ordal_1985
==========

M\. A\. Ordal, R\. J\. Bell, R\. W\. Alexander, Jr\., L\. L\. Long and M\. R\. Querry, "Optical properties of fourteen metals in the infrared and far infrared\: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W", Appl\. Opt\. 24, 4493\-4499 \(1985\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/ordal_1985.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/AO\.24\.004493 <https://doi.org/10.1364/AO.24.004493>`__

**Source kind:** measurement

**Recorded technique:** Copper \(Table II; also Ni and Fe, not transcribed\)\: the power reflectance measured against an aluminium mirror, corrected for that mirror's absolute reflectance 'using values measured by us'; a Perkin\-Elmer 580 at 180\-4000 cm\-1 and a Varian model 2300 at 4000\-50,000 cm\-1 \(p\. 4494\)\. A Kramers\-Kronig analysis of the reflectance gave n and k, from which epsilon\_1 and epsilon\_2 were calculated\. Wings for Cu\: below 180 cm\-1 a Drude extrapolation to 1 cm\-1 and a constant reflectance below that \(the Table II values\); above, the authors' data to 20,000 cm\-1 \(cut there 'arbitrarily', after 'essentially perfect agreement in the 17,000\-23,000\-cm\-1 range' with Weaver et al\.\), then Weaver et al\.'s data \(Ref\. 2\), then an inverse fourth power of the energy until the reflectance fell to ~4e\-4, then constant \(pp\. 4495\-4496\)\. Drude parameters of fourteen metals \(Table I\) fitted by trial and error \('a trial and error eyeball technique'\) to the compiled and new epsilon, starting from Eqs\. \(12\)\-\(13\) at the lowest frequencies with epsilon\_inf = 1 \(p\. 4494\)\.

**Materials in structured entries:** Ag, Al, Au, Cu

**Dataset quantities:** extinction\_coefficient, permittivity\_imaginary, permittivity\_real, refractive\_index

**Contents:** 4 datasets; 4 formulas.

Curation notes
--------------

Journal pages 4493\-4499 = PDF pages 1\-7\. Page 4499 also carries, below the references, an unrelated NASA Tech Briefs item \('Laser schlieren crystal\-growth imager'\)\. Identity checked against the first page \(the library flags warnings on the bibliographic record only\)\. The paper extends Ordal et al\. 1983 \(ordal\_1983, its Ref\. 1\) and is Ref\. 3 of Ordal et al\. 1988 \(ordal\_1988\)\.

TABLE II, COPPER \(p\. 4495\)\: the authors' own data, 56 wavenumbers 180\-19400 cm\-1 \(55\.6\-0\.517 um\), omega, lambda, \-epsilon\_1, epsilon\_2, n, k to three figures\. n and k are the Kramers\-Kronig result \(use = primary\); epsilon\_1 and epsilon\_2 were calculated from them \(use = check\)\. \-epsilon\_1 is stored as printed with scale = \-1\. lambda stays in printed\. Every row satisfies epsilon\_1 = n^2 \- k^2, epsilon\_2 = 2nk and lambda = 1e4 / omega to the printed rounding \(worst\: epsilon\_2 at 1900 cm\-1, 239 printed against 238\.05, 0\.80 of the rounding bound; checked 2026\-09\-28\)\: no misprint\. The paper says nothing of the copper sample \(bulk or film, preparation, surface\) or the temperature, and gives no uncertainty; its only statement of accuracy is the low\-frequency wing's effect\: 'The use of a Drude model low frequency wing changed the values of the optical constants at 180 cm\-1 by at most 4% relative to the case of a constant wing\. There was a \<1% difference in the optical constants at 500 cm\-1, with the difference becoming correspondingly smaller at higher frequencies' \(p\. 4495\)\. Fig\. 1 plots these data \(solid lines\) with the 1983 compilation's copper blocks \(ordal\_1983\) and the Drude fit\.

TABLE I \(p\. 4494\)\: omega\_tau and omega\_p of the Drude model, Eq\. \(2\), for fourteen metals, printed as 10^\-2 omega\_tau and 10^\-4 omega\_p \(cm\-1\), with the optical resistivity rho\_opt = 60 omega\_tau / omega\_p^2 \(Eq\. 16, ohm cm; printed in micro\-ohm cm\), the handbook dc resistivity rho\_0 \(footnote a\: Ref\. 5, the AIP Handbook, pp\. 9\-39, 9\-40\) and rho\_0 / rho\_opt\. Al, Cu, Au and Ag are the formulas below\. The others \(10^\-2 omega\_tau, 10^\-4 omega\_p, rho\_opt, rho\_0, rho\_0/rho\_opt as printed\)\: Co 2\.95, 3\.20, 17\.3, 5\.80, 0\.34; Fe 1\.47, 3\.30, 8\.10, 9\.80, 1\.20; Pb 16\.3, 5\.94, 27\.7, 21\.0, 0\.76; Mo 4\.12, 6\.02, 6\.82, 5\.33, 0\.78; Ni 3\.52, 3\.94, 13\.3, 7\.04, 0\.52; Pd 1\.24, 4\.40, 3\.84, 10\.55, 2\.8; Pt 5\.58, 4\.15, 19\.4, 10\.42, 0\.54; Ti 3\.82, 2\.03, 55\.6, 43\.1, 0\.78; V 4\.89, 4\.16, 17\.0, 19\.9, 1\.2; W 4\.87, 5\.17, 10\.9, 5\.33, 0\.49\. Against ordal\_1983's Table 13\: 'The Drude model parameters for Cu are revised \.\.\. due to the availability of additional data', Al, Au, Ag and W change slightly \('Refinements in our fitting technique'\), and 'The Drude model parameters for Pb correct a numerical error in our earlier tabulation' \(abstract\)\. The paper also corrects the 1983 paper's Eq\. \(5\) \(epsilon\_inf removed from omega\_p\) and Eq\. \(10\) \(the sign convention of the surface impedance; Eq\. \(10\) here, R\(omega\), is unchanged, so the 1983 numbers stand\)\.

THE OTHER TABLES \(not transcribed; the metals are not registered\)\. Table III, Ni \(p\. 4495, 180\-20000 cm\-1, the authors' data\)\: not extracted by the library \(its caption survives only as a note on Table II\)\. Table IV, Fe \(p\. 4498, tbl\_1b9df4038551, unlabelled in the library; 180\-19200 cm\-1, 56 rows, the authors' data\)\: consistent to the rounding except the last row \(19200 cm\-1\: \-epsilon\_1 2\.08, epsilon\_2 3\.11 printed with n = 5\.36, k = 13\.0, which give 140 and 139; a misprint of the page\)\. Table V, Mo \(tbl\_d6d1e12f21d0, 807\-20200 cm\-1, 24 rows, 'Weaver et al\.', Ref\. 2 p\. 148\)\: 5970 cm\-1 prints \-epsilon\_1 = 69\.7 against k^2 \- n^2 = 67\.9\. Table VI, V \(tbl\_8ff99e8acf56, 807\-53200 cm\-1, 30 rows, Weaver et al\., Ref\. 2 p\. 50\)\: epsilon\_2 at 968 and 1610 cm\-1 is 0\.7 % and 2 % from 2nk, and lambda at 1\.05E\+4 cm\-1 is printed 0\.984 um \(1e4 / omega = 0\.952\)\. The text says Tables II, III and IV are Cu, Fe and Ni; the captions on the page are Cu, Ni and Fe\. Fig\. 9's caption cites 'Ref\. 4\: Johnson and Christy', which is Ref\. 3 \(Ref\. 4 is Moravec et al\.\)\.

FIGURES 1\-9 \(pp\. 4496\-4497\)\: \-epsilon\_1 and epsilon\_2 against omega \(log\-log\) for Cu, Fe, Co, Ni, Pd, Ti, Pt, Mo and V, with the Drude fits of Table I \(dashed\) and the compiled or new data; not digitised\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

ordal\_1985/n\_Cu
~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "n_Cu",
     "material": "Cu",
     "file": "Cu/ordal_1985__n_Cu.csv",
     "table": "tbl_08c9b2542049",
     "quantity": "refractive_index",
     "abscissa_unit": "cm-1",
     "use": "primary",
     "parameters": {
       "technique": "reflectance and Kramers-Kronig analysis"
     }
   }

Table II, p\. 4495\: n of copper, 180\-19400 cm\-1 \(55\.6\-0\.517 um\), 56 rows; the Kramers\-Kronig analysis of the authors' reflectance \(record notes\)\. Sample and temperature not stated\. At 180 cm\-1 the low\-frequency wing's choice moves the values by up to 4 %, below 1 % from 500 cm\-1 \(p\. 4495\)\.

ordal\_1985/k\_Cu
~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "k_Cu",
     "material": "Cu",
     "file": "Cu/ordal_1985__k_Cu.csv",
     "table": "tbl_08c9b2542049",
     "quantity": "extinction_coefficient",
     "abscissa_unit": "cm-1",
     "use": "primary",
     "parameters": {
       "technique": "reflectance and Kramers-Kronig analysis"
     }
   }

Table II, p\. 4495\: k of copper, 180\-19400 cm\-1, 56 rows \(as n\_Cu\)\.

ordal\_1985/eps1\_Cu
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eps1_Cu",
     "material": "Cu",
     "file": "Cu/ordal_1985__eps1_Cu.csv",
     "table": "tbl_08c9b2542049",
     "quantity": "permittivity_real",
     "abscissa_unit": "cm-1",
     "scale": -1,
     "use": "check",
     "parameters": {
       "technique": "reflectance and Kramers-Kronig analysis"
     }
   }

Table II, p\. 4495\: the column headed '\-epsilon\_1', stored as printed with scale = \-1, so the values are epsilon\_1\. 56 rows\. Calculated from n and k \('The Kramers\-Kronig analysis of the reflectance data yielded n and k from which epsilon\_1 and epsilon\_2 were calculated', p\. 4494\)\: a check\.

ordal\_1985/eps2\_Cu
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eps2_Cu",
     "material": "Cu",
     "file": "Cu/ordal_1985__eps2_Cu.csv",
     "table": "tbl_08c9b2542049",
     "quantity": "permittivity_imaginary",
     "abscissa_unit": "cm-1",
     "use": "check",
     "parameters": {
       "technique": "reflectance and Kramers-Kronig analysis"
     }
   }

Table II, p\. 4495\: epsilon\_2, 56 rows, calculated from n and k\: a check\.

Formulas
--------

ordal\_1985/drude\_Al
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "drude_Al",
     "material": "Al",
     "equation": "Eq. (2), p. 4493, with Table I, p. 4494",
     "printed": "epsilon_c = epsilon_inf - omega_p^2 / (omega^2 + i omega omega_tau); Table I, Al: 10^-2 omega_tau (cm-1) 6.60; 10^-4 omega_p (cm-1) 11.9; rho_opt (micro-ohm cm) 2.80; rho_0 2.74; rho_0/rho_opt 0.98",
     "variable": "omega: wavenumber in cm-1; epsilon_inf = 1 ('with epsilon_inf taken to be unity', p. 4494); coefficients as printed under the headers 10^-2 omega_tau and 10^-4 omega_p, so omega_tau = 660 cm-1 and omega_p = 119,000 cm-1",
     "range": "The infrared data of the 1983 compilation (ordal_1983); no range is stated",
     "coefficients": {
       "omega_tau": "6.60",
       "omega_p": "11.9"
     },
     "check": "rho_opt = 60 omega_tau / omega_p^2 = 2.796 micro-ohm cm, printed 2.80. Against ordal_1983's Al blocks: at 313 cm-1, -epsilon_1 = 26,539, epsilon_2 = 55,963 against Bennett and Bennett's 2.60E+04, 5.56E+04 (+2.1 %, +0.7 %); at 1110 cm-1, +1.0 % and +0.6 %; against Shiles et al.'s block 15-40 % off (1050 cm-1: 9,206 + 5,787i against 6.93E+03 + 4.07E+03i). Against ordal_1988's Table I at 1000 cm-1: -9,863 + 6,510i against -7,562.9 + 4,687.1i. Checked 2026-09-28."
   }

The Drude fit ordal\_1988 quotes \(its drude\_ordal\_1985\_Al\)\. It follows Bennett and Bennett's Drude curve \(omega\_tau 663 cm\-1, ordal\_1983\), not Shiles et al\.'s data\.

ordal\_1985/drude\_Cu
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "drude_Cu",
     "material": "Cu",
     "equation": "Eq. (2), p. 4493, with Table I, p. 4494",
     "printed": "epsilon_c = epsilon_inf - omega_p^2 / (omega^2 + i omega omega_tau); Table I, Cu: 10^-2 omega_tau (cm-1) 0.732; 10^-4 omega_p (cm-1) 5.96; rho_opt (micro-ohm cm) 1.24; rho_0 1.70; rho_0/rho_opt 1.3",
     "variable": "omega: wavenumber in cm-1; epsilon_inf = 1; coefficients as printed under the headers 10^-2 omega_tau and 10^-4 omega_p, so omega_tau = 73.2 cm-1 and omega_p = 59,600 cm-1",
     "range": "Fitted to the lowest frequencies of Table II (from 180 cm-1); no range is stated",
     "coefficients": {
       "omega_tau": "0.732",
       "omega_p": "5.96"
     },
     "check": "rho_opt = 1.236 micro-ohm cm, printed 1.24 (rho_0/rho_opt = 1.37, printed 1.3). Against Table II: at 180 cm-1, -epsilon_1 = 94,080, epsilon_2 = 38,260 against 9.40E+4, 3.83E+4 (+0.1 %, -0.1 %); at 500 cm-1 +7 % and -45 %; at 1000 cm-1 -9 % and -75 %; epsilon_2 falls further below the data at higher omega (-91 % at 5000 cm-1), as Fig. 1 shows. Checked 2026-09-28."
   }

Revised from ordal\_1983/drude\_Cu \(278, 63,800\) with the new data of Table II\.

ordal\_1985/drude\_Au
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "drude_Au",
     "material": "Au",
     "equation": "Eq. (2), p. 4493, with Table I, p. 4494",
     "printed": "epsilon_c = epsilon_inf - omega_p^2 / (omega^2 + i omega omega_tau); Table I, Au: 10^-2 omega_tau (cm-1) 2.15; 10^-4 omega_p (cm-1) 7.28; rho_opt (micro-ohm cm) 2.43; rho_0 2.20; rho_0/rho_opt 0.91",
     "variable": "omega: wavenumber in cm-1; epsilon_inf = 1; coefficients as printed under the headers 10^-2 omega_tau and 10^-4 omega_p, so omega_tau = 215 cm-1 and omega_p = 72,800 cm-1",
     "range": "The infrared data of the 1983 compilation (ordal_1983); no range is stated",
     "coefficients": {
       "omega_tau": "2.15",
       "omega_p": "7.28"
     },
     "check": "rho_opt = 2.434 micro-ohm cm, printed 2.43. Against ordal_1983's gold blocks: Bennett and Bennett's at 313 and 1000 cm-1 to -0.4/-0.6 % and +0.3/-0.1 % (-epsilon_1/epsilon_2); Brandli and Sievers's at 31.4 cm-1 +30 %/+23 % and at 100 cm-1 -11 %/+5 %. Checked 2026-09-28."
   }

A slight refinement of ordal\_1983/drude\_Au \(216, 72,500\)\.

ordal\_1985/drude\_Ag
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "drude_Ag",
     "material": "Ag",
     "equation": "Eq. (2), p. 4493, with Table I, p. 4494",
     "printed": "epsilon_c = epsilon_inf - omega_p^2 / (omega^2 + i omega omega_tau); Table I, Ag: 10^-2 omega_tau (cm-1) 1.45; 10^-4 omega_p (cm-1) 7.27; rho_opt (micro-ohm cm) 1.65; rho_0 1.61; rho_0/rho_opt 0.98",
     "variable": "omega: wavenumber in cm-1; epsilon_inf = 1; coefficients as printed under the headers 10^-2 omega_tau and 10^-4 omega_p, so omega_tau = 145 cm-1 and omega_p = 72,700 cm-1",
     "range": "The infrared data of the 1983 compilation (ordal_1983); no range is stated",
     "coefficients": {
       "omega_tau": "1.45",
       "omega_p": "7.27"
     },
     "check": "rho_opt = 1.646 micro-ohm cm, printed 1.65. Against ordal_1983's silver blocks: Bennett and Bennett's at 313 and 1000 cm-1 to 0.0/-0.1 % and +0.7/+0.2 % (-epsilon_1/epsilon_2); Hagemann et al.'s epsilon_2 lies 21 % (807 cm-1) to 52 % (4030 cm-1) above it. Checked 2026-09-28."
   }

A slight refinement of ordal\_1983/drude\_Ag \(145, 72,500\)\.

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 </register>` for the checks and decisions.