JOURNAL OF RESEARCH of the National Bureau of Standards - A. Physics and Chemistry Refractive Indices of Fused Silica at Low Temperatures* R. M. Waxler and G. W. Cleek Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234 (April 7, 1971) The refractive indices of a commercial fused silica specimen were determined at ten wavelengths from 404.7 to 667.8 nm over the temperature range from -200 to +20 °C. The data are needed for the design of optical systems for space applications where the extremes of temperature are encountered. Values of the thermal coefficient of refractive index were found to be positive and varied from about 9 × 10-6/°C at room temperature to 3 × 10-6/°C at liquid nitrogen temperature. The data also showed that there is an increase in dispersion with increasing temperature. These results bear out the predictions of the theory for the thermo-optic behavior of solids. Key words: Fused silica; glasses; interferometry; optics; refractive index. 1. Introduction Data on the refractive indices of fused silica at low mperatures are needed in the design of optical sysems for space applications. A survey of the literature hows that Rinne [1, 2]1 made measurements to 160 °C for four spectral lines of helium radiation. He used the classic minimum deviation method with a rism of fused silica and a goniometer which read to s. The data are reported to 5 significant figure's. Austin and Pierce [3] have reported on refractive inices to 200 °C for one spectral line of helium at 87.6 nm. These authors used an optical interference method in which change in optical path length was easured, and the change in refractive index from an nitial value was calculated; the technique requires ata on linear thermal expansion. This method makes I possible to obtain index data to 6 significant figures. The source of the fused silica was not specified n either of the above investigations. In the present study, it was desired to obtain data on commerical used silica, Corning Code 7940,2 from +20 to -200 °C For 10 wavelengths from 404.7 to 667.8 nm. Fused silica is an interesting material for study, because it is known from earlier work that the change of refractive index with temperature, dn/dT, is very arge, being about 9 × 10-6/°C at room temperature, 3] whereas for most optical crown glasses it is about 2 or 3 × 10-6/°C [4, 5]. On the other hand, the coefficient of thermal expansion is extremely low, being about 0.5 × 10-6/°C [6, 7] while most optical glasses have *This work was sponsored by Langley Research Center, NASA. National Aeronautics and Space Administration, Washington, D.C. 20546. The figures in brackets indicate literature references at the end of this paper. Commercial materials are identified in this paper to specify the particular substance on which the data were obtained. In no instance does such identification imply recommendaion or endorsement by the National Bureau of Standards or that the material identified is necessarily the best for the purpose. values on the order of 8 to 10 × 10-6/°C [4]. There is, therefore, a large value of dn/dT for fused silica which cannot be attributed to change in volume. 2. Experimental Method The interference method employed by Austin and Pierce [3] offers the attractive feature of high precision of measurement. There is the additional feature that, since the specimen employed is small, thermal gradients constitute less of a problem. Moreover, a continuous record of change in optical path length may be obtained by using a continuously recording camera. For these several reasons it was decided to use this basic method with some amplifications to permit the photographing of fringe shifts for several spectral lines simultaneously. In the optical interference method the specimen in the form of a plate with flat, polished faces constitutes the interferometer. When this plate is viewed in reflection using collimated, monochromatic light, a pattern of localized, Fizeau-type interference fringes may be seen at the top surface. For a specimen of thickness, t, and refractive index, n, the fringe number N is given by 424-032 OL-71-3 mark and the change in thickness, together with data on the initial index and thickness, permit the calculation of An. The shift in interference fringes was recorded photographically on high speed film, using an optical system similar to the one described by Saunders [8]. It has been found that the proper adjustment of a prism in Saunders' apparatus permits the recording of fringe shifts for several spectral lines on the same film [9]. In the present investigation four spectral lines of helium, 471.3, 501.6, 587.6 and 667.8 nm were recorded on one film, four spectral lines of cadmium, 467.8, 480.0, 508.6, and 643.8 nm were recorded on a second and two lines of mercury, 404.7 and 435.8 nm were recorded on a third. The fused silica specimen was about 0.3 cm in thickness. This specimen was half-silvered on the front surface and fully silvered on the back surface in order to increase the brightness in the image plane. The specimen was enclosed in a cryostat, in which liquid nitrogen was used to effect the reduction in temperature; this apparatus has been described [10]. In the present experiment, liquid nitrogen was added, a little at a time, and, after each addition, a waiting period of about one-half hour was allowed for a quasiequilibrium condition to obtain. The temperature was measured at each plateau with a potentiometer and a calibrated copper-constantan thermocouple. Calculations showed that the sensitivity of measurement was 0.02 °C at room temperature and 0.5 °C at the lowest temperatures. In each run, eight to twelve temperature intervals provided data points from +20 to about - 192 °C. 3. Results and Discussion The experiments involved only measurement changes in optical path, and initial values of refractiv index at 20 °C for the various spectral lines were thos reported by Malitson [11]. The small corrections for th change in length, At, were taken from the data d Scheel and Heuse [6] which are recommended h Sosman in his compendium on silica [7]. With th information plus the measured values of AN, it wa possible to calculate An for each temperature interva It was estimated that shifts could be measured t one-tenth of an interference fringe, and calculation showed that this meant that the sensitivity of measure ment was about 2 × 10-5 in An. The calculated values of An were then fitted b computer to a cubic equation, and values of An a temperature intervals of 10 °C were printed out from +20 to 200 °C. These increments were added to th initial values of refractive index, and the results whic refer to air at 20 °C are shown in table 1. The standar deviation of each value of the original data was withi 1× 10−5. The initial values of refractive index used in th present study differed from those of the earlier in vestigators, but it is still possible to make a com parison of the changes in refractive index betwee two specified temperatures. The temperatures, 18 an - 160 °C were selected because Rinne [1, 2] report his data at these points, and Austin and Pierce [3] give an equation from which these values may be obtained In the present study, values at 18 °C were found from the computer run although they are not given in table l TABLE 1. Refractive index of fused silica, Corning Code 7940, as a function of temperature and wavelength + 20 +10 0 - 10 - 20 1.45573 -30 1.45565 - 40 1.45557 1.45623 1.45797 1.46136 1.46173 - 50 1.45550 1.45615 1.45789 1.45607 1.45670 1.45846 1.46186 1.46224 1.46350 1.46406 1.46429 1.46669 1.46962 the helium spectral line of 587.6 nm. The curve represents smoothed data taken from the computer run. The points represent values of An/AT calculated from the experimental data between two adjacent values of temperature and plotted at the mid-point. or the four wavelengths used by Rinne and the single FIGURE 1. Temperature variation of dn/dT for fused silica at avelength employed by Austin and Pierce. Condering that the sensitivity of measurement of the iterference method is 2x 10-5, the difference of × 10-5 for the two values of An at 587.6 nm (data of ustin and Pierce versus data of the present study) eems reasonable. Rinne's data are of lesser precision, ut, recognizing this, the agreement between the sets f data appears to be good. It should be noted that the data obtained here bear at the phenomenological theory for the thermal hange in the refractive index of solids which has een developed by Ramachandran [12, 5, 13]. Accordg to this theory, dn/dT in a solid depends upon (1) change in the number of dispersion centers and 2) a variation in the dispersion frequencies. This ariation in the dispersion frequencies, in turn, shows dependence upon volume change as the solid exands as well as an effect due purely to temperature. From data on commercial glasses [5] and fused ilica [13], Ramachandran has inferred that the variaon of the dispersion frequencies in these materials essentially independent of change in volume and is Imost solely dependent on temperature change itself. This is very apparent in the case of vitreous silica where the thermal expansion is extremely small, and he shift in the fundamental dispersion frequency ccounts almost entirely for the observed changes in n/dT. Values of dn/dT for the spectral line of 587.6 nm re shown as a function of temperature in figure 1. t can be seen in the figure that dn/dT decreases coninuously to the lowest temperatures investigated, ven though there is a maximum in the density of used silica at about — 80 °C [6, 7]. The theory also predicts that the magnitude of the emperature shift of the fundamental absorption band lecreases with fall of temperature, and probably anishes at low temperatures. In fused silica this is nanifested in the variation of dn/dT with temperature s shown in figure 1. For several commercial optical classes, Molby [4] has found that refractive index ersus temperature data exhibit a minimum at some educed temperature. The commercial glasses have an appreciable thermal expansion (in contrast to fused silica) with an accompanying contribution to dn/dT that is always negative because of the lessening in the number of dispersion centers. The data on the optical glasses may be explained by the reduced contribution to dn/dT by the temperature shift of the fundamental absorption band at low temperatures. Ramachandran has pointed out that the shift of fundamental absorption band with increasing temperature is toward longer wavelengths, so that there is an increase in dispersion. This is borne out by the data for fused silica shown in table 1, by subtracting the value of the refractive index for the spectral line of 667.8 nm from that at 404.7 nm, comparison shows that the differences are 0.01343 and 0.01355 at -200 and +20 °C, respectively. 4. References [1] Rinne, F., Nues Jahrb. Mineral, Beil. 39, 388 (1914). [3] Austin, J. B., and Pierce, R. H. H., Jr., Physics 6, 43 (1935). [5] Ramachandran, G. N., Proc. Indian Acad. Sci. 25A, 498 (1947). [6] Scheel, K., and Heuse, W., Verh. Deutsch. Physik, GES. 16:1-3. [7] Sosman, R. B., The Properties of Silica, (Chemical Catalog Co., New York, 1927) pp. 403-406. [8] [9] Saunders, J. B., J. Res. Nat. Bur. Stand. (U.S.) 35, 157-186 (1945) RP 1668. Waxler, R. M., Weir, C. E., and Schamp, H. W., Jr., J. Res. Nat. Bur. Stand. (U.S.), 68A (Phys. and Chem.) No. 5, 489498 (Sept.-Oct. 1964). [10] Wachtman, J. B., Jr., Scuderi, T. G., and Cleek, G. W., J. [11] Malitson, I. H., J. Opt. Soc. Am. 55 No. 10, 1205 (1965). (Paper 75A4-669) JOURNAL OF RESEARCH of the National Bureau of Standards-A. Physics and Chemistry Heat Capacity, High-Speed (Subsecond) Measurement of Heat A. Cezairliyan and J. L. McClure Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234 (April 14, 1971) Measurements of heat capacity, electrical resistivity, hemispherical total emittance, and normal spectral emittance of tungsten above 2000 K by a pulse heating technique are described. Duration of an individual experiment, in which the specimen is heated from room temperature to near its melting point, is less than one second. Temperature measurements are made with a photoelectric pyrometer. Experimental quantities are recorded with a digital data acquisition system, which has a full-scale signal resolution of one part in 8000. Time resolution of the entire system is 0.4 ms. Results on the above properties of tungsten in the range 2000 to 3600 K are reported and are compared with those in the literature. Estimated inaccuracy of measured properties in the above temperature range is: 2 to 3 percent for heat capacity, 1 percent for electrical resistivity, 3 percent for hemispherical total and normal spectral emittances. Key words: Electrical resistivity; emittance; heat capacity; high-speed measurements; high tempera- 1. Introduction Tungsten has the highest melting point (above 3600 K) of any known metal. Because of the difficulties involved in performing accurate experiments by conventional techniques at temperatures above approximately 2500 K, a high-speed method was developed to measure heat capacity, electrical resistivity, hemispherical total emittance and normal spectral emittance of electrical conductors. In this paper, application of this technique to measurements on tungsten in the temperature range 2000 to 3600 K is described. The method is based on rapid resistive self-heating of the specimen from room temperature to near its melting point. During the short experiment, which lasts less than 1 s, current flowing through the specimen, potential across the specimen and specimen temperature are measured. Temperature measure of relations for properties etc., are given in earlier publications [2, 3] in connection with measurements on molybdenum and tantalum. 2. Measurements The measurements were made in the temperature interval 1900 to 3600 K. To optimize the operation of the pyrometer, this temperature interval was divided into four ranges: low, 1900 to 2200 K; medium, 2150 to 2500 K; high, 2450 to 2900 K; and very high, 2850 to 3600 K. Two experiments were conducted in each range; and three additional experiments were conducted in the first three ranges in which the surface radiance of the specimen was measured. Before the start of the experiments, the specimen was annealed by subjecting it to approximately 30 heating pulses (up to 3200 K). -1 at The duration of the current pulses in the experiments ranged from 410 to 630 ms depending on the desired final temperature. The average heating rate of the specimen was: 7100 K s-1 at 2000 K, 5600 K s 3000 K, and 3700 K s-1 at 3600 K. At these temperatures, radiative heat losses from the specimen amounted to approximately 3, 12, and 27 percent of the input power, respectively. All of the experiments were conducted with the specimen in a vacuum environment of approximately 10-4 torr. The data on voltage, current, and temperature were used to obtain third degree polynomial functions for |