egan_2023#
P. F. Egan and Y. Yang, “Optical n(p, T90) Measurement Suite 1: He, Ar, and N2”, Int. J. Thermophys. 44, 181 (2023)
Source record · Catalogue · Review register
DOI: 10.1007/s10765-023-03291-2
Source kind: measurement
Recorded technique: Fabry-Perot cavity refractometry (NIST): a wire-suspended 15 cm titania-silicate cavity with the cavity mode and a capsule SPRT in one copper block, a He-Ne laser at 632.9908(1) nm (vacuum) referenced to an iodine-stabilised laser; pressure generated by a dimensionally characterised piston gauge (1.9e-6 p), temperature on ITS-90 (water, gallium and indium fixed points) converted to thermodynamic T with the consensus T - T90 (Fischer et al. 2011; Gaiser et al. 2022 at the gallium point). Refractivity from the change in resonance frequency between vacuum and gas, Eq. (1), with mirror phase-dispersion and Gouy corrections. The cavity compressibility kappa(T) is calibrated with helium, whose refractivity is taken from ab initio theory (Puchalski et al. 2016), Eq. (2): nine helium isotherms. Argon and nitrogen: nine isotherms each, 293-433 K, 19 pressures to 0.5 MPa repeated five times, regressed together to p = (n - 1) A [1 + (n - 1) B + (n - 1)^2 C] + eps_p (Eq. (5)), A = 2RT/(3 A_R), with B and C polynomials in T (Eq. (6)); 99.9999 % gases (pp. 2-5, 10-11, 16).
Materials in structured entries: Ar, N2
Dataset quantities: molar_refractivity
Contents: 2 datasets; 1 formula.
Curation notes#
Identity VALIDATED_WITH_WARNINGS in the library (the title’s math is garbled in the metadata; the registry record’s DOI, journal, volume 44, article 181, authors and year agree with the DOI and authors printed in the PDF). Page numbers are the library pdf pages (1-35). All uncertainties are one standard uncertainty, ‘approximately a 68 % confidence level’ (p. 8).
CORRECTED: the authors’ correction (egan_2024_correction, Int. J. Thermophys. 45, 177 (2024), DOI 10.1007/s10765-024-03473-6) finds the Gouy phase shift mistreated in Eq. (1) and the molar refractivities of Ar and N2 ‘fractionally small by 0.3 x 10^-6 A_R’; both values are corrected by the [[errata]] below (TC-707, TC-724).
What the paper measures (633 nm only; no 1542 nm data: those are Suite 3, Int. J. Thermophys. 45, 120 (2024), not in the library): (i) helium, as a standard of refractive index, calibrates the cavity compressibility, kappa_303 = 9.8255(7)e-12 Pa^-1 (1.3e-4 relative, Table 1): no helium optical property is measured; (ii) argon gives relative primary thermometry, T - T90 from 293 to 433 K (Table 2, not a refractive quantity), with the molar refractivity A_R of argon as the key parameter, fixed at the gallium melting point (T* = 302.9184(3) K); (iii) nitrogen’s molar refractivity and its temperature dependence (Eq. (8)); (iv) second density virial coefficients B_rho of Ar and N2 (Table 5) and the fit coefficients B, C (Table 4): equation-of-state quantities, not extracted. A_R is the zero-density Lorentz-Lorenz coefficient, A_R = A_eps(omega) + A_mu, electric plus magnetic (p. 5): the package’s refractive polarizability.
Argon (p. 11): A_R = 4.195735(13) cm^3/mol at 632.9908(1) nm, ‘effectively described by Table 3’ (3.0e-6 T, representative of 373 K); ‘increases 11.8 x 10^-6 A_R from the previous recommendation’ (egan_2019’s 4.195685(64): 11.9e-6 computed) with five times less uncertainty ‘because pressure has been generated by a dimensionally-characterized piston-gage’; ‘within 5.3 x 10^-6 A_R’ of Lesiuk and Jeziorski’s recommendation (lesiuk_2023, Gaiser and Fellmuth’s static value with the ab initio dispersion and chi_0) using its sixth-order coefficient. Reproduced (2026-09-29): with alpha_0 = 11.077183, S(-4) = 27.976, S(-6) = 95.02, S(-8) = 382.5 and chi_0 = -2.3004e-4 a.u. at 632.9908 nm, 4.195756 cm^3/mol, 5.0e-6 above this value (without S(-8): 4.195736, 0.3e-6); the 0.3e-6 between 5.0 and 5.3 is not resolved. A_R depends on T* through A_R = 2RT*/(3A), so a future change of the gallium point’s T - T90 moves it (p. 12).
Nitrogen (p. 17): A_R(T) = A_303 [1 + A_theta (T - 303)], A_303 = 4.446175(14) cm^3/mol, A_theta = 1.18(4) x 10^-6 K^-1 at 632.9908 nm; the uncertainty of A_303 is the quadrature of Table 3; that of A_theta is ‘dominated by the choice of T - T90’, and both depend on the T - T90 function used (Fischer et al. 2011 here; Gaiser et al. 2022 does not cover the range) (pp. 18-19). Against the same laboratory’s earlier values (Fig. 4): egan_2019 at T90 = 293.15 K agrees within 3.7e-6 A_R, Egan et al. 2016 at T90 = 302.914 K within 8.0e-6 (egan_2019’s 302.919 K is the thermodynamic temperature); the three rest on three pressure scales (mercury manometer, optical pressure scale, piston gauge), equivalent at (5.9 +- 4.3)e-6 p (p. 18). A_theta against theory: Sharipov et al. 1.14e-6 (static), Buldakov et al. 1.07e-6 (optical), 3.4 % from the measurement; experiments: Hohm and Kerl 1.8(11)e-6, Schmidt and Moldover 1.4(3)e-6 (static) K^-1 (p. 18).
Inputs the analysis assumed (not measured here): helium refractivity from Puchalski et al. (2016), argon B_R and C_R from Garberoglio and Harvey (2020, 2021), argon C_rho from Cencek et al. (2013) and B_rho from Lang et al. (2023, to fix C only); for nitrogen, B_R = 0.741 - 1.29e-3 (T/K - 303) cm^6/mol^2 (the mean of Montixi et al. 1983 and Achtermann et al. 1991, with Hohm’s 1993 temperature slope), C_R = -97.3 cm^9/mol^3, and Subramanian et al.’s C_rho (p. 22). Yang, Stone and Egan (yang_2025) used this paper’s B_rho for argon and nitrogen and the same apparatus: its A_eps are correlated with, not copies of, the values here.
Not extracted: Tables 1 and 3 (uncertainty budgets, summarised above), Table 2 (T - T90), Tables 4 and 5 (B, C and B_rho), the compressibility and expansivity of the cavity (p. 6-7), the n(p, T90) datasets (supplementary material, NIST repository doi 10.18434/mds2-3054, not in the library).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
egan_2023/A_R_Ar#
{
"id": "A_R_Ar",
"material": "Ar",
"table": "text",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 303.0
}
}
1 inline points in the source record.
p. 11: A_R = 4.195735(13) cm^3/mol ‘operating at lambda = 632.9908(1) nm’, from the 303 K isotherm (T90 = 303.107 K, Table 2) with T* = 302.9184(3) K, the consensus thermodynamic temperature of the gallium melting point; standard uncertainty (3.1e-6 relative). An independent measurement of egan_2019’s quantity with another apparatus and another pressure scale (a piston gauge, not the helium-calibrated optical scale): 11.9e-6 above egan_2019’s A_R_Ar, within its 15e-6.
egan_2023/A_R_N2#
{
"id": "A_R_N2",
"material": "N2",
"table": "text",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"temperature_k": 303.0
}
}
1 inline points in the source record.
p. 17: A_303 = 4.446175(14) cm^3/mol at 632.9908 nm, the 303 K value of the linear law Eq. (8) from nine isotherms 293-433 K (the formula n2_temperature), with the old consensus T - T90 (Fischer et al. 2011); standard uncertainty (3.1e-6 relative). Nitrogen’s A_R rises 1.18e-6 per K (source notes).
Formulas#
egan_2023/n2_temperature#
{
"id": "n2_temperature",
"material": "N2",
"equation": "Eq. (8), p. 17",
"printed": "A_R(T) = A_303 [1 + A_theta (T - 303)]; A_303 = 4.446175(14) cm^3 mol^-1, A_theta = 1.18(4) x 10^-6 K^-1 (at lambda = 632.9908 nm)",
"variable": "T: thermodynamic temperature in K (from T90 with Fischer et al.'s 2011 T - T90); A_R in cm^3/mol",
"state": "none (molar, zero density)",
"density": "none",
"range": "632.9908 nm only; 293-433 K",
"coefficients": {
"A_303": "4.446175",
"A_theta": "1.18e-6"
},
"check": "At 293.1529 K it gives 4.446123, 3.7e-6 above egan_2019's 4.446107(68) (the paper: 'within 3.7 x 10^-6'); at 302.919 K 4.4461746, 8.0e-6 above Egan et al. 2016's 4.446139(16) as quoted in egan_2019 ('within 8.0 x 10^-6'). Computed 2026-09-29."
}
The temperature dependence of nitrogen’s molar refractivity, ‘within 3.5 %’ (abstract), as calculated from vibrational and rotational averaging (Sharipov et al., Buldakov et al., p. 18); A_theta’s uncertainty is dominated by the choice of T - T90 (p. 17). The package’s N2 polarizability has no temperature dependence.
Corrections#
[
{
"dataset": "A_R_Ar",
"row": "632.9908",
"column": "value",
"printed": "4.195735",
"corrected": "4.1957363",
"reason": "The authors' correction (egan_2024_correction, p. 2): the Gouy phase shift was treated incorrectly in the working equation (Eq. (1) of this paper), and the reported molar refractivities of argon and nitrogen were 'fractionally small by 0.3 x 10^-6 A_R'. The correction applied: 4.195735 x (1 + 0.3e-6) = 4.1957363 (computed; not a printed value). One tenth of the 3.1e-6 standard uncertainty (TC-724).",
"evidence": "egan_2024_correction (library Egan_2024_CorrectionOptical90, pp. 1-2, text read 2026-09-29): the corrected Eq. (3) and the statement of the effect on A_R; the printed 4.195735(13) is on p. 11 of this paper."
},
{
"dataset": "A_R_N2",
"row": "632.9908",
"column": "value",
"printed": "4.446175",
"corrected": "4.4461763",
"reason": "The authors' correction (egan_2024_correction, p. 2): as for A_R_Ar, the reported molar refractivity was 'fractionally small by 0.3 x 10^-6 A_R'. The correction applied: 4.446175 x (1 + 0.3e-6) = 4.4461763 (computed). One tenth of the 3.1e-6 standard uncertainty (TC-724).",
"evidence": "egan_2024_correction (library Egan_2024_CorrectionOptical90, pp. 1-2, text read 2026-09-29); the printed A_303 = 4.446175(14) is on p. 17 of this paper."
}
]
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.