clergent_1999 ============= Y\. Clergent, C\. Durou and M\. Laurens, "Refractive Index Variations for Argon, Nitrogen, and Carbon Dioxide at lambda = 632\.8 nm \(He\-Ne Laser Light\) in the Range 288\.15 K \<= T \<= 323\.15 K, 0 \< p \< 110 kPa", J\. Chem\. Eng\. Data 44, 197 \(1999\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1021/je980133o `__ **Source kind:** measurement **Recorded technique:** Mach\-Zehnder interferometer with a 5 mW He\-Ne laser \(632\.8 nm\)\: two brass tubes of equal length L = 40\.64 cm \(at 25 degrees C\) in a thermostatted bath, one evacuated, the other slowly filled from vacuum to 110 kPa through a microvalve while an electronic counter counts the bright fringes N; \[n\(p, T\_i\) \- 1\] L = N lambda\. For each of eight bath temperatures T\_i from 15 to 50 degrees C, three runs, each fitted as N = alpha p \+ beta; mu = lambda T\_i alpha/L \(Eq\. 3\), and mu averaged over the 24 runs per gas\. Temperature by a K\-type thermocouple \(within 0\.2 K of a Pt reference, Delta T/T \<= 1e\-3\); absolute pressure by an electronic manometer \(linearity 4e\-4, calibrated against a SCHWIEN 140 absolute manometer\)\. Air Liquide gases \(Table 1\: impurities of Ar H2O 3, CnHm 1\.5, O2 3, N2 10 ppm; N2 H2O 3, CnHm 1\.5, O2 5 ppm; CO2 H2O 7, CnHm 5, O2 10, N2 25, CO 2, H2 1 ppm by volume\) \(pp\. 1\-3\)\. **Materials in structured entries:** Ar, CO2, N2 **Dataset quantities:** refractivity **Contents:** 6 datasets; 3 formulas. Curation notes -------------- Identity checked against the first page \(pp\. 197\-199 = pdf pages 1\-3; a 4\-page supplement holds the CO2 and Ar fringe counts\)\. Page numbers are pdf pages\. REDUCTION \(p\. 1\)\. The gases are taken as ideal and the Gladstone\-Dale form of Lorentz\-Lorenz as exact over 0\-110 kPa and 288\-323 K, so that n \- 1 = mu p/T \(Eq\. 1\) with one constant mu per gas; the N\-p plots are straight \(R^2 \> 0\.9999, Fig\. 2, Table 3\)\. Table 5's n \- 1 at 101\.325 kPa \(760 mmHg\) and 293\.15 K is mu p/T with Table 4's mu\. They are therefore the refractivity at that state, measured on the 20 degrees C isotherm and nearby ones\: the linear fit over 0\-110 kPa absorbs the second\-virial curvature, and the ideal\-gas law enters only in averaging mu over the eight isotherms \(for CO2, whose B p/RT is \-0\.5 % at 1 atm, this shifts the 20 degrees C value by about \-0\.05 %; less for Ar and N2; estimated here\)\. Recorded with density = 'real' for that reason \(the value at the state\), not the ideal\-gas reduction of Eq\. \(1\)\. Note also that mu p/T gives 263\.38 \(Ar\) and 279\.56 \(N2\) where Table 5 prints 263\.3 and 279\.5\: the table truncates \(CO2 418\.61, printed 418\.6\)\. WAVELENGTH\. 'lambda = 632\.8 nm' \(title, p\. 2\), the He\-Ne line, medium not stated; stored as a standard\-air wavelength \(632\.97 nm in vacuum\), as buckingham\_1968 does for 632\.8 nm\. UNCERTAINTY \(p\. 3\)\. Table 4's \+\- on mu is the 'confidence interval' of the mean of the 24 runs \(Tables 3 and S2, S4 print mean, confidence interval and standard deviation\: N2 808\.8, 1\.2, 2\.3; CO2 1211\.1, 1\.5, 2\.9; Ar 762\.0, 1\.2, 2\.2, x 1e\-9 K/Pa\)\. No level is stated; every interval equals 2\.576 x std dev/sqrt\(24\), a 99 % normal interval of the mean \(computed here\)\. Table 5's \+\- is Eq\. \(4\), the LINEAR sum Delta \(n \- 1\)/\(n \- 1\) = Delta mu/mu \+ Delta p/p \+ Delta T/T with Delta p/p = 4e\-4 and Delta T/T = 1e\-3 \(N2\: 1\.2/808\.8 \+ 0\.0014 = 0\.29 %, i\.e\. 0\.80 on 279\.5, as printed\)\: a worst\-case sum of the 99 % interval and instrument bounds; level 'not stated'\. FINDING \(computed 2026\-09\-26 with optmat's default models at 632\.8 nm standard air, i\.e\. 632\.975 nm vacuum, 101325 Pa, 293\.15 K, real\-gas density\)\: fit/Ar 261\.83e\-6, fit/N2 277\.33e\-6, fit/CO2 416\.51e\-6\. Clergent et al\. are HIGHER by \+0\.56 % \(Ar 263\.3\), \+0\.78 % \(N2 279\.5\) and \+0\.50 % \(CO2 418\.6\), about twice their own stated uncertainties \(0\.30, 0\.29, 0\.26 %\), while Hauf and Grigull's interpolated values \(261\.8, 278\.1, 417\.4\) agree with the models to \-0\.01 %, \+0\.28 % and \+0\.21 %\. The common \+0\.5 to \+0\.8 % offset points to a calibration error of the measurement; the authors themselves suggest 'differences in calibration of pressure and temperature measurements' \(p\. 3\)\. The models reach Clergent's values at 291\.5 K \(Ar\), 290\.9 K \(N2\) and 291\.7 K \(CO2\)\. Use as a check only\. WAHLSTRAND\. The Maryland group's absolute Kerr calibration \(wahlstrand\_2012 and the papers that follow it\) takes n0 \- 1 = 2\.795e\-4 for N2 at 633 nm and 1 atm from this paper\: it is Table 5's N2 value \(279\.5e\-6\) at 293\.15 K, 0\.78 % above optmat's N2 model at that state \(see the note added to wahlstrand\_2012\)\. Not extracted\: Table 4's mu is recorded as the formulas below \(it is not a quantity with a state\)\. Table 6, the specific refractivities r = \(2/3\)\(n \- 1\)RT/\(M p\) \(Eq\. 5; 10^3 m^3 kg^\-1\: Ar 0\.1057, N2 0\.1600, CO2 0\.1525; Hauf and Grigull 0\.1052, 0\.1592, 0\.1521; molar masses 39\.95, 28\.02, 44\.01\)\: derived from mu\. Table 7, dn/dT = \-mu p/T^2 at 101\.325 kPa and 293\.15 K \(\|dn/dT\| x 10^6 K^\-1\: Ar 0\.898, N2 0\.953, CO2 1\.428; Hauf and Grigull 0\.894, 0\.949, 1\.424\)\: derived from mu\. Table 2 \(N2\) and the supplement's tables \(CO2, Ar\)\: the raw fringe counts N at eight temperatures and nine pressures, three runs each; Table 3 and the supplement's\: alpha, beta, R^2 and mu of the 24 runs per gas \(N2 mu from 802\.61 to 812\.05 x 1e\-9 K/Pa\)\. Table 1\: impurities \(in the technique\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- clergent\_1999/refractivity\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refractivity_Ar", "material": "Ar", "file": "Ar/clergent_1999__refractivity_Ar.csv", "table": "tbl_4e3479144d9d", "quantity": "refractivity", "scale": 1e-06, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "state": "1atm_20C", "density": "real", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table 5 'our results'\: \(n \- 1\) x 10^6 = 263\.3 \+\- 0\.8 at 101\.325 kPa and 293\.15 K, 632\.8 nm \(mu p/T with mu = 762\.0 \+\- 1\.2 x 1e\-9 K/Pa; the '\+\-' extracts as '\('\)\. 0\.56 % above optmat's Ar model \(source notes\)\: a check\. Uncertainty the linear sum of Eq\. \(4\), level not stated\. clergent\_1999/refractivity\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refractivity_N2", "material": "N2", "file": "N2/clergent_1999__refractivity_N2.csv", "table": "tbl_4e3479144d9d", "quantity": "refractivity", "scale": 1e-06, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "state": "1atm_20C", "density": "real", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table 5 'our results'\: \(n \- 1\) x 10^6 = 279\.5 \+\- 0\.8 at 101\.325 kPa and 293\.15 K, 632\.8 nm \(mu = 808\.8 \+\- 1\.2 x 1e\-9 K/Pa\)\. 0\.78 % above optmat's N2 model\: a check\. The value wahlstrand\_2012 uses as n0 \- 1 = 2\.795e\-4 of N2 for its absolute calibration\. clergent\_1999/refractivity\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "refractivity_CO2", "material": "CO2", "file": "CO2/clergent_1999__refractivity_CO2.csv", "table": "tbl_4e3479144d9d", "quantity": "refractivity", "scale": 1e-06, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "state": "1atm_20C", "density": "real", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table 5 'our results'\: \(n \- 1\) x 10^6 = 418\.6 \+\- 1\.1 at 101\.325 kPa and 293\.15 K, 632\.8 nm \(mu = 1211\.1 \+\- 1\.5 x 1e\-9 K/Pa\)\. 0\.50 % above optmat's CO2 model\: a check\. clergent\_1999/hauf\_grigull\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "hauf_grigull_Ar", "material": "Ar", "file": "Ar/clergent_1999__hauf_grigull_Ar.csv", "table": "tbl_4e3479144d9d", "quantity": "refractivity", "scale": 1e-06, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "state": "1atm_20C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "W. Hauf and V. Grigull, Optical Methods in Heat Transfer, in Advances in Heat Transfer, Vol. 6 (Academic Press, New York, 1970), pp. 133-366" ] } Table 5 'Hauf and Grigull'\: \(n \- 1\) x 10^6 = 261\.8 at 101\.325 kPa, 293\.15 K, 632\.8 nm, which Hauf and Grigull \(1970; the second author printed 'V\. Grigull'\) 'calculated \.\.\. by interpolation from old data collected in the International Critical Tables' \(1930\) with a Cauchy formula n \- 1 = A/\(nu0^2 \- nu^2\) \(Eq\. 2, p\. 1\)\. Not a measurement at 632\.8 nm; no uncertainty\. Agrees with optmat's Ar model to 0\.01 %\. clergent\_1999/hauf\_grigull\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "hauf_grigull_N2", "material": "N2", "file": "N2/clergent_1999__hauf_grigull_N2.csv", "table": "tbl_4e3479144d9d", "quantity": "refractivity", "scale": 1e-06, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "state": "1atm_20C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "W. Hauf and V. Grigull, Optical Methods in Heat Transfer, in Advances in Heat Transfer, Vol. 6 (Academic Press, New York, 1970), pp. 133-366" ] } Table 5 'Hauf and Grigull'\: \(n \- 1\) x 10^6 = 278\.1, interpolated from the International Critical Tables \(see hauf\_grigull\_Ar\)\. 0\.28 % above optmat's N2 model\. clergent\_1999/hauf\_grigull\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "hauf_grigull_CO2", "material": "CO2", "file": "CO2/clergent_1999__hauf_grigull_CO2.csv", "table": "tbl_4e3479144d9d", "quantity": "refractivity", "scale": 1e-06, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "state": "1atm_20C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "W. Hauf and V. Grigull, Optical Methods in Heat Transfer, in Advances in Heat Transfer, Vol. 6 (Academic Press, New York, 1970), pp. 133-366" ] } Table 5 'Hauf and Grigull'\: \(n \- 1\) x 10^6 = 417\.4, interpolated from the International Critical Tables \(see hauf\_grigull\_Ar\)\. 0\.21 % above optmat's CO2 model\. Formulas -------- clergent\_1999/mu\_Ar ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mu_Ar", "material": "Ar", "equation": "Eq. (1), p. 1; Table 4, p. 3", "printed": "n - 1 = mu p/T; mu/(10^-9 K Pa^-1) = 762.0 +- 1.2 (Ar)", "variable": "p: pressure in Pa; T: temperature in K; lambda = 632.8 nm (He-Ne, medium not stated)", "state": "any p, T in range (ideal gas assumed)", "density": "ideal", "range": "288.15-323.15 K, 0-110 kPa, 632.8 nm", "coefficients": { "mu": "762.0e-9" }, "check": "mu x 101325/293.15 = 263.38e-6; Table 5 prints 263.3 +- 0.8 (truncated). The mean of the supplement's 24 Ar runs as printed there (762.0, confidence interval 1.2, std dev 2.2). Checked 2026-09-26." } \+\- 1\.2 is the confidence interval of the mean of 24 runs \(2\.576 std dev/sqrt\(24\)\: a 99 % interval; level not stated\)\. The Gladstone\-Dale and ideal\-gas assumptions are the authors' \(p\. 1\)\. clergent\_1999/mu\_N2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mu_N2", "material": "N2", "equation": "Eq. (1), p. 1; Table 4, p. 3", "printed": "n - 1 = mu p/T; mu/(10^-9 K Pa^-1) = 808.8 +- 1.2 (N2)", "variable": "p: pressure in Pa; T: temperature in K; lambda = 632.8 nm (He-Ne, medium not stated)", "state": "any p, T in range (ideal gas assumed)", "density": "ideal", "range": "288.15-323.15 K, 0-110 kPa, 632.8 nm", "coefficients": { "mu": "808.8e-9" }, "check": "mu x 101325/293.15 = 279.56e-6; Table 5 prints 279.5 +- 0.8 (truncated). Table 3 prints the 24 runs (mu from 802.61 to 812.05) and their mean 808.8, confidence interval 1.2, std dev 2.3 (x 1e-9 K/Pa). Checked 2026-09-26." } As mu\_Ar\. clergent\_1999/mu\_CO2 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mu_CO2", "material": "CO2", "equation": "Eq. (1), p. 1; Table 4, p. 3", "printed": "n - 1 = mu p/T; mu/(10^-9 K Pa^-1) = 1211.1 +- 1.5 (CO2)", "variable": "p: pressure in Pa; T: temperature in K; lambda = 632.8 nm (He-Ne, medium not stated)", "state": "any p, T in range (ideal gas assumed)", "density": "ideal", "range": "288.15-323.15 K, 0-110 kPa, 632.8 nm", "coefficients": { "mu": "1211.1e-9" }, "check": "mu x 101325/293.15 = 418.61e-6; Table 5 prints 418.6 +- 1.1. The supplement prints the mean of the 24 CO2 runs 1211.1, confidence interval 1.5, std dev 2.9. Checked 2026-09-26." } As mu\_Ar\. For CO2 the ideal\-gas form ignores B p/RT = \-0\.4 to \-0\.55 % at 1 atm over 288\-323 K\: n \- 1 = mu p/T is good to about 0\.1 % over the range, not better \(estimated here\)\. 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.