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 · Catalogue · 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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.