egan_2026 ========= P\. F\. Egan, Meas\. Sci\. Technol\. 37, 255003 \(2026\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/1361\-6501/ae6e94 `__ **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 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.