BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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Material property literature sources

Date: 2026-08-28 Purpose: One table per property family naming the literature behind every material fit, with the full bibliography Module: src/physics/materials

The material classes identify their data sources in comments within their create_*() routines. This document collects those statements in one place and presents them in a standardized form. The file:line positions in the class sources are authoritative. When a comment gives only a vague attribution, such as "literature value" or "experimental data", the table reports that wording instead of inventing a source. Model-level references for the E-J power law are in resistivity_laws.md; sources for homogenization are in alloy_homogenization.md; and sources for the Callaway model are in callaway_thermal_conductivity.md.

Property symbols: alpha denotes thermal expansion, cp specific heat, rho electrical resistivity (the quantity stored by the rho group of a generated database), E Young's modulus, and nu Poisson ratio.

Main table

Material alpha cp rho E nu
Copper Touloukian TPRC Touloukian TPRC Matula 1979 (Bloch-Grueneisen, 273.15 K anchor); Kohler: De Launay 1959, Benz 1969, Arentz 1982, Clausecker 1969, Strom-Olsen 1967 Wachtman fit vs Blanke 1989 copper.org / Wolfram Cloud (RT value)
Aluminum Touloukian TPRC Touloukian TPRC Hust-Lankford 1984 anchor; Debye curve: Desai 1984, Cook 1975; Kohler: Luethi 1960, Fickett 1972 Wachtman fit vs Blanke 1989 Grueneisen-consistent, RT value Wolfram Cloud
Chromium e3sconf 2024 (primary), Touloukian TPRC (secondary) unnamed literature spread (sanity: cp(293 K) = 451 vs 449) White-Woods 1959 anchor; Debye: Anderson 1970; Kohler: Kozlova-Kondorskii 1963, Arajs-Dunmyre 1965 Armstrong-Brown 1964 (scaled to 279 GPa at RT) Wolfram Cloud (RT value)
Silver Touloukian TPRC Touloukian TPRC Matula 1979 (273.15 K anchor); Kohler: Luethi 1960, Strom-Olsen 1967, Stout 1939, Iwasa 1993, Li 2015 Wachtman fit vs Blanke 1989 Wolfram Cloud (RT value)
Indium Touloukian TPRC (6..374 K, rms 0.005%) Touloukian TPRC; low-T gamma/beta: TPRC curve 3 White-Sondheimer via PhysRevB 23 3845 anchor; Kohler: Luethi 1960, PhysRev 120 1167 Kim-Ledbetter 1998 Kim-Ledbetter 1998
White tin Touloukian TPRC Touloukian TPRC; Sommerfeld/Debye: O'Neil 1965 White 1968 via Hariharan 1979 anchor; Debye high-T: Meaden 1965 via Hall 1968; Kohler: Luethi 1960 Wachtman fit vs Blanke 1989 Wolfram Cloud (RT value)
Lead Touloukian TPRC Touloukian TPRC White 1968 via Hariharan 1979 anchor; Debye high-T: Meaden 1965 via Hall 1968; Kohler: Luethi 1960 Wachtman fit vs Blanke 1989 Wolfram Cloud (RT value)
Iron Touloukian TPRC Touloukian TPRC (Curie anomaly smoothed) White-Woods 1959 (T < 295 K, RRR 40..104), Arajs-Colvin 1964 (300..1300 K), magnetization: Crangle-Goodman 1971; Kohler: Klaffky-Coleman 1974, Luethi 1960; valid to 860 K Wachtman fit vs Blanke 1989 Wolfram Cloud (RT value)
Nickel Touloukian TPRC Touloukian TPRC; gamma/beta: TPPM White-Woods 1959, Farrell-Greig 1968; magnetization: Crangle-Goodman 1971; Kohler: Luethi 1960 Wachtman fit vs Blanke 1989 (two curves across the Curie point) Wolfram Cloud (RT value)
Magnesia (MgO) Simon 1994, Durand 1936 Touloukian TPRC curve 4 + Simon 1994 n/a (insulator) Blanke 1989 (Simon 1994 judged too low for HTS tapes) Simon 1994
Hastelloy C-276 Lu 2008 Lu 2008 (15..120 K); RT Debye tail anchored at unnamed literature cp = 427 Lu 2008 (log-log above 10.73 K) Cryogenics 2006 + MATWEB Cryogenics 2006 + MATWEB
YBCO Salomons 1987 Baak 1989 (T < 20 K), Lang 1988 (50..350 K) Sommerfeld 2003 (Bloch-Grueneisen, RRR ~ 50) Lei-Ledbetter 1991 (normalized curve, user-scaled) Lei-Ledbetter 1991
Alloy (homogenized) see alloy_homogenization.md see alloy_homogenization.md see alloy_homogenization.md (Nordheim, Bruggeman, Hust-Lankford) see alloy_homogenization.md (Eshelby, Hill, Voigt/Reuss) see alloy_homogenization.md

The supporting property thermal conductivity, lambda, is included here because users often ask for it next. Copper, Aluminum, and Iron follow Hust-Lankford 1984. Silver is fitted to Mendelssohn 1952, Gerritsen 1956, and Li 2015; the class header notes that the RRR data are sparse. Indium, White tin, Lead, Magnesia, and Nickel follow Touloukian TPRC. YBCO uses the Callaway model fitted to Sommerfeld 2003, which the code flags as a degenerate interim fit. Hastelloy has no lambda source and uses only the Wiedemann-Franz construction.

Bibliography

Key Authors Year Journal / Publisher DOI or identifier
Touloukian TPRC Y. S. Touloukian et al. 1970 ff. Thermophysical Properties of Matter (TPRC data series), IFI/Plenum series; cited per curve in-code
TPPM Thermophysical Properties of Matter, vol. 1 1970 IFI/Plenum volume/page cited in-code
Matula 1979 R. A. Matula 1979 J. Phys. Chem. Ref. Data 8, 1147 10.1063/1.555614
Blanke 1989 W. Blanke (ed.) 1989 Thermophysikalische Stoffgroessen, Springer ISBN book
Hust-Lankford 1984 J. G. Hust, A. B. Lankford 1984 NBSIR 84-3007 / NBS SP 260-90 10.6028/nbs.ir.84-3007
White-Woods 1959 G. K. White, S. B. Woods 1959 Phil. Trans. R. Soc. A 251, 273 10.1098/rsta.1959.0004
De Launay 1959 J. De Launay et al. 1959 J. Phys. Chem. Solids 10.1016/0022-3697(59)90038-1
Benz 1969 M. G. Benz 1969 J. Appl. Phys. 40 10.1063/1.1657896
Arentz 1982 R. Arentz et al. 1982 Phys. Rev. B 26, 2727 10.1103/PhysRevB.26.2727
Clausecker 1969 K. Clausecker 1969 Z. Physik 10.1007/BF02422537
Strom-Olsen 1967 J. O. Strom-Olsen 1967 Proc. R. Soc. A jstor.org/stable/2415889
Desai 1984 P. D. Desai et al. 1984 J. Phys. Chem. Ref. Data 10.1063/1.555725
Cook 1975 J. G. Cook et al. 1975 ORNL-5079 report ORNL-5079
Luethi 1960 B. Luethi 1960 Dissertation, ETH Zuerich (Widerstandsaenderung von Metallen in hohen Magnetfeldern) thesis
Fickett 1972 F. R. Fickett 1972 FNAL report (Magnetoresistivity of Copper and Aluminum at Cryogenic Temperatures) report
Armstrong-Brown 1964 P. E. Armstrong, H. L. Brown 1964 Trans. AIME as cited in-code
Kozlova-Kondorskii 1963 N. Kozlova, E. Kondorskii 1963 Soviet Physics JETP as cited in-code
Arajs-Dunmyre 1965 S. Arajs, G. R. Dunmyre 1965 J. Appl. Phys. 10.1063/1.1703039
Anderson 1970 Anderson, Stewart, Ramsay 1970 phys. status solidi (b) 10.1002/pssb.19700370137
e3sconf 2024 (chromium expansion dataset) 2024 E3S Web of Conferences 10.1051/e3sconf/202459202009
Smith-Fickett 1995 D. R. Smith, F. R. Fickett 1995 J. Res. NIST 100 10.6028/jres.100.012
Mendelssohn 1952 K. Mendelssohn et al. 1952 Proc. Phys. Soc. A 65 10.1088/0370-1298/65/6/301
Gerritsen 1956 A. N. Gerritsen 1956 Physica 10.1016/S0031-8914(56)90035-0
Li 2015 Li et al. 2015 IOP Conf. Ser.: Mater. Sci. Eng. 102 10.1088/1757-899X/102/1/012027
Stout 1939 J. W. Stout et al. 1939 J. Am. Chem. Soc. 10.1021/ja01871a006
Iwasa 1993 Y. Iwasa et al. 1993 Cryogenics 10.1016/0011-2275(93)90199-X
Kim-Ledbetter 1998 S. Kim, H. Ledbetter 1998 Mater. Sci. Eng. A 10.1016/S0921-5093(98)00490-0
O'Neil 1965 H. R. O'Neal et al. 1965 Phys. Rev. 137, A748 (in-code cited as 1964) 10.1103/PhysRev.137.A748
White 1968 G. K. White 1968 Experimental Techniques in Low Temperature Physics (book) via Hariharan 1979
Hariharan 1979 Hariharan et al. 1979 Pramana 13, 117 10.1007/BF02872130
Meaden 1965 G. T. Meaden 1965 Electrical Resistance of Metals (book) via Hall, NBS TN 365 (1968)
Crangle-Goodman 1971 J. Crangle, G. M. Goodman 1971 Proc. R. Soc. A 10.1098/rspa.1971.0044
Arajs-Colvin 1964 S. Arajs, R. V. Colvin 1964 phys. status solidi 10.1002/pssb.19640060317
Klaffky-Coleman 1974 R. W. Klaffky, R. V. Coleman 1974 Phys. Rev. B 10, 2915 10.1103/PhysRevB.10.2915
Farrell-Greig 1968 T. Farrell, D. Greig 1968 J. Phys. C 1 10.1088/0022-3719/1/5/326
Simon 1994 N. J. Simon 1994 NISTIR 5030 report
Durand 1936 M. A. Durand 1936 Physics 7 10.1063/1.1745396
Lu 2008 J. Lu, E. S. Choi, H. D. Zhou 2008 J. Appl. Phys. 103 (Hastelloy C-276 at cryogenic temperatures) 10.1063/1.2899058
Cryogenics 2006 (Hastelloy mechanical dataset) 2006 Cryogenics 46 10.1016/j.cryogenics.2006.01.014
Cryogenics 2023 (Hastelloy composition) 2023 Cryogenics 10.1016/j.cryogenics.2023.103776
Salomons 1987 E. Salomons et al. 1987 Physica B+C 10.1016/0378-4363(87)90092-1
Baak 1989 J. Baak et al. 1989 Physica C 10.1016/0921-4534(89)91125-8
Lang 1988 M. Lang et al. 1988 Z. Phys. B 10.1007/BF01312506
Lei-Ledbetter 1991 M. Lei, H. Ledbetter 1991 NISTIR 3980, Fig. 4.3 report
Sommerfeld 2003 Sommerfeld et al. 2003 Phys. Rev. B 67, 174520 10.1103/PhysRevB.67.174520
CRC Handbook CRC Handbook of Chemistry and Physics n/a CRC Press (isotope masses and abundances) edition not stated in-code

Known gaps (as found in the sources, 2026-08-28)

  • The mass density ref_density is an uncited literal for every material except Silver, which cites Smith-Fickett 1995.
  • Hastelloy C-276 has no data source for lambda; it uses only the Wiedemann-Franz construction.
  • The Alloy class contains no in-code citations; its sources are documented exclusively in alloy_homogenization.md.
  • The iron and nickel spin-disorder resistivity amplitudes are described as "typical values" without a source.
  • The Debye curve for Indium and the Debye temperature of 275 K for YBCO are bare fits.
  • "Wolfram Cloud" is the room-temperature Poisson source for seven metals, although it is a lookup service rather than a primary reference.
  • Base-class model names such as Bloch-Grueneisen, Matthiessen, Kohler, Wachtman, Pippard, and Wiedemann-Franz are used throughout, but none has a bibliographic entry anywhere in the tree.

Citation defects in the sources (typos worth a cleanup pass)

Line numbers above are advisory; grep for the citation text when in doubt.