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Rubidium Bromide (RbBr)
Rubidium Bromide (RbBr) IVAN OHLiDAL Department of Solid State Physics Faculty of Sciences Masaryk University Brno Brno, Czech Republic and MILOSLAV OHLiDAL Institute of Physical Engineering Technical University Brno, Czech Republic
Single crystals of rubidium bromide exhibit the cubic structure of NaC1 (O~-Fm3m space group). Rubidium bromide is a hygroscopic material similar to the other rubidium halides. Surfaces of optical components fabricated from RbBr crystals must be prepared with great care. Roughness of the surfaces of the RbBr components achieved by the usual polishing procedures causes a considerable decrease in transmittance of these components, at shorter wavelengths in particular [1]. This is probably caused by the fact that these procedures cause surface roughness that is characterized by relatively large values of the heights of the surface irregularities [1]. In practice the spectral region 0.25-40 /xm can be considered as the region of transparency of RbBr. So far, only four sets of optical-constant data have been published for RbBr in the literature. Three of these sets are summarized in this work. The roomtemperature values of the refractive index n and the extinction coefficient k tabulated here (see Table I and Fig. 1) were obtained from the following papers: the 54.05 /xm (0.02294 eV) to 0.21 /zm (5.904 eV) values of n are calculated using the dispersion formula published in the Li paper [2]; the 0.656 /xm (1.890 eV) to 0.486 /~m (2.551 eV) values of n are from Sprockhoff [3]; and 222.2 /zm (45 cm -~) to 50.00 /xm (200 cm -~) values of n and k were presented by Pai e t al.[4]. 845 HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS III
Copyright 9 1998 by Academic Press. All rights of reproduction in any form reserved ISBN 0-12-544423-0/$25.00.
846
Ivan Ohlfdal and Miloslav Ohlidal
The Li formula employed for calculating the refractive-index data of RbBr in the region 54.00/xm _> ~ _> 0.21 /xm was constructed in the form n 2 = 1.45931 +
0.16301 ~2 0.29841 A2 + + A2 - (0.123) 2 A2 - (0.146) 2
0.17198 ~2 0.12186 ~2 + + ~ 2 _ (0.155)2 ,~2_ (0.178)2
(1)
0.13039 ~2 2.520 ~2 + ~2 _ (0.191)2 ~2 _ (114.29) 2 ' where A is in micrometers. The values of n calculated by means of the Li formula (see Table I) correspond to the RbBr single crystal because this formula was obtained on the basis of the important Kublitzky refractive-index data [5]. The primary Kublitzky data were measured for prisms formed with the RbBr single crystal by means of the method of minimum deviation at selected wavelengths in the spectral region 0.578 /xm -> A -> 0.219/.Lm [5]. Li constructed his formula of the Sellmeier type in such a way that the wavelengths of the ultraviolet absorption peaks and the wavelength of the fundamental infrared absorption peak ~, found by direct measurements are included in this formula. The values of the adjustable parameters of the formula mentioned (e.g., 0.16301) were sought by fitting the Kublitzky data by means of the leastsquares method [2]. This means that the values of the refractive index n can be calculated using the Li dispersion formula at wavelengths beyond the Kublitzky's data in both directions, that is, at wavelengths belonging to the near-UV and the IR regions. On the basis of the Kublitzky data, Radhakrishnan [6] also derived the following empirical dispersion formula expressing the spectral dependence of the refractive index n of the RbBr single crystal in the region 0.546 ~m >- ,~ -> 0.219/xm: n 2 = 1.4500 +
0.2000 ~2 + ~2 _ 0.015129
0.3651 ~2 ~2 _ 0.022650
+
0.3224 ,~2
(2)
~2 _ 0.033124 '
,~ is also in micrometers. This formula gives wavelengths of ultraviolet absorption peaks that agree closely with those obtained by direct measurements [7, 8] but gives no information concerning the infrared absorption peak. Extrapolated values of n for the long wavelengths, that is, for the IR wavelengths, as given by the Radhakrishnan formula have large uncertainties in contrast to those given by the Li formula expressed with Eq. (1). This means that the Radhakrish-
Rubidium Bromide (RbBr)
847
nan dispersion formula is not an adequate one for use in a wide wavelength range, that is, in both the mid-IR and the far-IR regions in particular. Thus, the Radhakrishnan formula only correlates the dispersion in both the visible and the near UV with absorption bands in the UV region. Sprockhoff [3] measured the values of n of RbBr using the method of minimum deviation as well. He determined the refractive-index value of the RbBr single crystal at the following wavelengths: 0.486, 0.589 and 0.656/xm (see Table I). The errors of the refractive-index data calculated using Eq. (1) are dependent on wavelength. (The greatest and/or smallest errors in n are equal to ___ 0.02 in the regions 0.21-0.22/xm and 40.00-60.00 ~m and/or _ 0.002 in the region 0.40-1.50 /xm.) In the Sprockhoff and Kublitzky data the errors of the values of n can be estimated as _ 0.001. Pai et al. [4] determined the spectral dependences of n and k characterizing RbBr bulk samples (i.e., single crystals) by means of amplitude and phase reflection measurements made by dispersive Fourier transform spectroscopy in the region 222.2 ~m -> A -> 50/zm. The errors in the optical constants n and k evaluated in this way are also dependent on wavelength. (The greatest and/or smallest errors in both n and k are equal to + 0.10 and/or _+ 0.01 at the wavelength of about 116/zm and/or in the interval 93/xm _> )t -> 50/xm [4].) Spectral dependences of n and k in the vicinity of the maximum value of k at the wavelength of the fundamental infrared absorption peak &z are related to the TO phonon mode. The fine structures in the curves of n and k in the far-IR region may be caused by multiple-phonon absorption processes. In the visible there is very good agreement between the refractive-index data calculated using the Li formula [2] and measured by Kublitzky [5] on one side and those presented by Sprockhoff [3] on the other side (see Table I). Similarly, one can see a relatively good agreement between the values of n calculated by means of the Li formula and those determined by Pai et al. [4] in the region 54.00 /zm _> )t _> 50.00 /zm (see Table I). Both the facts mentioned give support for the correctness and reliability of the opticalconstant data presented for the RbBr single crystal in this paper. From Eq. (1) and the spectral dependence of k determined by Pai et al. [4], one can see that there is a good agreement between the value of/~I used in the Li formula [2] and that implied by the data of Pai et al. It should be noted that in the parts of the IR region in which RbBr is a weakly absorbing material (k -< 0.1), more precise values of k can be determined by transmittance measurements of sufficiently thin RbBr slabs than by means of the experimental techniques used by Pai et al. [4]. Thus far, these measurements of the transmittance of the RbBr slabs have not been performed in the IR region. Unfortunately, measurements enabling us to evaluate the values of the extinction coefficient k of the RbBr single crystals or RbBr thin films in the UV region have not been carried out, either. The optical-constant data presented here are the room-temperature
848
Ivan Ohlidal and Miloslav Ohlidal
data, as pointed out earlier. However, strictly speaking, there are small differences at temperatures corresponding to the data summarized. Namely, the refractive-index data obtained by means of the Li dispersion formula [2], the values of n determined by Sprockhoff [3] and the values of n and k published by Pai et al. [4] correspond to 293 K, 298 K, and 300 K, respectively. Both the Radhakrishnan formula [6] and the Kublitzky data correspond to 308 K. This means that at first Li reduced the Kublitzky refractiveindex data from 308 to 293 K to obtain his formula in the form presented. He performed these corrections by using empirical parameters to construct a formula for dn/dT, enabling him to carry out the mentioned corrections of the Kublitzky values of n [2] (dn/dT denotes the derivative of the refractive index with respect to temperature T). In conclusion, it is possible to state that the optical-constant data summarized here represent the best values of the refractive index n characterizing the RbBr single crystal in the region 222.2/xm --- h -> 0.21/.~m and the best values of the extinction coefficient k of the same material in the region 222.2 tzm -> h -> 50/xm. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8.
D. E. McCarthy, Appl. Opt. 7, 1243 (1968). H. H. Li, J. Phys. Chem. Ref Data 5, 329 (1976). M. Sprockhoff, Neues Jahrb. Mineral Geol. Palaeontol., Beilageband 18, 117 (1904). K. E Pai, T. J. Parker, N. E. Tornberg, R. P. Lowndes, and W. G. Chambers, Infrared Phys. 18, 199 (1978). A. Kublitzky, Ann. Phys. 20, 793 (1934). T. Radhakrishnan, Proc. Indian Acad. Sci. Sect. A 27, 165 (1948). R. Hilsch and R. W. Pohl, Z. Phys. 59, 812 (1930). E. G. Schneider and H. M. O'Bryan, Phys. Rev. 51, 293 (1937).
Rubidium
Bromide
(RbBr)
10
849
'
'
'
'
''"1
'
'
'
'
''"1
'
'
'
'
''"1
I
L
I I I I I I I I I I I I
n,k
I
|
|
0.1
I I I I I I tI i I I I I I I I I I
0.01
,
0,1
, ,,,,,,I
,
1
, ,,,,,,I
,
.......
10
WAVELENGTH
'
,
100
[ p,m ]
Fig. 1. Log-log plot of n (solid line) and k (dashed line) versus wavelength in micrometers for RbBr.
850
Ivan Ohlidal and Miloslav Ohl[dal TABLE I Values of n and k for R u b i d i u m B r o m i d e as Obtained from Various References a
eV
cm - - 1
5.904 5.848 5.794 5.740 5.687 5.636 5.585 5.535 5.486 5.438 5.391 5.344 5.299 5.254 5.209 5.166 5.123 5.081 5.040 4.999 4.959 4.920 4.881 4.843 4.806 4.769 4.732 4.696 4.661 4.626 4.592 4.558 4.525 4.492 4.460 4.428 4.397 4.366 4.335 4.305 4.275 4.246 4.217 4.189 4.161
47,620 47,170 46,730 46,300 45,870 45,450 45,050 44,640 44,250 43,860 43,480 43,100 42,740 42,370 42,020 41,670 41,320 40,980 40,650 40,320 40,000 39,680 39,370 39,060 38,760 38,460 38,170 37,880 37,590 37,310 37,040 36,760 36,500 36,230 35,970 35,710 35,460 35,210 34,970 34,720 34,480 34,250 34,010 33,780 33,560
/zm 0.210 0.212 0.214 0.216 0.218 0.220 0.222 0.224 0.226 0.228 0.230 0.232 0.234 0.236 0.238 0.240 0.242 0.244 0.246 0.248 0.250 0.252 0.254 0.256 0.258 0.260 0.262 0.264 0.266 0.268 0.270 0.272 0.274 0.276 0.278 0.280 0.282 0.284 0.286 0.288 0.290 0.292 0.294 0.296 0.298
n 1.962 [2] 1.936 1.913 1.893 1.875 1.858 1.844 1.830 1.818 1.807 1.796 1.787 1.777 1.769 1.761 1.754 1.747 1.740 1.734 1.728 1.722 1.717 1.712 1.707 1.703 1.698 1.694 1.690 1.686 1.683 1.679 1.676 1.673 1.669 1.666 1.664 1.661 1.658 1.655 1.653 1.651 1.648 1.646 1.644 1.642
(continued) a
References given in brackets.
Rubidium Bromide (RbBr)
851 TABLE I
(Continued)
Rubidium Bromide
eV 4.133 4.065 4.000 3.936 3.875 3.815 3.757 3.701 3.647 3.594 3.542 3.493 3.444 3.397 3.351 3.306 3.263 3.220 3.179 3.139 3.100 3.024 2.952 2.883 2.818 2.755 2.695 2.638 2.583 2.551 2.530 2.480 2.431 2.384 2.339 2.296 2.254 2.214 2.175 2.138 2.105 2.101 2.066 2.000 1.937 1.890
cm-
1
33,330 32,790 32,260 31,750 31,250 30,770 30,300 29,850 29,410 28,990 28,570 28,170 27,780 27,400 27,030 26,670 26,320 25,970 25,640 25,320 25,000 24,390 23,810 23,260 22,730 22,220 21,740 21,280 20,830 20,580 20,410 20,000 19,610 19,230 18,870 18,520 18,180 17,860 17,540 17,240 16,980 16,950 16,670 16,130 15,630 15,240
/xm 0.300 0.305 0.310 0.315 0.320 0.325 0.330 0.335 0.340 0.345 0.350 0.355 0.360 0.365 0.370 0.375 0.380 0.385 0.390 0.395 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.486 0.490 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.589 0.590 0.600 0.620 0.640 0.656
1.640 1.635 1.630 1.626 1.622 1.618 1.615 1.612 1.609 1.606 1.603 1.601 1.598 1.596 1.594 1.592 1.590 1.588 1.587 1.585 1.583 1.580 1.578 1.575 1.573 1.571 1.569 1.567 1.566 1.565 [31 1.564 [21 1.563 1.561 1.560 1.559 1.558 1.557 1.556 1.555 1.554 1.553 [31 1.553 [2] 1.552 1.551 [2] 1.550 1.548 [3]
(continued)
852
Ivan Ohlidal and Miloslav Ohlfdal TABLE I (Continued) Rubidium Bromide
eV 1.879 1.823 1.771 1.722 1.675 1.631 1.590 1.550 1.512 1.476 1.442 1.409 1.378 1.348 1.319 1.292 1.265 1.240 1.181 1.127 1.078 1.033 0.9919 0.9537 0.9184 0.8856 0.8551 0.8266 0.7749 0.7293 0.6888 0.6526 0.6199 O.5636 O.5166 0.4769 0.4428 0.4133 0.3542 0.3100 O.2755 0.2480 0.2066 0.1771 0.1550 0.1378
--1 cm
15,150 14,710 14,290 13,890 13,510 13,160 12,820 12,500 12,200 11,900 11,630 11,360 11,110 10,870 10,640 10,420 10,200 10,000 9,524 9,091 8,696 8,333 8,000 7,692 7,407 7,143 6,897 6,667 6,250 5,882 5,556 5,263 5,000 4,545 4,167 3,846 3,571 3,333 2,857 2,500 2,222 2,000 1,667 1,429 1,250 1,111 ,,,
/xm 0.660 0.680 0.700 0.720 0.740 0.760 0.780 0.800 0.820 0.840 0.860 0.880 0.900 0.920 0.940 0.960 0.980 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.60 1.70 1.80 1.90 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00 4.50 5.00 6.00 7.00 8.00 9.00
1.548 [2] 1.547 1.546 1.546 1.545 1.544 1.543 1.543 1.542 1.542 1.541 1.541 1.540 1.540 1.539 1.539 1.539 1.538 1.538 1.537 1.537 1.536 1.536 1.535 1.535 1.535 1.535 1.534 1.534 1.534 1.533 1.533 1.533 1.532 1.532 1.532 1.532 1.532 1.531 1.531 1.530 1.530 1.529 1.528 1.527 1.526
Rubidium Bromide (RbBr)
853 TABLE I
(Continued)
Rubidium Bromide eV 0.1240 0.1127 0.1033 0.09537 0.08856 0.08266 0.07999 0.07749 0.07514 0.07293 0.07085 0.06888 0.06702 0.06526 0.06358 0.06199 0.06048 0.05904 0.05767 0.05636 0.05510 0.05391 0.05276 0.05166 0.05061 0.04959 0.04862 0.04769 0.04679 0.04592 0.04509 0.04428 0.04350 0.04275 0.04203 0.04133 0.04065 0.04000 0.03936 0.03875 0.03815 0.03757 0.03701 0.03647 0.03594 0.03542
cm-
1
,000 909.1 833.3 769.2 714.3 666.7 645.2 625.0 606.1 588.2 571.4 555.6 540.5 526.3 512.8 500.0 487.8 476.2 465.1 454.5 444.4 434.8 425.5 416.7 408.2 400.0 392.2 384.6 377.4 370.4 363.6 357.1 350.9 344.8 339.0 333.3 327.9 322.6 317.5 312.5 307.7 303.0 298.5 294.1 289.9 285.7
/xm lO.O 11.0 12.0 13.0 14.0 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0
1.525 1.524 1.522 1.521 1.519 1.517 1.516 1.515 1.514 1.513 1.511 1.510 1.509 1.508 1.506 1.505 1.504 1.502 1.501 1.499 1.498 1.496 1.495 1.493 1.491 1.489 1.488 1.486 1.484 1.482 1.480 1.478 1.476 1.474 1.471 1.469 1.467 1.465 1.462 1.460 1.457 1.455 1.452 1.449 1.446 1.444
(continued)
854
Ivan Ohlfdal and Miloslav Ohlidal TABLE I
(Continued)
Rubidium Bromide -1
/.~m
0.03493 0.03444 0.03397 0.03351 0.03306 0.03263 0.03220 0.03179 0.03139 0.03100 0.03061 0.03024 0.02988 0.02952 0.02917 0.02883 0.02850 0.02818 0.02786 0.02755 0.02725 0.02695 0.02666 0.02638 0.02610 0.02583 0.02556 0.02530 0.02505 0.02480
281.7 277.8 274.0 270.3 266.7 263.2 259.7 256.4 253.2 250.0 246.9 243.9 241.0 238.1 235.3 232.6 229.9 227.3 224.7 222.2 219.8 217.4 215.1 212.8 210.5 208.3 206.2 204.1 202.0 20O
35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.O 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.00
0.02418
195
51.28
0.02356
190
52.63
0.02294
185
54.05
0.02232 0.02170 0.02108 0.02046 0.02009 O.01984 0.01959 0.01934 0.01909
180 175 170 165 162 160 158 156 154
55.56 57.14 58.82 60.61 61.73 62.50 63.29 64.10 64.94
eV
cm
1.441 1.438 1.435 1.432 1.429 1.425 1.422 1.419 1.415 1.412 1.408 1.405 1.401 1.397 1.393 1.389 1.385 1.381 1.376 1.372 1.368 1.363 1.358 1.354 1.349 1.344 1.338 1.333 1.328 1.322 1.31 [4] 1.308 [2] 1.29 [4] 1.291 [2] 1.27 [4] 1.272 [2] 1.25 [4] 1.22 1.18 1.16 1.13 1.11 1.09 1.07 1.04 1.00
0.01 [4] 0.01 [4] 0.02 [4] 0.02 [4] 0.03 0.04 0.04 0.04 0.05 0.05 0.06 0.07 0.09
Rubidium Bromide (RbBr)
855 TABLE I
(Continued)
Rubidium Bromide eV 0.01885 0.01860 0.01835 0.01810 0.01785 0.01761 0.01736 0.01711 0.01686 0.01661 0.01637 0.01612 0.01587 0.01562 0.01537 0.01513 0.01488 0.01463 0.01438 0.01413 0.01389 0.01364 0.01339 0.01314 0.01289 0.01265 0.01240 0.01215 0.01190 0.01165 0.01141 0.01116 0.01091 0.01066 0.01041 0.01017 0.00992 0.00967 0.00942 0.00917 0.00893 0.00868 0.00843 0.00806 0.00744 0.00682 0.00620 0.00558
cm
-1
152 150 148 146 144 142 140 138 136 134 132 130 128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98.0 96.0 94.0 92.0 90.0 88.0 86.0 84.0 82.0 80.0 78.0 76.0 74.0 72.0 70.0 68.0 65.0 60.0 55.0 50.0 45.0
/xm 65.79 66.67 67.57 68.49 69.44 70.42 71.43 72.46 73.53 74.63 75.76 76.92 78.13 79.37 80.65 81.97 83.33 84.75 86.21 87.72 89.29 90.91 92.59 94.34 96.15 98.04 100.0 102.0 104.2 106.4 108.7 111.1 113.6 116.3 119.0 122.0 125.0 128.2 131.6 135.1 138.9 142.9 147.1 153.8 166.7 181.8 200.0 222.2
0.99 0.99 0.97 0.96 0.96 0.95 0.91 0.88 0.80 0.72 0.75 0.84 O.87 0.84 0.81 0.78 0.69 0.55 0.50 0.49 0.50 0.50 0.45 0.42 0.44 0.47 0.49 0.54 0.56 0.59 0.73 1.25 2.66 4.26 4.27 4.08 3.62 3.12 2.87 2.78 2.78 2.76 2.73 2.65 2.53 2.47 2.41 2.39
0.10 0.11 0.13 0.14 0.17 0.18 0.18 0.20 0.21 0.27 0.36 0.38 0.37 0.44 0.53 0.52 0.56 0.67 0.76 0.86 0.99 1.14 1.30 1.46 1.61 1.76 1.99 2.33 2.68 3.05 3.46 4.12 4.56 3.31 1.95 1.17 0.52 0.29 0.25 0.23 0.25 0.27 0.27 0.25 0.25 0. I9 0.18 0.13
Single crystals of rubidium bromide exhibit the cubic structure of NaC1 (O~-Fm3m space group). Rubidium bromide is a hygroscopic material similar to the other rubidium halides. Surfaces of optical components fabricated from RbBr crystals must be prepared with great care. Roughness of the surfaces of the RbBr components achieved by the usual polishing procedures causes a considerable decrease in transmittance of these components, at shorter wavelengths in particular [1]. This is probably caused by the fact that these procedures cause surface roughness that is characterized by relatively large values of the heights of the surface irregularities [1]. In practice the spectral region 0.25-40 /xm can be considered as the region of transparency of RbBr. So far, only four sets of optical-constant data have been published for RbBr in the literature. Three of these sets are summarized in this work. The roomtemperature values of the refractive index n and the extinction coefficient k tabulated here (see Table I and Fig. 1) were obtained from the following papers: the 54.05 /xm (0.02294 eV) to 0.21 /zm (5.904 eV) values of n are calculated using the dispersion formula published in the Li paper [2]; the 0.656 /xm (1.890 eV) to 0.486 /~m (2.551 eV) values of n are from Sprockhoff [3]; and 222.2 /zm (45 cm -~) to 50.00 /xm (200 cm -~) values of n and k were presented by Pai e t al.[4]. 845 HANDBOOK OF OPTICAL CONSTANTS OF SOLIDS III
Copyright 9 1998 by Academic Press. All rights of reproduction in any form reserved ISBN 0-12-544423-0/$25.00.
846
Ivan Ohlfdal and Miloslav Ohlidal
The Li formula employed for calculating the refractive-index data of RbBr in the region 54.00/xm _> ~ _> 0.21 /xm was constructed in the form n 2 = 1.45931 +
0.16301 ~2 0.29841 A2 + + A2 - (0.123) 2 A2 - (0.146) 2
0.17198 ~2 0.12186 ~2 + + ~ 2 _ (0.155)2 ,~2_ (0.178)2
(1)
0.13039 ~2 2.520 ~2 + ~2 _ (0.191)2 ~2 _ (114.29) 2 ' where A is in micrometers. The values of n calculated by means of the Li formula (see Table I) correspond to the RbBr single crystal because this formula was obtained on the basis of the important Kublitzky refractive-index data [5]. The primary Kublitzky data were measured for prisms formed with the RbBr single crystal by means of the method of minimum deviation at selected wavelengths in the spectral region 0.578 /xm -> A -> 0.219/.Lm [5]. Li constructed his formula of the Sellmeier type in such a way that the wavelengths of the ultraviolet absorption peaks and the wavelength of the fundamental infrared absorption peak ~, found by direct measurements are included in this formula. The values of the adjustable parameters of the formula mentioned (e.g., 0.16301) were sought by fitting the Kublitzky data by means of the leastsquares method [2]. This means that the values of the refractive index n can be calculated using the Li dispersion formula at wavelengths beyond the Kublitzky's data in both directions, that is, at wavelengths belonging to the near-UV and the IR regions. On the basis of the Kublitzky data, Radhakrishnan [6] also derived the following empirical dispersion formula expressing the spectral dependence of the refractive index n of the RbBr single crystal in the region 0.546 ~m >- ,~ -> 0.219/xm: n 2 = 1.4500 +
0.2000 ~2 + ~2 _ 0.015129
0.3651 ~2 ~2 _ 0.022650
+
0.3224 ,~2
(2)
~2 _ 0.033124 '
,~ is also in micrometers. This formula gives wavelengths of ultraviolet absorption peaks that agree closely with those obtained by direct measurements [7, 8] but gives no information concerning the infrared absorption peak. Extrapolated values of n for the long wavelengths, that is, for the IR wavelengths, as given by the Radhakrishnan formula have large uncertainties in contrast to those given by the Li formula expressed with Eq. (1). This means that the Radhakrish-
Rubidium Bromide (RbBr)
847
nan dispersion formula is not an adequate one for use in a wide wavelength range, that is, in both the mid-IR and the far-IR regions in particular. Thus, the Radhakrishnan formula only correlates the dispersion in both the visible and the near UV with absorption bands in the UV region. Sprockhoff [3] measured the values of n of RbBr using the method of minimum deviation as well. He determined the refractive-index value of the RbBr single crystal at the following wavelengths: 0.486, 0.589 and 0.656/xm (see Table I). The errors of the refractive-index data calculated using Eq. (1) are dependent on wavelength. (The greatest and/or smallest errors in n are equal to ___ 0.02 in the regions 0.21-0.22/xm and 40.00-60.00 ~m and/or _ 0.002 in the region 0.40-1.50 /xm.) In the Sprockhoff and Kublitzky data the errors of the values of n can be estimated as _ 0.001. Pai et al. [4] determined the spectral dependences of n and k characterizing RbBr bulk samples (i.e., single crystals) by means of amplitude and phase reflection measurements made by dispersive Fourier transform spectroscopy in the region 222.2 ~m -> A -> 50/zm. The errors in the optical constants n and k evaluated in this way are also dependent on wavelength. (The greatest and/or smallest errors in both n and k are equal to + 0.10 and/or _+ 0.01 at the wavelength of about 116/zm and/or in the interval 93/xm _> )t -> 50/xm [4].) Spectral dependences of n and k in the vicinity of the maximum value of k at the wavelength of the fundamental infrared absorption peak &z are related to the TO phonon mode. The fine structures in the curves of n and k in the far-IR region may be caused by multiple-phonon absorption processes. In the visible there is very good agreement between the refractive-index data calculated using the Li formula [2] and measured by Kublitzky [5] on one side and those presented by Sprockhoff [3] on the other side (see Table I). Similarly, one can see a relatively good agreement between the values of n calculated by means of the Li formula and those determined by Pai et al. [4] in the region 54.00 /zm _> )t _> 50.00 /zm (see Table I). Both the facts mentioned give support for the correctness and reliability of the opticalconstant data presented for the RbBr single crystal in this paper. From Eq. (1) and the spectral dependence of k determined by Pai et al. [4], one can see that there is a good agreement between the value of/~I used in the Li formula [2] and that implied by the data of Pai et al. It should be noted that in the parts of the IR region in which RbBr is a weakly absorbing material (k -< 0.1), more precise values of k can be determined by transmittance measurements of sufficiently thin RbBr slabs than by means of the experimental techniques used by Pai et al. [4]. Thus far, these measurements of the transmittance of the RbBr slabs have not been performed in the IR region. Unfortunately, measurements enabling us to evaluate the values of the extinction coefficient k of the RbBr single crystals or RbBr thin films in the UV region have not been carried out, either. The optical-constant data presented here are the room-temperature
848
Ivan Ohlidal and Miloslav Ohlidal
data, as pointed out earlier. However, strictly speaking, there are small differences at temperatures corresponding to the data summarized. Namely, the refractive-index data obtained by means of the Li dispersion formula [2], the values of n determined by Sprockhoff [3] and the values of n and k published by Pai et al. [4] correspond to 293 K, 298 K, and 300 K, respectively. Both the Radhakrishnan formula [6] and the Kublitzky data correspond to 308 K. This means that at first Li reduced the Kublitzky refractiveindex data from 308 to 293 K to obtain his formula in the form presented. He performed these corrections by using empirical parameters to construct a formula for dn/dT, enabling him to carry out the mentioned corrections of the Kublitzky values of n [2] (dn/dT denotes the derivative of the refractive index with respect to temperature T). In conclusion, it is possible to state that the optical-constant data summarized here represent the best values of the refractive index n characterizing the RbBr single crystal in the region 222.2/xm --- h -> 0.21/.~m and the best values of the extinction coefficient k of the same material in the region 222.2 tzm -> h -> 50/xm. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8.
D. E. McCarthy, Appl. Opt. 7, 1243 (1968). H. H. Li, J. Phys. Chem. Ref Data 5, 329 (1976). M. Sprockhoff, Neues Jahrb. Mineral Geol. Palaeontol., Beilageband 18, 117 (1904). K. E Pai, T. J. Parker, N. E. Tornberg, R. P. Lowndes, and W. G. Chambers, Infrared Phys. 18, 199 (1978). A. Kublitzky, Ann. Phys. 20, 793 (1934). T. Radhakrishnan, Proc. Indian Acad. Sci. Sect. A 27, 165 (1948). R. Hilsch and R. W. Pohl, Z. Phys. 59, 812 (1930). E. G. Schneider and H. M. O'Bryan, Phys. Rev. 51, 293 (1937).
Rubidium
Bromide
(RbBr)
10
849
'
'
'
'
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'
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I
L
I I I I I I I I I I I I
n,k
I
|
|
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I I I I I I tI i I I I I I I I I I
0.01
,
0,1
, ,,,,,,I
,
1
, ,,,,,,I
,
.......
10
WAVELENGTH
'
,
100
[ p,m ]
Fig. 1. Log-log plot of n (solid line) and k (dashed line) versus wavelength in micrometers for RbBr.
850
Ivan Ohlidal and Miloslav Ohl[dal TABLE I Values of n and k for R u b i d i u m B r o m i d e as Obtained from Various References a
eV
cm - - 1
5.904 5.848 5.794 5.740 5.687 5.636 5.585 5.535 5.486 5.438 5.391 5.344 5.299 5.254 5.209 5.166 5.123 5.081 5.040 4.999 4.959 4.920 4.881 4.843 4.806 4.769 4.732 4.696 4.661 4.626 4.592 4.558 4.525 4.492 4.460 4.428 4.397 4.366 4.335 4.305 4.275 4.246 4.217 4.189 4.161
47,620 47,170 46,730 46,300 45,870 45,450 45,050 44,640 44,250 43,860 43,480 43,100 42,740 42,370 42,020 41,670 41,320 40,980 40,650 40,320 40,000 39,680 39,370 39,060 38,760 38,460 38,170 37,880 37,590 37,310 37,040 36,760 36,500 36,230 35,970 35,710 35,460 35,210 34,970 34,720 34,480 34,250 34,010 33,780 33,560
/zm 0.210 0.212 0.214 0.216 0.218 0.220 0.222 0.224 0.226 0.228 0.230 0.232 0.234 0.236 0.238 0.240 0.242 0.244 0.246 0.248 0.250 0.252 0.254 0.256 0.258 0.260 0.262 0.264 0.266 0.268 0.270 0.272 0.274 0.276 0.278 0.280 0.282 0.284 0.286 0.288 0.290 0.292 0.294 0.296 0.298
n 1.962 [2] 1.936 1.913 1.893 1.875 1.858 1.844 1.830 1.818 1.807 1.796 1.787 1.777 1.769 1.761 1.754 1.747 1.740 1.734 1.728 1.722 1.717 1.712 1.707 1.703 1.698 1.694 1.690 1.686 1.683 1.679 1.676 1.673 1.669 1.666 1.664 1.661 1.658 1.655 1.653 1.651 1.648 1.646 1.644 1.642
(continued) a
References given in brackets.
Rubidium Bromide (RbBr)
851 TABLE I
(Continued)
Rubidium Bromide
eV 4.133 4.065 4.000 3.936 3.875 3.815 3.757 3.701 3.647 3.594 3.542 3.493 3.444 3.397 3.351 3.306 3.263 3.220 3.179 3.139 3.100 3.024 2.952 2.883 2.818 2.755 2.695 2.638 2.583 2.551 2.530 2.480 2.431 2.384 2.339 2.296 2.254 2.214 2.175 2.138 2.105 2.101 2.066 2.000 1.937 1.890
cm-
1
33,330 32,790 32,260 31,750 31,250 30,770 30,300 29,850 29,410 28,990 28,570 28,170 27,780 27,400 27,030 26,670 26,320 25,970 25,640 25,320 25,000 24,390 23,810 23,260 22,730 22,220 21,740 21,280 20,830 20,580 20,410 20,000 19,610 19,230 18,870 18,520 18,180 17,860 17,540 17,240 16,980 16,950 16,670 16,130 15,630 15,240
/xm 0.300 0.305 0.310 0.315 0.320 0.325 0.330 0.335 0.340 0.345 0.350 0.355 0.360 0.365 0.370 0.375 0.380 0.385 0.390 0.395 0.400 0.410 0.420 0.430 0.440 0.450 0.460 0.470 0.480 0.486 0.490 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.589 0.590 0.600 0.620 0.640 0.656
1.640 1.635 1.630 1.626 1.622 1.618 1.615 1.612 1.609 1.606 1.603 1.601 1.598 1.596 1.594 1.592 1.590 1.588 1.587 1.585 1.583 1.580 1.578 1.575 1.573 1.571 1.569 1.567 1.566 1.565 [31 1.564 [21 1.563 1.561 1.560 1.559 1.558 1.557 1.556 1.555 1.554 1.553 [31 1.553 [2] 1.552 1.551 [2] 1.550 1.548 [3]
(continued)
852
Ivan Ohlidal and Miloslav Ohlfdal TABLE I (Continued) Rubidium Bromide
eV 1.879 1.823 1.771 1.722 1.675 1.631 1.590 1.550 1.512 1.476 1.442 1.409 1.378 1.348 1.319 1.292 1.265 1.240 1.181 1.127 1.078 1.033 0.9919 0.9537 0.9184 0.8856 0.8551 0.8266 0.7749 0.7293 0.6888 0.6526 0.6199 O.5636 O.5166 0.4769 0.4428 0.4133 0.3542 0.3100 O.2755 0.2480 0.2066 0.1771 0.1550 0.1378
--1 cm
15,150 14,710 14,290 13,890 13,510 13,160 12,820 12,500 12,200 11,900 11,630 11,360 11,110 10,870 10,640 10,420 10,200 10,000 9,524 9,091 8,696 8,333 8,000 7,692 7,407 7,143 6,897 6,667 6,250 5,882 5,556 5,263 5,000 4,545 4,167 3,846 3,571 3,333 2,857 2,500 2,222 2,000 1,667 1,429 1,250 1,111 ,,,
/xm 0.660 0.680 0.700 0.720 0.740 0.760 0.780 0.800 0.820 0.840 0.860 0.880 0.900 0.920 0.940 0.960 0.980 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.60 1.70 1.80 1.90 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00 4.50 5.00 6.00 7.00 8.00 9.00
1.548 [2] 1.547 1.546 1.546 1.545 1.544 1.543 1.543 1.542 1.542 1.541 1.541 1.540 1.540 1.539 1.539 1.539 1.538 1.538 1.537 1.537 1.536 1.536 1.535 1.535 1.535 1.535 1.534 1.534 1.534 1.533 1.533 1.533 1.532 1.532 1.532 1.532 1.532 1.531 1.531 1.530 1.530 1.529 1.528 1.527 1.526
Rubidium Bromide (RbBr)
853 TABLE I
(Continued)
Rubidium Bromide eV 0.1240 0.1127 0.1033 0.09537 0.08856 0.08266 0.07999 0.07749 0.07514 0.07293 0.07085 0.06888 0.06702 0.06526 0.06358 0.06199 0.06048 0.05904 0.05767 0.05636 0.05510 0.05391 0.05276 0.05166 0.05061 0.04959 0.04862 0.04769 0.04679 0.04592 0.04509 0.04428 0.04350 0.04275 0.04203 0.04133 0.04065 0.04000 0.03936 0.03875 0.03815 0.03757 0.03701 0.03647 0.03594 0.03542
cm-
1
,000 909.1 833.3 769.2 714.3 666.7 645.2 625.0 606.1 588.2 571.4 555.6 540.5 526.3 512.8 500.0 487.8 476.2 465.1 454.5 444.4 434.8 425.5 416.7 408.2 400.0 392.2 384.6 377.4 370.4 363.6 357.1 350.9 344.8 339.0 333.3 327.9 322.6 317.5 312.5 307.7 303.0 298.5 294.1 289.9 285.7
/xm lO.O 11.0 12.0 13.0 14.0 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0
1.525 1.524 1.522 1.521 1.519 1.517 1.516 1.515 1.514 1.513 1.511 1.510 1.509 1.508 1.506 1.505 1.504 1.502 1.501 1.499 1.498 1.496 1.495 1.493 1.491 1.489 1.488 1.486 1.484 1.482 1.480 1.478 1.476 1.474 1.471 1.469 1.467 1.465 1.462 1.460 1.457 1.455 1.452 1.449 1.446 1.444
(continued)
854
Ivan Ohlfdal and Miloslav Ohlidal TABLE I
(Continued)
Rubidium Bromide -1
/.~m
0.03493 0.03444 0.03397 0.03351 0.03306 0.03263 0.03220 0.03179 0.03139 0.03100 0.03061 0.03024 0.02988 0.02952 0.02917 0.02883 0.02850 0.02818 0.02786 0.02755 0.02725 0.02695 0.02666 0.02638 0.02610 0.02583 0.02556 0.02530 0.02505 0.02480
281.7 277.8 274.0 270.3 266.7 263.2 259.7 256.4 253.2 250.0 246.9 243.9 241.0 238.1 235.3 232.6 229.9 227.3 224.7 222.2 219.8 217.4 215.1 212.8 210.5 208.3 206.2 204.1 202.0 20O
35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.O 45.5 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.00
0.02418
195
51.28
0.02356
190
52.63
0.02294
185
54.05
0.02232 0.02170 0.02108 0.02046 0.02009 O.01984 0.01959 0.01934 0.01909
180 175 170 165 162 160 158 156 154
55.56 57.14 58.82 60.61 61.73 62.50 63.29 64.10 64.94
eV
cm
1.441 1.438 1.435 1.432 1.429 1.425 1.422 1.419 1.415 1.412 1.408 1.405 1.401 1.397 1.393 1.389 1.385 1.381 1.376 1.372 1.368 1.363 1.358 1.354 1.349 1.344 1.338 1.333 1.328 1.322 1.31 [4] 1.308 [2] 1.29 [4] 1.291 [2] 1.27 [4] 1.272 [2] 1.25 [4] 1.22 1.18 1.16 1.13 1.11 1.09 1.07 1.04 1.00
0.01 [4] 0.01 [4] 0.02 [4] 0.02 [4] 0.03 0.04 0.04 0.04 0.05 0.05 0.06 0.07 0.09
Rubidium Bromide (RbBr)
855 TABLE I
(Continued)
Rubidium Bromide eV 0.01885 0.01860 0.01835 0.01810 0.01785 0.01761 0.01736 0.01711 0.01686 0.01661 0.01637 0.01612 0.01587 0.01562 0.01537 0.01513 0.01488 0.01463 0.01438 0.01413 0.01389 0.01364 0.01339 0.01314 0.01289 0.01265 0.01240 0.01215 0.01190 0.01165 0.01141 0.01116 0.01091 0.01066 0.01041 0.01017 0.00992 0.00967 0.00942 0.00917 0.00893 0.00868 0.00843 0.00806 0.00744 0.00682 0.00620 0.00558
cm
-1
152 150 148 146 144 142 140 138 136 134 132 130 128 126 124 122 120 118 116 114 112 110 108 106 104 102 100 98.0 96.0 94.0 92.0 90.0 88.0 86.0 84.0 82.0 80.0 78.0 76.0 74.0 72.0 70.0 68.0 65.0 60.0 55.0 50.0 45.0
/xm 65.79 66.67 67.57 68.49 69.44 70.42 71.43 72.46 73.53 74.63 75.76 76.92 78.13 79.37 80.65 81.97 83.33 84.75 86.21 87.72 89.29 90.91 92.59 94.34 96.15 98.04 100.0 102.0 104.2 106.4 108.7 111.1 113.6 116.3 119.0 122.0 125.0 128.2 131.6 135.1 138.9 142.9 147.1 153.8 166.7 181.8 200.0 222.2
0.99 0.99 0.97 0.96 0.96 0.95 0.91 0.88 0.80 0.72 0.75 0.84 O.87 0.84 0.81 0.78 0.69 0.55 0.50 0.49 0.50 0.50 0.45 0.42 0.44 0.47 0.49 0.54 0.56 0.59 0.73 1.25 2.66 4.26 4.27 4.08 3.62 3.12 2.87 2.78 2.78 2.76 2.73 2.65 2.53 2.47 2.41 2.39
0.10 0.11 0.13 0.14 0.17 0.18 0.18 0.20 0.21 0.27 0.36 0.38 0.37 0.44 0.53 0.52 0.56 0.67 0.76 0.86 0.99 1.14 1.30 1.46 1.61 1.76 1.99 2.33 2.68 3.05 3.46 4.12 4.56 3.31 1.95 1.17 0.52 0.29 0.25 0.23 0.25 0.27 0.27 0.25 0.25 0. I9 0.18 0.13