buckingham_1968#

A. D. Buckingham and D. A. Dunmur, Trans. Faraday Soc. 64, 1776 (1968)

Source record · Catalogue · Review register

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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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#

{
  "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 review register for the checks and decisions.