buckingham_1970 =============== A\. D\. Buckingham, M\. P\. Bogaard, D\. A\. Dunmur, C\. P\. Hobbs and B\. J\. Orr, "Kerr effect in some simple non\-dipolar gases", Trans\. Faraday Soc\. 66, 1548 \(1970\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1039/tf9706601548 `__ **Source kind:** measurement **Recorded technique:** Absolute dc Kerr effect at 632\.8 nm \(He\-Ne laser\) with the apparatus of Buckingham & Dunmur 1968 and Buckingham & Orr 1968, at temperatures between 243 and 343 K and pressures up to 10^7 N m^\-2 \(100 bar\); \(n\_par \- n\_perp\) V\_m/F^2 fitted at each temperature to Eq\. \(5\), A\_K \+ V\_m^\-1 \[B\_K \+ A\_K\(2 N alpha/3 eps0 \+ N a/6 eps0\)\], molar volumes from Dymond & Smith's second and third virial coefficients\. N2 and CO2 of purity greater than 99\.9 % \(mass spectrometry\), unpurified \(p\. 1549\)\. **Materials in structured entries:** CO2, N2 **Dataset quantities:** hyperpolarizability, kerr\_virial\_coefficient, molar\_kerr\_constant, polarizability\_anisotropy **Contents:** 10 datasets; 2 formulas. Curation notes -------------- Pages are the journal's \(1548\-1553; p\. = pdf page \+ 1547\)\. N2 AND CO2 ONLY are recorded; ethane, ethylene, acetylene and cyclopropane \(Tables 1\-3\) are out of scope and not transcribed\. DEFINITIONS \(pp\. 1548\-1549\)\. mK = 6 n \(n\_par \- n\_perp\) V\_m/\[\(n^2 \+ 2\)^2 \(eps \+ 2\)^2 F^2\] \(Eq\. 1\); mK = A\_K \+ B\_K V\_m^\-1 \+ \.\.\. \(Eq\. 2\); for non\-dipolar molecules A\_K = \(N/\(405 eps0\)\){5 gamma \+ \(3/\(2kT\)\)\(alpha\_ab a\_ab \- 3 a alpha\)} \(Eq\. 3\), alpha\_ab static and a\_ab optical polarizabilities; gamma = \(3 gamma\_ab,ab \- gamma\_aa,bb\)/10 \(Eq\. 4\)\: Buckingham's dc Kerr gamma\_K in the Taylor\-series convention\. For an axial molecule \(3/2\)\(alpha\_ab a\_ab \- 3 alpha a\) = \(alpha\_par \- alpha\_perp\)\(a\_par \- a\_perp\) \(p\. 1551\)\. Units S\.I\. as printed \(A\_K in C^2 m^5 J^\-2, per mole; B\_K in C^2 m^8 J^\-2, per mole squared\)\. The polarizabilities used in Eq\. \(5\), printed under each block of Table 1\: CO2 alpha = 3\.26 \(Johnston & Cole 1962\), a = 2\.93 \(Watson & Ramaswamy 1936\); N2 alpha = 1\.94 \(Orcutt & Cole 1967\), a = 1\.97 x 10^\-40 C^2 m^2 J^\-1 \(Watson & Ramaswamy\)\. EXTRACTION\. Table 1 is extracted as eight fragments without headers, the gases identified only by their label cells and order; checked against the page images of pp\. 1550\-1551\: CARBON DIOXIDE \(252\-337 K, nine temperatures\) then NITROGEN \(248\-334 K, seven\), as extracted\. ACCURACY \(p\. 1551\)\: 'The precision of the results for A\_K is \+\-2 %, but the absolute accuracy is limited to \+\-5 % due to calibration uncertainties\. The errors associated with B\_K are standard deviations on the least\-squares fit, and are much greater than any calibration error\.' Table 2's errors are not described\. TABLE 2 \(p\. 1551\) AND ITS ERRORS\. \(A\_K\)\_\(T^\-1 = 0\) = 4\.7 \+\- 0\.9 \(CO2\), 0\.8 \+\- 0\.1 \(N2\) x 10^\-28 C^2 m^5 J^\-2; dA\_K/dT^\-1 = 6\.84 \+\- 0\.47, 0\.67 \+\- 0\.04 x 10^\-25 C^2 m^5 J^\-2 K; gamma = 5\.6 \+\- 1\.2, 0\.9 \+\- 0\.1 x 10^\-61 C^4 m^4 J^\-3; \(alpha\_ab a\_ab \- 3 a alpha\) = 3\.75 \+\- 0\.26, 0\.366 \+\- 0\.025 x 10^\-80 C^4 m^4 J^\-2\. Checked \(2026\-09\-26\)\: gamma = 81 eps0/N x intercept \(5\.60, 0\.95\); an unweighted line through Table 1 reproduces the intercepts and slopes \(CO2 4\.68 and 6\.82, N2 0\.76 and 0\.67\), but its standard errors from the scatter are CO2 \+\-3\.5 and N2 \+\-0\.25 x 10^\-28 on the intercept \(75 % and 33 %\), not the printed \+\-0\.9 and \+\-0\.1 \(19 % and 12 %\)\. Dropping CO2's lowest\-temperature point \(252 K\) moves its intercept to \-0\.53 x 10^\-28 \(gamma \-0\.06 x 10^\-60\), as gentle\_1989 \(p\. 3037\: 'the intercept has an uncertainty \.\.\. of 75% rather than the quoted value of 21%'; \+0\.56 \+\- 0\.42 \-\> \-0\.06 \+\- 0\.18\) and shelton\_1986\_co2 \(\-61 \+\- 200 x 10^\-63\) found\. The gamma values come from a long extrapolation to 1/T = 0 \(T\_min/\(T\_max \- T\_min\) = 3\.0 for CO2, gentle\_1989\) and are 1\.6 \(N2, 1443 au\) and 7\.8 \(CO2, 8981 au\) times optmat's fitted static gamma\_0 \(920 and 1151 au, docs/nonlinear\.md\)\: recorded as 'check'\. 'at 300 K, gamma contributes 26, 17 \.\.\. % to the Kerr effect of nitrogen, carbon dioxide' \(p\. 1552\)\. TABLE 3 \(p\. 1552\)\: infrared atomic contributions delta alpha\_par, delta alpha\_perp \(CO2 0\.50, 0\.21; N2 0\.00, 0\.00 x 10^\-40 C^2 m^2 J^\-1\), the optical anisotropy at 632\.8 nm 'from ref\. \(6\)' \(Bridge & Buckingham 1966\: CO2 2\.34, N2 0\.774\), the static anisotropy derived by adding the atomic parts \(2\.63, 0\.774\), their product \(6\.15, 0\.599\) and the Kerr slope's \(3/2\)\(alpha\_ab a\_ab \- 3 alpha a\) \(5\.62 \+\- 0\.38, 0\.54 \+\- 0\.04\)\. B\_K 'in approximate accord with the theory, provided that allowance is made for the induced dipole\-induced dipole contribution' \(p\. 1553\)\. A footnote \(p\. 1552\) notes New & Ward's THG ratios for N2 and CO2, 'complicated by dispersion'\. Superseded for CO2 by gentle\_1989 \(A\_K \+\-2 % over 299\-490 K\)\. Reproductions elsewhere\: hattig\_1998/expt\_dc\_kerr\_N2 \(1443 \+\- 160 au = 0\.9 \+\- 0\.1 x 10^\-61 / 6\.2354e\-65\); shelton\_1986\_co2/table2\_dc\_kerr \(558 \+\- 120 x 10^\-63, excluded there\) and text\_dc\_kerr\_reanalysed; hellwarth\_1990/kerr\_buckingham\_1970\_N2 and kerr\_average\_N2 \(converted\); carusotto\_1985/table2\_ref6\_N2\_\* \(converted to K\)\. Not edited here, citing this paper\: lundeen\_1983, rosasco\_1985, ward\_1979\. The library's validation warnings are the uncaptioned fragments of Table 1\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- buckingham\_1970/table1\_A\_K\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_A_K_CO2", "material": "CO2", "file": "CO2/buckingham_1970__table1_A_K_CO2.csv", "table": "tbl_2089ba2fdb4d", "quantity": "molar_kerr_constant", "unit": "C2 m5 J-2", "scale": 1e-27, "abscissa": "temperature", "abscissa_unit": "K", "use": "primary", "uncertainty": { "relative": 0.05, "level": "not stated" }, "parameters": { "wavelength_nm": 632.8 } } Table 1 \(p\. 1550\), CARBON DIOXIDE\: A\_K at nine temperatures, 252\-337 K, 632\.8 nm, including the orientation term\. 'The precision of the results for A\_K is \+\-2 %, but the absolute accuracy is limited to \+\-5 % due to calibration uncertainties' \(p\. 1551\)\: the 5 % is recorded \(level not stated\)\. gentle\_1989 remeasured CO2 to \+\-2 % over 299\-490 K\. buckingham\_1970/table1\_A\_K\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_A_K_N2", "material": "N2", "file": "N2/buckingham_1970__table1_A_K_N2.csv", "table": "tbl_c5d4dfda3344", "quantity": "molar_kerr_constant", "unit": "C2 m5 J-2", "scale": 1e-27, "abscissa": "temperature", "abscissa_unit": "K", "use": "primary", "uncertainty": { "relative": 0.05, "level": "not stated" }, "parameters": { "wavelength_nm": 632.8 } } Table 1 \(p\. 1550\), NITROGEN \(a headerless fragment in the extraction; the gas from its label cell and the page image\)\: A\_K at seven temperatures, 248\-334 K, 632\.8 nm, including the orientation term\. Precision \+\-2 %, absolute accuracy \+\-5 % \(p\. 1551\)\: the 5 % is recorded \(level not stated\)\. buckingham\_1970/table1\_B\_K\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_B_K_CO2", "material": "CO2", "file": "CO2/buckingham_1970__table1_B_K_CO2.csv", "table": "tbl_2089ba2fdb4d", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-32, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "wavelength_nm": 632.8, "order": 2 } } Table 1 \(p\. 1550\)\: the second Kerr virial coefficient B\_K of CO2 at nine temperatures\. 'The errors associated with B\_K are standard deviations on the least\-squares fit, and are much greater than any calibration error' \(p\. 1551\)\. buckingham\_1970/table1\_B\_K\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_B_K_N2", "material": "N2", "file": "N2/buckingham_1970__table1_B_K_N2.csv", "table": "tbl_c5d4dfda3344", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-32, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "wavelength_nm": 632.8, "order": 2 } } Table 1 \(p\. 1550\)\: B\_K of N2 at seven temperatures, all within about one standard deviation of zero\. Standard deviations of the least\-squares fit \(p\. 1551\)\. buckingham\_1970/table2\_gamma\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_gamma_CO2", "material": "CO2", "file": "CO2/buckingham_1970__table2_gamma_CO2.csv", "table": "tbl_53d38067698d", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-61, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic_vibrational", "component": "K" } } Table 2 \(p\. 1551\)\: gamma = \(5\.6 \+\- 1\.2\) x 10^\-61 C^4 m^4 J^\-3 \(8981 \+\- 1924 au\) for CO2 at 632\.8 nm, from the 1/T = 0 intercept of A\_K \(Eq\. 3\)\: the dc Kerr gamma\_K, electronic plus vibrational\. A long extrapolation, driven by the lowest\-temperature point\: without it the intercept is negative \(computed here; gentle\_1989 and shelton\_1986\_co2 found the same\); the scatter gives \+\-75 %, not the printed \+\-21 %\. 7\.8 times optmat's fitted gamma\_0\. Superseded by gentle\_1989 \(0\.125 \+\- 0\.032 x 10^\-60\)\. Level of the error not stated\. buckingham\_1970/table2\_gamma\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_gamma_N2", "material": "N2", "file": "N2/buckingham_1970__table2_gamma_N2.csv", "table": "tbl_53d38067698d", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-61, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic_vibrational", "component": "K" } } Table 2 \(p\. 1551\)\: gamma = \(0\.9 \+\- 0\.1\) x 10^\-61 C^4 m^4 J^\-3 \(1443 \+\- 160 au\) for N2 at 632\.8 nm, from the 1/T = 0 intercept of A\_K \(Eq\. 3\)\: the dc Kerr gamma\_K, electronic plus vibrational \(the orientation term is the fitted 1/T part\)\. A long extrapolation over 248\-334 K\: the scatter of Table 1 gives an intercept of \(0\.76 \+\- 0\.25\) x 10^\-28 \(computed here\), a third, not the printed eighth\. 1\.6 times optmat's fitted static gamma\_0 \(920 au\)\. Level of the error not stated\. buckingham\_1970/table3\_anisotropy\_optical\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_anisotropy_optical_CO2", "material": "CO2", "file": "CO2/buckingham_1970__table3_anisotropy_optical_CO2.csv", "table": "tbl_a0c4c55e9fd4", "quantity": "polarizability_anisotropy", "unit": "SI", "scale": 1e-40, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966)" ], "uncertainty": { "level": "not stated" } } Table 3 \(p\. 1552\)\: the optical polarizability anisotropy \(a\_par \- a\_perp\) of CO2 at 632\.8 nm, 2\.34 x 10^\-40 C^2 m^2 J^\-1, 'from ref\. \(6\)' \(Bridge & Buckingham 1966, Rayleigh depolarisation\)\. No uncertainty printed\. buckingham\_1970/table3\_anisotropy\_optical\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_anisotropy_optical_N2", "material": "N2", "file": "N2/buckingham_1970__table3_anisotropy_optical_N2.csv", "table": "tbl_a0c4c55e9fd4", "quantity": "polarizability_anisotropy", "unit": "SI", "scale": 1e-40, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. A 295, 334 (1966)" ], "uncertainty": { "level": "not stated" } } Table 3 \(p\. 1552\)\: the optical polarizability anisotropy of N2 at 632\.8 nm, 0\.774 x 10^\-40 C^2 m^2 J^\-1, 'from ref\. \(6\)' \(Bridge & Buckingham 1966\)\. No uncertainty printed\. buckingham\_1970/table3\_anisotropy\_static\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_anisotropy_static_CO2", "material": "CO2", "file": "CO2/buckingham_1970__table3_anisotropy_static_CO2.csv", "table": "tbl_a0c4c55e9fd4", "quantity": "polarizability_anisotropy", "unit": "SI", "scale": 1e-40, "abscissa_unit": "nm", "use": "check", "uncertainty": { "level": "not stated" } } Table 3 \(p\. 1552\)\: the static anisotropy \(alpha\_par \- alpha\_perp\) of CO2, 2\.63 x 10^\-40 C^2 m^2 J^\-1, 'derived from optical values by including the atomic contributions' \(delta alpha\_par = 0\.50, delta alpha\_perp = 0\.21 from infrared intensities\); the electronic dispersion is neglected \(p\. 1551\)\. Not the Kerr measurement's value\: that is the slope's product \(3/2\)\(alpha\_ab a\_ab \- 3 alpha a\) = 5\.62 \+\- 0\.38 x 10^\-80 C^4 m^4 J^\-2, which with a\_par \- a\_perp = 2\.34 gives 2\.40 \(computed here; gentle\_1989 found 2\.41 \+\- 0\.08\)\. buckingham\_1970/table3\_anisotropy\_static\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_anisotropy_static_N2", "material": "N2", "file": "N2/buckingham_1970__table3_anisotropy_static_N2.csv", "table": "tbl_a0c4c55e9fd4", "quantity": "polarizability_anisotropy", "unit": "SI", "scale": 1e-40, "abscissa_unit": "nm", "use": "check", "uncertainty": { "level": "not stated" } } Table 3 \(p\. 1552\)\: the static anisotropy of N2, 0\.774 x 10^\-40 C^2 m^2 J^\-1, equal to the optical value \(no infrared atomic contribution; dispersion neglected\)\. The Kerr slope gives \(3/2\)\(alpha\_ab a\_ab \- 3 alpha a\) = 0\.54 \+\- 0\.04 x 10^\-80, i\.e\. 0\.70 with the optical 0\.774 \(computed here\)\. Formulas -------- buckingham\_1970/table2\_A\_K\_line\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_A_K_line_CO2", "material": "CO2", "equation": "Eq. (3), Table 2, p. 1551", "printed": "10^28 (A_K)_(T^-1 = 0) = 4.7 +- 0.9 C^2 m^5 J^-2; 10^25 (dA_K/dT^-1) = 6.84 +- 0.47 C^2 m^5 J^-2 K", "variable": "T: temperature in K; A_K = intercept + slope/T in C^2 m^5 J^-2 (per mole)", "range": "252-337 K (Table 1)", "coefficients": { "intercept": "4.7", "slope": "6.84" }, "coefficient_units": { "intercept": "1e-28 C^2 m^5 J^-2", "slope": "1e-25 C^2 m^5 J^-2 K" }, "check": "An unweighted line through Table 1 gives 4.68 and 6.82 (reproduced, 2026-09-26), but standard errors of 3.5 and 1.0 from the scatter against the printed 0.9 and 0.47; without the 252 K point the intercept is -0.53. It reproduces Table 1 with chi^2/dof = 2.6 at the stated 2 % precision." } The line A\_K\(1/T\) behind Table 2's gamma and anisotropy product\. The intercept is poorly determined \(see the record's notes\)\. buckingham\_1970/table2\_A\_K\_line\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_A_K_line_N2", "material": "N2", "equation": "Eq. (3), Table 2, p. 1551", "printed": "10^28 (A_K)_(T^-1 = 0) = 0.8 +- 0.1 C^2 m^5 J^-2; 10^25 (dA_K/dT^-1) = 0.67 +- 0.04 C^2 m^5 J^-2 K", "variable": "T: temperature in K; A_K = intercept + slope/T in C^2 m^5 J^-2 (per mole)", "range": "248-334 K (Table 1)", "coefficients": { "intercept": "0.8", "slope": "0.67" }, "coefficient_units": { "intercept": "1e-28 C^2 m^5 J^-2", "slope": "1e-25 C^2 m^5 J^-2 K" }, "check": "An unweighted line through Table 1 gives 0.76 and 0.67 (reproduced, 2026-09-26), with standard errors from the scatter of 0.25 and 0.07 against the printed 0.1 and 0.04; chi^2/dof = 1.1 at the stated 2 % precision." } The line A\_K\(1/T\) behind Table 2's gamma for N2\. 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.