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 `__ · :doc:`Catalogue ` · :doc:`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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ----------- .. code-block:: text [ { "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 :doc:`review register ` for the checks and decisions.