buckingham_1969 =============== A\. D\. Buckingham and B\. J\. Orr, "Kerr effect in methane and its four fluorinated derivatives", Trans\. Faraday Soc\. 65, 673 \(1969\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1039/tf9696500673 `__ **Source kind:** measurement **Recorded technique:** Absolute dc Kerr effect \(electric birefringence\) at 632\.8 nm \(He\-Ne laser\) with the apparatus of Boyle et al\. 1966, Buckingham & Dunmur 1968 and Buckingham & Orr 1968 \(phase\-sensitive detection; thermostat \-30 to \+60 C\); pressures to 2 bar on a glass line with a mercury manometer, to 100 bar on a steel line with a calibrated Budenberg gauge\. mK0 = \(2/27\) V \(n\_par \- n\_perp\) F^\-2 per measurement \(Eq\. 6\), fitted to mK0 = A\_K \+ \[B\_K \+ A\_K\(2 A\_eps \+ A\_R/2\)\] V^\-1 \(Eq\. 7\), molar volumes from literature virial coefficients \(CH4\: Schamp et al\. 1958\)\. CH4 \(commercial, purity better than 98 %, 'the only significant impurity being air'\) at 249\.7, 273\.6 and 303\.7 K, 8\-30 bar, 18\-20 measurements each \(pp\. 673\-675\)\. **Materials in structured entries:** CH4 **Dataset quantities:** hyperpolarizability, kerr\_virial\_coefficient, molar\_kerr\_constant **Contents:** 3 datasets; 0 formulas. Curation notes -------------- Pages are the journal's \(673\-681; p\. = pdf page \+ 672\)\. CH4 ONLY is recorded; the paper also measures CF4 \(gamma = 0\.093 \+\- 0\.005 x 10^\-60 C^4 m^4 J^\-3; A\_K 0\.078, B\_K 0\.422 at 288\.8 K\), CH3F, CH2F2 and CHF3 \(A\_K, B\_K against temperature; Table 3's beta, \(alpha\_33 \- alpha\), dipole moments, polarizabilities; Table 4's term\-by\-term A\_K at 300 K\), all out of scope and not transcribed\. DEFINITIONS \(pp\. 673\-674\)\. mK = 6 n V \(n\_par \- n\_perp\)\[\(n^2 \+ 2\)\(eps \+ 2\) F\]^\-2 \(Eq\. 1\); mK = A\_K \+ B\_K V^\-1 \(Eq\. 2\); A\_K = \(N/\(81 eps0\)\)\[gamma \+ \(kT\)^\-1\(\(2/3\) mu beta \+ \(9/5\) alpha^\(0\) alpha kappa^2\) \+ \(3/10\)\(kT\)^\-2 mu^2 \(alpha\_33 \- alpha\)\] \(Eq\. 3, S\.I\.\), with gamma = \(1/10\)\(3 gamma\_xi eta,xi eta \- gamma\_xi xi,eta eta\) \(Eq\. 5\)\: Buckingham's dc Kerr gamma\_K in the Taylor\-series convention\. 'For the tetrahedral molecules methane and tetrafluoromethane only the term involving gamma in eqn\. \(3\) is non\-zero, so that A\_K should be temperature\-independent' \(p\. 674\); A\_K = N gamma/81 eps0 \(Eq\. 8\)\. The S\.I\. units of Table 1 are printed 'C^2 m^5 J^\-2' for A\_K and 'C^2 m^8 J^\-2' for B\_K \(per mole and per mole squared implied\: N is Avogadro's number, V the molar volume\); the extraction reads the A\_K header as 'C^2m^3J^\-2', the image shows m^5\. Table 6 \(appendix\)\: 1 S\.I\. unit of gamma = 8\.0776 x 10^24 e\.s\.u\.; of mK, A\_K 0\.89876 x 10^15 e\.s\.u\.; of B\_K 0\.89876 x 10^21 e\.s\.u\. RESULT \(p\. 677\)\: 'Measurements of A\_K for CH4 \(table 1\) show no significant trend with temperature, which is consistent with eqn\. \(8\)\. Results in table 1 yield\: 10^60 gamma\(CH4\) = 0\.180 \+\- 0\.009 C^4 m^4 J^\-3'\. Checked \(2026\-09\-26\)\: 81 eps0/N\_A x mean A\_K \(0\.1507 x 10^\-27\) = 0\.179 x 10^\-60; the \+\-0\.009 is the 5 % absolute accuracy\. In au \(6\.235377e\-65\)\: 2887 \+\- 144 \(shelton\_1994 Table XII\: 2887 \+\- 140\)\. ACCURACY \(pp\. 675\-676\)\: 'The estimated precision of A\_K is \+\-2 %, but the absolute accuracy is \+\-5 % as a result of calibration uncertainties; the precision of B\_K for CH4, CF4 and CH2F2 is \+\-10 %'\. TABLE 2 \(p\. 676\), mK of CH4 at 298 K and 105\-425 bar\: Kuss & Stuart \(Physik\. Z\. 42, 95 \(1941\)\) 0\.24\-0\.27 x 10^\-27 against this work's linear extrapolation 0\.27\-0\.53 x 10^\-27 \('The uncertainties in the extrapolations vary from \+\-5 % at 105 bar to \+\-8 % at 425 bar'\); 'The deviation at high pressures \.\.\. might be due to the effect of a negative third Kerr virial coefficient'\. No quantity holds a finite\-density molar Kerr constant\: notes only\. TABLE 5 \(p\. 680\)\: B\_K\(obs\.\) of CH4 0\.30 \+\- 0\.03, 0\.28 \+\- 0\.03, 0\.24 \+\- 0\.02 x 10^\-31 at 250, 274, 304 K \(Table 1's values rounded, with the 10 %\) against B\_K\(calc\.\) 0\.34, 0\.31, 0\.27 from the pair\-anisotropy theory of Buckingham & Dunmur with alpha = 2\.90, alpha^\(0\) = 2\.88 x 10^\-40 C^2 m^2 J^\-1 and Lennard\-Jones eps/k = 148\.2 K, sigma = 0\.382 nm \(Hirschfelder, Curtiss & Bird\)\: 'The agreement is good for CH4' \(p\. 680\)\. Reproductions elsewhere\: shelton\_1986\_ch4/table2\_dc\_kerr \(180 \+\- 9 x 10^\-63 C^4 m^4 J^\-3, digit\-identical\), shelton\_1994/table12\_CH4\_dc\_kerr row 'ref 28' \(2887 \+\- 140 au\)\. Not edited here\: lundeen\_1983, ward\_1984 cite this paper's CH4 value too\. The library's validation findings are informational \(figure grouping, page headers\)\. **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\_1969/table1\_A\_K\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_A_K_CH4", "material": "CH4", "file": "CH4/buckingham_1969__table1_A_K_CH4.csv", "table": "tbl_d2bf39485ac8", "quantity": "molar_kerr_constant", "unit": "C2 m5 J-2", "scale": 1e-27, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "relative": 0.05, "level": "not stated" }, "parameters": { "wavelength_nm": 632.8 } } Table 1 \(p\. 675\), METHANE\: A\_K at 249\.7, 273\.6 and 303\.7 K \(8\-30 bar, 18\-20 measurements each\), 632\.8 nm, in S\.I\. units as printed \(C^2 m^5 J^\-2, per mole\)\. No orientation term for CH4\: A\_K = N gamma/81 eps0, so text\_gamma\_CH4 is these values averaged \(fit that one, not both\)\. Uncertainty\: the 'absolute accuracy is \+\-5 % as a result of calibration uncertainties' \(the precision is \+\-2 %\); level not stated\. buckingham\_1969/table1\_B\_K\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_B_K_CH4", "material": "CH4", "file": "CH4/buckingham_1969__table1_B_K_CH4.csv", "table": "tbl_d2bf39485ac8", "quantity": "kerr_virial_coefficient", "unit": "C2 m8 J-2", "scale": 1e-31, "abscissa": "temperature", "abscissa_unit": "K", "use": "check", "uncertainty": { "relative": 0.1, "level": "not stated" }, "parameters": { "wavelength_nm": 632.8, "order": 2 } } Table 1 \(p\. 675\), METHANE\: the second Kerr virial coefficient B\_K \(Eq\. 2\) at 249\.7, 273\.6 and 303\.7 K, in S\.I\. units as printed \(C^2 m^8 J^\-2, per mole squared\)\. 'the precision of B\_K for CH4, CF4 and CH2F2 is \+\-10 %' \(p\. 676; Table 5 prints these as 0\.30 \+\- 0\.03, 0\.28 \+\- 0\.03, 0\.24 \+\- 0\.02\)\. buckingham\_1969/text\_gamma\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_gamma_CH4", "material": "CH4", "table": "text", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-60, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "total", "component": "K" } } 1 inline points in the source record. p\. 677\: '10^60 gamma\(CH4\) = 0\.180 \+\- 0\.009 C^4 m^4 J^\-3' \(2887 \+\- 144 au\), the dc Kerr gamma\_K of CH4 at 632\.8 nm from the temperature\-independent A\_K of Table 1 by Eq\. \(8\)\. A tetrahedral molecule has no orientation term, so gamma is the total dc Kerr response \(electronic plus vibrational\)\. The error is the 5 % absolute accuracy \(calibration\); level not stated\. shelton\_1986\_ch4 finds it about 10 % above the ESHG\-predicted dc Kerr value\. 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.