egan_2011
=========

P\. Egan and J\. A\. Stone, Appl\. Opt\. 50, 3076 \(2011\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/egan_2011.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/AO\.50\.003076 <https://doi.org/10.1364/AO.50.003076>`__

**Source kind:** measurement

**Recorded technique:** Absolute refractometry with two Fabry\-Perot cavities of ULE glass \(143 and 329 mm, finesse about 400\) at NIST\: He\-Ne lasers locked to cavity modes, absolute frequencies from beats against an iodine\-stabilised He\-Ne laser; n \- 1 from the vacuum and gas\-filled resonant frequencies, the mode\-number change and the free spectral range \(Eq\. \(2\)\)\. The pressure\-induced length change is calibrated with helium, whose refractivity is calculated from first principles \(Stone and Stejskal 2004\), giving the ULE bulk modulus 33\.86 GPa\. Gases at \(100 \+\- 0\.5\) kPa and \(20 \+\- 0\.005\) C, scaled to 100 kPa and 20 C; pressure gauge u = 1\.6 Pa, thermistor\-referenced thermocouples u = 1\.3 mK \(pp\. 2\-5; page numbers are the library pdf pages\)\.

**Materials in structured entries:** Ar, N2

**Dataset quantities:** molar\_refractivity, refractivity

**Contents:** 10 datasets; 0 formulas.

Curation notes
--------------

Title as observed \(the record is UNVERIFIED in the library\)\: 'Absolute refractometry of dry gas to \+\-3 parts in 10^9'; the citation is Egan et al\.'s Ref\. 50 in egan\_2019 \(Appl\. Opt\. 50, 3076 \(2011\)\), which matches the library file name ao\-50\-19\-3076\.pdf\.

Wavelength\: the paper says '632\.8 nm' \(abstract, conclusion\) and 'lambda ~ 633 nm' \(Table 2\), the usual air\-wavelength label of the He\-Ne line; the lasers are He\-Ne lasers measured against an iodine\-stabilised He\-Ne\. Egan et al\. \(2019, p\. 12\) state that these measurements were 'made at the same wavelength' as theirs, 632\.9908 nm \(vacuum\), which is used here\. The difference from treating 632\.8 nm as a standard\-air wavelength \(about 632\.97 nm in vacuum\) is negligible for n \- 1 \(a few 1e\-9 relative\)\.

Table 2\: \(n \- 1\) x 10^8 at p = 100 kPa, T = 20 C\. This work 27368\.2 \+\- 0\.9 \(N2\) and 25838\.9 \+\- 0\.9 \(Ar\); the \+\- is the expanded uncertainty, 'an expanded uncertainty of \< 9 x 10^\-9 \(k = 2\) in the refractive index reference values for nitrogen and argon at specified temperature and pressure' \(p\. 7\)\. The dry\-gas refractometer alone has a standard uncertainty of 1\.41e\-9 \(Table 1, not extracted\: the budget\)\. The Birch, Hou and Thalmann and Achtermann et al\. rows are 'corresponding results obtained using the molar refractivity values given by' those authors \(p\. 9\)\: the authors' conversion of other work to 100 kPa and 20 C, reproduced; their uncertainty level is not stated\.

Molar refractivities \(text, p\. 9\)\: N2 4\.44585 and Ar 4\.19545 cm^3/mol, 'expanded uncertainty of 1\.2 x 10^\-4 cm^3/mol', computed from the refractivities with Dymond et al\.'s density virial coefficients and Achtermann et al\.'s \(1991\) refractivity virial coefficients \(so partly derived from literature virials\)\: inline datasets, check\.

REVISED BY THE AUTHORS\: Egan et al\. \(2019, p\. 12, Table III note a\) adjust these molar refractivities by \+19\.3e\-6 A\_R for two biases\: the difference T \- T\_90 = 2\.9 mK \(9\.9e\-6; the 2011 temperatures were ITS\-90\) and a blunder in the extrapolation of the helium\-permeation lengthening \(9\.4e\-6; a linear instead of the stated half\-linear, half\-quadratic extrapolation\), giving 4\.44594\(6\) and 4\.19553\(6\) \(egan\_2019, reproduced there as a check\), and 'consider the present measurements to supersede those of 2011'\. The helium blunder enters the refractivity itself and T \- T\_90 its temperature, so the Table 2 refractivities are presumably low by a similar amount \(about 5e\-9 in n \- 1, within the stated expanded uncertainty 9e\-9\); the paper's values are kept as printed and flagged in the register \(TC\-116\)\.

Not extracted\: Table 1 \(uncertainty budget\), the humidity and cavity\-comparison results \(air; figures\)\.

**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\_2011/refractivity\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_N2",
     "material": "N2",
     "file": "N2/egan_2011__refractivity_N2.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     }
   }

Table 2 'This work'\: \(n \- 1\) x 10^8 = 27368\.2 \+\- 0\.9 \(k = 2\) at 100 kPa, 20 C \(ITS\-90\), 632\.9908 nm \(vacuum; see source notes\)\. Later found by the authors to share a bias of about \-19e\-6 relative \(source notes; TC\-116\)\.

egan\_2011/refractivity\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_Ar",
     "material": "Ar",
     "file": "Ar/egan_2011__refractivity_Ar.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     }
   }

Table 2 'This work'\: \(n \- 1\) x 10^8 = 25838\.9 \+\- 0\.9 \(k = 2\) at 100 kPa, 20 C \(ITS\-90\), 632\.9908 nm \(vacuum\)\. Later found by the authors to share a bias of about \-19e\-6 relative \(source notes; TC\-116\)\.

egan\_2011/birch\_1991\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "birch_1991_N2",
     "material": "N2",
     "file": "N2/egan_2011__birch_1991_N2.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "reproduced",
     "reproduced_from": [
       "birch_1991"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2 'Birch'\: 27368 \+\- 4, computed by Egan and Stone from Birch's molar refractivity \(p\. 9\)\.

egan\_2011/birch\_1991\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "birch_1991_Ar",
     "material": "Ar",
     "file": "Ar/egan_2011__birch_1991_Ar.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "reproduced",
     "reproduced_from": [
       "birch_1991"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2 'Birch'\: 25838 \+\- 4, computed by Egan and Stone from Birch's molar refractivity \(p\. 9\)\.

egan\_2011/hou\_1994\_N2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "hou_1994_N2",
     "material": "N2",
     "file": "N2/egan_2011__hou_1994_N2.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "reproduced",
     "reproduced_from": [
       "W. Hou and R. Thalmann, Measurement 13, 307 (1994)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2 'Hou and Thalmann'\: 27367 \+\- 4, computed by Egan and Stone from Hou and Thalmann's molar refractivity \(p\. 9\)\. The original is not in the library\.

egan\_2011/hou\_1994\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "hou_1994_Ar",
     "material": "Ar",
     "file": "Ar/egan_2011__hou_1994_Ar.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "reproduced",
     "reproduced_from": [
       "W. Hou and R. Thalmann, Measurement 13, 307 (1994)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2 'Hou and Thalmann'\: 25839 \+\- 4, computed by Egan and Stone from Hou and Thalmann's molar refractivity \(p\. 9\)\. The original is not in the library\.

egan\_2011/achtermann\_1991\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "achtermann_1991_N2",
     "material": "N2",
     "file": "N2/egan_2011__achtermann_1991_N2.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "reproduced",
     "reproduced_from": [
       "achtermann_1991"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2 'Achtermann et al\.' \(Ref\. 22, the 1991 paper\)\: 27372 \+\- 3, computed by Egan and Stone from Achtermann et al\.'s molar refractivity \(p\. 9\)\.

egan\_2011/achtermann\_1991\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "achtermann_1991_Ar",
     "material": "Ar",
     "file": "Ar/egan_2011__achtermann_1991_Ar.csv",
     "table": "tbl_7d11225de36b",
     "quantity": "refractivity",
     "scale": 1e-08,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 293.15
     },
     "density": "real",
     "use": "reproduced",
     "reproduced_from": [
       "achtermann_1991"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2 'Achtermann et al\.'\: 25842 \+\- 1, computed from Achtermann et al\.'s molar refractivity; 'the argon measurements of Achtermann et al\. \.\.\. claim a much lower uncertainty than is assigned to the corresponding nitrogen results' and are the only values not consistent within the stated uncertainties \(p\. 9\)\.

egan\_2011/molar\_refractivity\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "molar_refractivity_N2",
     "material": "N2",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

1 inline points in the source record.

p\. 9\: A\_R = 4\.44585 cm^3/mol at 20 C, expanded uncertainty 1\.2e\-4 cm^3/mol, from refractivity\_N2 with Dymond et al\.'s density and Achtermann et al\.'s refractivity virial coefficients\: derived, and revised to 4\.44594\(6\) by Egan et al\. 2019 \(\+19\.3e\-6; source notes\)\. A check\.

egan\_2011/molar\_refractivity\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "molar_refractivity_Ar",
     "material": "Ar",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     }
   }

1 inline points in the source record.

p\. 9\: A\_R = 4\.19545 cm^3/mol, expanded uncertainty 1\.2e\-4 cm^3/mol, derived as for nitrogen; revised to 4\.19553\(6\) by Egan et al\. 2019\. A check\.

Formulas
--------

No formulas are recorded.

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 </register>` for the checks and decisions.