shiles_1980#
E. Shiles, T. Sasaki, M. Inokuti and D. Y. Smith, “Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: Applications to aluminum”, Phys. Rev. B 22, 1612-1628 (1980)
Source record · Catalogue · Review register
Source kind: compilation
Recorded technique: An iterative, self-consistent Kramers-Kronig analysis of published optical data on metallic aluminium at room temperature, 0.04-10000 eV, with the reflectance R as the starting function (Sec. II): measured R below the plasma energy; above it, R from measured extinction coefficients and trial n (Eq. 2.1); the phase by the subtracted Jahoda-Velicky relation (Eq. 3.1), evaluated at 506 energies from 0.04 to 10000 eV (trapezoidal rule over 0.038-11000 eV, analytic fits outside); n, kappa, epsilon_1, epsilon_2 from R and the phase (Eqs. 3.2-3.5); iterated (‘one or two full iterations’, reproducing the input to better than 0.5 %). The result tested by sum rules: the inertial rule for n, the dc-conductivity rule, the f-sum rules for epsilon_2, kappa and Im(1/epsilon), partial f sums per shell, and the mean excitation energy I. The measured kappa above the L edge was then reduced ad hoc by 14 % to satisfy the f-sum rule (Sec. V C).
Materials in structured entries: None recorded.
Dataset quantities: None recorded.
Contents: 0 datasets; 0 formulas.
Curation notes#
Journal pages 1612-1628 = PDF pages 1-17. Identity checked against the first page (the library flags warnings on the bibliographic record only). Nothing is extracted: the paper prints its optical functions only as figures, and its three tables hold quantities the vocabulary does not have (plasmon energy and width, effective electron numbers, mean excitation energy): notes only.
THE TABULATION IS ELSEWHERE (REF. 12). ‘A critical review of available experimental data and a full tabulation of our recommended values for the optical constants will be given elsewhere.12’ (p. 1613); ‘a tabular presentation will be given elsewhere.12’ (p. 1617). Ref. 12 is printed ‘E. Shiles and D. Y. Smith (unpublished).’ The tabulation appeared in J. H. Weaver, C. Krafka, D. W. Lynch and E. E. Koch, Optical Properties of Metals, Physics Data 18-2 (Fachinformationszentrum Karlsruhe, 1981), pp. 79-86: ‘Aluminum. [...] publication by E. Shiles, T. Sasaki, M. Inokuti, and D.Y. Smith in Phys. Rev. B 22, 1612 (1980) based on the following tabulation’, Energy (eV), epsilon_1, epsilon_2, n, k, Im(-1/epsilon), R(phi = 0), 0.040-1551 eV, three decimals (R four) (in the library since 2026-09-28 and curated as weaver_1981’s n_Al, k_Al, eps1_Al and eps2_Al, TC-638). Rakic (rakic_1995, Ref. 27) cites it as ‘tabulated in’ D. Y. Smith, E. Shiles and M. Inokuti, ‘The optical properties of metallic aluminum’, in Handbook of Optical Constants of Solids, ed. E. D. Palik (Academic, Orlando, 1985), pp. 369-408 (not in the library, and not needed: listed as missing only as the second printing).
DATA SOURCES BY RANGE (Sec. III A, pp. 1614-1616; Figs. 1-3, 8). Below 0.04 eV (0.0517 eV): a free-electron-model fit to Bennett, Silver and Ashley’s reflectance at 0.0517 eV (24 um) (footnote 33: from 0.0517 to 0.124 eV the free-electron fit is reasonable; below 0.0517 eV the measured R rises slightly faster, ~0.002 %). 0.0517-3.00 eV: Bennett, Silver and Ashley and Bennett and Bennett (UHV films, ~1e-10 torr); 3.00-11.75 eV: Endriz and Spicer (the smoothest film, free of surface-plasmon absorption, Fig. 3); between them a smooth interpolation from 1.66 to 3.0 eV, choosing the highest reflectances (no secondary structure assumed near 2 eV, on the weight of Bos and Lynch’s and Rosei and Lynch’s data); Mathewson and Myers’s UHV ellipsometry (0.7-2.5 eV) agrees and was kept as an independent check, not input. 11.75-18 eV: estimated, guided by electron-energy-loss spectra (Sec. IV; of four trial curves only curve d gives the loss peak at ~15.0 eV with ~0.5 eV width, Figs. 7-8). 15-30 eV: R computed from measured n and kappa (Ditchburn and Freeman; Daude, Savary, Jezequel and Robin; Madden, Canfield and Hass; Hunter). 30-4000 eV: Sasaki and Inokuti’s R (from experimental kappa, a composite listed in footnote 51: Lukirskii et al., Haensel et al., Gahwiller and Brown, Fomichev et al. ...). 4000-10000 eV: the same, supplemented by Henke and Elgin, Henke and Ebisu, Singman, Lublin et al., Hubbell et al. and Davisson’s photoelectric cross sections. Above 10000 eV: R proportional to omega^-4 (kappa ~ omega^-4 for the f sums, footnote 86). Soft-x-ray angular-reflectance determinations were not used. The L-shell absorption begins at 72.7 eV (72.65 eV), the K shell at 1557 eV.
THE 14 % REDUCTION (Sec. V C, pp. 1620-1622; Fig. 9; Table II). With the reported data all three f sums reach 14.08 instead of 13 electrons/atom; the partial sums place the excess in the L shell (9.3(5) against 8.3(3) from Hartree-Fock-Slater theory), which the paper attributes to surface (oxide) layers on the evaporated thin-film transmission samples (at 525 eV foils give kappa 10 % below films; Balzarotti et al. find ~15 % below). The ‘modified’ data: kappa reduced by 14 % from the L edge to 300 eV, then by a percentage falling linearly from 14 % at 300 eV to zero at 500 eV, chosen to satisfy both the f sum and the measured mean excitation energy (a 13.5 % reduction to 400 eV, tapering to 700 eV, also gives 13 electrons but I several eV lower). The change in n is small except near its 12 eV minimum, where n falls from 0.0353 to 0.0328 (Fig. 5 caption, p. 1617).
ELECTRON DENSITY AND COUNTS. The f-sum rules use Omega_p^2 = 4 pi N e^2/m with N the total electron density (13 electrons/atom); the paper prints no number for N, the atom density or the mass density (p. 1623 remarks only that evaporated films frequently have a lower density than bulk, which would make an interferometric-thickness absorption coefficient too low, the opposite of the excess found). Conduction electrons: n_eff,c = 3.1(1) e/atom with the core background epsilon_b = 1.04 (Eqs. 5.10-5.12, p. 1621), revised to 1.03(5) after the reduction (p. 1623); the conduction-electron plasma frequency omega_p,c^2 = 4 pi n_eff,c e^2/m.
SUM RULES AND OTHER TEXT VALUES. Inertial rule for n: zeta ~ -0.002 (Eq. 5.2; below 0.005 counts as consistent; Sasaki and Inokuti’s preliminary data gave 0.17; p. 1620). dc-conductivity rule (Eq. 5.3): sigma_0 = 3.21e17 s^-1 (esu), 2.80 uOhm cm, against 3.18e17 (2.83) and 3.28e17 s^-1 (2.74 uOhm cm) measured (p. 1620).
TABLE I (p. 1619, tbl_ba0e6952f3d5; image checked): bulk-plasmon peak energy omega_p and FWHM Delta E_1/2 (eV). Calculated, present composite: 15.0(5), 0.54(5). Experimental: Gibbons et al. (1976) 15.02 +- 0.03, 0.54 +- 0.03; Urner-Wille and Raether (1976) 15.1 +- 0.1; Petri and Otto (1975) 14.5 +- 0.15; Kloos (1973) 14.95 +- 0.05, 0.5 +- 0.05; Zacharias (1972) 14.95 +- 0.06, 0.52 +- 0.05; Geiger and Wittmaack (1966) 14.97 +- 0.02, 0.60 +- 0.02.
TABLE II (p. 1622, tbl_16d59c7b7d67; image checked): effective number of electrons n_eff(omega)|_epsilon per shell: occupation; ‘raw’ data; modified data; HFS theory. Conduction (3s^2, 3p): 3; 3.1(1); 3.1(1); 3.12. L shell (2s^2, 2p^6): 8; 9.3(5); 8.2(7); 8.33. K shell (1s^2): 2; 1.6(1); 1.6(1); 1.55. Total: 13; 14.0(8); 12.9(9); 13.00.
TABLE III (p. 1624, tbl_1a9cf773be76; image checked): mean excitation energy I (eV). Present work, unmodified epsilon data 165.6(7); modified 165.7(1); atomic oscillator strength (theory, Dehmer, Inokuti and Saxon) 124; experimental: Bichsel and Uehling (1960), Turner et al. (1970) 163; Tschalar and Bichsel 167. The part of I above 10 keV is 3.1 eV, uncertain by much less than 1 eV (footnote 108).
AGAINST HAGEMANN, GUDAT AND KUNZ (HGK, DESY SR-74/7; Sec. VI C, p. 1625): HGK’s kappa is very similar to the unmodified kappa here except below ~0.1 eV, where it is 10-20 % higher; HGK’s n exceeds this work’s below 0.08 eV and is smaller ‘by a factor of 2/3 over most of the region from 0.08 to 1.5 eV’, in ‘significant disagreement with direct measurements of n’; HGK’s f sums are 13.4, 13.6 and 13.6 (epsilon_2, kappa, Im 1/epsilon), and their n_eff|epsilon_2 falls below n_eff|kappa from 10 eV to the L edge (an inconsistency below 10 eV). Sasaki and Inokuti’s n has spurious structure at 6-12 eV (residual surface plasmon) (p. 1625).
FIGURES (not digitised): Figs. 1-3 R (the input); Fig. 4 the phase; Fig. 5 n; Fig. 6 kappa, with the measurements; Fig. 7 loss functions of the trial R curves; Fig. 8 R near the plasmon; Fig. 9 n_eff; Fig. 10 the cumulative I.
WHO USES THESE DATA. ordal_1988’s Table I rests on Shiles et al.’s optical constants (Weaver et al.’s compilation) from 320 cm-1 up, through its own Kramers-Kronig analysis (not a reprint of values); rakic_1995 took Shiles et al.’s kappa (Palik’s Handbook) as its input above 14.94 eV; franta_2013 and franta_2013b quote this paper’s sum-rule values. No curated record reprints tabulated values of this paper.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
No datasets are recorded.
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.