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Beryllium Oxide (BeO)
Beryllium Oxide (BeO) DAVID F. EDWARDS and RICHARD H. WHITE University of California Lawrence Livermore National Laboratory Livermore, California
The optical properties of crystalline synthetic beryllium oxide, BeO, have been reported for a very limited number of samples. The main reasons for this lack of data are probably the toxic properties of the material and the difficulty of growing large optical-quality crystals [1]. As pointed out by Peterson and Palma [2], BeO is a useful new optical material for the vacuum UV because of its high transmittance down to about 9.4 eV (1320 A) and its apparent resistance to UV radiation damage. In their report they show only the transmittance and, unfortunately, not enough data to estimate the n and k values for the 3 - 1 0 e V region. Calculations by White, Edwards, and Rathkopf [3] predict that overlayers of BeO on metallic reflectors should significantly enhance their hardness to X-ray radiation. Natural bromellite (BeO) and synthetically grown BeO crystals are uniaxially positive. Newkirk et al. [4], using the angle-of-minimumdeviation technique, have measured the ordinary and extraordinary refractive indices and their dependence on temperature from 0.430txm to 0.690 ~tm. Loh [5] has evaluated the ordinary and extraordinary infrared refractive indices and extinction coefficients for BeO from their polarized reflectance spectra. The n and k values were derived from parameters used to fit the classical oscillator dispersion formula to the reflectance spectra. The wellknown formula, as used by Loh, is g(o~) - - n 2o o - - (eo - -
n 2~ ) e O o /2( O ~
o-O~2 + iyt_O), 2
where eo is the static dielectric constant, and r t ~ 2 is the high-frequency dielectric constant. 7 is a phenomenological damping term, and ~Oo is the transverse optical resonance frequency. These classical dispersion parameters are given in Table I. The n and k values were determined from the HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS II
805
Copyright 9 1991 by Academic Press. All rights of reproduction in any form reserved. ISBN 0-12-544422-2
806
David F. Edwards and Richard H. White
complex dielectric constant and are included in Table II (and Fig. 1) for the infrared region 100 to 1400 cm -1 (100 to 7.14 ~tm). These calculations were extended beyond the measurement range (up to 400 cm -1) to 100 cm -1 in order to estimate the static dielectric constant, eo. From the classical dispersion analysis of Loh, eo(11)-7.65 and eo(_L)=6.94. From Table II, n([I) 2= 7.765 and n(_L)2 = 6.96 at 100cm -1. The indices of refraction between 0.440 ~tm and 7.0 ~tm have been fit to both a Herzberger-type and a modified Sellmeier-type dispersion formula. A total of 31 and 29 wavelengths were used for fitting the ordinary and extraordinary indices, respectively. The indices for wavelengths greater than 7.0 ~tm are from the lattice band spectra of Loh [5] and are not included in the dispersion formulas. The Herzberger-type dispersion formula for the index is [6] n = A + B L + C L 2 + D 2 2 + E 2 4,
where L = 1 / ( 2 2 - 2 . 8 0 x 106) with 2 in angstroms. As explained by Herzberger [6], the 2.80 x 10 6 is the square of the mean asymptote for the short-wavelength abrupt increase in the index for 14 materials (BeO not included). The coefficients for the room-temperature ordinary indices, evaluated by least squares, are A=1.699773, B=7.451288x102, C = -4.331397 x 1012, D = - 8.194535 x 10 -12, and E = - 1.659630 x 10 -2~ The RMS error between the measured values and the dispersion formula calculated indices is 0.355% for the 0.440 to 7.0 ~tm range. The coefficients for the extraordinary indices are A=1.715140, B=7.871215x105, C = - 4 . 7 8 2 7 1 1 x 1012, D = - 2.139439 x 10 -11, and E = - 1.390880 x 10 -2~ The RMS error is 0.263%. The calculated no and ne values are included in Table II. The modified Sellmeier-type dispersion formula [7] is n 2= 1 + A / ( 2 2 - B) + C22/(22- D), where the wavelength 2 is in angstroms. For the 31 ordinary and 29 extraordinary data points, the coefficients are as follows. For the ordinary index of refraction, A = 3.698124 x 10 -6, B = - 1.878147 x 10 -6, C = 1.953730, and D = 1.472502x 10 -6. The extraordinary coefficients are A = 3.257604 x 10 -6, B = - 1.609457 x 10 -6, C = 1.997330, and D = 1.548286 x 10 -6. The RMS errors are 0.228% and 0.216% for the ordinary and extraordinary indices, respectively. The Sellmeier-calculated indices are not tabulated here but the equation and coefficients are included for completeness. Worrell [8] has determined the infrared optical constants for commer-
Beryllium Oxide (BeO)
807
cially available ceramic beryllia, BeO. He evaluated n and k from a Kramers-Kronig analysis of the reflectance spectrum at near normal incidence. His results for one of the two measured samples are tabulated in Table III. The data for the second sample are not listed here but have the same general features with some variation in detail. Comparisons have been made of these ceramic data with those of Loh [5] for the crystalline BeO. The ceramic beryllia is optically isotropic compared with the uniaxial crystalline BeO. Plots of the ceramic data are not shown here but a comparison with the Loh data shows that the reststrahlen band is the same for the two materials: 1200 to 600 cm -1. The maximum reflectance at the center of this band (around 800 cm -~) is less than that of the crystalline BeO: approximately, 84% versus 96%. This lower reflectance is attributed to a lower density and the polycrystalline nature of the ceramic relative to the crystal. Differences in band profile are noted with the appearance of shoulder bands at approximately 1070 cm -1 and 710cm -1 in the ceramic materials. The peak values of the index and extinction coefficient are about 10 to 13 for the crystal and about half that for the ceramic. The n and k values outside of the reststrahlen band show greater variation with the Loh data. The reason is that corrections were not applied by Worrell [8] to the Kramers-Kronig analysis to account for truncations. Newkirk et al. [4] measured the ordinary and extraordinary indices at five different temperatures from - 12.06+_0.01~ to 44.85_0.01~ at five different wavelengths from 0.450 to 0.670 tam. They found the temperature coefficient of refractive index (dn/dT) to be essentially wavelength independent and linear with temperature. They report the ordinary coefficient to be + 8.18 x 10-6/~ and + 13.40 x 10-6/~ for the extraordinary index. REFERENCES 1. S. B. Austerman, "Growth of Beryllia Crystals," J. Am. Ceram. Soc. 46, 6 (1963). 2. C. W. Peterson and G. E. Palma, "BeO as a Window in the Vacuum UV," J. Opt. Soc. Am. 63, 387 (1973). 3. R. H. White, D. F. Edwards, and J. A. Rathkopf, "Hardening of Optical Coatings to the Effects of X-Rays," J. Appl. Phys. (in press). 4. H. W. Newkirk, D. K. Smith, and J. S. Kahn, "Synthetic Bromellite III. Some Optical Properties," Am. Mineral. 51, 141 (1966). 5. E. Loh, "Optical Phonons in BeO Crystals," Phys. Rev. 166, 673 (1968). 6. M. Herzberger and C. D. Salzberg, "Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses," J. Opt. Soc. Am. 52 420 (1962); M. Herzberger, "Colour Correction in Optical Systems and a New Dispersion Formula," Opt. Acta 6, 197 (1959). 7. D. F. Edwards and R. H. White, see KDP in this volume. 8. C. A. Worrell, "Infrared Optical Constants for CO2 Laser Waveguide Materials," J. Mater. Sci. 21,781 (1986); private communication, (1990).
808
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i0 ~ WAVELENGTH
~ , ,l,,nl
I01
I0 z
(~m)
Fig. 1. (a) Log-log plot of no (solid line) and ko (dashed line) versus wavelength in micrometers for beryllium oxide. (b) Log-log plot of n e (solid line) and k e (dashed line) versus wavelength in micrometers.
TABLE I Classical Dispersion Parameters for Evaluating the Infrared Optical Properties of BeO
r 2 to n| 2
-1)
Ordinary (_L)
Extraordinary (ll)
680 12.8 7.65 2.99
724 11.6 6.94 2.95
Beryllium Oxide (BeO)
809
TABLE II Values of n and k for Beryllium Oxide from Various References a
eV 2.818 2.696 2.583 2.480 2.385 2.296 2.214 2.138 2.067 2.0O0 1.938 1.879 1.824 1.771 1.722 1.676 1.632 1.590 1.550 1.378 1.240 0.6199 0.4133 O.3100 0.2480 0.2067 0.1771 0.1736 0.1674 0.1612 0.1550 0.1488 0.1457 0.1426 0.1395 0.1364 0.1333
cm
-1
22,727 21,739 20,833 20,000 19,231 18,519 17,857 17,241 16,667 16,129 15,625 15,152 14,706 14,286 13,889 13,514 13,158 12,821 12,500 11,111 10,000
5,000 3,333 2,500 2,000 1,667 1,429 1,400 1,350 1,300 1,250
1,200 1,175 1,150 1,125 1,100 1,075
lam 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.90 1.0 2.0 3.0 4.0 5.0 6.0 7.0 7.143 7.407 7.692 8.000 8.333 8.511 8.696 8.889 9 091 9.302
no (_L) 1.7288 [4] 1.7273 1.7258 1.7243 1.7229 1.7216 1.7203 1.7191 1.7180 1.7169 1.7160 1.7151 1.7142 1.7134 [6] 1.7127 1.7120 1.7114 1.7108 1.7102 1.7078 1.7060 1.6957 1.6798 1.6446 1.5759 1.4554 1.2613 1.230 [5] 1.166 1.086 0.981 0.834 0.735 0.604 0.411 O. 105 0.057
k ~ (_L)
n e (11)
k e (11)
0.0076 [51 0.008 0.011 0.014 0.021 0.026 0.036 0.060 0.267 0.568
1.7448 [4] 1.7434 1.7419 1.7403 1.7389 1.7375 1.7362 1.7349 1.7337 1.7326 1.7316 1.7306 1.7297 1.7289 [6] 1.7281 1.7273 1.7266 1.7259 1.7253 1.7226 1.7205 1.7063 1.6855 1.6458 1.5750 1.4581 1.2765 1.247 [5] 1.187 1.113 1.018 0.890 0.806 0.701 0.562 0.348 0.089
0.007 [5] o.008 0.011 0.014 0.019 0.024 o.03o 0.043 0.078 0.344
810
David F. Edwards and Richard H. White
TABLE II (Continued) Beryllium Oxide
eV 0.1302 0.1271 0.1240 0.1209 0.1178 0.1147 0.1116 0.1085 0.1054 0.1023 0.09919 0.09609 0.09299 0.08989 0.08679 0.08369 0.0[~059 0.07749 0.07439 0.07129 0.06819 0.06509 0.06199 0.05889 0.05579 0.05269 0.04959 0.04339 0.03720 0.03100 0.02480 0.01860 0.01240
cm "1 1,050 1,025 1,000 975 950 925 900 875 850 825 800 775 750 725 700 675 650 625 600 575 550 525 500 475 450 425 400 350 300 250 200 150 100
I.tm 9.524 9.756 10.00 10.26 10.53 10.81 11.11 11.43 11.76 12.12 12.50 12.90 13.33 13.79 14.29 14.81 15.38 16.00 16.67 17.39 18.18 19.05 20.00 21.05 22.22 23.53 25.00 28.57 33.3 40 50 66.7 100
no (.L)
k ~ (.L)
n e (11)
k e (11)
0.048 0.045 0.045 0.047 0.050 0.056 0.064 0.076 0.095 0.126 0.184 0.321 0.830 10.089 7.805 5.725 4.81.4 4.287 3.939 3.689 3.502 3.355 3.237 3.141 3.061 2.993 2.936 2.845 2.776 2.725 2.686 2.659 2.639
0.789 0.986 1.179 1.375 1.583 1.810 2.066 2.365 2.729 3.196 3.847 4.879 6.700 11.834 0.870 0.296 0.155 0.097 0.068 0.050 0.038 0.030 0.025 0.020 0.017 0.014 0.012 9.1x10-3 6.9x10-3 5.1x10-3 3.8x10-3 2.7x10-3 1.7x10-3
0.058 0.050 0.047 0.047 0.049 0.052 0.057 0.065 0.075 0.091 0.115 0.157 0.239 0.444 1.407 13.180 7.428 5.715 4.888 4.389 4.052 3.807 3.620 3.474 3.356 3.259 3.178 3.052 2.960 2.893 2.843 2.807 2.783
0.609 0.816 1.005 1.189 1.376 1.573 1.787 2.024 2.295 2.617 3.015 3.537 4.284 5.523 8.36 7.050 0.732 0.289 0.160 0.103 0.073 0.054 0.042 0.034 0.027 0.023 0.018 0.0136 0.010 7.4x10-3 5.4x10-3 3.8x10-3 2.4x10-3
a The no ,and ne values for wavelength 7.0 lam and smaller were calculated with the Herzbergertype formula. The n and k values for wavelength greater than 7.0 I.tm were calculated from the reststrahlen data. The bracketed numbers indicate the reference to the data.
Beryllium Oxide (BeO)
811
TABLE I11 Values of n and k for Ceramic Beryllium Oxide [8]
eV 0.02244 0.02360 0.02480 0.02606 0.02740 0.02852 0.02982 0.03104 0.03230 0.03346 0.03482 0.03605 0.03715 0.03846 0.03963 0.04104 0.04209 0.04357 0.04468 0.04581 0.04723 0.04838 0.04961 0.05086 0.05214 0.05320 0.05454 0.05591 0.05704 0.05819 0.05967 0.06086 0.06209 0.06335 0.06462 0.06592 0.06691 0.06826
cm
-1
181.0 190.3 200.0 210.2 221.0 230.0 240.5 250.3 260.5 269.8 280.8 290.7 299.6 310.2 319.6 331.0 339.4 351.4 360.3 369.4 380.9 390.2 400.1 410.2 420.5 429.0 439.8 450.9 460.0 469.3 481.2 490.8 500.7 510.8 521.1 531.6 539.6 550.5
lam
n
k
55.25 52.55 50.00 47.57 45.25 43.48 41.58 39.95 38.39 37.06 35.61 34.40 33.38 32.25 31.29 30.21 29.46 28.46 27.75 27.07 26.25 25.63 24.99 24.38 23.78 23.31 22.74 22.18 21.74 21.31 20.78 20.37 19.97 19.57 19.19 18.81 18.53 18.17
2.6208 2.6270 2.6336 2.6410 2.6491 2.6562 2.6650 2.6735 2.6828 2.6917 2.7027 2.7131 2.7227 2.7348 2.7459 2.7599 2.7707 2.7869 2.8009 2.8138 2.8327 2.8485 2.8683 2.8905 2.9165 2.9376 2.9683 2.9961 3.0179 3.0375 3.0734 3.1129 3.1595 3.2034 3.2464 3.2978 3.3361 3.3931
0.0799 0.0779 0.0784 0.0798 0.0819 0.0841 0.0871 0.0903 0.0938 0.0973 O. i 018 O.1061 0.1 I01 0.1151 0.1198 O. 1255 O. 1298 0.1360 0.1397 0.1457 O. 1522 O. 1564 O. 1602 0.1665 O. 1718 O. 1801 0.1928 0.2071 O. 2199 0.2277 0.2323 0.2375 0.2499 0.2701 0.2892 0.3091 0.3238 0.3382
812
David F. Edwards and Richard H. White
TABLE III (Continued) Beryllium Oxide
eV 0.06964 0.07069 0.07212 0.07320 0.07467 0.07580 0.07694 0.07811 0.07929 0.08048 0.08169 0.08334 0.08459 0.08587 0.08673 0.08804 0.0..8937 0.09071 0.09208 0.09300 0.09440 0.09583 0.09678 0.09825 0.09922 0.1007 0.1017 0.1033 0.1043 0.1054 0.1069 0.1080 0.1091 0.1107 0.1118 0.1130 0.1141 0.1152 0.1170
cm
-1
561.6 570.1 581.6 590.3 602.2 611.3 620.5 629.9 639.4 649.0 658.8 672.1 682.2 692.5 699.4 710.0 720.7 731.5 742.6 750.0 761.3 772.8 780.5 792.3 800.2 812.3 820.4 832.8 841.2 849.6 862.4 871.0 879.8 893.0 902.0 911.0 920.2 929.4 943.4
lam
n
17.81 17.54 17.19 16.94 16.61 16.36 16.12 15.88 15.64 15.41 15.18 14.88 14.66 14.44 14.30 14.08 13.88 13.67 13.47 13.33 13.14 12.94 12.81 12.62 12.50 12.31 12.19 12.01 11.89 11.77 11.60 11.48 11.37 11.20 11.09 10.98 10.87 10.76 10.60
3.4728 3.5387 3.6485 3.7442 3.9054 4.0367 4.1815 4.3584 4.5546 4.8086 5.1446 5.5384 5.6595 5.4389 5.1068 4.1266 2.9343 2.1243 1.6565 1.4092 1.0695 0.7918 0.6559 0.5184 0.4551 0.3912 0.3630 0.3359 0.3224 0.3125 0.2959 0.2872 0.2804 0.2704 0.2622 0.2525 0.2424 0.2320 0.2151
0.3566 0.3662 0.3993 0.4173 0.4786 0.5445 0.6166 0.7298 0.8448 1.0489 1.3233 2.0507 2.8332 3.7439 4.3753 5.1834 5.2651 4.8910 4.5246 4.3319 4.0385 3.7230 3.5065 3.2061 3.0236 2.7791 2.6336 2.4419 2.3282 2.2235 2.0818 1.9938 1.9097 1.7957 1.7242 1.6550 1.5876 1.5215 1.4235
Beryllium Oxide (BeO)
813
TABLE III (Continued)
Beryllium Oxide
-1
eV
cm
0.1182 0.1193 0.1205 0.1217 0.1230 0.1242 0.1254 0.1267 0.1280 0.1293 0.1305 0.1319 0.1332 0.1345 0.1352 0.1365 0.1379 0.1393 0.1414 0.1428 0.1442 0.1457 O. 1464 0.1479 0.1494 0.1501 0.1516 0.1524 0.1539 0.1554 0.1562 0.1578 0.1594 0.1602 0.1618 0.1626 0.1642 0.1650 0.1667
952.9 962.4 972.1 981.8 991.7 1001.6 1011.6 1021.8 1032.0 1042.4 1052.8 1063.4 1074.0 1084.8 1090.2 1101.2 1112.2 1123.3 1140.3 1151.7 1163.3 1174.9 1180.8 1192.6 1204.6 1210.6 1222.7 1228.9 1241.2 1253.6 1259.9 1272.5 1285.3 1291.7 1304.6 1311.2 1324.3 1330.9 1344.3
lam
n
10.49 10.39 10.29 10.19 10.08 9.984 9.885 9.787 9.690 9.593 9.498 9.404 9.311 9.218 9.173 9.081 8.991 8.902 8.770 8.683 8.596 8.511 8.469 8.385 8.302 8.260 8.179 8.137 8.057 7.977 7.937 7.859 7.780 7.742 7.665 7.627 7.551 7.514 7.439
0.2032 0.1911 0.1791 0.1669 O. 1564 0.1488 0.1453 0.1466 0.1510 0.1531 0.1507 O. 1463 O. 1602 0.2098 0.2469 0.3590 0.4797 0.5733 0.6778 0.7388 0.7874 0.8354 0.8586 0.8996 0.9347 0.9476 0.9770 0.9900 1.0180 1.0484 1.0621 1.0858 1.1072 1.1169 1.1369 1.1469 1.1670 1.1744 1.1850
1.3580 1.2919 1.2248 1.1556 1.0832 1.0080 0.9309 0.8535 0.7783 0.7041 0.6246 0.5277 0.4103 0.2794 0.2173 0.1216 0.0777 0.0678 0.0587 0.0555 0.0523 0.0505 0.0512 0.0553 0.0604 0.0632 0.0623 0.0633 0.0607 0.0621 0.0638 0.0695 0.0760 0.0786 0.0802 0.0822 0.0916 0.0969 0.1058
814
David F. Edwards and Richard H. White
TABLE III (Continued)
Beryllium Oxide
-1
eV
cm
0.1675 0.1692 0.1701 0.1718 0.1726 0.1735 0.1752 0.1761 0.1779 0.1787 0.1823 0.1917 0.2015 0.2226 0.2460
1351.0 1364.5 1371.4 1385.1 1392.0 1399.0 1413.0 1420.1 1434.3 1441.5 1470.5 1545.8 1624.8 1795.2 1983.5
lam
n
7.402 7.329 7.292 7.220 7.184 7.148 7.077 7.042 6.972 6.937 6.800 6.469 6.155 5.570 5.042
1.1900 1.2002 1.2040 1.1972 1.1838 1.1714 1.1636 1.1711 1.1968 1.2132 1.2617 1.3150 1.3571 1.4255 1.4726
0.1087 0.1185 0.1259 0.1430 0.1435 0.1354 0.1006 0.0831 0.0611 0.0544 0.0586 0.0697 0.0743 0.0735 0.1125
The optical properties of crystalline synthetic beryllium oxide, BeO, have been reported for a very limited number of samples. The main reasons for this lack of data are probably the toxic properties of the material and the difficulty of growing large optical-quality crystals [1]. As pointed out by Peterson and Palma [2], BeO is a useful new optical material for the vacuum UV because of its high transmittance down to about 9.4 eV (1320 A) and its apparent resistance to UV radiation damage. In their report they show only the transmittance and, unfortunately, not enough data to estimate the n and k values for the 3 - 1 0 e V region. Calculations by White, Edwards, and Rathkopf [3] predict that overlayers of BeO on metallic reflectors should significantly enhance their hardness to X-ray radiation. Natural bromellite (BeO) and synthetically grown BeO crystals are uniaxially positive. Newkirk et al. [4], using the angle-of-minimumdeviation technique, have measured the ordinary and extraordinary refractive indices and their dependence on temperature from 0.430txm to 0.690 ~tm. Loh [5] has evaluated the ordinary and extraordinary infrared refractive indices and extinction coefficients for BeO from their polarized reflectance spectra. The n and k values were derived from parameters used to fit the classical oscillator dispersion formula to the reflectance spectra. The wellknown formula, as used by Loh, is g(o~) - - n 2o o - - (eo - -
n 2~ ) e O o /2( O ~
o-O~2 + iyt_O), 2
where eo is the static dielectric constant, and r t ~ 2 is the high-frequency dielectric constant. 7 is a phenomenological damping term, and ~Oo is the transverse optical resonance frequency. These classical dispersion parameters are given in Table I. The n and k values were determined from the HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS II
805
Copyright 9 1991 by Academic Press. All rights of reproduction in any form reserved. ISBN 0-12-544422-2
806
David F. Edwards and Richard H. White
complex dielectric constant and are included in Table II (and Fig. 1) for the infrared region 100 to 1400 cm -1 (100 to 7.14 ~tm). These calculations were extended beyond the measurement range (up to 400 cm -1) to 100 cm -1 in order to estimate the static dielectric constant, eo. From the classical dispersion analysis of Loh, eo(11)-7.65 and eo(_L)=6.94. From Table II, n([I) 2= 7.765 and n(_L)2 = 6.96 at 100cm -1. The indices of refraction between 0.440 ~tm and 7.0 ~tm have been fit to both a Herzberger-type and a modified Sellmeier-type dispersion formula. A total of 31 and 29 wavelengths were used for fitting the ordinary and extraordinary indices, respectively. The indices for wavelengths greater than 7.0 ~tm are from the lattice band spectra of Loh [5] and are not included in the dispersion formulas. The Herzberger-type dispersion formula for the index is [6] n = A + B L + C L 2 + D 2 2 + E 2 4,
where L = 1 / ( 2 2 - 2 . 8 0 x 106) with 2 in angstroms. As explained by Herzberger [6], the 2.80 x 10 6 is the square of the mean asymptote for the short-wavelength abrupt increase in the index for 14 materials (BeO not included). The coefficients for the room-temperature ordinary indices, evaluated by least squares, are A=1.699773, B=7.451288x102, C = -4.331397 x 1012, D = - 8.194535 x 10 -12, and E = - 1.659630 x 10 -2~ The RMS error between the measured values and the dispersion formula calculated indices is 0.355% for the 0.440 to 7.0 ~tm range. The coefficients for the extraordinary indices are A=1.715140, B=7.871215x105, C = - 4 . 7 8 2 7 1 1 x 1012, D = - 2.139439 x 10 -11, and E = - 1.390880 x 10 -2~ The RMS error is 0.263%. The calculated no and ne values are included in Table II. The modified Sellmeier-type dispersion formula [7] is n 2= 1 + A / ( 2 2 - B) + C22/(22- D), where the wavelength 2 is in angstroms. For the 31 ordinary and 29 extraordinary data points, the coefficients are as follows. For the ordinary index of refraction, A = 3.698124 x 10 -6, B = - 1.878147 x 10 -6, C = 1.953730, and D = 1.472502x 10 -6. The extraordinary coefficients are A = 3.257604 x 10 -6, B = - 1.609457 x 10 -6, C = 1.997330, and D = 1.548286 x 10 -6. The RMS errors are 0.228% and 0.216% for the ordinary and extraordinary indices, respectively. The Sellmeier-calculated indices are not tabulated here but the equation and coefficients are included for completeness. Worrell [8] has determined the infrared optical constants for commer-
Beryllium Oxide (BeO)
807
cially available ceramic beryllia, BeO. He evaluated n and k from a Kramers-Kronig analysis of the reflectance spectrum at near normal incidence. His results for one of the two measured samples are tabulated in Table III. The data for the second sample are not listed here but have the same general features with some variation in detail. Comparisons have been made of these ceramic data with those of Loh [5] for the crystalline BeO. The ceramic beryllia is optically isotropic compared with the uniaxial crystalline BeO. Plots of the ceramic data are not shown here but a comparison with the Loh data shows that the reststrahlen band is the same for the two materials: 1200 to 600 cm -1. The maximum reflectance at the center of this band (around 800 cm -~) is less than that of the crystalline BeO: approximately, 84% versus 96%. This lower reflectance is attributed to a lower density and the polycrystalline nature of the ceramic relative to the crystal. Differences in band profile are noted with the appearance of shoulder bands at approximately 1070 cm -1 and 710cm -1 in the ceramic materials. The peak values of the index and extinction coefficient are about 10 to 13 for the crystal and about half that for the ceramic. The n and k values outside of the reststrahlen band show greater variation with the Loh data. The reason is that corrections were not applied by Worrell [8] to the Kramers-Kronig analysis to account for truncations. Newkirk et al. [4] measured the ordinary and extraordinary indices at five different temperatures from - 12.06+_0.01~ to 44.85_0.01~ at five different wavelengths from 0.450 to 0.670 tam. They found the temperature coefficient of refractive index (dn/dT) to be essentially wavelength independent and linear with temperature. They report the ordinary coefficient to be + 8.18 x 10-6/~ and + 13.40 x 10-6/~ for the extraordinary index. REFERENCES 1. S. B. Austerman, "Growth of Beryllia Crystals," J. Am. Ceram. Soc. 46, 6 (1963). 2. C. W. Peterson and G. E. Palma, "BeO as a Window in the Vacuum UV," J. Opt. Soc. Am. 63, 387 (1973). 3. R. H. White, D. F. Edwards, and J. A. Rathkopf, "Hardening of Optical Coatings to the Effects of X-Rays," J. Appl. Phys. (in press). 4. H. W. Newkirk, D. K. Smith, and J. S. Kahn, "Synthetic Bromellite III. Some Optical Properties," Am. Mineral. 51, 141 (1966). 5. E. Loh, "Optical Phonons in BeO Crystals," Phys. Rev. 166, 673 (1968). 6. M. Herzberger and C. D. Salzberg, "Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses," J. Opt. Soc. Am. 52 420 (1962); M. Herzberger, "Colour Correction in Optical Systems and a New Dispersion Formula," Opt. Acta 6, 197 (1959). 7. D. F. Edwards and R. H. White, see KDP in this volume. 8. C. A. Worrell, "Infrared Optical Constants for CO2 Laser Waveguide Materials," J. Mater. Sci. 21,781 (1986); private communication, (1990).
808
D a v i d F. E d w a r d s a n d R i c h a r d H. W h i t e
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i0 ~ WAVELENGTH
~ , ,l,,nl
I01
I0 z
(~m)
Fig. 1. (a) Log-log plot of no (solid line) and ko (dashed line) versus wavelength in micrometers for beryllium oxide. (b) Log-log plot of n e (solid line) and k e (dashed line) versus wavelength in micrometers.
TABLE I Classical Dispersion Parameters for Evaluating the Infrared Optical Properties of BeO
r 2 to n| 2
-1)
Ordinary (_L)
Extraordinary (ll)
680 12.8 7.65 2.99
724 11.6 6.94 2.95
Beryllium Oxide (BeO)
809
TABLE II Values of n and k for Beryllium Oxide from Various References a
eV 2.818 2.696 2.583 2.480 2.385 2.296 2.214 2.138 2.067 2.0O0 1.938 1.879 1.824 1.771 1.722 1.676 1.632 1.590 1.550 1.378 1.240 0.6199 0.4133 O.3100 0.2480 0.2067 0.1771 0.1736 0.1674 0.1612 0.1550 0.1488 0.1457 0.1426 0.1395 0.1364 0.1333
cm
-1
22,727 21,739 20,833 20,000 19,231 18,519 17,857 17,241 16,667 16,129 15,625 15,152 14,706 14,286 13,889 13,514 13,158 12,821 12,500 11,111 10,000
5,000 3,333 2,500 2,000 1,667 1,429 1,400 1,350 1,300 1,250
1,200 1,175 1,150 1,125 1,100 1,075
lam 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.90 1.0 2.0 3.0 4.0 5.0 6.0 7.0 7.143 7.407 7.692 8.000 8.333 8.511 8.696 8.889 9 091 9.302
no (_L) 1.7288 [4] 1.7273 1.7258 1.7243 1.7229 1.7216 1.7203 1.7191 1.7180 1.7169 1.7160 1.7151 1.7142 1.7134 [6] 1.7127 1.7120 1.7114 1.7108 1.7102 1.7078 1.7060 1.6957 1.6798 1.6446 1.5759 1.4554 1.2613 1.230 [5] 1.166 1.086 0.981 0.834 0.735 0.604 0.411 O. 105 0.057
k ~ (_L)
n e (11)
k e (11)
0.0076 [51 0.008 0.011 0.014 0.021 0.026 0.036 0.060 0.267 0.568
1.7448 [4] 1.7434 1.7419 1.7403 1.7389 1.7375 1.7362 1.7349 1.7337 1.7326 1.7316 1.7306 1.7297 1.7289 [6] 1.7281 1.7273 1.7266 1.7259 1.7253 1.7226 1.7205 1.7063 1.6855 1.6458 1.5750 1.4581 1.2765 1.247 [5] 1.187 1.113 1.018 0.890 0.806 0.701 0.562 0.348 0.089
0.007 [5] o.008 0.011 0.014 0.019 0.024 o.03o 0.043 0.078 0.344
810
David F. Edwards and Richard H. White
TABLE II (Continued) Beryllium Oxide
eV 0.1302 0.1271 0.1240 0.1209 0.1178 0.1147 0.1116 0.1085 0.1054 0.1023 0.09919 0.09609 0.09299 0.08989 0.08679 0.08369 0.0[~059 0.07749 0.07439 0.07129 0.06819 0.06509 0.06199 0.05889 0.05579 0.05269 0.04959 0.04339 0.03720 0.03100 0.02480 0.01860 0.01240
cm "1 1,050 1,025 1,000 975 950 925 900 875 850 825 800 775 750 725 700 675 650 625 600 575 550 525 500 475 450 425 400 350 300 250 200 150 100
I.tm 9.524 9.756 10.00 10.26 10.53 10.81 11.11 11.43 11.76 12.12 12.50 12.90 13.33 13.79 14.29 14.81 15.38 16.00 16.67 17.39 18.18 19.05 20.00 21.05 22.22 23.53 25.00 28.57 33.3 40 50 66.7 100
no (.L)
k ~ (.L)
n e (11)
k e (11)
0.048 0.045 0.045 0.047 0.050 0.056 0.064 0.076 0.095 0.126 0.184 0.321 0.830 10.089 7.805 5.725 4.81.4 4.287 3.939 3.689 3.502 3.355 3.237 3.141 3.061 2.993 2.936 2.845 2.776 2.725 2.686 2.659 2.639
0.789 0.986 1.179 1.375 1.583 1.810 2.066 2.365 2.729 3.196 3.847 4.879 6.700 11.834 0.870 0.296 0.155 0.097 0.068 0.050 0.038 0.030 0.025 0.020 0.017 0.014 0.012 9.1x10-3 6.9x10-3 5.1x10-3 3.8x10-3 2.7x10-3 1.7x10-3
0.058 0.050 0.047 0.047 0.049 0.052 0.057 0.065 0.075 0.091 0.115 0.157 0.239 0.444 1.407 13.180 7.428 5.715 4.888 4.389 4.052 3.807 3.620 3.474 3.356 3.259 3.178 3.052 2.960 2.893 2.843 2.807 2.783
0.609 0.816 1.005 1.189 1.376 1.573 1.787 2.024 2.295 2.617 3.015 3.537 4.284 5.523 8.36 7.050 0.732 0.289 0.160 0.103 0.073 0.054 0.042 0.034 0.027 0.023 0.018 0.0136 0.010 7.4x10-3 5.4x10-3 3.8x10-3 2.4x10-3
a The no ,and ne values for wavelength 7.0 lam and smaller were calculated with the Herzbergertype formula. The n and k values for wavelength greater than 7.0 I.tm were calculated from the reststrahlen data. The bracketed numbers indicate the reference to the data.
Beryllium Oxide (BeO)
811
TABLE I11 Values of n and k for Ceramic Beryllium Oxide [8]
eV 0.02244 0.02360 0.02480 0.02606 0.02740 0.02852 0.02982 0.03104 0.03230 0.03346 0.03482 0.03605 0.03715 0.03846 0.03963 0.04104 0.04209 0.04357 0.04468 0.04581 0.04723 0.04838 0.04961 0.05086 0.05214 0.05320 0.05454 0.05591 0.05704 0.05819 0.05967 0.06086 0.06209 0.06335 0.06462 0.06592 0.06691 0.06826
cm
-1
181.0 190.3 200.0 210.2 221.0 230.0 240.5 250.3 260.5 269.8 280.8 290.7 299.6 310.2 319.6 331.0 339.4 351.4 360.3 369.4 380.9 390.2 400.1 410.2 420.5 429.0 439.8 450.9 460.0 469.3 481.2 490.8 500.7 510.8 521.1 531.6 539.6 550.5
lam
n
k
55.25 52.55 50.00 47.57 45.25 43.48 41.58 39.95 38.39 37.06 35.61 34.40 33.38 32.25 31.29 30.21 29.46 28.46 27.75 27.07 26.25 25.63 24.99 24.38 23.78 23.31 22.74 22.18 21.74 21.31 20.78 20.37 19.97 19.57 19.19 18.81 18.53 18.17
2.6208 2.6270 2.6336 2.6410 2.6491 2.6562 2.6650 2.6735 2.6828 2.6917 2.7027 2.7131 2.7227 2.7348 2.7459 2.7599 2.7707 2.7869 2.8009 2.8138 2.8327 2.8485 2.8683 2.8905 2.9165 2.9376 2.9683 2.9961 3.0179 3.0375 3.0734 3.1129 3.1595 3.2034 3.2464 3.2978 3.3361 3.3931
0.0799 0.0779 0.0784 0.0798 0.0819 0.0841 0.0871 0.0903 0.0938 0.0973 O. i 018 O.1061 0.1 I01 0.1151 0.1198 O. 1255 O. 1298 0.1360 0.1397 0.1457 O. 1522 O. 1564 O. 1602 0.1665 O. 1718 O. 1801 0.1928 0.2071 O. 2199 0.2277 0.2323 0.2375 0.2499 0.2701 0.2892 0.3091 0.3238 0.3382
812
David F. Edwards and Richard H. White
TABLE III (Continued) Beryllium Oxide
eV 0.06964 0.07069 0.07212 0.07320 0.07467 0.07580 0.07694 0.07811 0.07929 0.08048 0.08169 0.08334 0.08459 0.08587 0.08673 0.08804 0.0..8937 0.09071 0.09208 0.09300 0.09440 0.09583 0.09678 0.09825 0.09922 0.1007 0.1017 0.1033 0.1043 0.1054 0.1069 0.1080 0.1091 0.1107 0.1118 0.1130 0.1141 0.1152 0.1170
cm
-1
561.6 570.1 581.6 590.3 602.2 611.3 620.5 629.9 639.4 649.0 658.8 672.1 682.2 692.5 699.4 710.0 720.7 731.5 742.6 750.0 761.3 772.8 780.5 792.3 800.2 812.3 820.4 832.8 841.2 849.6 862.4 871.0 879.8 893.0 902.0 911.0 920.2 929.4 943.4
lam
n
17.81 17.54 17.19 16.94 16.61 16.36 16.12 15.88 15.64 15.41 15.18 14.88 14.66 14.44 14.30 14.08 13.88 13.67 13.47 13.33 13.14 12.94 12.81 12.62 12.50 12.31 12.19 12.01 11.89 11.77 11.60 11.48 11.37 11.20 11.09 10.98 10.87 10.76 10.60
3.4728 3.5387 3.6485 3.7442 3.9054 4.0367 4.1815 4.3584 4.5546 4.8086 5.1446 5.5384 5.6595 5.4389 5.1068 4.1266 2.9343 2.1243 1.6565 1.4092 1.0695 0.7918 0.6559 0.5184 0.4551 0.3912 0.3630 0.3359 0.3224 0.3125 0.2959 0.2872 0.2804 0.2704 0.2622 0.2525 0.2424 0.2320 0.2151
0.3566 0.3662 0.3993 0.4173 0.4786 0.5445 0.6166 0.7298 0.8448 1.0489 1.3233 2.0507 2.8332 3.7439 4.3753 5.1834 5.2651 4.8910 4.5246 4.3319 4.0385 3.7230 3.5065 3.2061 3.0236 2.7791 2.6336 2.4419 2.3282 2.2235 2.0818 1.9938 1.9097 1.7957 1.7242 1.6550 1.5876 1.5215 1.4235
Beryllium Oxide (BeO)
813
TABLE III (Continued)
Beryllium Oxide
-1
eV
cm
0.1182 0.1193 0.1205 0.1217 0.1230 0.1242 0.1254 0.1267 0.1280 0.1293 0.1305 0.1319 0.1332 0.1345 0.1352 0.1365 0.1379 0.1393 0.1414 0.1428 0.1442 0.1457 O. 1464 0.1479 0.1494 0.1501 0.1516 0.1524 0.1539 0.1554 0.1562 0.1578 0.1594 0.1602 0.1618 0.1626 0.1642 0.1650 0.1667
952.9 962.4 972.1 981.8 991.7 1001.6 1011.6 1021.8 1032.0 1042.4 1052.8 1063.4 1074.0 1084.8 1090.2 1101.2 1112.2 1123.3 1140.3 1151.7 1163.3 1174.9 1180.8 1192.6 1204.6 1210.6 1222.7 1228.9 1241.2 1253.6 1259.9 1272.5 1285.3 1291.7 1304.6 1311.2 1324.3 1330.9 1344.3
lam
n
10.49 10.39 10.29 10.19 10.08 9.984 9.885 9.787 9.690 9.593 9.498 9.404 9.311 9.218 9.173 9.081 8.991 8.902 8.770 8.683 8.596 8.511 8.469 8.385 8.302 8.260 8.179 8.137 8.057 7.977 7.937 7.859 7.780 7.742 7.665 7.627 7.551 7.514 7.439
0.2032 0.1911 0.1791 0.1669 O. 1564 0.1488 0.1453 0.1466 0.1510 0.1531 0.1507 O. 1463 O. 1602 0.2098 0.2469 0.3590 0.4797 0.5733 0.6778 0.7388 0.7874 0.8354 0.8586 0.8996 0.9347 0.9476 0.9770 0.9900 1.0180 1.0484 1.0621 1.0858 1.1072 1.1169 1.1369 1.1469 1.1670 1.1744 1.1850
1.3580 1.2919 1.2248 1.1556 1.0832 1.0080 0.9309 0.8535 0.7783 0.7041 0.6246 0.5277 0.4103 0.2794 0.2173 0.1216 0.0777 0.0678 0.0587 0.0555 0.0523 0.0505 0.0512 0.0553 0.0604 0.0632 0.0623 0.0633 0.0607 0.0621 0.0638 0.0695 0.0760 0.0786 0.0802 0.0822 0.0916 0.0969 0.1058
814
David F. Edwards and Richard H. White
TABLE III (Continued)
Beryllium Oxide
-1
eV
cm
0.1675 0.1692 0.1701 0.1718 0.1726 0.1735 0.1752 0.1761 0.1779 0.1787 0.1823 0.1917 0.2015 0.2226 0.2460
1351.0 1364.5 1371.4 1385.1 1392.0 1399.0 1413.0 1420.1 1434.3 1441.5 1470.5 1545.8 1624.8 1795.2 1983.5
lam
n
7.402 7.329 7.292 7.220 7.184 7.148 7.077 7.042 6.972 6.937 6.800 6.469 6.155 5.570 5.042
1.1900 1.2002 1.2040 1.1972 1.1838 1.1714 1.1636 1.1711 1.1968 1.2132 1.2617 1.3150 1.3571 1.4255 1.4726
0.1087 0.1185 0.1259 0.1430 0.1435 0.1354 0.1006 0.0831 0.0611 0.0544 0.0586 0.0697 0.0743 0.0735 0.1125