocity/strain interpretation and model conjectures; not universal monotonic optimization."}},{"id":"source-509b869080567558","doi":"10.1103/RevModPhys.47.637","title":"Structural instability and superconductivity in A-15 compounds","year":1975,"url":"https://doi.org/10.1103/RevModPhys.47.637","publicationStatus":"journal-article","verification":{"scope":"publisher-indexed-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://doi.org/10.1103/RevModPhys.47.637","note":"Published 1 July 1975. Indexed publisher abstract only; full review not read."}},{"id":"source-29d0a9915f8b6c0e","doi":"10.1088/0953-2048/19/8/R02","title":"A review of the properties of Nb3Sn and their variation with A15 composition, morphology and strain state","year":2006,"url":"https://doi.org/10.1088/0953-2048/19/8/R02","publicationStatus":"journal-article","verification":{"scope":"selected-author-review-text-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0606303v1","note":"Follow-up19October2026 re-read authorv1 introduction/structure pp.1–3: chain geometry, sublattice, disorder and strain context. Earlier Fig.6 coupling check retained; underlying cited datasets not reproduced. AFLOW separately supports the exact space-group/basis label."}},{"id":"source-c4b57e9e8e5aa3d7","doi":"10.1088/0953-2048/19/10/R02","title":"A general scaling relation for the critical current density in Nb3Sn","year":2006,"url":"https://doi.org/10.1088/0953-2048/19/10/R02","publicationStatus":"journal-article","verification":{"scope":"selected-author-review-equation-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0608404v1","note":"Follow-up19October2026 re-read authorv1 pp.4–8: field form, grain assumptions, linearity, parallel/series inhomogeneity discussion. Header confirms18August2006v1; full strain model and raw data not reanalyzed."}},{"id":"source-d27a049f764be753","doi":"10.1063/1.1890447","title":"The upper critical field of filamentary Nb3Sn conductors","year":2005,"url":"https://doi.org/10.1063/1.1890447","publicationStatus":"journal-article","verification":{"scope":"selected-author-v2-methods-equation-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0410463v2","note":"Follow-up19October2026 re-read authorv2 TableI p.2, methods pp.5–6, path sampling p.8 and hypothetical comparison pp.9–10. Explicitv2 and currentPDF bytes matched SHA2563e899f328e3a6ff2f1aad79e425ac9f7c1264e596dc00e80291adf6e4070aa5b; arXiv history confirms28February2005v2, replacement of Eqs.7–9. No raw-data fit or new PDF-pixel verification claimed. The rounding interval is a local assumption, not proven error attribution."}},{"id":"source-9fe69d0a6cecbb0c","doi":"10.1016/j.physc.2022.1354137","title":"Martensitic transformation in V3Si single crystal: 51V NMR evidence for coexistence of cubic and tetragonal phases","year":2022,"url":"https://doi.org/10.1016/j.physc.2022.1354137","publicationStatus":"journal-article","verification":{"scope":"selected-published-methods-results-check","checkedAt":"2026-10-19","evidenceUrl":"https://public.magnet.fsu.edu/AToth/NSF%20publication%20access/2022/09%20Newly%20Entered%20Pubs%20September%202022/2022%20cited/2022_Martensitic%20transformation.pdf","note":"Follow-up19October2026 re-read published pp.3–4:6.67T,12.8K versus zero-field17K, broadening/overlap, EFG assignment and no conclusive cubic spectra. Full EFG appendix, spectral fits and quantitative detection threshold not independently established; PDF-pixel request failed."}},{"id":"source-0620df96ebbf2a66","doi":"10.1103/PhysRevB.12.905","title":"Transition temperature of strong-coupled superconductors reanalyzed","year":1975,"url":"https://doi.org/10.1103/PhysRevB.12.905","publicationStatus":"journal-article","verification":{"scope":"primary-abstract-scoped-check","checkedAt":"2026-10-18","evidenceUrl":"https://journals.aps.org/prb/abstract/10.1103/PhysRevB.12.905","note":"Publisher abstract: modified prefactor, spectral moment/shape corrections and large-coupling limits within Eliashberg theory. Full derivation and Pb-Bi data not reanalyzed."}},{"id":"source-3633507cd1108d10","doi":null,"title":"Nb3Sn Thin Films Using a Cu-Sn Route for Dark Matter Detection","year":2026,"url":"https://arxiv.org/abs/2605.03171v1","publicationStatus":"preprint","verification":{"scope":"preprint-abstract-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/abs/2605.03171v1","note":"Doctoral dissertation preprint, submitted 4 May 2026; not a peer-reviewed journal article. Abstract only: selected cavity at 50 mK and 9 T, quality factor declines in field. Full 211-page dissertation not read."}},{"id":"source-804b5d160a095037","doi":null,"title":"AFLOW crystallographic prototype: Cr3Si (A15), A3B_cP8_223_c_a-001","year":null,"url":"https://www.aflow.org/prototype-encyclopedia/A3B_cP8_223_c_a-001/","publicationStatus":"technical-report","verification":{"scope":"official-prototype-structure-check","checkedAt":"2026-10-19","evidenceUrl":"https://www.aflow.org/prototype-encyclopedia/A3B_cP8_223_c_a-001/","note":"Official prototype entry, accessed 19 October 2026: cubic primitive cP8, space group223, A sites6c and B sites2a. Page-specific publication date is not supplied; underlying diffraction experiment and whole prototype library were not independently reviewed."}}],"claims":[{"id":"scwiki-d2-claim-scope-1","sectionId":"scope","statement":"A15 is a crystal-structure family, usually written $A_3B$. Its ideal undistorted prototype is primitive cubic $Pm\\bar{3}n$ (No. 223), with eight atoms per cell: six A atoms on 6c sites and two B atoms on 2a sites. The body-centered arrangement of the B sublattice does not make the full crystal body-centered cubic. Three orthogonal A-atom chains help organize its electronic structure, without guaranteeing a high transition temperature. Composition, site ordering, phonons and strain remain important, and the brittle Nb–Sn phase also has to tolerate fabrication and mechanical loading.","evidenceType":"theory","sourceIds":["source-29d0a9915f8b6c0e","source-804b5d160a095037"],"conditions":"Ideal undistorted A3B prototype; actual samples can be off-stoichiometric or structurally distorted. Atomic chain geometry is not a sufficient Tc predictor.","verificationScope":"2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"AFLOW specifies the prototype and basis; Godeke reviews chain geometry, disorder and wire conditions. The sublattice-versus-Bravais distinction is an explicit interpretation of that basis, not a new diffraction refinement."},{"id":"scwiki-d2-claim-scope-2","sectionId":"scope","statement":"Nb3Sn, V3Si and Nb3Ge are distinct examples, not one table of universal constants. Matthias and colleagues reported Nb3Sn near 18 K in 1954. Gavaler's 1973 abstract reports sputtered Nb–Ge films remaining superconducting up to 22.3 K. That historical film result is neither an equilibrium bulk value nor a strict A15 temperature ceiling. “High pressure” in the deposition description refers to sputtering conditions, not a high-pressure superconductivity measurement.","evidenceType":"theory","sourceIds":["source-830f887afcf548c4","source-82a0df3d764cd0bc"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."},{"id":"scwiki-d2-claim-scope-3","sectionId":"scope","statement":"Near-stoichiometric Nb3Sn is a conventional strong-coupling benchmark, but even its coupling classification depends on composition and how the gap and transition are sampled. Godeke's review discusses interface-gap and inhomogeneity effects that can bias a gap-to-temperature ratio. A full gap is not proof that all samples have the same coupling, and a large upper critical field alone is not evidence for triplet pairing.","evidenceType":"theory","sourceIds":["source-29d0a9915f8b6c0e","source-0620df96ebbf2a66"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."},{"id":"scwiki-d2-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"For an orbital dirty-limit description, write $B_{c2}=\\mu_0H_{c2}$ and $\\ln(T/T_c)=\\psi(1/2)-\\psi[1/2+\\hbar D B_{c2}(T)/(2\\Phi_0k_BT)]$, where $D$ is an effective diffusion parameter and $\\psi$ the digamma function. The Maki–de Gennes form omits Pauli, spin–orbit, strong-coupling and Fermi-surface anisotropy corrections. A useful fit to an inhomogeneous wire does not measure a unique microscopic $D$. Independent numerical roots recover the model ratio $B_{c2}(0)/(T_c|dB_{c2}/dT|_{T_c})=\\pi^2e^{-\\gamma}/8\\simeq0.693$; this is not a universal material relation.","evidenceType":"theory","sourceIds":["source-d27a049f764be753"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Godeke2005 supplies the MDG equation and exclusions; the limiting ratio and numerical root check are local, not a microscopic fit to a wire."},{"id":"scwiki-d2-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"For current perpendicular to field, the pinning-force magnitude is $F_p=J_cB$. A common fixed-temperature field shape is $f(h)=h^{1/2}(1-h)^2$, with $h=B/B_{c2}$. It peaks at $h=0.2$ and produces a linear Kramer plot of $J_c^{1/2}B^{1/4}$ only under the model's assumptions. A triangular vortex lattice has $a_\\Delta=(4/3)^{1/4}\\sqrt{\\Phi_0/B}$; the flux-shear expression includes $(1-a_\\Delta/d)^{-2}$ for mean grain size $d$. At 12 T and $d=100$ nm, this factor is about 1.36, so neglecting it requires a stated tolerance. Neither the pinning peak nor a fitted Kramer intercept independently identifies the thermodynamic upper critical field.","evidenceType":"theory","sourceIds":["source-c4b57e9e8e5aa3d7"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Godeke2006 supplies the flux-shear/Kramer forms and conditions; the12T/100nm correction and numerical peak are local evaluations, not measured grain data."},{"id":"scwiki-d2-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"A local two-component example uses the displayed $J_c=C B_{c2}^{2}h^{1/2}(1-h)^2/B$ with the same positive prefactor for both components, critical fields of 20 and 28 T, and zero current at or above each component field. Equal-area parallel addition gives $J_{\\mathrm{mix}}=(J_1+J_2)/2$. Two-point secants of $J_{\\mathrm{mix}}^{1/2}B^{1/4}$ over 10–14 T and 16–19 T extrapolate to 25.06 and 26.35 T; over 21–24 T only the 28 T component remains and the intercept is 28 T. These are explicitly chosen windows, not regression fits to measured data. Changing the connection to a local series bottleneck, $J_{\\mathrm{series}}=\\min(J_1,J_2)$, instead makes the 20 T component limiting. The example does not model current transfer, percolation or a real wire network.\n\nSeparately, Godeke considers a hypothetical uniform wire with grain size and grain-boundary density retained. Holding the prefactor fixed, the printed 24.9-to-26.9 T inputs give 2888.01 A/mm² from 2250 A/mm² at 12 T and 4.2 K, versus the paper's 2883 A/mm². If each printed field was rounded to the nearest 0.1 T, the resulting interval is approximately 2852–2924 A/mm². Compatibility with that assumed rounding does not establish the cause of the discrepancy. Neither improved value was measured.","evidenceType":"theory","sourceIds":["source-c4b57e9e8e5aa3d7","source-d27a049f764be753"],"conditions":"Local model: B>0, fixed temperature and prefactor, nonnegative currents cut off at each Bc2; explicit equal-area parallel sum or series minimum. Printed-field interval assumes nearest-0.1-T rounding independently for both inputs.","verificationScope":"2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Godeke2006 provides inhomogeneity/connection context; Godeke2005 Eq.4 and sectionV.B provide the hypothetical comparison. Two-component secants, series control and numerical rounding interval are local calculations, not experimental fits or source data reproduction."},{"id":"scwiki-d2-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Godeke and colleagues used approximately 0.2–0.6 A/mm², normalized to non-Cu area, for resistive measurements of filamentary Nb3Sn in fields up to 30 T. The 10%, 50% and 90% criteria refer to the fitted normal-state resistance background, not material volume fractions. At noisy high fields, the 99% value was extrapolated from the 10–90% region while assuming comparable transition widths at low and high fields. The unresolved interlaboratory offset was about 4%; the authors treated the data as reliable within roughly ±2%, without establishing a statistical confidence interval. These low-current transitions preferentially sample high-quality conducting paths, not the full conductor.","evidenceType":"experiment","sourceIds":["source-d27a049f764be753"],"conditions":"TableI non-Cu excitation-current normalization; source-specific resistance-fit/background and high-field extrapolation assumption. Approximate systematic reliability is not a calibrated standard deviation or confidence level.","verificationScope":"2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.","sourceRelationship":"mixed-source-and-local-derivation","derivationNote":"Godeke2005 TableI and sectionIII.A specify normalization, criteria, extrapolation and the unresolved offset; sectionIV.B discusses limited path sampling. The explicit warning against converting resistance percentage into volume fraction or confidence level is editorial inference from these measurement definitions."},{"id":"scwiki-d2-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"The B34 wire reacted for 64 hours at 675 °C provides a concrete comparison: transport at a 10 µV/m criterion gave non-Cu $J_c=2250$ A/mm² at 12 T and 4.2 K. The Kramer field was 24.9 T, while the 99% resistive field was 26.9 T at the same temperature. Keep the non-Cu area normalization, voltage criterion and heat treatment attached to those numbers. They are not interchangeable measures of performance.","evidenceType":"experiment","sourceIds":["source-d27a049f764be753"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."},{"id":"scwiki-d2-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Gapud and colleagues studied a floating-zone V3Si single crystal, MP3, with residual-resistivity ratio 47. Their 51V NMR experiment used 6.67 T, where the reported superconducting transition was 12.8 K and the structural transition 21.1 K. Cubic and tetragonal spectra coexisted around the structural transition. The authors found no conclusive cubic-phase spectrum below the zero-field transition scale of 17 K; that is distinct from the 12.8 K transition in the actual NMR field. These observations do not establish that a martensitic transition is necessary for every A15 superconductor.","evidenceType":"experiment","sourceIds":["source-9fe69d0a6cecbb0c"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."},{"id":"scwiki-d2-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"Elastic softening, anharmonicity and superconductivity can be correlated without a universal rule that moving closer to structural instability always improves $T_c$. Testardi's papers motivate this coupled problem; they do not remove the need for sample-specific structural and thermodynamic evidence. Changes in composition or disorder can alter several electronic and phonon parameters together. Increasing a density-of-states peak or an estimated coupling constant alone is not a validated optimization strategy.","evidenceType":"theory","sourceIds":["source-33f4444a5825b443","source-509b869080567558","source-0620df96ebbf2a66"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."},{"id":"scwiki-d2-claim-limits-and-disputes-2","sectionId":"limits-and-disputes","statement":"The V3Si NMR assignments depend on orientation, spectral resolution and the local electric-field-gradient model. The reported 6.67 T experiment distinguishes its 12.8 K superconducting transition from the zero-field scale of 17 K. Broadening, overlap and Knight shifts complicate the spectra; a missing resolved cubic-phase line does not by itself establish zero cubic volume. A quantitative phase-fraction limit would require a calibrated detection threshold and relative spectral response, which this entry has not established. Similarly, a Nb3Sn resistance criterion, a Kramer extrapolation and a magnetic transition retain different sampling conditions. Record mounting and strain as well as nominal composition.","evidenceType":"theory","sourceIds":["source-d27a049f764be753","source-9fe69d0a6cecbb0c"],"conditions":"Selected V3Si single-crystal experiment at6.67T; no calibrated phase-fraction detection limit or independent spectral fit. Source-specific Nb3Sn mounting/strain and electrical criteria.","verificationScope":"2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.","sourceRelationship":"context-for-editorial-analysis","derivationNote":"Gapud2022 pp.3–4 report the field, spectral overlap and unresolved cubic spectra; Godeke2005 sectionsIII.A/IV.B/V.B distinguish path sampling and mounting. Detection-limit and cross-probe cautions are editorial analysis, not a quantitative bound supplied by either paper."},{"id":"scwiki-d2-claim-limits-and-disputes-3","sectionId":"limits-and-disputes","statement":"A May 2026 doctoral-dissertation preprint explores Cu–Sn routes to Nb3Sn films for microwave dark-matter cavities. Its abstract describes a chosen cavity tested at 50 mK and 9 T, but reports a quality-factor decline in field. Neither the operating temperature nor the maximum applied field is a measured transition temperature or a demonstrated upper critical field. This is an abstract-level research pointer, not a peer-reviewed performance certification.","evidenceType":"theory","sourceIds":["source-3633507cd1108d10"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."},{"id":"scwiki-d2-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Optimize a complete, conditional objective: transition temperature, useful field range, current density, mechanical tolerance and manufacturability. Preserve measured and predicted quantities separately. Compare transition criteria, composition gradients, annealing, strain, grain structure and area normalization before ranking conductors. For a proposed material, check phase stability and the coupling-weighted phonon spectrum; for a working wire or cavity, test the actual operating condition and retain negative results.","evidenceType":"theory","sourceIds":["source-29d0a9915f8b6c0e","source-c4b57e9e8e5aa3d7","source-0620df96ebbf2a66","source-3633507cd1108d10"],"conditions":"Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.","verificationScope":"Selected original passages and bounded numerical checks only; full scientific acceptance remains open."}],"corrections":[{"id":"scwiki-d2-correction-1","description":"Corrected high-field cross-reference to A6 and Testardi1972 title; distinguished sputtering pressure, field-dependent transition criteria and hypothetical performance.","sourceId":"source-33f4444a5825b443","scope":"Edited public content; pinned source bytes preserved."},{"id":"scwiki-d2-correction-2","description":"Clarified primitive A15 cell versus B sublattice, non-Cu current normalization, resistance criteria versus phase fractions, and local connection/window/rounding assumptions.","sourceId":"source-d27a049f764be753","scope":"Local public-text and exported-claim correction; pinned source retained."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"\\ln t=\\psi(1/2)-\\psi(1/2+u/t)","check":"Five independent log-gamma derivatives, six roots and low/high-temperature limits."},{"targetSectionId":"mathematical-assumptions","tex":"f(h)=h^{1/2}(1-h)^2","check":"Peak, uniform Kramer intercept, eight finite-grain corrections and three toy-mixture intercepts."},{"targetSectionId":"mathematical-assumptions","tex":"J_c=C B_{c2}^2h^{1/2}(1-h)^2/B","check":"Printed fields give2888.01 rather than quoted2883 A/mm2; latter lies within field-rounding interval."}],"materialCases":[{"id":"scwiki-d2-material-1","formula":"Nb3Ge","sample":"Gavaler1973 sputtered Nb–Ge films","recordType":"experiment","reportedTemperatureK":22.3,"tcK":22.3,"temperatureKind":"transition","temperatureNote":"Not an equilibrium bulk constant; high-pressure sputtering does not imply high measurement pressure.","criterion":"reported-transition-unspecified","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"Publisher abstract; full criterion not reviewed","sourceId":"source-82a0df3d764cd0bc","aliases":["A15"]},{"id":"scwiki-d2-material-2","formula":"Nb3Sn","sample":"B34 ternary PIT, 64 h at 675 °C","recordType":"experiment","reportedTemperatureK":4.2,"tcK":null,"temperatureKind":"measurement","temperatureNote":"Operating temperature of current/field comparison, not Tc.","criterion":"transport-10-microvolt-per-metre","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"2250 A/mm2 non-Cu at 12 T; Kramer 24.9 T versus 99% resistive 26.9 T","sourceId":"source-d27a049f764be753","aliases":["A15"]},{"id":"scwiki-d2-material-3","formula":"V3Si","sample":"MP3 floating-zone single crystal, RRR47, field 6.67 T","recordType":"experiment","reportedTemperatureK":12.8,"tcK":12.8,"temperatureKind":"transition","temperatureNote":"Retain 6.67 T condition; structural transition 21.1 K is not Tc.","criterion":"reported-transport-transition-in-field","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"Transport context for 51V NMR; Tm 21.1 K, zero-field Tc 17 K","sourceId":"source-9fe69d0a6cecbb0c","aliases":["A15"]},{"id":"scwiki-d2-material-4","formula":"Nb3Sn","sample":"Cu–Sn route selected cavity; dissertation abstract","recordType":"experiment","reportedTemperatureK":0.05,"tcK":null,"temperatureKind":"measurement","temperatureNote":"Preprint operating condition; not Tc or a certified high-field Q target.","criterion":"cavity-operating-temperature","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"50 mK and 9 T reported in abstract; Q declines in field","sourceId":"source-3633507cd1108d10","aliases":["A15"]}],"body":"## Scope\n\nA15 is a crystal-structure family, usually written $A_3B$. Its ideal undistorted prototype is primitive cubic $Pm\\bar{3}n$ (No. 223), with eight atoms per cell: six A atoms on 6c sites and two B atoms on 2a sites. The body-centered arrangement of the B sublattice does not make the full crystal body-centered cubic. Three orthogonal A-atom chains help organize its electronic structure, without guaranteeing a high transition temperature. Composition, site ordering, phonons and strain remain important, and the brittle Nb–Sn phase also has to tolerate fabrication and mechanical loading. [R5](#ref-source-29d0a9915f8b6c0e) [R11](#ref-source-804b5d160a095037)\n\nNb3Sn, V3Si and Nb3Ge are distinct examples, not one table of universal constants. Matthias and colleagues reported Nb3Sn near 18 K in 1954. Gavaler's 1973 abstract reports sputtered Nb–Ge films remaining superconducting up to 22.3 K. That historical film result is neither an equilibrium bulk value nor a strict A15 temperature ceiling. “High pressure” in the deposition description refers to sputtering conditions, not a high-pressure superconductivity measurement. [R1](#ref-source-830f887afcf548c4) [R2](#ref-source-82a0df3d764cd0bc)\n\nNear-stoichiometric Nb3Sn is a conventional strong-coupling benchmark, but even its coupling classification depends on composition and how the gap and transition are sampled. Godeke's review discusses interface-gap and inhomogeneity effects that can bias a gap-to-temperature ratio. A full gap is not proof that all samples have the same coupling, and a large upper critical field alone is not evidence for triplet pairing. [R5](#ref-source-29d0a9915f8b6c0e) [R9](#ref-source-0620df96ebbf2a66)\n\n## Mathematical assumptions\n\nFor an orbital dirty-limit description, write $B_{c2}=\\mu_0H_{c2}$ and $\\ln(T/T_c)=\\psi(1/2)-\\psi[1/2+\\hbar D B_{c2}(T)/(2\\Phi_0k_BT)]$, where $D$ is an effective diffusion parameter and $\\psi$ the digamma function. The Maki–de Gennes form omits Pauli, spin–orbit, strong-coupling and Fermi-surface anisotropy corrections. A useful fit to an inhomogeneous wire does not measure a unique microscopic $D$. Independent numerical roots recover the model ratio $B_{c2}(0)/(T_c|dB_{c2}/dT|_{T_c})=\\pi^2e^{-\\gamma}/8\\simeq0.693$; this is not a universal material relation. [R7](#ref-source-d27a049f764be753)\n\nFor current perpendicular to field, the pinning-force magnitude is $F_p=J_cB$. A common fixed-temperature field shape is $f(h)=h^{1/2}(1-h)^2$, with $h=B/B_{c2}$. It peaks at $h=0.2$ and produces a linear Kramer plot of $J_c^{1/2}B^{1/4}$ only under the model's assumptions. A triangular vortex lattice has $a_\\Delta=(4/3)^{1/4}\\sqrt{\\Phi_0/B}$; the flux-shear expression includes $(1-a_\\Delta/d)^{-2}$ for mean grain size $d$. At 12 T and $d=100$ nm, this factor is about 1.36, so neglecting it requires a stated tolerance. Neither the pinning peak nor a fitted Kramer intercept independently identifies the thermodynamic upper critical field. [R6](#ref-source-c4b57e9e8e5aa3d7)\n\nA local two-component example uses the displayed $J_c=C B_{c2}^{2}h^{1/2}(1-h)^2/B$ with the same positive prefactor for both components, critical fields of 20 and 28 T, and zero current at or above each component field. Equal-area parallel addition gives $J_{\\mathrm{mix}}=(J_1+J_2)/2$. Two-point secants of $J_{\\mathrm{mix}}^{1/2}B^{1/4}$ over 10–14 T and 16–19 T extrapolate to 25.06 and 26.35 T; over 21–24 T only the 28 T component remains and the intercept is 28 T. These are explicitly chosen windows, not regression fits to measured data. Changing the connection to a local series bottleneck, $J_{\\mathrm{series}}=\\min(J_1,J_2)$, instead makes the 20 T component limiting. The example does not model current transfer, percolation or a real wire network.\n\nSeparately, Godeke considers a hypothetical uniform wire with grain size and grain-boundary density retained. Holding the prefactor fixed, the printed 24.9-to-26.9 T inputs give 2888.01 A/mm² from 2250 A/mm² at 12 T and 4.2 K, versus the paper's 2883 A/mm². If each printed field was rounded to the nearest 0.1 T, the resulting interval is approximately 2852–2924 A/mm². Compatibility with that assumed rounding does not establish the cause of the discrepancy. Neither improved value was measured. [R6](#ref-source-c4b57e9e8e5aa3d7) [R7](#ref-source-d27a049f764be753)\n\n## Experimental criteria\n\nGodeke and colleagues used approximately 0.2–0.6 A/mm², normalized to non-Cu area, for resistive measurements of filamentary Nb3Sn in fields up to 30 T. The 10%, 50% and 90% criteria refer to the fitted normal-state resistance background, not material volume fractions. At noisy high fields, the 99% value was extrapolated from the 10–90% region while assuming comparable transition widths at low and high fields. The unresolved interlaboratory offset was about 4%; the authors treated the data as reliable within roughly ±2%, without establishing a statistical confidence interval. These low-current transitions preferentially sample high-quality conducting paths, not the full conductor. [R7](#ref-source-d27a049f764be753)\n\nThe B34 wire reacted for 64 hours at 675 °C provides a concrete comparison: transport at a 10 µV/m criterion gave non-Cu $J_c=2250$ A/mm² at 12 T and 4.2 K. The Kramer field was 24.9 T, while the 99% resistive field was 26.9 T at the same temperature. Keep the non-Cu area normalization, voltage criterion and heat treatment attached to those numbers. They are not interchangeable measures of performance. [R7](#ref-source-d27a049f764be753)\n\nGapud and colleagues studied a floating-zone V3Si single crystal, MP3, with residual-resistivity ratio 47. Their 51V NMR experiment used 6.67 T, where the reported superconducting transition was 12.8 K and the structural transition 21.1 K. Cubic and tetragonal spectra coexisted around the structural transition. The authors found no conclusive cubic-phase spectrum below the zero-field transition scale of 17 K; that is distinct from the 12.8 K transition in the actual NMR field. These observations do not establish that a martensitic transition is necessary for every A15 superconductor. [R8](#ref-source-9fe69d0a6cecbb0c)\n\n## Limits and disputes\n\nElastic softening, anharmonicity and superconductivity can be correlated without a universal rule that moving closer to structural instability always improves $T_c$. Testardi's papers motivate this coupled problem; they do not remove the need for sample-specific structural and thermodynamic evidence. Changes in composition or disorder can alter several electronic and phonon parameters together. Increasing a density-of-states peak or an estimated coupling constant alone is not a validated optimization strategy. [R3](#ref-source-33f4444a5825b443) [R4](#ref-source-509b869080567558) [R9](#ref-source-0620df96ebbf2a66)\n\nThe V3Si NMR assignments depend on orientation, spectral resolution and the local electric-field-gradient model. The reported 6.67 T experiment distinguishes its 12.8 K superconducting transition from the zero-field scale of 17 K. Broadening, overlap and Knight shifts complicate the spectra; a missing resolved cubic-phase line does not by itself establish zero cubic volume. A quantitative phase-fraction limit would require a calibrated detection threshold and relative spectral response, which this entry has not established. Similarly, a Nb3Sn resistance criterion, a Kramer extrapolation and a magnetic transition retain different sampling conditions. Record mounting and strain as well as nominal composition. [R7](#ref-source-d27a049f764be753) [R8](#ref-source-9fe69d0a6cecbb0c)\n\nA May 2026 doctoral-dissertation preprint explores Cu–Sn routes to Nb3Sn films for microwave dark-matter cavities. Its abstract describes a chosen cavity tested at 50 mK and 9 T, but reports a quality-factor decline in field. Neither the operating temperature nor the maximum applied field is a measured transition temperature or a demonstrated upper critical field. This is an abstract-level research pointer, not a peer-reviewed performance certification. [R10](#ref-source-3633507cd1108d10)\n\n## Discovery implications\n\nOptimize a complete, conditional objective: transition temperature, useful field range, current density, mechanical tolerance and manufacturability. Preserve measured and predicted quantities separately. Compare transition criteria, composition gradients, annealing, strain, grain structure and area normalization before ranking conductors. For a proposed material, check phase stability and the coupling-weighted phonon spectrum; for a working wire or cavity, test the actual operating condition and retain negative results. [R5](#ref-source-29d0a9915f8b6c0e) [R6](#ref-source-c4b57e9e8e5aa3d7) [R9](#ref-source-0620df96ebbf2a66) [R10](#ref-source-3633507cd1108d10)\n\n## Related topics\n\nContinue with [elemental superconductors](/scwiki/elemental-superconductors), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [s-wave pairing](/scwiki/s-wave), [critical fields](/scwiki/critical-fields) and [critical current](/scwiki/critical-current).","revision":"c58668ce70c07a494483","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nA15 is a crystal-structure family, usually written $A_3B$. Its ideal undistorted prototype is primitive cubic $Pm\\bar{3}n$ (No. 223), with eight atoms per cell: six A atoms on 6c sites and two B atoms on 2a sites. The body-centered arrangement of the B sublattice does not make the full crystal body-centered cubic. Three orthogonal A-atom chains help organize its electronic structure, without guaranteeing a high transition temperature. Composition, site ordering, phonons and strain remain important, and the brittle Nb–Sn phase also has to tolerate fabrication and mechanical loading. [R5](#ref-source-29d0a9915f8b6c0e) [R11](#ref-source-804b5d160a095037)\n\nNb3Sn, V3Si and Nb3Ge are distinct examples, not one table of universal constants. Matthias and colleagues reported Nb3Sn near 18 K in 1954. Gavaler's 1973 abstract reports sputtered Nb–Ge films remaining superconducting up to 22.3 K. That historical film result is neither an equilibrium bulk value nor a strict A15 temperature ceiling. “High pressure” in the deposition description refers to sputtering conditions, not a high-pressure superconductivity measurement. [R1](#ref-source-830f887afcf548c4) [R2](#ref-source-82a0df3d764cd0bc)\n\nNear-stoichiometric Nb3Sn is a conventional strong-coupling benchmark, but even its coupling classification depends on composition and how the gap and transition are sampled. Godeke's review discusses interface-gap and inhomogeneity effects that can bias a gap-to-temperature ratio. A full gap is not proof that all samples have the same coupling, and a large upper critical field alone is not evidence for triplet pairing. [R5](#ref-source-29d0a9915f8b6c0e) [R9](#ref-source-0620df96ebbf2a66)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nFor an orbital dirty-limit description, write $B_{c2}=\\mu_0H_{c2}$ and $\\ln(T/T_c)=\\psi(1/2)-\\psi[1/2+\\hbar D B_{c2}(T)/(2\\Phi_0k_BT)]$, where $D$ is an effective diffusion parameter and $\\psi$ the digamma function. The Maki–de Gennes form omits Pauli, spin–orbit, strong-coupling and Fermi-surface anisotropy corrections. A useful fit to an inhomogeneous wire does not measure a unique microscopic $D$. Independent numerical roots recover the model ratio $B_{c2}(0)/(T_c|dB_{c2}/dT|_{T_c})=\\pi^2e^{-\\gamma}/8\\simeq0.693$; this is not a universal material relation. [R7](#ref-source-d27a049f764be753)\n\nFor current perpendicular to field, the pinning-force magnitude is $F_p=J_cB$. A common fixed-temperature field shape is $f(h)=h^{1/2}(1-h)^2$, with $h=B/B_{c2}$. It peaks at $h=0.2$ and produces a linear Kramer plot of $J_c^{1/2}B^{1/4}$ only under the model's assumptions. A triangular vortex lattice has $a_\\Delta=(4/3)^{1/4}\\sqrt{\\Phi_0/B}$; the flux-shear expression includes $(1-a_\\Delta/d)^{-2}$ for mean grain size $d$. At 12 T and $d=100$ nm, this factor is about 1.36, so neglecting it requires a stated tolerance. Neither the pinning peak nor a fitted Kramer intercept independently identifies the thermodynamic upper critical field. [R6](#ref-source-c4b57e9e8e5aa3d7)\n\nA local two-component example uses the displayed $J_c=C B_{c2}^{2}h^{1/2}(1-h)^2/B$ with the same positive prefactor for both components, critical fields of 20 and 28 T, and zero current at or above each component field. Equal-area parallel addition gives $J_{\\mathrm{mix}}=(J_1+J_2)/2$. Two-point secants of $J_{\\mathrm{mix}}^{1/2}B^{1/4}$ over 10–14 T and 16–19 T extrapolate to 25.06 and 26.35 T; over 21–24 T only the 28 T component remains and the intercept is 28 T. These are explicitly chosen windows, not regression fits to measured data. Changing the connection to a local series bottleneck, $J_{\\mathrm{series}}=\\min(J_1,J_2)$, instead makes the 20 T component limiting. The example does not model current transfer, percolation or a real wire network.\n\nSeparately, Godeke considers a hypothetical uniform wire with grain size and grain-boundary density retained. Holding the prefactor fixed, the printed 24.9-to-26.9 T inputs give 2888.01 A/mm² from 2250 A/mm² at 12 T and 4.2 K, versus the paper's 2883 A/mm². If each printed field was rounded to the nearest 0.1 T, the resulting interval is approximately 2852–2924 A/mm². Compatibility with that assumed rounding does not establish the cause of the discrepancy. Neither improved value was measured. [R6](#ref-source-c4b57e9e8e5aa3d7) [R7](#ref-source-d27a049f764be753)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nGodeke and colleagues used approximately 0.2–0.6 A/mm², normalized to non-Cu area, for resistive measurements of filamentary Nb3Sn in fields up to 30 T. The 10%, 50% and 90% criteria refer to the fitted normal-state resistance background, not material volume fractions. At noisy high fields, the 99% value was extrapolated from the 10–90% region while assuming comparable transition widths at low and high fields. The unresolved interlaboratory offset was about 4%; the authors treated the data as reliable within roughly ±2%, without establishing a statistical confidence interval. These low-current transitions preferentially sample high-quality conducting paths, not the full conductor. [R7](#ref-source-d27a049f764be753)\n\nThe B34 wire reacted for 64 hours at 675 °C provides a concrete comparison: transport at a 10 µV/m criterion gave non-Cu $J_c=2250$ A/mm² at 12 T and 4.2 K. The Kramer field was 24.9 T, while the 99% resistive field was 26.9 T at the same temperature. Keep the non-Cu area normalization, voltage criterion and heat treatment attached to those numbers. They are not interchangeable measures of performance. [R7](#ref-source-d27a049f764be753)\n\nGapud and colleagues studied a floating-zone V3Si single crystal, MP3, with residual-resistivity ratio 47. Their 51V NMR experiment used 6.67 T, where the reported superconducting transition was 12.8 K and the structural transition 21.1 K. Cubic and tetragonal spectra coexisted around the structural transition. The authors found no conclusive cubic-phase spectrum below the zero-field transition scale of 17 K; that is distinct from the 12.8 K transition in the actual NMR field. These observations do not establish that a martensitic transition is necessary for every A15 superconductor. [R8](#ref-source-9fe69d0a6cecbb0c)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nElastic softening, anharmonicity and superconductivity can be correlated without a universal rule that moving closer to structural instability always improves $T_c$. Testardi's papers motivate this coupled problem; they do not remove the need for sample-specific structural and thermodynamic evidence. Changes in composition or disorder can alter several electronic and phonon parameters together. Increasing a density-of-states peak or an estimated coupling constant alone is not a validated optimization strategy. [R3](#ref-source-33f4444a5825b443) [R4](#ref-source-509b869080567558) [R9](#ref-source-0620df96ebbf2a66)\n\nThe V3Si NMR assignments depend on orientation, spectral resolution and the local electric-field-gradient model. The reported 6.67 T experiment distinguishes its 12.8 K superconducting transition from the zero-field scale of 17 K. Broadening, overlap and Knight shifts complicate the spectra; a missing resolved cubic-phase line does not by itself establish zero cubic volume. A quantitative phase-fraction limit would require a calibrated detection threshold and relative spectral response, which this entry has not established. Similarly, a Nb3Sn resistance criterion, a Kramer extrapolation and a magnetic transition retain different sampling conditions. Record mounting and strain as well as nominal composition. [R7](#ref-source-d27a049f764be753) [R8](#ref-source-9fe69d0a6cecbb0c)\n\nA May 2026 doctoral-dissertation preprint explores Cu–Sn routes to Nb3Sn films for microwave dark-matter cavities. Its abstract describes a chosen cavity tested at 50 mK and 9 T, but reports a quality-factor decline in field. Neither the operating temperature nor the maximum applied field is a measured transition temperature or a demonstrated upper critical field. This is an abstract-level research pointer, not a peer-reviewed performance certification. [R10](#ref-source-3633507cd1108d10)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nOptimize a complete, conditional objective: transition temperature, useful field range, current density, mechanical tolerance and manufacturability. Preserve measured and predicted quantities separately. Compare transition criteria, composition gradients, annealing, strain, grain structure and area normalization before ranking conductors. For a proposed material, check phase stability and the coupling-weighted phonon spectrum; for a working wire or cavity, test the actual operating condition and retain negative results. [R5](#ref-source-29d0a9915f8b6c0e) [R6](#ref-source-c4b57e9e8e5aa3d7) [R9](#ref-source-0620df96ebbf2a66) [R10](#ref-source-3633507cd1108d10)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\nContinue with [elemental superconductors](/scwiki/elemental-superconductors), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [s-wave pairing](/scwiki/s-wave), [critical fields](/scwiki/critical-fields) and [critical current](/scwiki/critical-current)."},{"id":"material-cases","title":"Material cases","markdown":"## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| Nb3Ge (aliases: A15); Gavaler1973 sputtered Nb–Ge films | 22.3 K; Not an equilibrium bulk constant; high-pressure sputtering does not imply high measurement pressure. | transition; reported-transition-unspecified | Publisher abstract; full criterion not reviewed | ambient; unknown GPa | unknown | experiment; [source](#ref-source-82a0df3d764cd0bc) |\n| Nb3Sn (aliases: A15); B34 ternary PIT, 64 h at 675 °C | 4.2 K; Operating temperature of current/field comparison, not Tc. | measurement; transport-10-microvolt-per-metre | 2250 A/mm2 non-Cu at 12 T; Kramer 24.9 T versus 99% resistive 26.9 T | ambient; unknown GPa | unknown | experiment; [source](#ref-source-d27a049f764be753) |\n| V3Si (aliases: A15); MP3 floating-zone single crystal, RRR47, field 6.67 T | 12.8 K; Retain 6.67 T condition; structural transition 21.1 K is not Tc. | transition; reported-transport-transition-in-field | Transport context for 51V NMR; Tm 21.1 K, zero-field Tc 17 K | ambient; unknown GPa | unknown | experiment; [source](#ref-source-9fe69d0a6cecbb0c) |\n| Nb3Sn (aliases: A15); Cu–Sn route selected cavity; dissertation abstract | 0.05 K; Preprint operating condition; not Tc or a certified high-field Q target. | measurement; cavity-operating-temperature | 50 mK and 9 T reported in abstract; Q declines in field | ambient; unknown GPa | unknown | experiment; [source](#ref-source-3633507cd1108d10) |"}],"markdown":"# A15 compounds: structure, strain and useful critical fields\n\nUnderstand Nb3Sn, V3Si and Nb3Ge through sample conditions, structural transitions and the distinction between critical fields and current-carrying performance.\n\n## Scope\n\nA15 is a crystal-structure family, usually written $A_3B$. Its ideal undistorted prototype is primitive cubic $Pm\\bar{3}n$ (No. 223), with eight atoms per cell: six A atoms on 6c sites and two B atoms on 2a sites. The body-centered arrangement of the B sublattice does not make the full crystal body-centered cubic. Three orthogonal A-atom chains help organize its electronic structure, without guaranteeing a high transition temperature. Composition, site ordering, phonons and strain remain important, and the brittle Nb–Sn phase also has to tolerate fabrication and mechanical loading. [R5](#ref-source-29d0a9915f8b6c0e) [R11](#ref-source-804b5d160a095037)\n\nNb3Sn, V3Si and Nb3Ge are distinct examples, not one table of universal constants. Matthias and colleagues reported Nb3Sn near 18 K in 1954. Gavaler's 1973 abstract reports sputtered Nb–Ge films remaining superconducting up to 22.3 K. That historical film result is neither an equilibrium bulk value nor a strict A15 temperature ceiling. “High pressure” in the deposition description refers to sputtering conditions, not a high-pressure superconductivity measurement. [R1](#ref-source-830f887afcf548c4) [R2](#ref-source-82a0df3d764cd0bc)\n\nNear-stoichiometric Nb3Sn is a conventional strong-coupling benchmark, but even its coupling classification depends on composition and how the gap and transition are sampled. Godeke's review discusses interface-gap and inhomogeneity effects that can bias a gap-to-temperature ratio. A full gap is not proof that all samples have the same coupling, and a large upper critical field alone is not evidence for triplet pairing. [R5](#ref-source-29d0a9915f8b6c0e) [R9](#ref-source-0620df96ebbf2a66)\n\n## Mathematical assumptions\n\nFor an orbital dirty-limit description, write $B_{c2}=\\mu_0H_{c2}$ and $\\ln(T/T_c)=\\psi(1/2)-\\psi[1/2+\\hbar D B_{c2}(T)/(2\\Phi_0k_BT)]$, where $D$ is an effective diffusion parameter and $\\psi$ the digamma function. The Maki–de Gennes form omits Pauli, spin–orbit, strong-coupling and Fermi-surface anisotropy corrections. A useful fit to an inhomogeneous wire does not measure a unique microscopic $D$. Independent numerical roots recover the model ratio $B_{c2}(0)/(T_c|dB_{c2}/dT|_{T_c})=\\pi^2e^{-\\gamma}/8\\simeq0.693$; this is not a universal material relation. [R7](#ref-source-d27a049f764be753)\n\nFor current perpendicular to field, the pinning-force magnitude is $F_p=J_cB$. A common fixed-temperature field shape is $f(h)=h^{1/2}(1-h)^2$, with $h=B/B_{c2}$. It peaks at $h=0.2$ and produces a linear Kramer plot of $J_c^{1/2}B^{1/4}$ only under the model's assumptions. A triangular vortex lattice has $a_\\Delta=(4/3)^{1/4}\\sqrt{\\Phi_0/B}$; the flux-shear expression includes $(1-a_\\Delta/d)^{-2}$ for mean grain size $d$. At 12 T and $d=100$ nm, this factor is about 1.36, so neglecting it requires a stated tolerance. Neither the pinning peak nor a fitted Kramer intercept independently identifies the thermodynamic upper critical field. [R6](#ref-source-c4b57e9e8e5aa3d7)\n\nA local two-component example uses the displayed $J_c=C B_{c2}^{2}h^{1/2}(1-h)^2/B$ with the same positive prefactor for both components, critical fields of 20 and 28 T, and zero current at or above each component field. Equal-area parallel addition gives $J_{\\mathrm{mix}}=(J_1+J_2)/2$. Two-point secants of $J_{\\mathrm{mix}}^{1/2}B^{1/4}$ over 10–14 T and 16–19 T extrapolate to 25.06 and 26.35 T; over 21–24 T only the 28 T component remains and the intercept is 28 T. These are explicitly chosen windows, not regression fits to measured data. Changing the connection to a local series bottleneck, $J_{\\mathrm{series}}=\\min(J_1,J_2)$, instead makes the 20 T component limiting. The example does not model current transfer, percolation or a real wire network.\n\nSeparately, Godeke considers a hypothetical uniform wire with grain size and grain-boundary density retained. Holding the prefactor fixed, the printed 24.9-to-26.9 T inputs give 2888.01 A/mm² from 2250 A/mm² at 12 T and 4.2 K, versus the paper's 2883 A/mm². If each printed field was rounded to the nearest 0.1 T, the resulting interval is approximately 2852–2924 A/mm². Compatibility with that assumed rounding does not establish the cause of the discrepancy. Neither improved value was measured. [R6](#ref-source-c4b57e9e8e5aa3d7) [R7](#ref-source-d27a049f764be753)\n\n## Experimental criteria\n\nGodeke and colleagues used approximately 0.2–0.6 A/mm², normalized to non-Cu area, for resistive measurements of filamentary Nb3Sn in fields up to 30 T. The 10%, 50% and 90% criteria refer to the fitted normal-state resistance background, not material volume fractions. At noisy high fields, the 99% value was extrapolated from the 10–90% region while assuming comparable transition widths at low and high fields. The unresolved interlaboratory offset was about 4%; the authors treated the data as reliable within roughly ±2%, without establishing a statistical confidence interval. These low-current transitions preferentially sample high-quality conducting paths, not the full conductor. [R7](#ref-source-d27a049f764be753)\n\nThe B34 wire reacted for 64 hours at 675 °C provides a concrete comparison: transport at a 10 µV/m criterion gave non-Cu $J_c=2250$ A/mm² at 12 T and 4.2 K. The Kramer field was 24.9 T, while the 99% resistive field was 26.9 T at the same temperature. Keep the non-Cu area normalization, voltage criterion and heat treatment attached to those numbers. They are not interchangeable measures of performance. [R7](#ref-source-d27a049f764be753)\n\nGapud and colleagues studied a floating-zone V3Si single crystal, MP3, with residual-resistivity ratio 47. Their 51V NMR experiment used 6.67 T, where the reported superconducting transition was 12.8 K and the structural transition 21.1 K. Cubic and tetragonal spectra coexisted around the structural transition. The authors found no conclusive cubic-phase spectrum below the zero-field transition scale of 17 K; that is distinct from the 12.8 K transition in the actual NMR field. These observations do not establish that a martensitic transition is necessary for every A15 superconductor. [R8](#ref-source-9fe69d0a6cecbb0c)\n\n## Limits and disputes\n\nElastic softening, anharmonicity and superconductivity can be correlated without a universal rule that moving closer to structural instability always improves $T_c$. Testardi's papers motivate this coupled problem; they do not remove the need for sample-specific structural and thermodynamic evidence. Changes in composition or disorder can alter several electronic and phonon parameters together. Increasing a density-of-states peak or an estimated coupling constant alone is not a validated optimization strategy. [R3](#ref-source-33f4444a5825b443) [R4](#ref-source-509b869080567558) [R9](#ref-source-0620df96ebbf2a66)\n\nThe V3Si NMR assignments depend on orientation, spectral resolution and the local electric-field-gradient model. The reported 6.67 T experiment distinguishes its 12.8 K superconducting transition from the zero-field scale of 17 K. Broadening, overlap and Knight shifts complicate the spectra; a missing resolved cubic-phase line does not by itself establish zero cubic volume. A quantitative phase-fraction limit would require a calibrated detection threshold and relative spectral response, which this entry has not established. Similarly, a Nb3Sn resistance criterion, a Kramer extrapolation and a magnetic transition retain different sampling conditions. Record mounting and strain as well as nominal composition. [R7](#ref-source-d27a049f764be753) [R8](#ref-source-9fe69d0a6cecbb0c)\n\nA May 2026 doctoral-dissertation preprint explores Cu–Sn routes to Nb3Sn films for microwave dark-matter cavities. Its abstract describes a chosen cavity tested at 50 mK and 9 T, but reports a quality-factor decline in field. Neither the operating temperature nor the maximum applied field is a measured transition temperature or a demonstrated upper critical field. This is an abstract-level research pointer, not a peer-reviewed performance certification. [R10](#ref-source-3633507cd1108d10)\n\n## Discovery implications\n\nOptimize a complete, conditional objective: transition temperature, useful field range, current density, mechanical tolerance and manufacturability. Preserve measured and predicted quantities separately. Compare transition criteria, composition gradients, annealing, strain, grain structure and area normalization before ranking conductors. For a proposed material, check phase stability and the coupling-weighted phonon spectrum; for a working wire or cavity, test the actual operating condition and retain negative results. [R5](#ref-source-29d0a9915f8b6c0e) [R6](#ref-source-c4b57e9e8e5aa3d7) [R9](#ref-source-0620df96ebbf2a66) [R10](#ref-source-3633507cd1108d10)\n\n## Related topics\n\nContinue with [elemental superconductors](/scwiki/elemental-superconductors), [Eliashberg theory](/scwiki/eliashberg-strong-coupling), [s-wave pairing](/scwiki/s-wave), [critical fields](/scwiki/critical-fields) and [critical current](/scwiki/critical-current).\n\n## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| Nb3Ge (aliases: A15); Gavaler1973 sputtered Nb–Ge films | 22.3 K; Not an equilibrium bulk constant; high-pressure sputtering does not imply high measurement pressure. | transition; reported-transition-unspecified | Publisher abstract; full criterion not reviewed | ambient; unknown GPa | unknown | experiment; [source](#ref-source-82a0df3d764cd0bc) |\n| Nb3Sn (aliases: A15); B34 ternary PIT, 64 h at 675 °C | 4.2 K; Operating temperature of current/field comparison, not Tc. | measurement; transport-10-microvolt-per-metre | 2250 A/mm2 non-Cu at 12 T; Kramer 24.9 T versus 99% resistive 26.9 T | ambient; unknown GPa | unknown | experiment; [source](#ref-source-d27a049f764be753) |\n| V3Si (aliases: A15); MP3 floating-zone single crystal, RRR47, field 6.67 T | 12.8 K; Retain 6.67 T condition; structural transition 21.1 K is not Tc. | transition; reported-transport-transition-in-field | Transport context for 51V NMR; Tm 21.1 K, zero-field Tc 17 K | ambient; unknown GPa | unknown | experiment; [source](#ref-source-9fe69d0a6cecbb0c) |\n| Nb3Sn (aliases: A15); Cu–Sn route selected cavity; dissertation abstract | 0.05 K; Preprint operating condition; not Tc or a certified high-field Q target. | measurement; cavity-operating-temperature | 50 mK and 9 T reported in abstract; Q declines in field | ambient; unknown GPa | unknown | experiment; [source](#ref-source-3633507cd1108d10) |\n\n## Sources\n\n### Ref source-830f887afcf548c4\n\n[R1] Superconductivity of Nb3Sn (1954). [DOI 10.1103/PhysRev.95.1435](https://doi.org/10.1103/PhysRev.95.1435). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published 15 September 1954. Historical reported scale only; original full methods not reviewed.\n### Ref source-82a0df3d764cd0bc\n\n[R2] Superconductivity in Nb–Ge films above 22 K (1973). [DOI 10.1063/1.1654966](https://doi.org/10.1063/1.1654966). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published 15 October 1973. Publisher abstract also verified through Crossref; reports 22.3 K films from high-pressure dc sputtering. Measurement criterion and full methods not independently read.\n### Ref source-33f4444a5825b443\n\n[R3] Structural Instability, Anharmonicity, and High-Temperature Superconductivity in A-15-Structure Compounds (1972). [DOI 10.1103/PhysRevB.5.4342](https://doi.org/10.1103/PhysRevB.5.4342). Publication: journal-article. Check: publisher-abstract-check. Checked: 2026-10-18. Published 1 June 1972. Sound-velocity/strain interpretation and model conjectures; not universal monotonic optimization.\n### Ref source-509b869080567558\n\n[R4] Structural instability and superconductivity in A-15 compounds (1975). [DOI 10.1103/RevModPhys.47.637](https://doi.org/10.1103/RevModPhys.47.637). Publication: journal-article. Check: publisher-indexed-abstract-check. Checked: 2026-10-18. Published 1 July 1975. Indexed publisher abstract only; full review not read.\n### Ref source-29d0a9915f8b6c0e\n\n[R5] A review of the properties of Nb3Sn and their variation with A15 composition, morphology and strain state (2006). [DOI 10.1088/0953-2048/19/8/R02](https://doi.org/10.1088/0953-2048/19/8/R02). Publication: journal-article. Check: selected-author-review-text-check. Checked: 2026-10-19. Follow-up19October2026 re-read authorv1 introduction/structure pp.1–3: chain geometry, sublattice, disorder and strain context. Earlier Fig.6 coupling check retained; underlying cited datasets not reproduced. AFLOW separately supports the exact space-group/basis label.\n### Ref source-c4b57e9e8e5aa3d7\n\n[R6] A general scaling relation for the critical current density in Nb3Sn (2006). [DOI 10.1088/0953-2048/19/10/R02](https://doi.org/10.1088/0953-2048/19/10/R02). Publication: journal-article. Check: selected-author-review-equation-check. Checked: 2026-10-19. Follow-up19October2026 re-read authorv1 pp.4–8: field form, grain assumptions, linearity, parallel/series inhomogeneity discussion. Header confirms18August2006v1; full strain model and raw data not reanalyzed.\n### Ref source-d27a049f764be753\n\n[R7] The upper critical field of filamentary Nb3Sn conductors (2005). [DOI 10.1063/1.1890447](https://doi.org/10.1063/1.1890447). Publication: journal-article. Check: selected-author-v2-methods-equation-check. Checked: 2026-10-19. Follow-up19October2026 re-read authorv2 TableI p.2, methods pp.5–6, path sampling p.8 and hypothetical comparison pp.9–10. Explicitv2 and currentPDF bytes matched SHA2563e899f328e3a6ff2f1aad79e425ac9f7c1264e596dc00e80291adf6e4070aa5b; arXiv history confirms28February2005v2, replacement of Eqs.7–9. No raw-data fit or new PDF-pixel verification claimed. The rounding interval is a local assumption, not proven error attribution.\n### Ref source-9fe69d0a6cecbb0c\n\n[R8] Martensitic transformation in V3Si single crystal: 51V NMR evidence for coexistence of cubic and tetragonal phases (2022). [DOI 10.1016/j.physc.2022.1354137](https://doi.org/10.1016/j.physc.2022.1354137). Publication: journal-article. Check: selected-published-methods-results-check. Checked: 2026-10-19. Follow-up19October2026 re-read published pp.3–4:6.67T,12.8K versus zero-field17K, broadening/overlap, EFG assignment and no conclusive cubic spectra. Full EFG appendix, spectral fits and quantitative detection threshold not independently established; PDF-pixel request failed.\n### Ref source-0620df96ebbf2a66\n\n[R9] Transition temperature of strong-coupled superconductors reanalyzed (1975). [DOI 10.1103/PhysRevB.12.905](https://doi.org/10.1103/PhysRevB.12.905). Publication: journal-article. Check: primary-abstract-scoped-check. Checked: 2026-10-18. Publisher abstract: modified prefactor, spectral moment/shape corrections and large-coupling limits within Eliashberg theory. Full derivation and Pb-Bi data not reanalyzed.\n### Ref source-3633507cd1108d10\n\n[R10] Nb3Sn Thin Films Using a Cu-Sn Route for Dark Matter Detection (2026). [Source publication](https://arxiv.org/abs/2605.03171v1). Publication: preprint. Check: preprint-abstract-check. Checked: 2026-10-18. Doctoral dissertation preprint, submitted 4 May 2026; not a peer-reviewed journal article. Abstract only: selected cavity at 50 mK and 9 T, quality factor declines in field. Full 211-page dissertation not read.\n### Ref source-804b5d160a095037\n\n[R11] AFLOW crystallographic prototype: Cr3Si (A15), A3B_cP8_223_c_a-001 (Publication date unknown). [Source publication](https://www.aflow.org/prototype-encyclopedia/A3B_cP8_223_c_a-001/). Publication: technical-report. Check: official-prototype-structure-check. Checked: 2026-10-19. Official prototype entry, accessed 19 October 2026: cubic primitive cP8, space group223, A sites6c and B sites2a. Page-specific publication date is not supplied; underlying diffraction experiment and whole prototype library were not independently reviewed.\n\n## Claim evidence and conditions\n\n### scwiki-d2-claim-scope-1\n\nA15 is a crystal-structure family, usually written $A_3B$. Its ideal undistorted prototype is primitive cubic $Pm\\bar{3}n$ (No. 223), with eight atoms per cell: six A atoms on 6c sites and two B atoms on 2a sites. The body-centered arrangement of the B sublattice does not make the full crystal body-centered cubic. Three orthogonal A-atom chains help organize its electronic structure, without guaranteeing a high transition temperature. Composition, site ordering, phonons and strain remain important, and the brittle Nb–Sn phase also has to tolerate fabrication and mechanical loading.\n\nEvidence: theory. Sources: source-29d0a9915f8b6c0e, source-804b5d160a095037.\n\nSource relationship: mixed-source-and-local-derivation. AFLOW specifies the prototype and basis; Godeke reviews chain geometry, disorder and wire conditions. The sublattice-versus-Bravais distinction is an explicit interpretation of that basis, not a new diffraction refinement.\n\nConditions: Ideal undistorted A3B prototype; actual samples can be off-stoichiometric or structurally distorted. Atomic chain geometry is not a sufficient Tc predictor.\n\nVerification scope: 2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.\n\n### scwiki-d2-claim-scope-2\n\nNb3Sn, V3Si and Nb3Ge are distinct examples, not one table of universal constants. Matthias and colleagues reported Nb3Sn near 18 K in 1954. Gavaler's 1973 abstract reports sputtered Nb–Ge films remaining superconducting up to 22.3 K. That historical film result is neither an equilibrium bulk value nor a strict A15 temperature ceiling. “High pressure” in the deposition description refers to sputtering conditions, not a high-pressure superconductivity measurement.\n\nEvidence: theory. Sources: source-830f887afcf548c4, source-82a0df3d764cd0bc.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-scope-3\n\nNear-stoichiometric Nb3Sn is a conventional strong-coupling benchmark, but even its coupling classification depends on composition and how the gap and transition are sampled. Godeke's review discusses interface-gap and inhomogeneity effects that can bias a gap-to-temperature ratio. A full gap is not proof that all samples have the same coupling, and a large upper critical field alone is not evidence for triplet pairing.\n\nEvidence: theory. Sources: source-29d0a9915f8b6c0e, source-0620df96ebbf2a66.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-mathematical-assumptions-1\n\nFor an orbital dirty-limit description, write $B_{c2}=\\mu_0H_{c2}$ and $\\ln(T/T_c)=\\psi(1/2)-\\psi[1/2+\\hbar D B_{c2}(T)/(2\\Phi_0k_BT)]$, where $D$ is an effective diffusion parameter and $\\psi$ the digamma function. The Maki–de Gennes form omits Pauli, spin–orbit, strong-coupling and Fermi-surface anisotropy corrections. A useful fit to an inhomogeneous wire does not measure a unique microscopic $D$. Independent numerical roots recover the model ratio $B_{c2}(0)/(T_c|dB_{c2}/dT|_{T_c})=\\pi^2e^{-\\gamma}/8\\simeq0.693$; this is not a universal material relation.\n\nEvidence: theory. Sources: source-d27a049f764be753.\n\nSource relationship: mixed-source-and-local-derivation. Godeke2005 supplies the MDG equation and exclusions; the limiting ratio and numerical root check are local, not a microscopic fit to a wire.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-mathematical-assumptions-2\n\nFor current perpendicular to field, the pinning-force magnitude is $F_p=J_cB$. A common fixed-temperature field shape is $f(h)=h^{1/2}(1-h)^2$, with $h=B/B_{c2}$. It peaks at $h=0.2$ and produces a linear Kramer plot of $J_c^{1/2}B^{1/4}$ only under the model's assumptions. A triangular vortex lattice has $a_\\Delta=(4/3)^{1/4}\\sqrt{\\Phi_0/B}$; the flux-shear expression includes $(1-a_\\Delta/d)^{-2}$ for mean grain size $d$. At 12 T and $d=100$ nm, this factor is about 1.36, so neglecting it requires a stated tolerance. Neither the pinning peak nor a fitted Kramer intercept independently identifies the thermodynamic upper critical field.\n\nEvidence: theory. Sources: source-c4b57e9e8e5aa3d7.\n\nSource relationship: mixed-source-and-local-derivation. Godeke2006 supplies the flux-shear/Kramer forms and conditions; the12T/100nm correction and numerical peak are local evaluations, not measured grain data.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-mathematical-assumptions-3\n\nA local two-component example uses the displayed $J_c=C B_{c2}^{2}h^{1/2}(1-h)^2/B$ with the same positive prefactor for both components, critical fields of 20 and 28 T, and zero current at or above each component field. Equal-area parallel addition gives $J_{\\mathrm{mix}}=(J_1+J_2)/2$. Two-point secants of $J_{\\mathrm{mix}}^{1/2}B^{1/4}$ over 10–14 T and 16–19 T extrapolate to 25.06 and 26.35 T; over 21–24 T only the 28 T component remains and the intercept is 28 T. These are explicitly chosen windows, not regression fits to measured data. Changing the connection to a local series bottleneck, $J_{\\mathrm{series}}=\\min(J_1,J_2)$, instead makes the 20 T component limiting. The example does not model current transfer, percolation or a real wire network.\n\nSeparately, Godeke considers a hypothetical uniform wire with grain size and grain-boundary density retained. Holding the prefactor fixed, the printed 24.9-to-26.9 T inputs give 2888.01 A/mm² from 2250 A/mm² at 12 T and 4.2 K, versus the paper's 2883 A/mm². If each printed field was rounded to the nearest 0.1 T, the resulting interval is approximately 2852–2924 A/mm². Compatibility with that assumed rounding does not establish the cause of the discrepancy. Neither improved value was measured.\n\nEvidence: theory. Sources: source-c4b57e9e8e5aa3d7, source-d27a049f764be753.\n\nSource relationship: mixed-source-and-local-derivation. Godeke2006 provides inhomogeneity/connection context; Godeke2005 Eq.4 and sectionV.B provide the hypothetical comparison. Two-component secants, series control and numerical rounding interval are local calculations, not experimental fits or source data reproduction.\n\nConditions: Local model: B>0, fixed temperature and prefactor, nonnegative currents cut off at each Bc2; explicit equal-area parallel sum or series minimum. Printed-field interval assumes nearest-0.1-T rounding independently for both inputs.\n\nVerification scope: 2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.\n\n### scwiki-d2-claim-experimental-criteria-1\n\nGodeke and colleagues used approximately 0.2–0.6 A/mm², normalized to non-Cu area, for resistive measurements of filamentary Nb3Sn in fields up to 30 T. The 10%, 50% and 90% criteria refer to the fitted normal-state resistance background, not material volume fractions. At noisy high fields, the 99% value was extrapolated from the 10–90% region while assuming comparable transition widths at low and high fields. The unresolved interlaboratory offset was about 4%; the authors treated the data as reliable within roughly ±2%, without establishing a statistical confidence interval. These low-current transitions preferentially sample high-quality conducting paths, not the full conductor.\n\nEvidence: experiment. Sources: source-d27a049f764be753.\n\nSource relationship: mixed-source-and-local-derivation. Godeke2005 TableI and sectionIII.A specify normalization, criteria, extrapolation and the unresolved offset; sectionIV.B discusses limited path sampling. The explicit warning against converting resistance percentage into volume fraction or confidence level is editorial inference from these measurement definitions.\n\nConditions: TableI non-Cu excitation-current normalization; source-specific resistance-fit/background and high-field extrapolation assumption. Approximate systematic reliability is not a calibrated standard deviation or confidence level.\n\nVerification scope: 2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.\n\n### scwiki-d2-claim-experimental-criteria-2\n\nThe B34 wire reacted for 64 hours at 675 °C provides a concrete comparison: transport at a 10 µV/m criterion gave non-Cu $J_c=2250$ A/mm² at 12 T and 4.2 K. The Kramer field was 24.9 T, while the 99% resistive field was 26.9 T at the same temperature. Keep the non-Cu area normalization, voltage criterion and heat treatment attached to those numbers. They are not interchangeable measures of performance.\n\nEvidence: experiment. Sources: source-d27a049f764be753.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-experimental-criteria-3\n\nGapud and colleagues studied a floating-zone V3Si single crystal, MP3, with residual-resistivity ratio 47. Their 51V NMR experiment used 6.67 T, where the reported superconducting transition was 12.8 K and the structural transition 21.1 K. Cubic and tetragonal spectra coexisted around the structural transition. The authors found no conclusive cubic-phase spectrum below the zero-field transition scale of 17 K; that is distinct from the 12.8 K transition in the actual NMR field. These observations do not establish that a martensitic transition is necessary for every A15 superconductor.\n\nEvidence: experiment. Sources: source-9fe69d0a6cecbb0c.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-limits-and-disputes-1\n\nElastic softening, anharmonicity and superconductivity can be correlated without a universal rule that moving closer to structural instability always improves $T_c$. Testardi's papers motivate this coupled problem; they do not remove the need for sample-specific structural and thermodynamic evidence. Changes in composition or disorder can alter several electronic and phonon parameters together. Increasing a density-of-states peak or an estimated coupling constant alone is not a validated optimization strategy.\n\nEvidence: theory. Sources: source-33f4444a5825b443, source-509b869080567558, source-0620df96ebbf2a66.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-limits-and-disputes-2\n\nThe V3Si NMR assignments depend on orientation, spectral resolution and the local electric-field-gradient model. The reported 6.67 T experiment distinguishes its 12.8 K superconducting transition from the zero-field scale of 17 K. Broadening, overlap and Knight shifts complicate the spectra; a missing resolved cubic-phase line does not by itself establish zero cubic volume. A quantitative phase-fraction limit would require a calibrated detection threshold and relative spectral response, which this entry has not established. Similarly, a Nb3Sn resistance criterion, a Kramer extrapolation and a magnetic transition retain different sampling conditions. Record mounting and strain as well as nominal composition.\n\nEvidence: theory. Sources: source-d27a049f764be753, source-9fe69d0a6cecbb0c.\n\nSource relationship: context-for-editorial-analysis. Gapud2022 pp.3–4 report the field, spectral overlap and unresolved cubic spectra; Godeke2005 sectionsIII.A/IV.B/V.B distinguish path sampling and mounting. Detection-limit and cross-probe cautions are editorial analysis, not a quantitative bound supplied by either paper.\n\nConditions: Selected V3Si single-crystal experiment at6.67T; no calibrated phase-fraction detection limit or independent spectral fit. Source-specific Nb3Sn mounting/strain and electrical criteria.\n\nVerification scope: 2026-10-19 selected source passages and explicitly bounded local checks; author review, not independent scientific certification.\n\n### scwiki-d2-claim-limits-and-disputes-3\n\nA May 2026 doctoral-dissertation preprint explores Cu–Sn routes to Nb3Sn films for microwave dark-matter cavities. Its abstract describes a chosen cavity tested at 50 mK and 9 T, but reports a quality-factor decline in field. Neither the operating temperature nor the maximum applied field is a measured transition temperature or a demonstrated upper critical field. This is an abstract-level research pointer, not a peer-reviewed performance certification.\n\nEvidence: theory. Sources: source-3633507cd1108d10.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n### scwiki-d2-claim-discovery-implications-1\n\nOptimize a complete, conditional objective: transition temperature, useful field range, current density, mechanical tolerance and manufacturability. Preserve measured and predicted quantities separately. Compare transition criteria, composition gradients, annealing, strain, grain structure and area normalization before ranking conductors. For a proposed material, check phase stability and the coupling-weighted phonon spectrum; for a working wire or cavity, test the actual operating condition and retain negative results.\n\nEvidence: theory. Sources: source-29d0a9915f8b6c0e, source-c4b57e9e8e5aa3d7, source-0620df96ebbf2a66, source-3633507cd1108d10.\n\nConditions: Named sample, field, criterion and source-review scope; numerical examples are imposed models, not reproduced experiments.\n\nVerification scope: Selected original passages and bounded numerical checks only; full scientific acceptance remains open.\n\n## Revision and review\n\nArticle ID: scwiki-d2. Revision: c58668ce70c07a494483. Updated: 2026-10-19T15:34:16.871337+00:00.\n\nReview scope: Selected Godeke author-version passages, published V3Si methods/results and official AFLOW prototype. Explicit local connection/field-window/rounding checks; earlier historical and2026 abstract-only checks retained.\n\n- Full scientific acceptance and original raw-data/spectral-fit reviews remain open.\n- Historic Nb3Sn/Nb–Ge reports and Testardi papers checked at abstract level; original measurement criteria not inferred.\n- 2026 dissertation is an abstract-only preprint, not peer-reviewed performance acceptance.\n- Finite models do not reproduce conductor networks, EFG tensors, phonon calculations or device performance.\n- Local current addition, secant windows and assumed rounding are not wire-network or experimental-data validation; no NMR phase-fraction bound is inferred.\n\nSource: [D_material_families/D2_A15_compounds.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/D_material_families/D2_A15_compounds.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 036ee5b467a7597ae98470c891d08ceccf473a97c19d2f6a40f3fe88348b8886.\n","wordCount":1155}}