Pt, Ag, Ti, and W in the infrared and far infrared - MURI...

Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd,Pt, Ag, Ti, and W in the infrared and far infrared

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward

Infrared optical constants collected from the literature are tabulated. The data for the noble metals andAl, Pb, and W can be reasonably fit using the Drude model. It is shown that -El(W) = E2(W) 2/(2w') at

the damping frequency c = c,. Also -El(w T) _ - (1/2) el(0), where the plasma frequency is op.

1. Introduction

Many measurements of the optical constants ofmetals have been made, primarily at near IR, visible,and UV wavelengths. Brandli and Sievers' havemeasured Au and Pb in the far IR. For the near and farIR we have compiled these data and have tabulated thereal and imaginary parts of the dielectric function, Eland e2, respectively, the index of refraction n and theextinction index k for each metal. Drude model2 pa-rameters giving a reasonable fit to the data are given forAu, Ag, Cu, Al, Pb, and W. In general, the Drude modelis not expected to be appropriate for transition metalsin the near and middle IR, but a good fit can be obtainedfor W with a Drude model dielectric function.

Weaver et al. 3 have compiled extensive tables oroptical properties of metals which have been recentlypublished. Most of their tables do not extend beyond12-yum wavelength, while our compilation extends to thelongest wavelength for which data are available. An-other standard compilation is that of Haas and Hadleyin the AMERICAN INSTITUTE OF PHYSICSHANDBOOK. 4 However, this includes data only upto 1967. Except for a few cases, the data presented hereare more recent.

Bennett and Bennett5 have shown that the Drudemodel fits the measured reflectance of gold, silver, andaluminum in the 3-30-/Im wavelength range with one

adjustable parameter; i.e., the Drude model parameterswere obtained from the dc resistivity and fitted with onefree electron per atom for gold and silver and 2.6 freeelectrons per atom for aluminum. Brandli and Sievershave shown that the Drude model is an excellent fit totheir far IR measurements on lead and provides a goodfit for gold with no adjustable parameters.

11. Definitions and Equations

In keeping with IR spectroscopic notation, allfrequencies will be expressed in cm-1 . The complexdielectric function es and the complex index of refrac-tion n, are defined as

(1)EC -el + ie2 n (n + ik)2 .

The Drude model dielectric function is2

C = E- - 2 . I

(1 + I co w T

where c, cop, and '-v, have units of cm-'. Separating thereal and imaginary parts yields

(3)

(4)

W2

el = E-co 2

2= ++ U2

In these equations, the plasma frequency6 is1 47rNe 2

1/2

,(cm-l) = _2rc me (5)

(2)

When this work was done all authors were with University of Mis-souri-Rolla, Physics Department, Rolla, Missouri 65401; C. A. W.Krebs is now with McDonnell Douglas Astronautics Company,Electrooptic Technology, P.O. Box 516, St. Louis Missouri 63166; S.E. Bell and R. R. Bell are now at Route 4, Box 124, Rolla, Missouri65401.

Received 12 October 1982.0003-6935/83/071099-21$01.00/0.© 1983 Optical Society of America.

where N is the free electron density, e is the electroncharge, m * is the effective mass of the electrons, and e-

is the high frequency dielectric constant. The dampingfrequency w expressed in cm-, is

W (Cm-l) = 1 27rc T

(6)

where r is the electron lifetime in seconds and c is thevelocity of light. Note that for low frequencies

1 April 1983 / Vol. 22, No. 7 / APPLIED OPTICS 1099

105

14)N

Z

In

102

101

100102 103

FREQUENC.W (CM'1)

106

105

14)

ZInkV

102

101

100105

Fig. 1. Aluminum: -el(w) and 2(M) vs frequency. The solid lineis the Drude model. The data from Ref. 7 are: Shiles et al., o forboth -el and 2; Bennett and Bennett * for -El and 2; Schulz, 0 for

-el and 2-

10100 l2 103

FREQUENCY, W (CM')

00 102 103

FREQUENCY, W (CM'l

Fig. 3. Gold: -e,(w) and e2(W) vs frequency. The solid line is theDrude model. The data from Ref. 9 are: Bennett and Bennett, *for both -el and e2; Schulz, 0 for both; Motulevich and Shubin, forboth; Padalka and Shklyarevskii, 0 for both; Bolotin et al., x for both;

Brandli and Sievers, + for both; Weaver et al., A for both.

104

I nL

Z 3a: 10tv

10'

104 105

Fig. 2. Copper: -el(W) and 2(O) vs frequency. The solid line isthe Drude model. The data from Ref. 8 are: Schulz, 0 for both -eland 2; Lenham and Treherne, * for -el and 2; Robusto andBraunstein, o3 for both; Hageman et al., X for both; and Dold and

Mecke, A for both.

10a102 103

FREQUENCY, W (CM1)

Fig. 4. Lead: -e l(w) and e2(u) vs frequency. The solid line rep-resents the Drude model. The data from Ref. 10 are: Brandli andSievers, x for -el and + for 2; and Golovashkin and Motulevich, A

for -el and oI for 2-

1100 APPLIED OPTICS / Vol. 22, No. 7 / 1 April 1983

106

105

14)

C3Z 3a: 10

W(I

101

ino

105

105

14

r-In

10' SILVER

xx

100 o 0 11 5

10 10I 102 10 10

FREQUENCY,W (CM']

Fig. 5. Silver: -l(co) and E2(0) vs frequency. The solid line is theDrude model. The data from Ref. 11 are: Bennett and Bennett, *for both -el and e2; Schulz, 0 for both; and Hagemann et al., X for

both.

10L1

1 03

14)1

MM 2a: 10

101

1001o'

I I I I I

+ -E

+x

2 ExIn,

A +

A+

XMEn

xooA A.W0A

,< 4, , I A

0 D

X 40

COBRLT 0101

4,

1 1 1 I I I~~~~~~~~~~~~~4

103 104

FREQUENCT, W (CM')

104

14)

InZ 2

a: 10

14)

10I

100t02

3 103 104

FREQUENCT,W (CMI)

105

Fig. 7. Iron: -el(w) and f2() vs frequency. The data from Ref.13 are: Weaver et al., X for -El and A for E2; Bolotin et al., 0 for-El

and 0 for f2-

103

14)

In

za: 102

10'

100105

Fig. 6. Colbalt: -el(c) and 2(M) vs frequency. The data from Ref.12 are: Kirillova and Charikov, + for -el and 0 for e2; Johnson andChristy, 0 for -el and 0 for 42; and Weaver et al, x for -el and A for

e2.

105103 104

FREQUENCY. W (CM')

Fig. 8. Nickel: -el(co) and 42(W) vs frequency. The data from Ref.14 are: Lynch et al., X for-c and A for E2; Johnson and Christy, 0

for -el and 0 for 2-


0'&x

O 0AX

ox

it A

°x

XAOA

4,-X

IRONX

X

x

x _-Ex I

A X

A X

A x

-E x2 A"

X

A,

A

X

X0 a

NICKEL

. . . . . .

16I I I

t2

1011 i101 I I

-4

I n

2 4,0

-E2 ,C+ ,,+

+ 0 xA

In + 0

In

_ x **

PRLLRDIUM AxX.&

x

I I I I I I

103 104

FREQUENCT, W (CM')

c~14J

2J _

10

10 5 102 103 104 105

FREQUENCY,W (CM'I)

Fig. 9. Palladium: -(W) and 42(C) vs frequency. The data fromRef. 15 are: Weaver and Benbow, 0 for -el and 0 for 2; Bolotin etal., + for -el and for 2; Johnson and Christy, X for -el and A for

42.

14)

10'

10 0 3

103 104

FREQUENCT, W (CM )

Fig. 11. Titanium: -el(w) and 42(W) vs frequency. The data fromRef. 17 are: Kirillova and Charikov, for both -el and 2; Lynch etal., A for both; Johnson and Christy, 0 for both; Kirillova and

Charikov, + for both; Bolotin et al., X for both.

106

105

104

14

In

102

100

10010O

Fig. 10. Platinum: -(co) and 42(W) vs frequency. The data fromRef. 16 are Weaver et al., A for -el and 03 for 42.

lOu 102 103

FREQUENCY, W (CMI)

Fig. 12. Tungsten: -l(w) and 42(W) vs frequency. The solid lineis the Drude model. The data from Ref. 18 are: Nomerovannaya et

al., 03 for both -el and 42; Weaver et al., A for both.


z 102

10'

1001o'

7- -- ,_. I I I I I I

A _EIn

A A

IA_ A

-E2 n AIn

In

A A

BMmaA

A

. ~ ~~~~ I

A

PLRTINUM

. .

-

104 104

103

1.

14

TABLE 1. Al, ALUMINUME. Shiles, T. Sasaki, M.(1980)

w(cm-')

3.23E+023.39E+023.71E+024.03E+024.36E+024.68E+025.OOE+025.32E+025.81E+026.45E+027. 10E+027.74E+028.87E+021.05E+031.21E+031.37E+031.61E+032.02E+032.42E+032.82E+033.23E+034.84E+036.45E+038.07E+031.21E+041.61E+04

x(Pm)

3. 10E+Ol 2.95E+O 2.70E+O12.48E+Ol 2.30E+O 12. 14E+12.OOE+O 1.88E+Ol1.72E+O11.55E+O 11.41E+O11.29E+O 11. 13E+O 9.54E+OO8.27E+OO7.29E+OO6.20E+OO4.96E+OO4. 13E+O3.54E+O3. 10E+OO2.07E+OO1.55E+OO1.24E+OO8.27E-Ol 6.20E-Ol

Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612

- 1

3. 18E+043.0 1E+042.68E+042.43E+042.14E+041.95E+041.80E+041.66E+041.50E+041.32E+041. 18E+041.05E+048.77E+036.93E+035.58E+034.51E+033.39E+032.25E+031.63E+031.24E+039.71E+024.53E+022.52E+021.54E+026. 15E+O15.42E+O 1

42

4.02E+043.62E+043.03E+042.59E+042.24E+042.0 1E+041.79E+041.60E+041.38E+041. 13E+049.49E+037.89E+035.94E+034.07E+032.86E+032.05E+031.39E+038.28E+025.54E+023.87E+022.80E+029. 73E+O 14.61E+O 3.02E+O 4.56E+O 11 .95E+O l

n

9.86E+O 19.22E+O 18.26E+O17.50E+O 6.93E+Ol 6.52E+O 6.07E+O 15.67E+O15.20E+O 4.58E+Ol 4.09E+O 3.62E+Ol 3.02E+O I2.35E+O 1.86E+O I1.49E+O 1. 17E+O I8.59E+OO6.76E+OO5.44E+OO4.45E+OO2.27E+OO1.44E+OO1.21E+OO2.75E+OO1.30E+OO

K

2.04E+021.96E+021.83E+021.73E+021.62E+021.54E+021.47E+021.41E+021.33E+021.24E+021.16E+021.09E+029.84E+O18.65E+O I7.70E+O 16.BBE+O 15.94E+OI4.82E+O 14. 10E+Ol 3.56E+O 13. 15E+O12. 14E+O11.60E+O11.25E+Ol 8.31E+OO7.48E+oo

TABLE 1. Al, ALUMINUM (Continued)H. E. Bennett and J. M. Bennett, Optical Properties and ElectronicsStructure of Metals and Alloys, ed. F. Abeles (North-Holland, 1966),p. 175.

Wo cm-1)

3. 13E+023.23E+023.33E+023.45E+023.57E+023.70E+023.85E+024.OOE+024. 17E+024.35E+024.55E+O024.76E+025.OOE+025.26E+025.56E+025.88E+ 026.25E+026.67E+027.14E+027.69E+028.33E+029.09E+021.00E+031. 1 1E+031.25E+03

X(I'm)

3.20E+ 13. 10E+013.OOE+O I2.90E+ 12.80E+O12.70E+O 12.60E+O 12.50E+O I2.40E+O12.30E+O 12.20E+O 12. 10E+012.OOE+O11.90E+O11.80E+O 11.70E+011.60E+011.50E+011.40E+011.30E+011.20E+O11. 10E+0 I1.OOE+019.00E+008.00E+00

- 1

2.60E+042.58E+042.56E+042.54E+042.47E+042.45E+042.38E+042.36E+042.3 1E+042.25E+042.19E+042. 1OE+042.05E+041.96E+041.88E+041.80E+041.69E+041.58E+041.47E+041.37E+ 041.24E+041. 10E+049.84E+038.4 1E+037.02E+03

42

5.56E+045.3 1E+045.08E+044.84E+044.59E+044.36E+044. 12E+043.91E+043.64E+043.42E+043.18E+042.93E+042.7 1E+042.47E+042.24E+042.02E+041.79E+041.58E+ 041.37E+041. 18E+049.88E+038.06E+036.49E+035.02E+033.72E+03

n

1.33E+021.29E+021.25E+021.21E+021. 17E+021. 13E+021.09E+021.05E+021.00E+02

9.60E+O 19. 15E+018.68E+0 18.2 IE+O 17.73E+0 17.24E+0 16.74E+0 16.23E+ 015.71E+O 15. 19E+014.67E+0 14. 15E+O13.63E+013. 12E+012.63E+O 12. 15E+0 1

P.

2.09E+022.06E+022.03E+022.OOE+021.96E+021.93E+021.89E+021.86E+021.82E+021.78E+021.74E+021.69E+021.65E+021.60E+021.55E+021.50E+021.44E+021.38E+021.32E+021.26E+021. 19E+021. 1 1E+021.04E+029.54E+ 018.65E+0 I


TABLE 1. Al, ALLUINUM (Continued)L. . Schulz, J. Opt. Soc. Am. 44, 357 (1954) and 362 (1954).

((cm-l) (I'm) -41 s2 n k

1.05E+04 9.50E-01 6.92E+01 2.98E+01 1.75E+00 8.50E+OOl.1lE+04 9.OOE-01 5.54E+01 3.02E+01 1.96E+00 7.70E+OO1.18E+04 8.50E-01 4.68E+01 2.97E+01 2.08E+00 7.15E+001.25E+04 8.00E-01 4.57E+01 2.81E+01 1.99E+00 7.05E+OO1.33E+04 7.50E-01 4.75E+01 2.56E+01 1.80E+00 7.12E+OO1.43E+04 7.OOE-01 4.66E+01 2.17E+01 1.55E+00 7.OOE+OO1.54E+04 6.50E-01 4.20E+01 1.64E+01 1.24E+00 6.60E+OO1.67E+04 6.OOE-01 3.51E+01 1.16E+01 9.70E-01 6.OOE+OO1.82E+04 5.50E-01 2.77E+01 8.09E+00 7.60E-01 5.32E+OO2.OOE+04 5.OOE-01 2.27E+01 5.95E+00 6.20E-01 4.80E+OO2.22E+04 4.50E-01 1.84E+01 4.23E+00 4.90E-01 4.32E+OO2.50E+04 4.OOE-01 1.52E+01 3.14E+00 4.OOE-01 3.92E+OO

TABLE 2. Cu, COPPERL. G. Schulz, J. Opt. Am. 44, 357 and 362 (1954).

((cm-') )(Um) -S1 42 n k

1.05E+04 9.50E-01 3.87E+01 1.62E+00 1.30E-01 6.22E+OO1.1lE+04 9.OOE-01 3.43E+01 1.52E+00 1.30E-01 5.86E+OO1.18E+04 8.50E-01 2.99E+01 1.31E+00 1.20E-01 5.47E+OO1.25E+04 8.00E-01 2.57E+01 1.22E+00 1;20E-01 5.07E+OO1.33E+04 7.50E-01 2.13E+O1 1.11E+OO 1.20E-01 4.62E+OO1.43E+04 7.OOE-01 1.74E+O1 1.OOE+OO 1.20E-01 4.17E+OO1.54E+04 6.50E-01 1.33E+01 9.49E-01 1.30E-01 3.65E+OO1.67E+04 6.OOE-01 9.40E+00 1.04E+00 1.70E-01 3.07E+OO1.82E+04 5.50E-01 5.34E+00 3.48E+00 7.20E-01 2.42E+OO2.OOE+04 5.OOE-O1 5.08E+00 4.26E+00 8.80E-01 2.42E+OO2.22E+04 4.50E-01 4.08E+00 3.83E+00 8.70E-01 2.20E+OO

TABLE 2. Cu, COPPER (Continued)A. P. Lnham and D. M. Treherne, J. Opt. Soc. Am. 56, 683 (1966).

(cm-') (lAm) -41 42 n P

5.OOE+02 2.OOE+01 1.35E+04 7.61E+03 3.16E+01 1.20E+025.56E+02 1.80E+01 1.15E+04 6.IIE+03 2.76E+OI 1.1lE+026.25E+02 1.60E+01 9.OOE+03 4.64E+03 2.37E+01 9.78E+Ol7.14E+02 1.40E+01 6.80E+03 3.36E+03 1.98E+01 8.48E+O18.33E+02 1.20E+O1 5.05E+03 2.29E+03 1.57E+01 7.28E+O11.OOE+03 I.OOE+O1 3.50E+03 1.40E+03 1.16E+01 6.03E+Ol1.25E+03 8.00E+00 2.20E+03 7.28E+02 7.66E+00 4.7SE+O11.67E+03 6.OOE+00 1.30E+03 3.24E+02 4.46E+00 3.63E+O12.OOE+03 5.OOE+OO l.OOE+03 1.40E+02 2.21E+00 3.17E+O12.50E+03 4.00E+00 6.22E+02 8.80E+OI 1.76E+00 2.SOE+O1

TABLE 2. Cu, Copper (Continued)P. F. Robusto and Braunstein, Phys. Stat. Sol. (b) 107, 443 (1981).

w(cm-1) %(lm) -41 42 n I

1.56E+04 6.40E-01 7.69E+00 1.70E+00 3.04E-01 2.79E+OO1.67E+04 6.OOE-01 5.98E+00 1.70E+00 3.44E-01 2.47E+OO1.79E+04 5.60E-01 4.09E+00 2.20E+00 5.26E-01 2.09E+OO1.92E+04 5.20E-01 3.71E+00 6.99E+00 1.45E+00 2.41E+OO2.08E+04 4.80E-01 3.10E+00 7.01E+00 1.51E+00 2.32E+OO2.27E+04 4.40E-01 2.39E+00 6.79E+00 1.55E+00 2.19E+OO2.50E+04 4.OOE-01 1.81E+00 5.92E+00 1.48E+00 2.OOE+OO


TABLE 2. Cu, COPPER (Continued)H. J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 6, 742 (1975).

w(cm-1) -4 1 42 n IC

8.07E+02 1.24E+01 4.24E+03 4.25E+03 2.97E+01 7.16E+O14.03E+03 2.48E+00 3.08E+02 6.03E+01 1.71E+00 1.76E+O18.07E+03 1.24E+00 7.17E+01 7.46E+00 4.40E-01 8.48E+OO1.21E+04 8.27E-01 2.76E+01 2.74E+00 2.60E-01 5.26E+OO1.37E+04 7.29E-01 1.96E+01 1.95E+00 2.20E-01 4.43E+OO1.41E+04 7.OE-01 1.80E+01 1.79E+00 2.10E-01 4.25E+OO1.45E+04 6.89E-01 1.63E+01 1.70E+00 2.10E-01 4.04E+OO1,49E+04 6.70E-01 1.48E+01 1.69E+00 2.20E-01 3.85E+OO1.S3E+04 6.53E-01 1.34E+01 1.54E+00 2.10E-01 3.67E+OO1.61E+04 6.20E-01 1.04E+01 1.75E+00 2.70E-01 3.24E+00

TABLE 2. Cu, COPPER (Continued)B. Dold and R. Mecke, Optik 22, 435 (1965).

w(cm-l) x(lLm) -41 42 n k

1.OOE+03 1.OOE+O1 2.27E+03 1.14E+03 1.16E+01 4.90E+O11.llE+03 9.OOE+00 1.99E+03 9.05E+02 9.90E+00 4.57E+O11.25E+03 8.OOE+00 1.66E+03 6.72E+02 8.10E+00 4.15E+O11.43E+03 7.OOE+00 1.31E+03 4.71E+02 6.40E+00 3.68E+O11.67E+03 6.OOE+00 9.99E+02 3.17E+02 4.95E+00 3.20E+O12.OOE+03 5.OOE+00 6.95E+02 1.92E+02 3.60E+00 2.66E+O12.50E+03 4.OOE+00 4.56E+02 1.05E+02 2.45E+00 2.15E+O13.33E+03 3.OOE+00 2.54E+02 4.80E+O1 l.50E+OO 1.60E+O15.OOE+03 2.OOE+00 1.12E+02 1.80E+01 8.50E-01 1.06E+O16.67E+03 1.SOE+OO 6.37E+01 9.28E+00 5.80E-01 8.OOE+OO8.00E+03 1.25E+00 4.46E+01 6.57E+00 4.90E-01 6.70E+OO

TABLE 3. Au, GOLDH. E. Bennett and J. M. Bennett, Optical Properties and ElectronicStructure of Metals and Alloys edited by F. Abeles (North-Holland,Amsterdam, 1966), p. 175.

W(cm-1) )(I'm) -41 42 n I

3.13E+02 3.20E+01 3.69E+04 2.54E+04 6.28E+01 2.02E+023.33E+02 3.OOE+01 3.37E+04 2.17E+04 5.66E+01 1.92E+023.57E+02 2.80E+01 3.06E+04 1.84E+04 5.05E+01 1.82E+023.85E+02 2.60E+01 2.73E+04 1.53E+04 4.46E+01 1.71E+024.17E+02 2.40E+01 2.41E+04 1.24E+04 3.89E+01 1.60E+024.55E+02 2.20E+01 2.08E+04 9.89E+03 3.34E+01 1.48E+025.OOE+02 2.OOE+01 1.77E+04 7.67E+03 2.82E+01 1.36E+025.56E+02 1.80E+01 1.48E+04 5.78E+03 2.33E+01 1.24E+026.25E+02 1.60E+01 1.22E+04 4.19E+03 1.87E+01 1.12E+027.14E+02 1.40E+01 9.51E+03 2.86E+03 1.45E+01 9.86E+O18.33E+02 1.20E+01 7.14E+03 1.84E+03 1.08E+01 8.52E+O1l.OOE+03 l.OOE+Ol 5.05E+03 1.09E+03 7.62E+00 7.15E+O11.25E+03 8.00E+00 3.29E+03 5.68E+02 4.93E+00 5.76E+O11.43E+03 7.OOE+00 2.54E+03 3.83E+02 3.79E+00 5.05E+Ol1.67E+03 6.OOE+00 1.88E+03 2.42E+02 2.79E+00 4.34E+Ol2.OOE+03 5.OOE+OO 1.31E+03 1.41E+02 1.95E+00 3.62E+O12.50E+03 4.OOE+00 8.39E+02 7.25E+01 1.25E+00 2.90E+O13.33E+03 3.OOE+00 4.75E+02 3.07E+01 7.04E-01 2.18E+O1


TABLE 3. Au, Gold (Continued)L. G. Schulz, J. Opt. Soc. Am. 44, 357 and 362 (1954).

W(cm-l) (Im) -41 42 n I

1.05E+04 9.50E-01 3.72E+01 2.32E+00 1.90E-01 6.10E+OOl.llE+04 9.OOE-01 3.27E+01 2.06E+00 1.80E-01 5.72E+OO1.25E+04 8.OOE-01 2.34E+01 1.55E+00 1.60E-01 4.84E+OO1.43E+04 7.OOE-01 1.57E+01 1.35E+00 1.70E-01 3.97E+OO1.67E+04 6.OOE-01 8.77E+00 1.37E+00 2.30E-01 2.97E+OO2.OOE+04 5.OOE-O1 2.68E+00 3.09E+00 8.40E-01 1.84E+OO2.22E+04 4.50E-01 1.57E+00 5.26E+00 1.40E+00 1.88E+0O

TABLE 3. Au, GOLD (Continued)G. P. Motulevich and A. A. Shubin, Soviet Phys. JETP 20, 560 (1965).

W(cm-1) %(0m) -41 42 n I

8.33E+02 1.20E+01 6.24E+03 2.48E+03 1.54E+01 8.05E+O11.OOE+03 l.OOE+O1 4.42E+03 1.55E+03 1.15E+01 6.75E+Ol1.25E+03 8.OOE+00 2.92E+03 8.54E+02 7.82E+OO 5.46E+O11.67E+03 6.OOE+00 1.72E+03 3.92E+02 4.70E+00 4.17E+Q12.OOE+03 5.OOE+00 1.23E+03 2.30E+02 3.27E+00 3.52E+Ol2.50E+03 4.OOE+00 7.74E+02 1.14E+02 2.04E+00 2.79E+O13.33E+03 3.OOE+00 4.40E+02 4.91E+01 1.17E+00 2.10E+Ol4.OOE+03 2.50E+00 2.99E+02 2.84E+01 8.20E-01 1.73E+O15.OOE+03 2.OOE+00 1.93E+02 1.52E+01 5.46E-01 1.39E+O16.67E+03 1.50E+00 1.08E+02 7.43E+00 3.57E-01 1.04E+O11.OOE+04 1.OOE+OO 4.50E+01 3.01E+00 2.24E-01 6.71E+OO

TABLE 3. Au, GOLD (Continued)V. G. Padalka and . N. Shklyarevskii, Opt. Spectr. U.S.S.R. 11, 285(1961).

AXcm-l) (1m) -41 42 n k

9.09E+02 l.lOE+O1 3.31E+03 l.O1E+03 8.71E+OO 5.82E+O11.OOE+03 1.OOE+O1 2.80E+03 7.91E+02 7.41E+00 5.34E+O11.llE+03 9.OOE+00 2.32E+03 6.04E+02 6.21E+00 4.86E+O11.25E+03 8.OOE+00 1.87E+03 4.39E+02 5.05E+00 4.35E+O11.43E+03 7.OOE+00 1.45E+03 3.04E+02 3.97E+00 3.83E+O11.67E+03 6.OOE+00 1.08E+03 1.99E+02 3.01E+00 3.30E+012.OOE+03 5.OOE+00 7.62E+02 1.21E+02 2.19E+00 2.77E+O12.50E+03 4.OOE+00 4.91E+02 6.62E+01 1.49E+00 2.22E+O13.33E+03 3.OOE+00 2.78E+02 3.11E+01 9.30E-01 1.67E+O15.OOE+03 2.OOE+00 1.25E+02 1.21E+01 5.40E-01 1.12E+O11.OOE+04 1.OOE+OO 3.10E+01 3.46E+00 3.10E-01 5.58E+OO

TABLE 3. Au, GOLD (Continued)G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, andB. A. Charikov, Phys. Met. and Mt. 13, 823 (1962).

w(cm-l) )(I'm) -s1 42 n k

1.05E+03 9.50E+00 2.44E+03 1.1OE+03 1.09E+01 5.06E+O11.1lE+03 9.OOE+00 2.19E+03 9.58E+02 1.OOE+Ol 4.7?E+O11.18E+03 8.50E+00 1.98E+03 8.86E+02 9.72E+00 4.56E+O11.25E+03 8.00E+00 1.87E+03 6.95E+02 7.90E+00 4.40E+O11.43E+03 7.OOE+00 1.51E+03 5.22E+02 6.62E+00 3.94E+O11.54E+03 6.SOE+00 1.37E+03 4.10E+02 5.48E+00 3.74E+O11.67E+03 6.00E+00 1.17E+03 3.25E+02 4.71E+00 3.45E+O12.OOE+03 5.OOE+00 8.05E+02 1.54E+02 2.71E+00 2.85E+O12.22E+03 4.50E+00 6.35E+02 1.15E+02 2.28E+00 2.53E+O12.50E+03 4.OOE+00 5.35E+02 8.72E+01 1.88E+00 2.32E+O13.33E+03 3.OOE+00 3.08E+02 4.40E+01 1.25E+00 1.76E+O14.OOE+03 2.50E+00 2.07E+02 1.99E+01 6.90E-01 1.44E+O1


TABLE 3. Au, Gold (Continued)B. Brandli and A. J. Sievers, Phy.

w(cm- 1) - 1

Rev. B , 3550 (1972) .

42 n

3.14E+01 3.18E+02 8.62E+04 6.23E+05 5.21E+02 5.98E+023.72E+01 2.69E+02 8.74E+04 5.37E+05 4.78E+02 5.62E+024.24E+01 2.36E+02 9.47E+04 4.81E+05 4.45E+02 5.41E+025.OOE+01 2.OOE+02 9.18E+04 4.OOE+05 3.99E+02 5.O1E+026.06E+01 1.65E+02 9.87E+04 3.37E+05 3.55E+02 4.74E+026.99E+01 1.43E+02 9.60E+04 2.82E+05 3.18E+02 4.44E+028.OOE+01 1.25E+02 9.97E+04 2.47E+05 2.89E+02 4.28E+029.01E+01 1.1E+02 1.OOE+05 2.15E+05 2.62E+02 4.1lE+02l.OOE+02 l.OOE+02 1.06E+05 1.93E+05 2.39E+02 4.04E+021.10E+02 9.09E+01 1.03E+05 1.68E+O5 2.17E+02 3.88E+021.20E+02 8.33E+01 1.04E+05 1.49E+05 1.97E+02 3.78E+021.30E+02 7.69E+01 9.72E+04 1.30E+05 1.80E+02 3.60E+021.40E+02 7.14E+01 9.66E+04 1.14E+05 1.63E+02 3.51E+021.50E+02 6.67E+01 8.51E+04 1.OOE+05 1.52E+02 3.29E+02

TABLE 3. Au, Gold (Continued)J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch (with C. G. Olson),Physics Data, Optical Properties of Metals, (Fach-Information Zentrum,Kalsrube, FOR, 1981).

W(cm-1) %(Im) -41 42 n k

8.07E+02 1.24E+01 6.79E+03 1.35E+03 8.17E+00 8.28E+011.21E+03 8.27E+00 3.07E+03 4.12E+02 3.71E+00 5.56E+011.61E+03 6.20E+OD 1.74E+03 1.78E+02 2.13E+00 4.17E+Ol2.02E+03 4.96E+00 1.11E+03 9.29E+01 1.39E+00 3.34E+012.42E+03 4.13E+00 7.73E+02 5.51E+01 9.90E-01 2.78E+012.82E+03 3.54E+00 5.67E+02 3.57E+01 7.50E-01 2.38E+0l3.23E+03 3.10E+00 4.34E+02 2.46E+01 5.90E-01 2.08E+0l3.63E+03 2.76E+00 3.42E+02 1.74E+01 4.70E-01 1.85E+014.03E+03 2.48E+00 2.76E+02 1.30E+01 3.90E-01 1.66E+014.44E+03 2.25E+00 2.27E+02 9.95E+00 3.30E-01 1.51E+014.84E+03 2.07E+00 1.90E+02 7.72E+00 2.80E-01 1.38E+O0l5.24E+03 1.9IE+00 1.61E+02 6.09E+00 2.40E-01 1.27E+015.65E+03 1.77E+00 1.38E+02 5.17E+00 2.20E-01 1.18E+016.05E+03 1.65E+00 1.19E+02 4.15E+00 1.90E-01 1.09E+016.45E+03 1.55E+00 1.04E+02 3.68E+00 1.80E-01 1.02E+0l6.86E+03 1.46E+00 9.16E+01 3.06E+00 1.60E-01 9.57E+007.26E+03 1.38E+00 8.12E+01 2.70E+00 1.50E-0l 9.01E+007.66E+03 1.31E+00 7.21E+01 2.38E+00 1.40E-01 8.49E+O08.07E+03 1.24E+00 6.45E+01 2.09E+00 1.30E-01 8.03E+001.21E+04 8.27E-01 2.48E+01 7.97E-01 8.00E-02 4.98E+001.61E+04 6.20E-01 9.97E+00 8.22E-01 1.30E-01 3.16E+00

TABLE 4. Pb, LEADG. Brandli and A. J. Sievers, Phys. Rev. 5, 3550 (1972).

W(cm-1) x(Im) -41 42 n k

6.25E+00 1.60E+03 1.99E+03 4.43E+05 4.69E+02 4.71E+021.17E+01 8.57E+02 1.74E+03 2.21E+05 3.31E+02 3.34E+021.78E+01 5.63E+02 2.21E+03 1.64E+05 2.85E+02 2.89E+022.61E+01 3.83E+02 2.40E+03 1.17E+05 2.39E+02 2.44E+023.38E+01 2.96E+02 2.14E+03 8.49E+04 2.03E+02 2.09E+024.41E+01 2.27E+02 2.10E+03 6.44E+04 1.77E+02 1.82E+025.38E+01 1.86E+02 2.09E+03 5.27E+04 1.59E+02 1.66E+026.28E+01 1.59E+02 2.05E+03 4.47E+04 1.46E+02 1.53E+027.19E+01 1.39E+02 2.01E+03 3.87E+04 1.35E+02 1.43E+027.96E+01 1.26E+02 2.02E+03 3.50E+04 1.28E+02 1.36E+028.92E+01 1.12E+02 1.85E+03 2.98E+04 1.18E+02 1.26E+021.02E+02 9.80E+01 1.71E+03 2.51E+04 1.08E+02 1.16E+021.12E+02 8.96E+01 1.64E+03 2.24E+04 1.02E+02 1.10E+021.21E+02 8.25E+01 1.61E+03 2.05E+04 9.72E+01 1.05E+02


kx0tm)

TABLE 4. Pb, LEAD (Continued)A. . Golovashkin and . P. Motulevich, Soviet Physics JETP 26, 881(1968)

WO m- 1)

8.33E+029.09E*021 .OOE+031. 1 I1E*031 .25E+031 .43E+031 .67E+032.OOE+032.5OE*032.86E+033.33E+033.85E+034.OOEt034. 17E*034.35E+034.55E*034.76E+035.OOE'035.88E+036. 67E+ 037.69E+031 .OOE+041. 1E+041. 18E+04

..25E+ 04I1.33E+041 .43E*041.54E*041 .67E+041.82E+042.OOEt042.22E.04

%dIxm)

1 .20E+011. 1E+0 I1.OOE+01I9. OOE+08.OOE+007.OOE+006.ODOE. 005.OOE+004.OOE+03.5OE+0O3. OOE+0O2.60E+02.50E+002.40E+OD2.30E.002.20E+002. 1E+02.OOE+001 .70E+001.50E+ 00I1.3OE+001.OOE+0O9. OOE-0 18.SO0E-0 B.ODOE-O I7. 50E- 17. OOE-D 16.SOE-0 16. OOE-0 15.SOE-0 15. OOE- 14. 50E-0OI

-i 1

I1.04E+039.98E+029.58E+029.32E'028.60E*027.56E+026.53E+025.33E+023.89E*023. 17E+ 022.5 1E+021. 95E+021 .83E+021.65E+D21 .56E+021.42E+02I1.31E+021 .20E+028.61E+016.62E+ 17.43E-0 2.64E+O 1

..99E+01I1. 68E+O1I1. 45E+D1I1. 17E+ 19. 58E+0 08.67E+008. 25E+008.2 1E+008.OO 0E+ 0O8.04E+0O

42

1.99E+031.82E+031.57E*031 .34E+031. 1E.038.7 1E+026.5BE+024.48E+022.74E+022. 0 1E+021 .40E+029.94E+O1I8.95E+O1IS.OO0E+ 17.27E+01I6.42E+O 15.78E+0O15.20E+0 13.58E+0 2.72E+0 15. 19E00I. 47E+ 0 11 .3IE+O011. 25E+ 0 11. 23E+01I1. .21E+0 I. 27E+0 11. 34E+ 0 1. 32E+0 11. 24E+O 11. 12E+O 9. 16E+00

n

2. 46E+O012.32E+O 12. IOE+0 11. 87E*0 1. 64E+ 011. 4E+O1I1. 17E+0 I9.04E*006.58E+005.39E+004.27E+003.45E+003.22E+003.03E+002.84E'002.63E+002.47E*002.32E+001 .89E+01 .64E+0O1. 50E+ 001 .38E+00I1.40E+0O1 .44E+0O1 .SOE+001 .60E+01.78E+OD1 .91E+00I1.91E+0O1 .83E+01 .70E+01 .44E+00

k

4.05E+ 13. 92E* 0 13. 74E+OI 3.58E+0 13.36E+0 13.09E+ 12.8 1E+0 12. 48E+0 12.08E*01I1. 86E+D 11. 64E+0 11. 44E+01I1. 39E 0 11. 32E+0 11. 28E+ 0 11. 22E+ 0 11. 17E+0 1. 12E+D 19.47E*008.30E+001 .73E+05.32E+O04. 68E+04.35EiDD4. 09E+03.78E+003.57EO003.5 1E+003.45E*DO3.40EO003.30E*-003. 1BE4DO

TABLE 5. Ag, SILVERH. E. Bennett and J. MI. Bennett in Optical Properties and ElectronicStructure o Metals and Alloys, edited by F. Abeles (North-Holland,Amsterdam, 1966), p. 175.

io cm- 1)

3. 13E+023. 33E+023. 57E* 023.8B5E+024. 17E+024. 55E+025.OOE.D25.56E+026.2hE+ 027. 14E+028. 33E. 02

.OE+03

..ZSE+031 .43E+031 .67E+032.ODOE. 032. 50E. 033. 33E+035. OOE+03

xC Im)

3.20E.0 I3.DOE.O 12. 80E.01I2.SOE.D 12.40E+0 I2.20E.D I2. OOE.01II .0E.O1I

.D0E+0 11 40E 0 11 .20E.01I1 .DOE.018. ODE.007 .ODE. DO6. ODE. 005.ODE.OD4. OOE.003. OOE.002. OOE+0O

-4 1

4 .44E.043.98E.D43. 55E. 043. 1DE.042.71IE.042.31IE.041 .95E.041 .59E+041 .28E.049.90 E +037. 34E. 035. 14E+033.32E.032. 55E. 03

.BSE.031 .31E.038.34E.024.7 1E.022. OE*02

2

2.OSE. 041 .74E.041 .44E.041. 17E.049.45E.037.39E.035.67E+034. 17E.032. 919E + 0 32.02E.03I1.28E.037. 49E.023.87E.022. SDE.02I1.64E.029.56E.0 I4.88SE+01I2.06E* 16. 15E00

n

4.78E+0 4.26E.D 13.76E+0 I3.28E+0 12. 83E 0 12.40E.0 I2. 0 IEtO I1 . 64E+ 0 1I. .31E+0 1I .OIE.017. 46E+OO5.2 1E.003. 35E. 002.57EO00

.9E 001 .32E+008. 44E-01I4.74E- 12. 12E-O1I

I.

2. 1E+022. 04E. 021 .?2E.021 .79,E.02I1.67E+02I1.54E.021 .41E.02I1.27E.021. 14E+02I1.OOE.028.S6O17. 19E.01I5.77E+01I5.OSE.01I4.34E.01I3.62E.01I2.89E+0 12. 17E.01II. 45E+01I

1108 APOPTICS / Vol. 22, No. 7 / 1 April 19831108 APPLIED

TABLE 5. Ag, SILVER (Continued)L. G. Schulz, J. Opt. Soc. Am. 44,

w(cm-') MItm) -4 1

p. 357 and 362 (1954).

42 n

1.OSE+04 9.50E-01 4.30E+01 1.44E+OO 1.IOE-O1 6.56E+001.11E+04 9.O0E-01 3.87E+01 1.31E+00 1.05E-01 6.22E+OO1.18E+04 8.50E-01 3.42E+01 1.17E+OO 1.OOE-O1 5.85E+0O1.25E+04 8.00E-01 2.97E+01 9.81E-01 9.OOE-02 5.45E+OO1.33E+04 7.50E-01 2.55E+01 8.08E-01 8.00E-02 5.05E+OO1.43E+04 7.00E-01 2.13E+01 6.93E-01 7.50E-02 4.62E+OO1.54E+04 6.50E-01 1.76E+01 5.88E-01 7.O0E-02 4.20E+OO1.67E+04 6.00E-01 1.41E+01 4.50E-01 6.OE-02 3.75E+OO1.82E+04 5.50E-O1 1.1OE+O1 3.65E-O1 5.SOE-02 3.32E+OO2.OOE+04 5.00E-01 8.23E+00 2.87E-01 5.00E-02 2.87E+OO2.22E+04 4.50E-01 5.55E+00 2.66E+OO S.50E-01 2.42E+OO2.50E+04 4.OE-01 3.72E+00 2.90E-01 7.50E-02 1.93E+OO

TABLE 5. Ag, Silver (Continued)H. J. Hageman, W. Gudat, and C. Kunz, J. Opt. Sac. Am. 65, 742 (1975).

((cmn1) X(Pm) -c1 42 n K

8.07E+02 1.24E+01 8.05E+03 1.79E+03 9.91E+00 9.03E+O11.61E+03 6.20E+00 2.08E+03 2.60E+02 2.84E+00 4.57E+O12.42E+03 4.13E+00 9.29E+02 8.60E+01 1.41E+00 3.05E+O13.23E+03 3.10E+00 5.23E+02 4.17E+01 9.10E-01 2.29E+O14.03E+03 2.48E+00 3.35E+02 2.45E+01 6.70E-01 1.83E+O18.07E+03 1.24E+00 8.15E+01 5.06E+00 2.80E-01 9.03E+OO1.21E+04 8.27E-01 3.35E+01 3.13E+00 2.70E-01 5.79E+OO1.61E+04 6.20E-01 1.74E+01 2.26E+00 2.70E-01 4.18E+OO

TABLE 6. Co, COBALTM. M. Kirillova and B. A. Charikov, Opt. Spectry. 17, 134 (1964).

(cm 1 ) x(m) -41 42 n K

5.OOE+02 2.OOE+01 2.44E+03 1.57E+03 1.52E+01 5.17E+O15.26E+02 1.90E+01 2.18E+03 1.46E+03 1.49E+01 4.90E+Ol5.88E+02 1.70E+01 1.84E+03 1.22E+03 1.35E+01 4.50E+O16.67E+02 1.50E+01 1.51E+03 9.07E+02 1.12E+01 4.05E+O17.14E+02 1.40E+01 1.34E+03 7.75E+02 1.02E+01 3.80E+O18.33E+02 1.20E+01 1.12E+03 6.25E+02 9.00E+00 3.47E+O19.09E+02 l.IOE+O1 9.97E+02 5.28E+02 8.10E+00 3.26E+Ol1.OOE+03 1.OOE+O1 8.20E+02 4.19E+02 7.10E+00 2.95E+O11.1lE+03 9.OOE+00 6.97E+02 3.57E+02 6.56E+00 2.72E+O11.25E+03 8.00E+00 5.42E+02 2.78E+02 5.80E+00 2.40E+O11.43E+03 7.00E+00 4.08E+02 2.26E+02 5.40E+00 2.09E+O11.54E+03 6.50E+00 3.45E+02 2.01E+02 5.20E+00 1.93E+O11.67E+03 6.OOE+00 2.81E+02 1.75E+02 5.00E+00 1.75E+Ol1.82E+03 5.50E+00 2.40E+02 1.54E+02 4.76E+00 1.62E+O12.OE+03 5.OOE+00 1.94E+02 1.38E+02 4.70E+00 1.47E+O12.22E+03 4.50E+00 1.36E+02 1.20E+02 4.78E+00 1.26E+O12.50E+03 4.OE+00 9.89E+01 1.03E+02 4.70E+OO 1.IOE+O13.33E+03 3.OE+00 4.78E+01 8.26E+01 4.88E+00 8.46E+04.OOE+03 2.50E+00 3.48E+01 7.96E+01 5.10E+00 7.80E+OO


PI

TABLE 6. Co, COBALT (Continued)P. B. Johnson and R. W. Christy, Phys. B 9, 5056 (1974).

w(cm-i)

5. 16E+036.2lE+037. 18E+038.23E+039. 19E+031.02E+041. 12E+041.22E+041.32E+041.42E+041.52E+041.62E+041.72E+041.82E+041.92E+042.02E+042. 12E+042.22E+042.32E+042.42E+042.52E+042.62E+042.72E+042.82E+042.92E+043.02E+043.12E+043.22E+043.32E+043.42E+043.52E+043.62E+043.72E+043.82E+043.92E+044.02E+044.12E+044.22E+044.32E+044.42E+044.52E+044.62E+044.72E+044.82E+044.92E+045.02E+045.12E+045.22E+045.32E+04

X(0m)

1.94E+OO1.61E+0O1.39E+01.22E+O1.09E+OO9.84E-D 18.92E-Ol8.21E-O17.56E-Ol7.04E- I6.59E-0 16. 17E-O15.82E-0l5.49E-O 15.2 IE-O I4.96E-O I4.71E-OI4.51E-Ol 4.30E-O14. 13E-OI3.97E-O13.8 IE-O 13.68E-OI3.54E-O 13.42E-O13.3 IE-O 13.20E-O13.1 IE-Ol3.0 E-DI2.92E-OI2.84E-OI2.76E-O I2.69E-OI2.62E- 12.55E-Ol 2.49E-O 12.43E-OI2.37E-D 12.31E-Ol 2.26E-O12.21E-O12. 16E-Ol2. 12E-O12.07E-O 12.03E-Ol1.99E- 11.95E-O11.92E-Ol1.88E-Ol

-4 1

4.57E+O 13.97E+ 13.41E+O I2.98E+O 12.59E+OI2.25E+O 11.96E+11. 74E+Ol 1.58E+ 11.45E+O11.32E+O11.21E+O1l. I IE+O 1.04E+O19.66E+O09.07E+OO8.35E+OO7.73E+OO7.26E+OO6.71E+OO6.12E+OO5.61E+OO5.09E+OO4.59E+OO4. 16E+OO3.82E+O3.5lE+O3.26E+OO2.99E+0O2.72E+OO2.51E+OO2.29E+OO2.09E+O1.97E+O1.78E+OO1.62E+OO1.52E+O01.41E+OO1.34E+O1.36E+OO1.38E+O01.40E+OO1.41E+OO1.32E+OO1.32E+0O1.26E+Oo1.20E+oo1. 19E+OO1. 18E+OO

42

6.03E+O 15.24E+ 14.63E+O I4.OE+DO13.46E+Ol3.06E+Ol 2.73E+ I2.47E+O 2.23E+O 2.06E+Ol1.92E+11.80E+Ol 1.69E+O 11.57E+O11.45E+O11.33E+ 11.23E+011. 14E+O I1.06E+Ol9.82E+OO9.20E+o8.63E+OO8. 13E+OO7.78E+O7.46E+O07. 12E+O6.87E+OO6.65E+06.48E+06.31E+OO6. 16E+006.02E+OO5.88E+OO5.79E+OO5.7lE+OO5.60E+OO5.58E+OO5.56E+OO5.50E+OO5.39E+05.29E+O05. 19E+OO5.02E+OO4.84E+OO4.62Et004.41E+OO4.21E+OO3.94E+O3.69E+OO

n

3.87E+OO3.61E+OO3.42E+OO3.17E+OO2.94E+OO2.78E+O2.65E+OO2.53E+O2.40E+O02.31E+OO2.25E+02.19E+O2.13E+O02.05E+OO1.97E+OO1.88E+OO1.81E+OO1.74E+O1.67E+01.61E+OO1.57E+001.53E+Ol.50E+OO1.49E+OO1.48E+OO1.46E+OO1.45E+OO1.44E+OO1.44E+O1.44E+DD1.44E+O1.44E+OO1.44E+OO1.44E+O1.45E+O1.45E+OO1.46E+OO1.47E+OO1.47E+01.45E+OO1.43E+OO1.41E+OO1.38E+OO1.36E+O1.32E+OO1.29E+OO1.26E+0O1.21E+OO1. 16E+0

P

7.79E+OO7.26E+OO6.77E+0O6.31E+OO5.88E+0O5.50E+OO5. 16E+OO4.88E+OO4.64E+OO4.45E+OO4.27E+O04.1 1E+OO3.96E+OO3.82E+O3.68E+OO3.55E+OO3.41E+0O3.28E+OO3.17E+OO3.05E+O2.93E+OO2.82E+OO2.71E+02.61E+OO2.52E+OO2.44E+O02.37E+O02.31E+OO2.25E+OO2. 19E+OO2. 14E+O2.09E+OO2.04E+0O2.0 IE+OO1.97E+OO1.93E+OO1.91E+O1.89E+OO1.87E+OO1.86E+OO1.85E+OO1.84E+OO1.82E+OO1.78E+OO1.75E+OO1.71E+O1.67E+OO1.63E+OO1.59E+OO

TABLE 6. Co, COBALT (Continued)J. H. Weaver, E. Colavita, D. W. Lynch and R. Rosei, Phys. Rev. B 19,3850 (1979).

w(cm-) X(Im) -41 42 n K

8.07E+02 1.24E+01 1.39E+03 5.08E+02 6.71E+00 3.79E+011.05E+03 9.54E+00 9.05E+02 3.29E+02 5.38E+00 3.06E+O11.21E+03 8.27E+00 6.27E+02 2.37E+02 4.66E+00 2.55E+O11.61E+03 6.20E+00 3.40E+02 1.33E+02 3.55E+00 1.88E+O12.02E+03 4.96E+00 1.97E+02 1.16E+02 3.98E+00 1.46E+012.42E+03 4.13E+00 1.32E+02 9.83E+01 4.04E+00 1.22E+O12.82E+03 3.54E+00 9.03E+01 8.68E+01 4.18E+00 1.04E+O13.23E+03 3.10E+00 6.54E+01 7.74E+01 4.24E+00 9.13E+OO3.63E+03 2.76E+00 4.80E+01 6.89E+01 4.24E+00 8.12E+O4.03E+03 2.48E+00 3.22E+01 6.34E+01 4.41E+00 7.19E+OO4.84E+03 2.07E+00 1.35E+01 6.02E+01 4.91E+00 6.13E+0O5.65E+03 1.77E+00 6.76E+00 6.13E+01 5.24E+00 5.85E+OO6.45E+03 1.5SE+00 7.96E+00 6.09E+01 5.17E+00 5.89E+07.26E+03 1.38E+OO 1.1OE+O1 5.88E+01 4.94E+00 5.95E+OO8.07E+03 1.24E+00 1.44E+01 5.23E+01 4.46E+00 5.86E+09.68E+03 1.03E+00 1.42E+01 4.08E+01 3.81E+00 5.36E+OO1.21E+04 8.27E-01 1.50E+01 3.08E+01 3.1OE+00 4.96E+OO1.61E+04 6.20E-O1 1.11E+O1 1.77E+01 2.21E+00 4.00E+O


TABLE 7. Fe, IronJ. H. Weaver, E. Colavi3850 (1979).

W(cm-i)

8.07E+021.05E+031.2 1E+031.37E+031.6 1E+031.77E+ 031.94E+032. 10E+032.26E+032.42E+032.58E+032.74E+032.90E+033.06E+033.23E+034.03E+034.84E+035.65E+036.45E+037.26E+038.07E+038.87E+039.68E+031.OSE+041. 13E+041.21E+041.29E+041.37E+041.45E+041.53E+041.61E+04

X(Pm)

1.24E+O1 9.54E+OO8.27E+OO7.29E+OO6.20E+OO5.64E+OO5.17E+OO4.77E+004.43E+004.13E+OO3.87E+OO3.65E+003.44E+003.26E+OO3. 10E+OO2.48E+O02.07E+OO1.77E+OO1.55E+OO1.38E+001.24E+OO1. 13E+001.03E+009.54E-0 18.86E-O IB. 27E-0 17.75E-O I7.29E-O I6.89E-O 16.53E-O 16.20E-0 1

ta, D. W. Lynch, and R. Rosei, Phys. Rev. B 19,

-4 1

1.05E+036.79E+024.82E+023.82E+023. 19E+022.16E+021.88E+021.62E+021.43E+021.21E+021.1 1E+029.69E+O 18.71E+O 18.00E+O 17.5SE+O 14.72E+0 3.29E+O 12.38E+O 1.80E+O11.42E+O I1. 12E+O 1.03E+O I7.65E+o06.58E+0O5.24E+OO4.9 lE+OO3.96E+OO3.5 1E+03.45E+OO3.OOE+O03. 1 1E+OO

42

4.24E+023.36E+022.86E+022.58E+021.34E+021.48E+021.45E+021.36E+021.23E+021. 17E+021.09E+021.03E+029.77E+O 19.32E+0 I8.62E+O I6.64E+O 5.46E+O 14.66E+O 14.09E+O 3.63E+ 13.29E+0 13.08E+O 2.76E+0 12.57E+0 12.4 1E+O I2.30E+O 12. 16E+0 12. 10E+0 2.02E+O 1 .95E+O 1.92E+0

n

6.41E+O06.26E+006.26E+OO6.28E+003.68E+OO4.80E+0O4.96E+OO4.98E+OO4.78E+004.87E+004.73E+OO4.70E+OO4.68E+004.63E+OO4.42E+OO4.14E+OO3.93E+003.78E+OO3.65E+003.52E+0O3.43E+003.33E+0O3.24E+OO3.16E+OO3.12E+OO3.05E+OO3.OE+OO2.98E+OO2.92E+002.89E+OO2.86E+OO

PI

3.31E+O 2.68E+O 2.28E+0 I2.05E+O1 1.82E+ 11.55E+O 1.46E+0 I1.37E+ 11.29E+O1 1.21E+O 1. ISE+O 1.09E+O 1.04E+O 11.0 1E+O 19.75E+OO8.02E+OO6.95E+ 006.17E+O05.60E+0O5.16E+004.79E+OO4.62E+004.26E+OO4.07E+OO3.87E+OO3.77E+003.60E+03.52E+OO3.46E+OO3.37E+0O3.36E+00

TABLE 7. Fe, Iron (Continued)6. A. Bolotin, M. M. Kirillova, and27(2) 31 (1969).

w( cm- 1

)

5.26E+025.56E+025.88E+026.25E+026.67E+027. 14E+027.69E+028.33E+029.09E+021. OOE+031. 1 1E+031.25E+031.43E+031.67E+032.OOE+032.SOE+033.33E+034.17E+035.OOE+036.67E+031.DOE+04

X(01m)

1.90E+O11.80E+OI1.70E+O 1.60E+O 11. SOE+O 11.40E+O 11.30E+O 1 .20E+O I1. 1E+O 1 .DOE+019.OOE+OO8.00E+OO7.OOE+OO6.OE+OO5.OOE+OO4.OOE+OO3.OE+OO2.40E+OO2.OOE+OO1.SOE+00I .OOE+OO

- 1

1.92E+031.58E+031.41E+031.27E+031. ISE+031.06E+039.52E+028.43E+027.20E+026.06E+024.67E+023.46E+022.68E+021.89E+021.39E+028.36E+ 14.72E+O 14.0 IE+O 2.98E+0 12.O0E+O 1.5IE+O I

V. M. Mayevskiy, Phys. Met. Metall,

42

1.09E+039.52E+028.70E+028.04E+027.62E+027. 18E+026.63E+025.47E+024.48E+023.58E+022.98E+022.56E+021.94E+021.35E+021.04E+02B. 10E+O 16. 16E+ 14.37E+O I3.97E+0 13.02E+O 12.08E+0 1

n

1.20E+O11. 15E+O 1. 1 1E+O 1.08E+O 1.07E+O I1.05E+0 11.02E+O19.OOE+008.00E+0O7.0OE+006.60E+OO6.50E+OO5.60E+OO4.65E+OO4. 15E+OO4.05E+OO3.90E+0O3. 10E+OO3. 15E+OO2.85E+OO2.30E+OO

k

4.54E+O 14. 14E+ 13.92E+O I3.72E+0 13.56E+O I3.42E+O 3.25E+0 13.04E+O 2.80E+O 2.56E+0 12.26E+O 11.97E+O 1.73E+ 011.45E+O 1.25E+ 011.OOE+017.90E+OO7.05E+OO6.30E+O05.30E+OO4.52E+OO

1 April 1983 / Vol. 22, No.-7 / APPLIED OPTICS 1111

TABLE 8. Ni,D. W. Lynch,2195 (1971).

w( cm-1 )

8.07E+028.87E+029.03E+031.OSE+031. 13E+031.21E+031.29E+031.37E+031.45E+031.53E+031.61E+031.69E+031.77E+031.86E+031.94E+032.02E+032. 10E+032. 18E+032.26E+032.34E+032.42E+032.66E+032.82E+032.98E+033. 15E+033.23E+033.63E+034.03E+034.44E+034.84E+035.24E+035.65E+036.05E+036.45E+036.86E+037.26E+037.66E+038.07E+038.47E+038.87E+039.28E+039.68E+03l.O1E+041.OSE+041.09E+041. 13E+041. 17E+041.21E+041.25E+041.29E+04

NICKELR. Rosei and

X( Lm)

1.24E+0 1. 13E+Ol 1. lE+OO9.54E+OO8.86E+OO8.27E+OO7.75E+0O7.29E+OO6.89E+06.53E+OO6.20E+OO5.90E+OO5.64E+OO5.39E+OO5. 17E+04.96E+OO4.77E+O04.59E+OO4.43E+O04.28E+OO4. 13E+OO3.76E+O3.54E+003.35E+OO3. 18E+OO3. 10E+OO2.76E+OO2.48E+OO2.25E+OO2.07E+OO1.91E+OO1.77E+OO1.65E+OO1.55E+OO1.46E+0O1.38E+OO1.31E+O01.24E+OO1. 18E+0O1. 13E+OO1.08E+OO1.03E+OO9.92E-O19.54E-O19.8 BE-Ol8.86E-O18.55E-0 18.27E-O 8.OOE-O 17.75E-O I

J. H. Weaver, Solid State Comnun. 9,

- 1

2.0 IE+031.68E+031.4lE+031.21E+031.04E+039.04E+027.95E+026.98E+026. 17E+025.48E+024.88E+024.35E+023.92E+023.54E+023.22E+022.95E+022.73E+022.54E+022.37E+022.22E+022.09E+021.73E+021.54E+021.38E+021.23E+021. 16E+028.62E+O 17.67E+O16.44E+O15.SOE+O 14.91E+O14.3 1E+O 13.87E+013.5 1E+O 13. 17E+O12.87E+O 12.61E+Ol 2.36E+O I2. 17E+O12.0 1E+O 11.90E+011.79E+O11.69E+O11.60E+Ol 1.51E+Ol 1.44E+Ol1.40E+O11.36E+O I1.30E+O11.27E+O 1

42

8.74E+026.79E+025.44E+024.55E+023.82E+023.33E+022.86E+022.5lE+022.25E+022.05E+021.85E+021.76E+021.66E+021.60E+021.53E+021.50E+021.46E+021.42E+021.38E+021.32E+021.26E+021. 13E+021.05E+029.84E+O 19. 12E+O18.78E+O 18.56E+O17.77E+O 6.96E+O16.4 1E+O 5.84E+Ol 5.37E+Ol 4.98E+O I4.61E+Ol 4.26E+013.96E+O l3.72E+ 13.5 IE+O 3.34E+O I3.20E+O I3.05E+Ol 2.91E+O I2.78E+O 12.66E+O 2.54E+O 2.45E+O 12.36E+O12.26E+O 12. 17E+Ol2.09E+Ol

n

9.54E+OO8.12E+OO7. 1lE+OO6.44E+OO5.83E+O05.45E+OO5.OOE+0O4.68E+OO4.45E+OO4.30E+OO4.12E+OO4. 13E+OO4.1 IE+0O4.14E+OO4.16E+OO4.25E+OO4.29E+0O4.30E+OO4.30E+OO4.26E+OO4.19E+OO4. 10E+OO4.03E+003.97E+OO3.88E+O03.84E+OO4.20E+0O4.03E+OO3.90E+OO3.84E+OO3.69E+OO3.59E+OO3.49E+OO3.38E+OO3.27E+OO3.18E+OO3.1 IE+OO3.06E+OO3.0 lE+OO2.97E+OO2.91E+OO2.85E+OO2.80E+OO2.74E+OO2.69E+02.65E+OO2.59E+OO2.53E+OO2.48E+OO2.43E+OO

k

4.58E+Ol 4. 18E+O13.83E+Ol3.53E+O I3.28E+Ol 3.06E+O 2.86E+O 12.68E+12.52E+O 2.38E+O I2.25E+O 12. 13E+12.02E+O 1.93E+O 11.84E+011.77E+O 11.71E+011.65E+O 11.60E+O11.55E+O11.51E+O11.38E+ 11.31E+O I1. 24E+Ol 1. 18E+O I1. 14E+O 1.02E+O19.64E+OO8.92E+OO8.35E+OO7.92E+0O7.48E+OO7. 13E+0O6.82E+OO6.5lE+OO6.23E+0O5.98E+OO5.74E+0O5.S5E+OO5.38E+065.24E+OO5. 10E+OO4.97E+0O4.8SE+OO4.73E+OO4.63E+OO4.55E+0O4.47E+OO4.38E+OO4.31E+OO

TABLE 8. Ni, Nickel (Continued)B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

w(cm-1) X(lm) -41 42 n k

5.16E+03 1.94E+00 7.06E+01 6.31E+01 3.47E+00 9.09E+006.21E+03 1.61E+00 5.35E+01 5.OOE+01 3.14E+00 7.96E+O07.18E+03 1.39E+00 4.14E+01 4.19E+01 2.96E+00 7.08E+0O8.23E+03 1.22E+00 3.36E+01 3.59E+01 2.79E+00 6.43E+009.19E+03 1.09E+00 2.81E+01 3.14E+01 2.65E+O0 5.93E+01.02E+04 9.84E-01 2.47E+01 2.75E+01 2.48E+0O 5.55E+001.12E+04 8.92E-01 2.16E+01 2.51E+01 2.40E+00 5.23E+OO1.22E+04 8.21E-01 1.96E+01 2.25E+01 2.26E+00 4.97E+OO1.32E+04 7.56E-01 1.78E+01 2.0lE+01 2.13E+00 4.73E+001.42E+04 7.04E-01 1.60E+01 1.85E+01 2.06E+00 4.50E+OO1.52E+04 6.59E-01 1.42E+01 1.70E+01 1.99E+00 4.26E+001.62E+04 6.17E-01 1.22E+01 1.60E+01 1.99E+00 4.02E+O01.72E+04 5.82E-01 1.06E+01 1.49E+01 1.96E+00 3.80E+001.82E+04 5.49E-01 9.35E+00 1.39E+01 1.92E+00 3.61E+OO1.92E+04 5.21E-01 8.27E+00 1.27E+0.1 1.85E+00 3.42E+002.02E+04 4.96E-01 7.25E+00 1.18E+0 1.82E+00 3.25E+0D


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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00e t 0 0 0 0 0 t t t t 6 N es N e t4 4 s 4 N ts N-NNoeotwcooeXl>rco0Nbno~-~tsc

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C4N0.

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TABLE 10. Pt, PlatinumJ. H. Weaver, Phys. Rev.

W(cm2 1) ),(Pm)

B 11, 1416 (1975).

-41 i2

8.07E+02 1.24E+01 1.83E+03 1.18E+03 1.32E+01 4.47E+O11.OSE+03 9.54E+00 1.25E+03 7.28E+02 9.91E+00 3.67E+011.21E+03 8.27E+00 9.04E+02 5.1OE+02 8.18E+00 3.12E+O11.37E+03 7.29E+00 6.92E+02 3.68E+02 6.78E+00 2.72E+O11.61E+03 6.20E+00 5.39E+02 2.83E+02 5.90E+00 2.40E+02.42E+03 4.13E+00 2.46E+02 1.27E+02 3.92E+00 1.62E+013.23E+03 3.10E+00 1.22E+02 6.40E+01 2.81E+00 1.14E+O14.03E+03 2.48E+00 4.42E+01 6.03E+01 3.91E+00 7.71E+O04.84E+03 2.07E+00 1.92E+01 6.93E+O1 5.13E+00 6.75E+005.65E+03 1.77E+00 1.40E+01 7.80E+01 5.71E+00 6.83E+OO6.45E+03 l.S5E+00 2.14E+01 7.48E+O1 5.31E+00 7.04E+0O8.07E+03 1.24E+00 2.58E+01 5.63E+01 4.25E+00 6.62E+001.21E+04 8.27E-01 1.72E+01 2.96E+01 2.92E+00 5.07E+OO1.61E+04 6.20E-01 1.13E+01 1.87E+01 2.30E+00 4.07E+O0

TABLE 10. Pt, PLATINUM (Continued)J. H. Weaver, D. W. Lynch, and C. G. Olson, Phys. Rev. B 10, 501 (1974).

w(cm-l) X(Pm) -(1 42 n I

8.06E+02 1.24E+01 1.62E+03 9.28E+02 1.llE+O1 4.18E+O11.20E+03 8.30E+00 8.02E+02 4.16E+02 7.12E+00 2.92E+Ol1.61E+03 6.20E+00 4.75E+02 2.30E+02 5.14E+00 2.24E+Ol2.42E+03 4.13E+00 2.17E+02 1.02E+02 3.39E+00 1.51E+O12.82E+03 3.54E+00 1.56E+02 7.19E+01 2.81E+00 1.28E+Ol3.23E+03 3.10E+00 1.08E+02 5.24E+01 2.45E+00 1.07E+O13.62E+03 2.76E+00 6.93E+01 4.77E+01 2.72E+00 8.76E+OO4.03E+03 2.48E+00 4.33E+01 5.47E+01 3.64E+00 7.52E+OO4.44E+03 2.25E+00 3.09E+O1 5.59E+01 4.06E+00 6.88E+OO4.83E+03 2.07E+00 2.21E+01 6.0lE+01 4.58E+00 6.56E+OO5.24E+03 1.91E+00 1.89E+01 6.26E+01 4.82E+00 6.49E+OO5.65E+03 1.77E+00 1.86E+01 6.35E+01 4.88E+00 6.51E+OO6.06E+03 1.65E+00 2.OOE+01 6.32E+01 4.81E+00 6.57E+OO6.45E+03 l.SSE+OO 2.18E+01 6.1lE+01 4.64E+00 6.58E+OO6.85E+03 1.46E+00 2.37E+01 5.74E+01 4.38E+00 6.55E+OO7.25E+03 1.38E+00 2.47E+01 5.28E+01 4.10E+00 6.44E+OO8.06E+03 1.24E+00 2.40E+01 4.49E+01 3.67E+00 6.12E+OO8.85E+03 1.13E+00 2.22E+01 3.87E+01 3.35E+00 5.78E+OO9.71E+03 1.03E+00 2.04E+01 3.35E+01 3.07E+00 5.46E+OO1.05E+04 9.50E-01 1.85E+01 2.96E+01 2.86E+00 5.17E+OO1.12E+04 8.90E-01 1.68E+01 2.63E+01 2.68E+00 4.90E+OO1.20E+04 8.30E-O1 1.55E+01 2.35E+01 2.52E+00 4.67E+OO1.30E+04 7.70E-01 1.41E+01 2.13E+01 2.39E+00 4.45E+001.37E+04 7.30E-01 1.30E+01 1.93E+01 2.27E+00 4.26E+OO1.45E+04 6.90E-01 1.19E+01 1.77E+01 2.17E+00 4.08E+001.49E+04 6.70E-O1 1.1SE+Ol 1.70E+01 2.12E+00 4.00E+001.54E+04 6.50E-O1 1.11E+01 1.64E+01 2.09E+00 3.93E+6O1.56E+04 6.40E-01 l.1E+O1 1.57E+01 2.02E+00 3.89E+O01.61E+04 6.20E-01 1.06E+01 1.49E+01 1.96E+00 3.80E+O0


n IC

TABLE 11. Ti, TITANIRIM. M. Kirillova and B.

(cm-i) X(Im)

5.OOE+025.26E+025.56E+025.88E+026.25E+026.67E+027.14E+028.33E+029.09E+021.OOE+031. 1E+031. 18E+031.25E+031.33E+031.43E+031.54E+031.67E+031.82E+032.OOE+032.22E+032.50E+032.86E+033.33E+034.OOE+03

2.O0E+Ol1.90E+O11.80E+O11.70E+O11.60E+O11.50E+O11.40E+11.20E+OI1. 1OE+Ol 1.OOE+O19.O0E+OO8.50E+OO8.OOE+OO7.50E+OO7.O0E+OO6.50E+OO6.O0E+0O5.50E+OO5.O0E+OO4.50E+OO4.O0E+OO3.50E+OO3.OOE+O02.50E+OO

A. Charikov, Opt. Spectry 17, 134 (1964).

- 1

8.43E+026.85E+026.54E+025.96E+025.65E+025. 1 IE+024.74E+023.36E+023.24E+022.81E+022.22E+022.1 IE+021.76E+021.53E+021.38E+021. 17E+029.87E+Ol 8.04E+O16.06E+O 14.32E+O 13.1 1E+Ol 2.25E+Ol 1.31E+O18. 17E+OO

n

1. 17E+031.04E+038.82E+027.67E+027.05E+026.14E+025.25E+023.77E+023.38E+022.90E+022.42E+022.24E+021.94E+021.75E+021.58E+021.37E+021.22E+021.04E+028.94E+Ol7.5 1E+O 6.78E+O16.O0E+O 15.33E+O I4.93E+ 1

1.73E+Ol1.68E+O 1.49E+Ol1.37E+O11.30E+O11.20E+O 1.08E+O19.20E+OO8.50E+OO7.85E+0O7.30E+OO6.96E+OO6.56E+OO6.31E+OO5.99E+0O5.63E+OO5.38E+OO5.07E+OO4.87E+OO4.66E+OO4.66E+04.56E+OO4.57E+OO4.57E+OO

k

3.38E+ 13. 1IE+OI2.96E+O 2.80E+O 2.71E+O 12.56E+O 12.43E+Ol 2.05E+O I1.99E+O11.85E+O 1.66E+O11.61E+O11.48E+11.39E+O11.32E+O 11.22E+0 1. 13E+O 11.03E+O I9.18E+OO8.06E+0O7.27E+0O6.58E+OO5.83E+OO5.39E+OO

TABLE 11. Ti, TITANIUM (Continued)D. W. Lynch, C. G. Olson, and J. H. Weaver, Phys. Rev. B 11, 3617 (1975).

W(cm-l) XUt M) -41 42 n K

8.07E+02 1.24E+01 5.21E+02 2.35E+02 5.03E+00 2.34E+O19.68E+02 1.03E+01 3.76E+02 1.54E+02 3.90E+00 1.98E+O11.05E+03 9.54E+00 3.20E+02 1.27E+02 3.49E+00 1.82E+011.21E+03 8.27E+00 2.38E+02 9.43E+01 3.OE+00 1.57E+O11.61E+03 6.20E+00 1.24E+02 4.8lE+01 2.12E+00 1.13E+O11.69E+03 5.90E+00 1.08E+02 4.33E+01 2.04E+00 1.06E+O1

TABLE 11. Ti, TITANIUM (Continued)P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974).

w(cmnr) X(I'm) -41 (2 n P

5.16E+03 1.94E+00 1.46E+01 3.64E+01 3.51E+00 5.19E+OO6.21E+03 1.61E+00 8.47E+00 3.47E+01 3.69E+00 4.70E+OO7.18E+03 1.39E+00 5.63E+00 3.21E+01 3.67E+00 4.37E+008.23E+03 1.22E+00 4.12E+00 3.OOE+01 3.62E+00 4.15E+OO9.19E+03 1.09E+00 3.91E+00 2.81E+01 3.50E+00 4.02E+OO1.02E+04 9.84E-01 4.54E+00 2.66E+01 3.35E+00 3.97E+OO1.12E+04 8.92E-01 4.86E+00 2.61E+01 3.29E+00 3.96E+OO1.22E+04 8.21E-01 5.78E+00 2.57E+01 3.21E+00 4.0lE+OO


TABLE 11. Ti, TITANIUM (Continued)M. M. Kirillova and B. A. Charikov,

w( cm-i)

2.50E+032.86E+033.33E+034.O0E+034.17E+034.35E+034.55E+035.O0E+035.56E+035.88E+036.25E+036.45E+036.67E+036.90E+037. 14E+037.41E+037.69E+038.00E+038.33E+03

X(Pm)

4.O0E+OO3.50E+OO3.OOE+OO2.50E+OO2.40E+OO2.30E+OO2.20E+OO2.O0E+O1.80E+OO1.70E+O1.60E+O1.55E+OO1.50E+O1.45E+01.40E+OO1.35E+OO1.30E+OO1.25E+0O1.20E+OO

-4 1

3. 17E+O12.29E+O I1.44E+O18.20E+OO9.17E+OO6.94E+OO7.36E+O7.12E+OO4.76E+005.8lE+OO5.36E+O6.56E+O4.48E+O4.37E+OO5.04E+OO3.75E+OO4.84E+OO8.47E+0O5.60E+OO

Phys. Met. 1, 138 (1963).

42

6.79E+O 16.0 lE+O 15.2 IE+O 4.62E+O 4.6lE+O 4.25E+O I4.20E+Ol3.93E+Ol 3.73E+O13.42E+ 13.38E+0 13.33E+O I3.3 E+O 13. ISE+O12.98E+0 12.80E+O I2.75E+O 2.90E+O12.42E+O l

n

4.65E+OO4.55E+OO4.45E+0O4.40E+OO4.35E+OO4.25E+OO4.20E+OO4.05E+OO4.05E+0O3.80E+0O3.80E+OO3.70E+OO3.80E+O3.70E+OO3.55E+OO3.50E+OO3.40E+OO3.30E+OO3. 10E+OO

k

7.30E+O06.60E+OO5.85E+OO5.25E+OO5.30E+OO5.OOE+OO5.OOE+O04.85E+OO4.60E+OO4.50E+OO4.45E+0O4.50E+O4.35E+0O4.25E+OO4.20E+0O4.O0E+OO4.05E+OO4.40E+0O3.90E+O

TABLE 11. Ti, TITANIUM (Continued)G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, andB. A. Charikov, Phys. Met. and Met. 13, 823 (1962).

w(cm-') X(lm) -41 42 n k

1.60E+03 1.OOE+O1 2.36E+02 3.21E+02 9.O1E+00 1.78E+O11.OSE+03 9.50E+00 2.19E+02 2.93E+02 8.56E+00 1.71E+O11.11E+03 9.OE+00 2.18E+02 2.51E+02 7.56E+00 1.66E+011.18E+03 8.50E+00 2.11E+02 2.24E+02 6.96E+O0 1.61E+O11.25E+03 8.OOE+00 1.76E+02 1.94E+02 6.56E+00 1.48E+O11.33E+03 7.50E+00 1.53E+02 1.75E+02 6.31E+00 1.39E+011.43E+03 7.OOE+00 1.38E+02 1.58E+02 5.99E+00 1.32E+O11.54E+03 6.50E+00 1.17E+02 1.37E+02 5.63E+00 1.22E+011.67E+03 6.00E+00 9.87E+01 1.22E+02 5.38E+00 1.13E+O11.82E+03 5.50E+00 8.04E+01 1.04E+02 5.07E+00 1.03E+O12.OOE+03 5.OOE+00 6.06E+01 8.94E+01 4.87E+00 9.18E+OO2.22E+03 4.50E+00 4.34E+01 7.52E+01 4.66E+00 8.07E+0O2.50E+03 4.OOE+00 3.1IE+01 6.78E+01 4.66E+00 7.27E+OO2.86E+03 3.50E+00 2.25E+01 6.OOE+01 4.56E+00 6.58E+OO3.33E+03 3.OE+00 1.31E+01 5.33E+01 4.57E+00 5.83E+OO4.OOE+03 2.50E+00 8.17E+00 4.93E+01 4.57E+00 5.39E+0O5.OOE+03 2.OOE+00 4.24E+00 4.24E+01 4.38E+00 4.84E+O

E,(O) - -W(c)2 (7) RM@ = 47r (@@7)1/1 _ , + + @ ) ] C 2 + + (2]1/2Rco (op coF co, i

The dc conductivity o is related to cp and Cw by

a0 = c'/(47rwr) (8)

with 6o having units of cm-1 . This can be expressed interms of the dc resistivity po:

oo(cm'1) = 1[2rcp 0(s)] = (9 X 1")/[2rcpo(Q cm)]. (9)

To analyze the data of Brandli, and Sievers1 it isconvenient to write the surface impedance Z(cc) for theDrude model2 :

Z(w) _ RW + iX(w) = 47r ( + (w 1/2 + i 11/2

(10)

We shall need only R (c):

111. Determination of Drude Model Parameters

All data in the form of n and k were changed to e1 andE2. Equations (3) and (4) were solved for co,, eliminating

Ce2

(1-el) (12)

This equation was solved to determine c using E1 andC2 at some frequency c. Then cop was obtained from

2 = (1-el) (co2 + ). (13)

This was done for several values of co to obtain severalpairs of co, and cop, which produce the curve with thebest eyeball fit to the data.


(11)

TABLE 12. W, TUNGSTENL. V. Nomerovannaya, M.17, 134 (1964).

w(cm-1) X(Im)

5.OOE+025.26E+025.56E+025.88E+026.25E+026.67E+027.14E+027.69E+028.33E+029.09E+021.OOE+031.OSE+031. 1E+031. 18E+031.21E+031.25E+031.29E+031.33E+031.38E+031.43E+031.48E+031.54E+031.60E+031.67E+031.74E+031.82E+031.90E+032.OE+032.1 1E+032.22E+032.27E+032.38E+032.44E+032.50E+032.56E+032.70E+032.78E+032.94E+033.03E+033.13E+033.23E+033.33E+033.45E+033.57E+033.70E+033.85E+034.00E+034.17E+03

2.OOE+0 11.90E+O11.80E+011.70E+OI1.60E+O11.50E+Ol1.40E+Ol1.30E+O11.20E+O11. 1OE+ I1.OOE+O19.50E+OO9.OOE+OO8. SOE+O08.25E+0O8.00E+0O7.76E+0O7.50E+OO7.25E+O07.O0E+006.75E+OO6.SOE+OO6.25E+O06.00E+OO5.75E+OO5.50E+OO5.25E+O05.OOE+OO4.75E+OO4.50E+0O4.40E+0O4.20E+OO4. 10E+OO4.OOE+0O3.90E+003.70E+O03.60E+003.40E+O03.30E+003.20E+OO3. 10E+003.OOE+0O2.90E+0O2.80E+OO2.70E+0O2.60E+02.50E+O02.40E+OO

M. Kirillova, and M.M. Noskov, Opt. Spectry.

- 1

4.32E+033.70E+033.56E+033.37E+033.32E+033.19E+032.94E+032.65E+032.42E+032.05E+031.65E+031.51E+031.36E+031. 18E+031. 13E+031.07E+03l.O1E+039.34E+028.43E+027.72E+026.68E+025.90E+025.42E+024.87E+025.OOE+024.82E+024.80E+024.37E+023.81E+023.88E+023.85E+023.55E+023.48E+023.30E+023.15E+022.81E+022.68E+022.35E+022.17E+022.08E+021.97E+021.84E+021.76E+021.80E+021.54E+021.39E+021.28E+021.28E+02

42

2.38E+032.05E+031.90E+031.80E+031.91E+031.69E+031.43E+031. 13E+031. 1OE+038.80E+026.85E+025.85E+025.49E+024.48E+024. 10E+024.06E+023.49E+023.19E+023.07E+023.03E+022.85E+022.49E+022.33E+022.19E+022.05E+022.0 1E+021.83E+021.48E+021.32E+021. 13E+021.05E+029.50E+Ol 8.65E+O 18. 16E+O17.95E+ 17.44E+O 16.60E+O17. 19E+16.73E+016.48E+O16.25E+O17. 18E+O16.89E+O16.26E+Ol 5.29E+O 15. 16E+0 14.71E+O14.95E+O 1

n

1.75E+O11. 63E+O 11.54E+011.50E+O 11.60E+O1.45E+ 11.28E+O 11.07E+O11.09E+0l9.50E+OO8.25E+007.40E+OO7.30E+0O6.40E+OO6.OOE+OO6. 10E+OO5.40E+OO5. 15E+OO5.20E+OO5.35E+OO5.40E+0O5.03E+OO4.90E+OO4.85E+OO4.SOE+OO4.48E+OO4. 11E+OO3.48E+OO3.33E+O02.85E+OO2.65E+0O2.SOE+OO2.30E+002.23E+OO2.22E+OO2.20E+0O2.OOE+O02.32E+0O2.26E+002.22E+OO2.20E+0O2.60E+O02.55E+OO2.30E+OO2. 10E+002.1SE+OO2.05E+OO2.15E+OO

P.

6.80E+O 6.30E+O 16. 16E+O16.OOE+O 15.98E+ 15.83E+ 15.57E+0 15.26E+Ol 5.04E+Ol 4.63E+ 14. 15E+O13.95E+ 13.76E+O 13.SOE+O 3.42E+O 13.33E+O 13.23E+O 13. 10E+O12.95E+O12.83E+O 2.64E+Ol 2.48E+O 12.38E+O12.26E+O 2.28E+O 12.24E+Ol 2.23E+0 12. 12E+O11.98E+011.99E+ 11.98E+O11.90E+Ol1.88E+O11.83E+O11.79E+0 11.69E+O11.65E+0l1.55E+O11.49E+OI1.46E+Ol1.42E+O11.38E+O l1.35E+011.36E+O11.26E+011.20E+OI1. 15E+O 1. 15E+O

TABLE 12. W TUNGSTEN (Continued)

w(cm-1 ) X(lm) -41 42 n K

4.35E+03 2.30E+00 9.80E+01 4.04E+01 2.OE+0 1.OIE+O14.55E+03 2.20E+00 8.85E+01 3.65E+01 1.90E+00 9.60E+OO4.76E+03 2.10E+00 7.58E+01 3.29E+01 1.85E+00 8.90E+OO5.OOE+03 2.OOE+00 6.09E+01 2.80E+01 1.75E+00 8.00E+OO5.26E+03 1.90E+00 4.86E+01 2.90E+01 2.00E+00 7.25E+OO5.56E+03 1.80E+00 4.12E+01 2.84E+01 2.10E+00 6.75E+OO5.71E+03 1.75E+00 3.89E+01 2.62E+01 2.O0E+00 6.55E+OO5.88E+03 1.70E+00 3.34E+01 2.58E+01 2.10E+00 6.15E+OO6.02E+03 1.66E+00 3.27E+01 2.98E+01 2.40E+00 6.20E+OO6.25E+03 1.60E+00 3.88E+01 3.51E+01 2.60E+00 6.75E+0O6.45E+03 1.55E+00 2.51E+01 2.80E+01 2.50E+00 5.60E+OO6.67E+03 1.50E+00 2.08E+01 3.13E+01 2.90E+00 5.40E+OO6.90E+03 1.45E+00 1.75E+01 3.09E+01 3.OE+00 5.15E+007.14E+03 1.40E+00 1.73E+01 3.36E+01 3.20E+00 5.25E+OO7.4lE+03 1.35E+00 1.64E+01 3.30E+01 3.20E+00 5.16E+O07.69E+03 1.30E+00 1.53E+01 3.23E+01 3.20E+00 5.05E+O08.33E+03 1.20E+00 1.15E+01 2.85E+01 3.10E+00 4.60E+OO9.09E+03 1.1OE+OO 9.78E+00 2.61E+01 3.0IE+00 4.34E+O01.OOE+04 1.OOE+OO 3.25E+00 2.10E+01 3.OOE+00 3.50E+OO


TABLE 12. W, TNGSTEN (Continued)J. H. Weaver, D. W. Lynch and C. G. Olson, Phys. Rev. B 12, 1293 (1975).

( cm-l)

4.84E+025.65E+026.45E+027.26E+028.07E+029.68E+021. 13E+031.29E+031.61E+032.42E+033.23E+034.03E+034.84E+035.65E+036.6 1E+037.26E+038.07E+031.21E+041.61E+04

)(Pm)

2.07E+O 1.77E+0 11.55E+ 011.38E+O 11.24E+O 11.03E+O 8.86E+007.75E+OO6.20E+OO4.13E+OO3. 10E+OO2.48E+O02.07E+OO1.77E+001.51E+OO1.38E+OO1.24E+008.27E-0 6.20E-O

- 1

5.68E+034.75E+033.83E+033.31E+032.80E+032.05E+031.56E+031.21E+037.86E+023.32E+021.70E+021.09E+026. 19E+O l3.50E+O I1.57E+O11 .OOE+O l8.80E+OO

-4.33E+OQ-4.61E+O0

(2

5.71E+033.9 1E+032.73E+032.04E+031.54E+039.37E+026.09E+024.18E+022.19E+026.71E+O 15. 11E+Ol2.95E+O 11.93E+ 011.95E+0 12. 18E+O 2.76E+O 12.71E+O 11.94E+O 12.08E+O

n

3.45E+O 2.65E+O 12.09E+O 1.70E+O 11.41E+O11.0 1E+O 17.58E+005.92E+OO3.87E+001.83E+001.94E+OO1.40E+OO1.2 1E+OO1.59E+O02.36E+003.1 IE+OO3.14E+OO3.48E+OO3.60E+OO

k1

8.29E+0 I7.39E+O 16.53E+ 016.OOE+O 5.47E+014.64E+O I4.02E+O 3.53E+O 12.83E+ 011.83E+O 1.32E+O 1.05E+O17.96E+006. 13E+OO4.6 1E+OO4.44E+OO4.32E+OO2.79E+OO2.89E+00

Table 13. Optical Parameters Found using a Drude Model Fit of the Experimental Dielectric Functions for Six Metals for which the Dielectric Functionscould be Fit; here w, Is the Frequency at which the Fit is Forced, and -e1(0) is -el (w) at dc; the Crossover Frequency Applies to -el e2

2f (cm1)for fit ofdata in IR

WT (cm- )IR fit

(cm1)IR fit

-Sl (O)p elT0

WT (cm )from dc

resistivitiesand p

W, (cm- )crossover on

el 2 lot

Noble Metals andAl and Pb

Al l.11x103 6.47xlO2 l.l9x1O 5 3.37xl04 6.45xlO2 7.00xlo2

Cu 2.O0x1O3 2.78xl02 6.38xl04 5.27xl04 1.15xl02 2.55xl02

Au 8.06xl0 2 2.16xlo2 7.25xl04 1.13xlO 5 1.93xlo2 2.16xlo2

Pb 5.00xlOl 1.45xl03 6.20xl04 1.33xl03 1.35xl03 1.55xl03

Ag l.00x103 1.45xlo2 7.25xlO4 2.50xl05 1.41xlo2 1.52x102

Transition Metals

W 8.06xlO2 4.33xl02 4.84xl04 1.25xl04 2.16x102 4.30xl02

The one exception to this process was the measure-ments of Brandli and Sievers' for Au and Pb. Theyreported values of R(w)/Zo where Zo = (47r)/c. For thefar IR, Eq. (11) reduces to

Z &2) (14)

cw1 was obtained from this data using co, from the nearIR fit. This value of c, was used for gold and leadrather than the co obtained from the near IR fit.

We note from Eq. (12) the frequency for which -el(co)e2((.) is very nearly w = cT since -el >> 1. With w =

OT, both components (-El and 2) of the dielectricfunction are cw2/(2co 2). Thus the Drude parameters, co,and cop, can be determined at the crossover from co = c,and the value of the dielectric function. Note that-E 1(O) wco2/Cd2 ; so -/2el(0) - E(Cr)-

IV. Data

Figures 1-12 are plots of -EI(c) and e2(W) for thetwelve metals. The high frequency termination occurswhere the Drude model becomes invalid. The solidlines are calculated from the Drude model with theparameters listed in Table 13. Tables 1-12 present thecollected values of El, E2, n and k. Table 13 summarizesthe Drude model parameters from our fit (for Ag, Au,Cu, Al, Pb, and W) as well as co, calculated from cop andthe AIP Handbook 9 values of the dc resistivity. Di-electric functions for all metals considered in this articleexcept Pb have been tabulated by Weaver et al. for theUV, visible, and near IR.

Finally, we disclaim any physical signficance for theDrude model. The intent is only to parametrize theoptical constants for these metals even when there is

1118 APPLIED OPTICS / Vol. 22, No.7 / 1 April 1983

,2

some question as to the physical meaning of the pa-rameters. The transition metals show interbandtransitions and cannot be fit with a Drude model in theIR (with the exception of W). Even the noble metalsin the IR can have small interband contributions to thedielectric constants.20

References1. G. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972).2. P. Drude, Theory of Optics (Longmans, Green, New York, 1922;

Dover, New York, 1968). A more modern reference is F. Wooten,Optical Properties of Solids (Academic, New York, 1972), p. 52.For the Drude model and surface impedance see B. Donovan,Elementary Theory of Metals (Pergamon, New York, 1967), p.220.

3. J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, "Part 1:The Transition Metals," "Part 2, Noble Metals, Aluminum,Scandium, Yttrium, the Lanthanides, and the Actinides," inPhysics Data, Optical Properties of Metals (Fachinformati-onszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Fed-eral Republic of Germany, 1981).

4. G. Haas and L. Hadley, in American Institute of PhysicsHandbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p.6-118.

5. H. E. Bennett and J. M. Bennett, in Optical Properties andElectronic Structure of Metals and Alloys, F. Abeles, Ed.,(North-Holland, Amsterdam; Wiley, New York, 1966), Sec. 1.6,p. 175. For Ag, Au, and AL for co, they estimated 145, 216, and663 cm-', respectively.

6. For a single carrier type (electrons) the plasma frequency isas given in Eq. (5) where the dielectric constant is e- (the con-tribution from the core electrons at high frequencies). Often m*= m and c- = 1 are assumed. For discussion see H. Ehrenreichand M. H. Cohen, Phys. Rev. 1 5, 786 (1959); the last paragraphon p. 790 is most relevant.

7. Al: E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev.B 22, 1612 (1980); H. E. Bennett and J. M. Bennett, OpticalProperties and Electronic Structure of Metals and Alloys, F.Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G.Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).

8. Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); A. P.Lenham and D. M. Treherne, J. Opt. Soc. Am. 56,683 (1966); P.F. Robusto and R. Braunstein, Phys. Status Solidi B 107, 443(1981); H. J. Hageman, W. Gudat, and C. Kunz, J. Opt, Soc. Am.65, 742 (1975); B. Dold and R. Mecke, Optik 22, 435 (1965).

9. Au: H. E. Bennett and J. M. Bennett, Optical Properties andElectronic Structure of Metals and Alloys, F. Abeles, Ed.(North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt.Soc. Am. 44, 357,362 (1954); G. P. Motulevich and A. A. Shubin,Sov. Phys. JETP 20, 560 (1965); V. G. Padalka and I. N. Shkly-arevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N.Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, andB. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brandliand A. J. Sievers, Phys. Rev. B 5, 3550 (1972).

10. Pb: G. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A.I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 26, 881(1968).

11. Ag: H. E. Bennett and J. M. Bennett, in Optical Properties andElectronic Structure of Metals and Alloys F. Abeles, Ed.(North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt.Soc. Am. 44,357, and 362 (1954); H. J. Hagemann, W. Endat, andC. Kunz, J. Opt. Soc. Am. 65, 742 (1975).

12. Co: M. M. Kirillova and B. A. Charikov, Opt. Spectrosc. 17, 134(1964); P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056(1974); J. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei,Phys. Rev. B 19, 3850 (1979).

13. Fe: J. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei, Phys.Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, and V. M.Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).

14. Ni: D. W. Lynch, R. Rosei, and J. H. Weaver, Solid State Com-mun. 9,2195 (1973); P. B. Johnson and R. W. Christy, Phys. Rev.B 9, 5056 (1974).

15. Pd: J. H. Weaver and R. L. Benbow, Phys. Rev. B 12,3509 (1975);G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, and M. M.Noskov, Fiz. Met. Mettalloved. 23,463 (1967); P. B. Johnson andR. W. Christy, Phys. Rev. B 9, 5056 (1974).

16. Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); J. H. Weaver, C.G. Olson, and D. W. Lynch, Phys. Rev. B 10, 501 (1974).

17. Ti: M. M. Kirillova and B. A. Charikov, Opt. Spectrosc. 17, 134(1964); D. W. Lynch, C. G. Olson, and J. H. Weaver, Phys. Rev.B 11, 3617 (1975); P. B. Johnson and R. W. Christy, Phys. Rev.B 9, 5056 (1974); M. M. Kirillova and B. A. Charikov, Phys. Met.15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov,A. V. Sokolov, and B. A. Charikov, Phys. Met. Metallogr. USSR13, 823 (1962).

18. W: L. V. Nomerovannaya, M. M. Kirillova, and M. M. Noskov,Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, andC. G. Olson, Phys. Rev. B 12,1293 (1975).

19. J. Babiskin and J. R. Anderson, in American Institute of PhysicsHandbook, (McGraw-Hill, New York, 1972), p. 9-39.

20. G. R. Parkins, W. E. Lawrence, and R. W. Christy, Phys. Rev. B23, 6408 (1981).

This work was partially supported by the U.S. Army,DAAK-11-82-C-0052. We gratefully acknowledge thevaluable advice of Jean M. Bennett, David Begley,David Bryan, Kul Bhasin, and W. F. Parks.

0


Optical Activities continued from page 1069

6 Close-up of polishing setup.

7 Interferogram showing creditable accuracy of the concave 8 Grinding the cone using a flat diamond wheel and the correctsurface. tilt angle. The work rotates at 100 rpm, the diamond wheel at

5000 surface ft/min.


Pt, Ag, Ti, and W in the infrared and far infrared - MURI...

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