buckingham_1968 =============== A\. D\. Buckingham and D\. A\. Dunmur, Trans\. Faraday Soc\. 64, 1776 \(1968\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1039/tf9686401776 `__ **Source kind:** measurement **Recorded technique:** Absolute dc Kerr effect \(electric\-field\-induced birefringence\) of He, Ne, Ar, Kr, Xe and SF6 at 23 C and 632\.8 nm \(50 mW He\-Ne laser\), relative to a carbon disulphide Kerr cell calibrated by the Senarmont method; gas cell with 46 cm stainless\-steel electrodes 0\.476 cm apart, pressures up to 80 atm \(Budenberg gauge\), fields 30\-50 esu \(rms voltage on an electrostatic voltmeter\); densities from pressure and temperature with the second and third virial coefficients of Table 1; the birefringence per F^2 extrapolated to zero density \(linear fit for He and Ne, quadratic for the others\), each point weighted by its density \(pp\. 1777\-1778\)\. **Materials in structured entries:** Ar, He, Kr, Ne, SF6, Xe **Dataset quantities:** hyperpolarizability **Contents:** 7 datasets; 0 formulas. Curation notes -------------- DEFINITIONS \(pp\. 1776\-1777, 1780\)\. The polarizability in a field is Pi\_ab = alpha\_ab \+ \(1/2\) gamma\_ab,cd F\_c F\_d \+ \.\.\. \(Eq\. 1\), 'expanded as a Taylor series in the electric field' \(Buckingham's convention\: the Taylor\-series gamma of Shelton & Rice, 'T'\); gamma in esu \(cm^5 statvolt^\-2 = cm^6 erg^\-1\) per molecule\. n = 1 \+ 2 pi N rho Pi\_bar \(Eq\. 2; N Avogadro's number, rho in mol/cm^3\); n\_xx \- n\_yy = 2 pi N rho \(Pi\_xx \- Pi\_yy\) \(Eq\. 3\) = pi N rho F\_x^2 \(gamma\_xx,xx \- gamma\_yy,xx\) \(Eq\. 4\); for spheres with the static\-limit symmetry gamma\_xxyy = gamma\_xxxx/3 = gamma/3\: n\_xx \- n\_yy = \(2/3\) pi N rho F\_x^2 gamma \(Eq\. 5\); 'In the general case, gamma in \(5\) is \(3 gamma\_ab,ab \- gamma\_aa,bb\)/10, which simplifies to gamma\_aabb/5 when gamma is symmetric in all suffixes' \(p\. 1777\)\: the dc Kerr gamma\_K of Shelton & Rice \(the optical frequency is treated as far below resonance\)\. F is the applied \(rms\) field\. Molar Kerr constant at low density A\_K = \(2/27\)\[\(n\_xx \- n\_yy\)/F\_x^2 rho\]\_{F \-\> 0, rho \-\> 0} = 4 pi N gamma/81 \(Eq\. 6\); the general molar Kerr constant mK = 6n/\[\(n^2 \+ 2\)^2 \(eps\_0 \+ 2\)^2\] \[\(n\_xx \- n\_yy\)/F\_x^2 rho\] = A\_K \+ B\_K rho \+ \.\.\. \(Eq\. 7\), and for axial centrosymmetric molecules mK = \(4 pi N/405\){5 gamma \+ \(alpha\_par \- alpha\_perp\)\(alpha\_par\(0\) \- alpha\_perp\(0\)\)/kT} \(Eq\. 8\)\. Parts\: the atoms have no orientational term; the measured gamma is electronic \(for SF6 electronic \+ vibrational\)\. TABLE 1 \(p\. 1780\), also\: 10^14 A\_K \(esu\) He 0\.25 \+\- 0\.02, Ne 0\.48 \+\- 0\.04, Ar 5\.5 \+\- 0\.4, Kr 13 \+\- 1, Xe 36 \+\- 3, SF6 11 \+\- 1 \(A\_K = 4 pi N gamma/81 restates gamma; not stored separately\: FORMAT GAP, kerr\_constant requires a state, which a zero\-density molar constant has not\); second virial coefficients at 23 C \(cm^3/mol\) 11\.7, 11\.4, \-16\.2, \-53\.3, \-132, \-280 and third \(cm^6/mol^2\) 72, 234, 1160, 2620, 6130, 73600 \(equation\-of\-state inputs, not extracted\)\. Shelton & Rice 1994 derive SF6's 2338 au from A\_K \(81 x 11e\-14 / \(4 pi N\) = 1\.177e\-36 esu\) and He's 53\.6 au from gamma\. TABLE 2 \(p\. 1781; second Kerr virial coefficients at 23 C, esu; no matching quantity, recorded here\)\: \(1/27\)\[d^2/d rho^2 {\(n\_xx \- n\_yy\)/F\_x^2}\]\_rho=0 x 10^12\: Ar 4\.7 \+\- 0\.6, Kr 18 \+\- 14, Xe 74 \+\- 22, SF6 300 \+\- 40; 10^12 B\_K expt\.\: Ar 4\.1 \+\- 0\.6, Kr 16 \+\- 14, Xe 65 \+\- 22, SF6 300 \+\- 40; calc\. \(dipole\-induced\-dipole pair anisotropy 6 alpha^2/r^3 and Lennard\-Jones potentials, Eqs\. 10\-13\)\: 5\.6, 26, 140, 170\. 'The measured B\_K for argon, krypton and xenon are significantly lower than B\_K \(calc\.\)' \(short\-range effects\); SF6's is larger\. Table 2 also lists polarizabilities \(10^24 alpha, static and at 6328 A\: Ar 1\.642/1\.663, Kr 2\.484/2\.517, Xe 4\.045/4\.113, SF6 6\.505/4\.470 cm^3\) from Orcutt & Cole 1967, Dalgarno & Kingston 1960 \(dalgarno\_1960\), Buckingham & Raab 1961 and Watson & Ramaswamy 1936 \(watson\_1936\)\: reproductions, not extracted; and Lennard\-Jones eps/k, r\_0\. ACCURACY\. 'The precision of a set of measurements on a gas was greater than the overall accuracy of the results\. For this reason the error limits quoted are greater than those indicated by the standard deviations' \(p\. 1778\)\. Purity\: inert gases \>= 99\.95 %, SF6 \> 98 % \('the only important impurity being air'\)\. Later assessments\: the He value is 20\-30 % above the ab initio result \(Shelton & Rice 1994 Table VI; shelton\_1989's Table I caption\: 'the dc\-Kerr experimental value for gamma\_He is 30% larger than the accurate ab initio result'\); Kr and Xe are 10\-20 % below the ESHG\-predicted curves \(shelton\_1986\_krxe Table II and Fig\. 3\)\. 'These results for the second hyperpolarizabilities of the inert gases and sulphur hexafluoride are the first experimental determinations of these quantities' \(p\. 1782\)\. Pages\: the journal's \(1776\-1783; the PDF page plus 1775\)\. The library's validation notes unmatched figure captions \(Figs 1\-6 on one page\); the table cells agree with the images, the raised decimal points \('0·027'\) written as '\.'\. **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\_1968/gamma\_He ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_He", "material": "He", "file": "He/buckingham_1968__gamma_He.csv", "table": "tbl_23a492df71b3", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic", "temperature_k": 296.15 } } Table 1 \(p\. 1780\)\: the dc Kerr second hyperpolarizability 10^36 gamma \(esu\) of He at 23 C and 632\.8 nm \(He\-Ne laser\), from the zero\-density limit of \(n\_xx \- n\_yy\)/F\_x^2 rho \(linear fit against density\) through Eq\. \(5\)\. Error limits 'greater than those indicated by the standard deviations of the least\-squares lines' \(p\. 1778; level not stated\)\. In au \(1 au = 5\.0367e\-40 esu, shelton\_1994 Table II\)\: about 53\.6 au \(computed here; not a value of the paper\)\. 'The new value for the second hyperpolarizability of helium differs only slightly from the earlier one' \(Boyle et al\. 1966, p\. 1782\)\. Later judged too high\: Shelton & Rice 1994 Table VI \(53\.6 \+\- 4 au against Bishop & Pipin's 44\.211\); Mizrahi & Shelton \(mizrahi\_1985\_h2d2, footnote 18\) suggest a systematic error of 20 % or more in the He Kerr measurement\. buckingham\_1968/gamma\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne", "material": "Ne", "file": "Ne/buckingham_1968__gamma_Ne.csv", "table": "tbl_23a492df71b3", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic", "temperature_k": 296.15 } } Table 1 \(p\. 1780\)\: the dc Kerr second hyperpolarizability 10^36 gamma \(esu\) of Ne at 23 C and 632\.8 nm \(He\-Ne laser\), from the zero\-density limit of \(n\_xx \- n\_yy\)/F\_x^2 rho \(linear fit against density\) through Eq\. \(5\)\. Error limits 'greater than those indicated by the standard deviations of the least\-squares lines' \(p\. 1778; level not stated\)\. In au \(1 au = 5\.0367e\-40 esu, shelton\_1994 Table II\)\: about 101\.3 au \(computed here; not a value of the paper\)\. shelton\_1992 converts it to 101 \+\- 8 au and compares with the ESHG\-predicted 111 \+\- 2 au \('fair agreement'\)\. buckingham\_1968/gamma\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ar", "material": "Ar", "file": "Ar/buckingham_1968__gamma_Ar.csv", "table": "tbl_23a492df71b3", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic", "temperature_k": 296.15 } } Table 1 \(p\. 1780\)\: the dc Kerr second hyperpolarizability 10^36 gamma \(esu\) of Ar at 23 C and 632\.8 nm \(He\-Ne laser\), from the zero\-density limit of \(n\_xx \- n\_yy\)/F\_x^2 rho \(quadratic fit against density\) through Eq\. \(5\)\. Error limits 'greater than those indicated by the standard deviations of the least\-squares lines' \(p\. 1778; level not stated\)\. In au \(1 au = 5\.0367e\-40 esu, shelton\_1994 Table II\)\: about 1171 au \(computed here; not a value of the paper\)\. 'Kuss obtained a single value for the Kerr constant of argon at 350 atm, and this gives a value for the second hyperpolarizability of 0\.7 x 10^\-36 e\.s\.u\.' \(p\. 1782; text\_kuss\_Ar\)\. buckingham\_1968/gamma\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Kr", "material": "Kr", "file": "Kr/buckingham_1968__gamma_Kr.csv", "table": "tbl_23a492df71b3", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic", "temperature_k": 296.15 } } Table 1 \(p\. 1780\)\: the dc Kerr second hyperpolarizability 10^36 gamma \(esu\) of Kr at 23 C and 632\.8 nm \(He\-Ne laser\), from the zero\-density limit of \(n\_xx \- n\_yy\)/F\_x^2 rho \(quadratic fit against density\) through Eq\. \(5\)\. Error limits 'greater than those indicated by the standard deviations of the least\-squares lines' \(p\. 1778; level not stated\)\. In au \(1 au = 5\.0367e\-40 esu, shelton\_1994 Table II\)\: about 2780 au \(computed here; not a value of the paper\)\. buckingham\_1968/gamma\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Xe", "material": "Xe", "file": "Xe/buckingham_1968__gamma_Xe.csv", "table": "tbl_23a492df71b3", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic", "temperature_k": 296.15 } } Table 1 \(p\. 1780\)\: the dc Kerr second hyperpolarizability 10^36 gamma \(esu\) of Xe at 23 C and 632\.8 nm \(He\-Ne laser\), from the zero\-density limit of \(n\_xx \- n\_yy\)/F\_x^2 rho \(quadratic fit against density\) through Eq\. \(5\)\. Error limits 'greater than those indicated by the standard deviations of the least\-squares lines' \(p\. 1778; level not stated\)\. In au \(1 au = 5\.0367e\-40 esu, shelton\_1994 Table II\)\: about 7743 au \(computed here; not a value of the paper\)\. buckingham\_1968/gamma\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_SF6", "material": "SF6", "file": "SF6/buckingham_1968__gamma_SF6.csv", "table": "tbl_23a492df71b3", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic_vibrational", "temperature_k": 296.15 } } Table 1 \(p\. 1780\)\: the dc Kerr second hyperpolarizability 10^36 gamma \(esu\) of SF6 at 23 C and 632\.8 nm \(He\-Ne laser\), from the zero\-density limit of \(n\_xx \- n\_yy\)/F\_x^2 rho \(quadratic fit against density\) through Eq\. \(5\)\. Error limits 'greater than those indicated by the standard deviations of the least\-squares lines' \(p\. 1778; level not stated\)\. In au \(1 au = 5\.0367e\-40 esu, shelton\_1994 Table II\)\: about 2383 au \(computed here; not a value of the paper\)\. SF6 has no permanent dipole or polarizability anisotropy, so no orientational term enters \(Eq\. 8 with Delta alpha = 0\); the value includes any vibrational hyperpolarizability \(shelton\_1988 calculates gamma^v\_Kerr ~ 0\.3e\-62 C^4 m^4 J^\-3 at 20000 cm^\-1\)\. Purity \> 98 %, 'the only important impurity being air' \(p\. 1780\)\. buckingham\_1968/text\_kuss\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_kuss_Ar", "material": "Ar", "table": "text", "quantity": "hyperpolarizability", "unit": "esu", "scale": 1e-36, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "E. Kuss, Dissertation, University of Berlin (1940)" ], "uncertainty": { "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic" } } 1 inline points in the source record. p\. 1782\: 'Kuss obtained a single value for the Kerr constant of argon at 350 atm, and this gives a value for the second hyperpolarizability of 0\.7 x 10^\-36 e\.s\.u\.' \(converted by the authors\)\. The wavelength of Kuss's measurement is not stated \(the conversion assumes the static\-limit symmetry of Eq\. 5\)\. At 350 atm the pair contribution \(B\_K\) is large\. 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 ` for the checks and decisions.