egan_2026#
P. F. Egan, Meas. Sci. Technol. 37, 255003 (2026)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Fabry-Perot cavity refractometer (Yang et al.’s apparatus) interrogated simultaneously at 0.6329908 and 1.542383 um (vacuum), both lasers referenced to a frequency comb; pressure from a dimensionally characterized piston gauge (1.9e-6 p), ITS-90 temperature by a capsule SPRT in a borehole of the vessel lid (1e-6 T); cavity compression calibrated with helium. Nine isotherms from 20 to 100 C up to 0.5 MPa per gas, regressed to p = (n - 1) A [1 + (n - 1) B + (n - 1)^2 C] + eps_p (Eq. 4), A = 2RT/(3 A_R) (pp. 3-4). Baseline relative standard uncertainty 2.3e-6.
Materials in structured entries: Ar, CO2, N2, O2
Dataset quantities: molar_refractivity
Contents: 2 datasets; 5 formulas.
Curation notes#
Measured gases: CO2, O2, two N2 + O2 mixtures, natural dry air (Niwot Ridge) and water vapour. The mixtures, air and water are not curated species and are skipped (water’s refractivity ratio 0.97569(8) at 1542/633 nm, 100 C, and the adjusted Voronin and Zheltikov Sellmeier of Table 5 included). All uncertainties are one standard uncertainty (p. 6).
Molar refractivity A_R (the zero-density Lorentz-Lorenz coefficient, Eq. 2) at 303 K, with a linear temperature dependence A_R(T) = A_303 [1 + A_theta (T/K - 303)] (Eq. 5); the parenthesised figures after A_303 are statistical only, the combined standard uncertainties are CO2 4.6e-6 A_303 and O2 7.2e-6 A_303 (pp. 6, 8). A_theta: CO2 4.22(9)e-6 at 633 nm and 4.13(9)e-6 at 1542 nm (combined u 8.0 %); O2 2.11(4)e-6 and 2.02(5)e-6 (combined u 9.4 %) (pp. 4, 7-8). ITS-90 nonlinearity (up to 9 mK) limits A_theta and leaves up to 2.7e-5 relative error in A_R(T).
Comparisons (pp. 5, 10): Birch’s A_R at 0.633 um, CO2 6.6418(5) and O2 4.0278(3) cm^3/mol (birch_1991); Zhang et al.’s (zhang_2008) O2 at 0.800 um is 4.5e-4 (n - 1) below Eq. (8) and their CO2 is also discrepant; Kren’s inferred O2 Sellmeier (kren_2011) is within 8e-5 at 0.633 um and 1.7e-4 at 1.542 um of Eq. (8).
Second density virial coefficients B_rho (Tables 1, 2, 4) and the N2-O2 cross virial (Table 3) are equation-of-state quantities, not refractive ones, and are not extracted (the vocabulary’s refractivity_virial_coefficient is B_R). They were derived with the second refractivity virial coefficients b_R(sigma, T) (B_R = A_R b_R) recorded below as formulas.
Table 6 (tbl_15c8e9be0440, image checked) gives beta, the slope of the refractivity ratio (n_633 - 1)/(n_1542 - 1) against n_1542 - 1 at 30 C (Eq. 15), which measures the dispersion of b_R (Eq. 18); the format has no quantity for it and it is not extracted. Values x 10^-3 (this apparatus; He, Ne, Ar, N2 from Yang, Stone and Egan, Phys. Rev. Appl. 23, 064041 (2025), ref. 15): He -1.20(25), Ne -0.70(25), Ar 2.62(25), N2 2.17(25), O2 4.73(25), CO2 4.83(25); Keeling’s ultraviolet values reduced by 4.95: Ar 2.99, N2 2.71, CO2 4.21; Hohm’s heuristic: He -0.18, Ne 0.20, Ar 2.81, N2 2.25, O2 3.21, CO2 4.29; ab initio (Garberoglio and Harvey): He -1.20, Ne -0.67, Ar 1.93.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
egan_2026/A_R_CO2#
{
"id": "A_R_CO2",
"material": "CO2",
"table": "text",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "um",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"relative": 4.6e-06,
"level": "1 sigma"
}
}
2 inline points in the source record.
p. 4: A_303 = 6.64337(3) cm^3/mol at 0.6329908 um and 6.50541(3) at 1.542383 um (statistical u in parentheses), molar refractivity at 303 K from nine isotherms 20-100 C. Combined standard uncertainty 4.6e-6 A_303 (apparatus 2.3e-6, fit 3.6e-6, nitrogen impurity bias 1.6e-6; p. 6). Temperature dependence A_theta = 4.22(9)e-6 and 4.13(9)e-6 per K.
egan_2026/A_R_O2#
{
"id": "A_R_O2",
"material": "O2",
"table": "text",
"quantity": "molar_refractivity",
"unit": "cm3/mol",
"abscissa_unit": "um",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"relative": 7.2e-06,
"level": "1 sigma"
}
}
2 inline points in the source record.
p. 7: A_303 = 4.027716(7) cm^3/mol at 0.633 um and 3.968990(7) at 1.542 um (statistical u in parentheses; the wavelengths are the apparatus’s 0.6329908 and 1.542383 um), at 303 K. Combined standard uncertainty 7.2e-6 A_303 (apparatus 2.3e-6, fit 1.8e-6, possible krypton impurity bias 4.0e-6; p. 8). A_theta = 2.11(4)e-6 and 2.02(5)e-6 per K. Oxygen’s optical A_R excludes the microwave orientational (magnetic-dipole) contribution (p. 10).
Formulas#
egan_2026/o2_sellmeier#
{
"id": "o2_sellmeier",
"form": "dn_sigma2",
"terms": {
"scale": "1e-8",
"A": "0",
"B": [
"5627886.8",
"197258.6"
],
"C": [
"281.0",
"45.4"
]
},
"range_nm": [
254.0,
1542.4
],
"material": "O2",
"equation": "Eq. (8), p. 9",
"printed": "10^8 (n_os - 1) = 5627886.8/(281.0 - sigma^2) + 197258.6/(45.4 - sigma^2)",
"variable": "sigma = um/lambda, lambda the vacuum wavelength",
"state": {
"pressure_pa": 100000.0,
"temperature_c": 20.0
},
"density": "real",
"range": "fitted to Ladenburg and Wolfsohn's (1932) visible-ultraviolet data, Hohm's five visible points (offset -2.1e-3 (n - 1)), this work's 0.633 and 1.542 um values and Keeling et al.'s 0.436/0.254 um ratio (1.097922)",
"coefficients": {
"B1": "5627886.8",
"C1": "281.0",
"B2": "197258.6",
"C2": "45.4"
},
"check": "With the package's real-gas density at 20 C and 100 kPa (CoolProp) and Lorentz-Lorenz, Eq. (8) gives A_R = 4.027691 cm^3/mol at 0.6329908 um and 3.968977 at 1.542383 um, 6.3e-6 and 3.4e-6 below this work's A_303 (within its 7.2e-6). A_R carried to 293.15 K with A_theta would be 2.1e-5 lower (4.027632), which suggested that Eq. (8) takes A_303 at 20 C without the temperature dependence; that is not established: with the paper's own density virial (-17.0 cm^3/mol), refractivity virial and A_theta, Eq. (8) is +1.8e-6 and +4.4e-6 off, both within 7.2e-6, and the package has no refractivity virial for O2 (an 8.6e-6 effect) (second reading, 2026-09-25; TC-157). Checked 2026-09-25."
}
At ‘standard conditions 20 C and 100 kPa’ (n_os after Ciddor). ‘Consistent within 1e-6 (n - 1) of the two-color measurement of this work and the Keeling et al ratio’; the fit is not robust in the ultraviolet (a Cauchy alternative differs by 7.7e-6 (n - 1) at zero frequency). Not valid at microwave frequencies (the 60 GHz O2 band adds 2.7e-3 (n - 1)); the 0.76 um A band perturbs n locally at 1e-5 (n - 1). The reproduced data it rests on are not in this record (Ladenburg and Wolfsohn 1932, Hohm, Keeling et al.).
egan_2026/co2_b_R#
{
"id": "co2_b_R",
"material": "CO2",
"equation": "p. 5",
"printed": "b_R / (cm^3 mol^-1) = (0.291 + 0.00575 sigma^2) [1 - 3.2 x 10^-3 (T/K - 303)]",
"variable": "sigma = um/lambda (vacuum); T in K; B_R = A_R b_R",
"range": "0.633-1.542 um, 293-373 K",
"coefficients": {
"b_eps": "0.291",
"b_R2": "0.00575",
"b_theta": "-3.2e-3"
},
"reproduced_from": [
"achtermann_1991"
],
"check": "Not checked (the reference value is Achtermann et al.'s B_R at 323 K and 0.633 um; the sigma^2 and T dependences are this work's beta analysis). At 0.633 um and 303 K, B_R = 6.64337 x 0.30535 = 2.029 cm^6/mol^2 (computed here)."
}
The second refractivity virial coefficient b_R = B_R / A_R (Eq. 2), ‘this work recommends’; assumed 10 % uncertainty (p. 6).
egan_2026/o2_b_R#
{
"id": "o2_b_R",
"material": "O2",
"equation": "p. 8",
"printed": "b_R / (cm^3 mol^-1) = (0.194 + 0.00641 sigma^2) [1 + 1.4 x 10^-3 (T/K - 303)]",
"variable": "sigma = um/lambda (vacuum); T in K",
"range": "0.633-1.542 um, 293-373 K",
"coefficients": {
"b_eps": "0.194",
"b_R2": "0.00641",
"b_theta": "1.4e-3"
},
"reproduced_from": [
"U. Hohm, Z. Naturforsch. A 48, 505 (1993) (heuristic b_epsilon)"
],
"check": "Checked against the paper's text (p. 8), 2026-10-01: the formula, the 50 % uncertainty and 'tied to Hohm's b_eps estimate, but the sigma^2 and T dependencies are derived from this work' (TC-794). b_epsilon is Hohm's heuristic estimate, the sigma^2 and T dependences this work's (Hohm's b_R^(2) 50 % too small, his temperature slope of the wrong sign)."
}
egan_2026/n2_b_R#
{
"id": "n2_b_R",
"material": "N2",
"equation": "p. 11",
"printed": "b_nn / (cm^3 mol^-1) = (0.195 + 0.00211 sigma^2) [1 + 0.0 x 10^-3 (T/K - 303)]",
"variable": "sigma = um/lambda (vacuum); T in K",
"range": "0.633-1.542 um, 293-373 K",
"coefficients": {
"b_eps": "0.195",
"b_R2": "0.00211",
"b_theta": "0.0"
},
"reproduced_from": [
"achtermann_1991"
],
"check": "Not checked. Based on Achtermann et al.'s 0.633 um measurements ('7% uncertainty'); a 10 % uncertainty is used for dry air."
}
egan_2026/ar_b_R#
{
"id": "ar_b_R",
"material": "Ar",
"equation": "p. 14",
"printed": "b_rr / (cm^3 mol^-1) = (0.412 + 0.00321 sigma^2) [1 - 0.3 x 10^-3 (T/K - 303)]",
"variable": "sigma = um/lambda (vacuum); T in K",
"range": "0.633-1.542 um, 293-373 K",
"coefficients": {
"b_eps": "0.412",
"b_R2": "0.00321",
"b_theta": "-0.3e-3"
},
"reproduced_from": [
"G. Garberoglio and A. H. Harvey, J. Res. Natl. Inst. Stand. Technol. 125, 125022 (2020)"
],
"check": "Not checked. b_R^(2) from this apparatus's beta (Yang, Stone and Egan 2025, ref. 15); 10 % uncertainty assumed."
}
Corrections#
No dataset errata are recorded in this source record.
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.