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 · Catalogue · 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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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

{
  "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 review register for the checks and decisions.