UNIVERSITY OF PENNSYLVANIA OPTICAL CONSTANTS OF THE BINARY ALLOYS OF SILVER WITH COPPER AND PLATINUM BY LOUIS K. OPPITZ A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY PRESS OF THE NEW ERA PRINTING COMPANY LANCASTER, PA. UNIVERSITY OF PENNSYLVANIA OPTICAL CONSTANTS OF THE BINARY ALLOYS OF SILVER WITH COPPER AND PLATINUM BY LOUIS K. OPPITZ *N\ A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY PRESS OF THE NEW ERA PRINTING COMPANY LANCASTER, PA. IQI7 [Reprinted from the PHYSICAL REVIEW, N. S., Vol. X, No. 2, August, 1917.] OPTICAL CONSTANTS OF THE BINARY ALLOYS OF SILVER WITH COPPER AND PLATINUM. T BY Louis K. OPPITZ. HISTORICAL INTRODUCTION. HE first studies in the optical constants of alloys were those of Drude 1 who investigated three alloys: (a) one of 18 k. gold alloyed with silver, copper, and a small quantity of iron; (&) one of copper-nickel; and (c) Wood's alloy. He made no attempt, however, to study any complete series of alloys related according to some well conceived prop- erty. Willi Meier 2 measured the optical constants of Wood's alloy and those of an alloy of gold and silver of equal parts by weight. His main interest was in the study of optical constants for a series of wave lengths which extended into the ultra-violet region. Bernouilli 3 measured the optical constants of a number of alloys, that form solid solutions; but restricted his examinations to small concen- trations, that is to dilute solid solutions. His work includes a study of the optical constants of Ag-Tl, Ag-Sn, Cd-Hg, Cu-Sn and Cu-Ni. The main interest in his work is his method, 4 which consisted of the measure- ment of the minimum azimuth of restored polarization. Voigt 5 has criticized the mathematical formula employed by Bernouilli as an illegitimate approximation. Littleton 6 was the first to study the variation of optical constants for entire alloy series. He investigated the alloy series of Cu-Ni, Fe-Mn, Ni-Fe, Ni-Si, Al-Cu and Cu-Fe. These alloys seem not to have been chosen for the purpose of studying group characteristics. In 1912, Eckhardt 7 investigated a series of gold-silver alloys. Gold and silver form an unbroken series of solid solutions. The series investi- gated consisted of ten members of progressively varying compositions. The concentration-refractivity curve of the series is continuous and shows 1 Drude, Ann. d. Phys., N. F., Vol. 39, 1890, pp. 481-554. 2 Willi Meier, Ann. d. Phys., Ser. 4, Vol. 31, 1910, pp. 1017-1099. 3 Bernouilli, Zeitschr. d. Elektro-chem., 15, pp. 646-648. 4 Ann. d. Phys., Ser. 4, Vol. 29, pp. 585 et seq. 5 Voigt, Ann. d. Phys., Ser. 4, Vol. 29, 1909, pp. 956 et seq. 6 Littleton, PHYS. REV., Vol. 32, 1911, pp. 453 et seq. r Eckhardt, Doctor's Thesis, University of Pennsylvania. 444337 157 LOUIS K. OPPITZ. [S?S a distinct but weak maximum, while the absorptive index curve shows a distinct minimum at about the same concentration. The indices of refraction of nearly all of the gold-silver alloys are higher than those of either component forming the series. OBJECT, THEORY AND METHOD OF THE PRESENT INVESTIGATION. The object of the present investigation is a study of the optical con- stants of two complete series of binary alloys, silver-copper and platinum- silver. The copper used in the alloys was electrolytic copper, while the silver was 1,000 fine assay silver. The alloys were approximately of the same size and mass. The masses of the metals constituting the alloys were carefully determined on a chemical balance. The alloys were also weighed after being fused. In no case was there a greater loss due to evaporation than one part in about three hundred. The boiling point of silver is about 1950 C. In order to avoid the loss of silver by evaporation, the platinum was first fused, and the silver was introduced gradually into the melted platinum. The regulus was then carefully stirred by means of a carbon rod and was kept at red heat for several hours, to insure a homogeneous mixture. The alloys were fused in graphite crucibles in a resistor furnace. They are free from graphite, as is shown by the values of the optical constants of the pure metals. The source of energy was an alternating current passed through a step-down transformer. POLISHING OF THE MIRRORS. The method of polishing was approximately that of Drude. After the alloy had cooled it was mounted and a plane face was turned on it in a jeweler's lathe. It was then treated with emery. Fine grades of French emery paper of four degrees of fineness (i. e.j o, oo, ooo, oooo) were used. The process of polishing began with the use of the o grade that being the coarsest. The specimen was stroked in a definite direction against the emery paper. The emery paper was held on a smooth plate of plane glass. Each mirror required individual treatment. The pressure of the stroke was adapted to the hardness of the particular alloy. The surface of the alloy was stroked so as to give to the scratches a single definite direction. Then the mirror was stroked in a direction at right angles to the scratches imparted to it by the coarsest grade of emery paper, against an emery paper of the next grade of fineness and so on until the finest grade of emergy paper had been used. Each succeeding grade of emery paper thus tended to remove or to render less deep the No L *2 X '] OPTICAL CONSTANTS OF BINARY ALLOYS. 158 scratches introduced by the preceding, and to insure a plane surface. If any scratches remained after the finest emery had been used, recourse was had to a burnishing tool like that used by silversmiths. Much care was exercised to keep the surface of the emery paper free from dust and other forms of contamination. Drude's criterion for a satisfactory optical surface was used: the azi- muths of restored polarization for light parallel and perpendicular to the scratches must be approximately equal. The phase change was found to be invariable for a given angle of incidence so long as the mirror remained free from surface layers. OPTICAL METHODS. The source of light was a Bunsen flame colored by means of fused NaCl. This light was filtered though an aqueous solution of K 2 Cr 2 O 7 which rendered the resulting light practically that of the D lines of sodium. The light incident upon the surface to be studied was plane polarized at an azimuth of 45. This light after reflection became elliptically polarized and was reconverted into plane polarized light by means of a Soleil-Babinet compensator. The azimuth of restored plane polarization was determined by means of an analyzing half-shadow-nicol system. Then the analyzing nicol was set for extinction and the phase change was determined by the use of the compensator. The angle at which the plane polarized light became incident upon the surface of reflection was carefully determined by reading the position of the telescope from the goniometer circle. In order to determine the azimuth of restored polari- zation, a modified form of the Zehnder 1 half-shadow polarimeter was used. This consisted of the usual analyzing nicol and a movable smoked glass wedge, adjacent to the nicol and moving over a fixed smoked glass wedge. In its original form the polarimeter was made up of an analyzing nicol adjacent to a fixed smoked glass plate. The intensity of the light used for studying the optical properties of the surfaces was found to vary for different angles of incidence and for different optically reflecting surfaces. It was therefore found that relatively large angles of incidence were the most favorable. At suggestion of Dr. Eckhardt, of this laboratory, the fixed smoked glass plate to which reference has been made was replaced by a movable smoked glass wedge, which could be varied so as to change the length of the path traversed by the light passing through it. This rendered it possible to adapt the length of the path to the intensity of the light traversing the polarimeter. This gave half shadow equality through a range varying from 7 to 21. The determination of the position of 1 Zehnder, Ann. d. Phys., 26, 1908, pp. 985-1018. 159 LOUIS K. OPPITZ. extinction of the analyzing nicol with the polarizer depended upon judging half-shadow equality. Half-shadow equality is most easily judged when the illumination through the analyzing nicol and smoked glass appears homogeneous and intense. Two half-shadow equality positions were viewed, one on each side of the extinction position of the analyzing nicol. Then the analyzing nicol half-shadow device was rotated ap- proximately 1 80 and two other half-shadow equality positions were found. Thus, there were four readings in all from which to find the extinction position of the nicol. The arithmetical mean of the positions before and after extinction gives the extinction position. Much practice was necessary for attaining proficiency in the judgment of half-shadow equality. After considerable preliminary practice, the initial step in the experimental work was to determine the optical con- stants of electrolytic copper. The experimental values obtained for pure copper are as follows : nK K .640 2.63 4.10 Drude, .620 2.57 4.14 L.K.O. The difference in the two sets of values is probably explainable on the basis that the two specimens of copper used, differed in purity. After determining these optical constants for pure copper, those of nine different alloys of silver-copper, of eight alloys of silver-platinum and pure silver and pure platinum were measured. The entire eleven points of the silver- copper curves (Fig. 3) and the entire ten points of the platinum-silver curves were experimentally determined (Fig. 4). In the figures, the variation in the composition of the alloys is ex- pressed in terms of the atomic per cent, of copper. The reflecting power was obtained by calculation, and not by direct measurement. No ex- planation is at present offered for the anomalously high reflecting power of the silver-copper alloy of 4.99 per cent, concentration. WORKING FORMULA. The well known formulae of Drude were in the calculation of the optical constants : w 2 (i + K 2 } = tan 2 P sin 2 tan 2 0. (i) The atomic per cent, of one component is given by loop x = - , p + (100 - p) - VOL. X.I No. 2. J OPTICAL CONSTANTS OF BINARY ALLOYS. 160 where p = per cent, by weight of this- component, a = its atomic weight and b = the atomic weight of the other component. K = tan Q (2) tan A = sin Q tan 2 P (3) cos 2\f/ = cos Q sin 2P (4) h i 2n R = where n 2 (i (5) n = the index of refraction, K = the absorptive index, A = the phase change, i// = the azimuth of restored polarization, R = the reflecting power, = the angle of incidence. EXPERIMENTAL RESULTS. Silver- Copper Alloys. Silver and copper form a series of alloys in which there are two limited series of solid solutions, separated by a gap. This gap consists of a series i of eutectiferous alloys. As one withdraws from pure silver, silver crystals, i. e., crystal type I. sepa- rate out, and this lowers the melt- ing point. At 8.5 per cent, of copper concentration, the solid so- lutions of silver are saturated, being incapable of taking up any further quantity of copper. After that, the crystals contain varying amounts of silver imbedded in the melt. At 40 per cent., the melt solidifies about the crystals. The saturation point for copper is 96 per cent. Likewise from 100 per cent, copper to 40 per cent., the crystals vary in the amount of copper contained. At 40 per cent, of concentration, the solid solutions are in equilib- rium with the melt, and therefore a eutectic mixture is formed. These thermal relationships obtained from Guertler's Metallographie are given in Fig. i. Fig. 1. 161 LOUIS K. OPPITZ. The optical constants of these alloys are shown in Table I. while Fig. 3 is a graphical representation of the same. TABLE I. Silver-Copper Series. Wt. Per Cent. of~Cu. Atom. Per Cent, of Cu. n K nK R .202 17.08 3.44 94 3 4.99 .252 11.35 2.86 98.8 6 10J27 .517 6.51 3.31 84.87 10 16.49' .492 7.51 3.69 87.68 30 42.12 .36 6.61 2.40 80.92 50 62,94 .312 7.57 2.37 82.92 72 40.00 .244 13.78 3.36 93.26 80 87.14 .416 7.05 2.93 84.35 90 93.87 .507 5.71 2.90 80.98 95 96.99 .643 5.01 3.22 80.26 100 100.00 .620 4.14 2.57 73.11 The concentration-refractivity curve shows a minimum near the eutec- tic point, the index of refraction being the lowest here excepting that of pure silver. As the eutectic point is left in either direction, there is an increase in the index of refrac- tion. The absorptive index-concentra- tion curve shows a relative maxi- mum near eutectic point, but the absorptive index of every alloy is higher than of copper and always lower than of silver. Platinum-Silver Alloys. Similarly platinum and silver form two series of solid solutions separated by a gap. This gap con- sists of a region of heterogeneous mixture of silver and platinum ex- tending from approximately 34.8 per cent, to 83.5 per cent, of plat- Fig. 2. inum concentration. Beyond these points in either direction, we find solid solutions. These relations are found in Fig. 2. This was also obtained from Guertler. VOL. X.I No. 2. J OPTICAL CONSTANTS OF BINARY ALLOYS. 162 Hf. : Co flee nt r^ion it R+omie. "/, oj. Pfr. Fig. 3. Fig. 4. The optical constants of these alloys are found in Table II. while their graphical representation is embodied in Fig. 4. TABLE II. Platinum-Silver Series. Wt. Per Cent, of Pt. Atom. Per Cent. ofPt. 7* K nK R Loss in Mass of Alloy After Fusing. 15 8.9 .202 .71 17.08 5.92 3.44 4.26 94% 86.54 0.000 gr. 0.035 30 19.18 1.05 3.69 3.91 78.85 0.020 40 26.97 1.13 2.736 3.09 67.95 0.032 45 31.18 1.26 2.42 3.10 65.56 0.000 48 33.83 1.45 2.29 3.33 65.98 0.000 50 35.64 1.57 2.15 3.39 65.27 0.000 62 47.47 1.74 1.82 3.18 60.41 0.000 90 83.39 2.12 1.85 3.95 66.24 0.000 100 100.00 2.03 1.96 3.80 65.61 0.000 Good working surfaces of the platinum-silver alloys were easily ob- tained. The concentration refractive index curve shows an unmistakable in- crease toward pure platinum. The concentration absorptive index curve indicates a very sudden drop from pure silver to the next member of the series. After that the decrease is very gradual. The absorptive index I 63 LOUIS K. OPPITZ. of pure platinum is slightly lower than that of the solid solutions of crystal type II. in Fig. 2. In general, for platinum-silver alloys as well as silver-copper alloys when solid solutions are formed, an index of refraction which increases with the concentration indicates a decreasing absorptive index. A typical sample of the readings (those on the eutectic alloy of silver and copper) is included below: Sample Series of Observations for Mirror No. I Atomic per cent. Cu =40. Eutectic Alloy of Silver and Copper. Angle of Incidence = 74 7'. I. Scratches Parallel to Plane of Incidence. Polarizer at 285 59'. 28 10' 47 20' 204 45' 230 30' 25 46 50 205 10 35 10 47 25 204 50 50 20 10 55 40 2 20 15 205 00 40 28 17 47 12 204 56 230 39 Aver. 37 44' Aver. 2 17 47' Polarizer at 195 59'. 295 35' 327 55' 121 40' 142 35' 35 328 00 10 45 296 05 327 40 15 10 295 40 50 30 30 40 45 20 30 295 43 327 51 121 23 142 30 Aver. 311 47' Aver. 131 56' Polarizer at 105 59'. 28 05' 47 20' 204 45' 230 45' 27 55 05 205 05 25 28 15 15 204 55 35 00 25 205 10 40 15 20 00 50 28 06 47 17 204 59 230 39 Aver. 37 41' Aver. 217 49' Polarizer at 375 59'. 296 05' 328 05' 121 25' 142 15' 295 35 327 40 10 50 296 10 328 00 10 30 295 35 327 45 15 35 296 20 328 15 20 40 295 57 328 15 121 16 142 34 Aver. 311 57' Aver. 131 55' 2^ = 217 47' - 131 56' = 85 51' TT - 2^ = 311 47' - 217 47' = 94 VOL. X.I No. 2. J OPTICAL CONSTANTS OF BINARY ALLOYS. 164 II. Scratches Perpendicular to Plane of Incidence. Polarizer at 285 59'. 28 10' 46 50' 15 47 00 25 46 55 20 47 20 20 25 28 18 47 06 Aver. 37 42' 295 15' 328 59' 30 327 40 20 50 45 45 40 55 295 30 327 50 Aver. 311 40' 28 15' 46 50' 30 47 00 20 15 25 20 2 20 10 28 22 47 07 Aver. 37 44' 295 20' 327 35' 40 328 05 35 327 40 50 50 20 55 295 33 327 49 Polarizer at 195 59'. Polarizer at 105 59'. Polarizer at 375 59'. 205 00' 230 30' 204 45 50 50 35 205 10 40 204 55 35 204 56 230 38 Aver. 217 47' 122 05' 141 55' 121 30 142 10 40 30 15 20 20 20 121 24 142 15 Aver. 131 49' 204 40' 230 40' 50 45 55 35 205 10 40 00 50 204 55 230 42 Aver. 217 48' 121 55' 142 05' 25 141 50 30 142 15 15 25 40 30 121 33 142 13 Aver. 311 41' Aver. 131 53' = 217 47' - 131 49' = 85 58' Compensator Readings. Before Extinction. After Extinction. Main Scale. Scale. Main Scale. Scale. 16.00 04 17.00 19 15.75 97 34 16.00 48 47 14 77 09 86 Av 16 00 14 17.00 52 General Average: 16.50, 33 divisions. 165 LOUIS K. OPPITZ. HER?ES D SUMMARY OF RESULTS. 1. Near the eutectic point, the index of refraction is lower than that of any other member in the silver-copper series, except that of pure silver, while the absorptive index is a relative maximum for the same concen- tration. 2. The indices of refraction of the alloys at the saturation points in the two regions of solid solutions for silver-copper are higher than that of the pure metal near these points. 3. From the eutectic point of the silver-copper series, there is a marked increase in the index of refraction in either direction until saturated solid solutions are formed. The absorptive index shows a behavior which is approximately the inyerse of that shown by the index of refraction. 4. The reflecting power of a metal of relatively low reflecting power is in general improved by mixing this metal with one of relatively higher reflecting power. This is in agreement with the work of others. 5. Whenever solid solutions are formed an increasing index of refraction indicates a decreasing index of absorption. This is borne out by the studies of both the silver-copper and platinum-silver series. In conclusion, I wish to record my grateful appreciation to Dr. H. C. Richards for placing at my disposal the facilities of the Randal Morgan Laboratory of Physics. Not only has he shown interest throughout the en- tire progress of this work but it is to him that I owe my first interest in the subject of optical constants. It is also with pleasure that I acknowledge my indebtedness to Dr. E. A. Eckhardt who has aided me with numerous valuable suggestions in every detail of the work. THE RANDAL MORGAN LABORATORY OF PHYSICS, UNIVERSITY OF PENNSYLVANIA. UNIVERSITY OF CALIFORNIA LIBRARY