Vol. 64
EDWIN RII. LARSENA N D DONALD R. VISSERS
i
I T 5°C
267.
A
2
i
447*
Time. Fig. 9.-A comparison between the differential thermal analysis curves of non-irradiated sublimed ;hrT&C104 and irradiated “4ClO4 carried out in air a t atmospheric Dyessure. Total absorbed dose 5.4 x 10-2 e.v./molec. Heating rate 5’/min., 250-mg. samples. Downward direction endothermal, u ward direction exothermal: 1, non-irradiated sublimed h?H&l04; 2, irradiated “4ClOn.
259’
q4. 236’
398.
for the sublimate. The sublimate appears to consist of agglomerates of spherical particles of about 5 p in diameter. Samples of uiiirradiated Time. Fig. 8.-Differential thermal analysis curves for am- ammonium perchlorate ground gently to approximonium perchlorate containin 1 mole % iodide ion heated mately the same average particle size did not exin air at atmospheric ressure,gheating rate 5’/min., 250-mg. hibit a decomposition spectrum similar to that of samples. DifTerentiaf temperature us. reference tempera- the sublimate. Spheroidal shape may indicate e.v./molec. Downward ture. Absorbed dose 7.0 x direction endothermal upward direction exothermal: curve poorly ordered crystals, as was confirmed by appreciable X-ray line broadening. 1, non-irradiated; ciirve 2, irradiated. Acknowledgment.-The authors wish to acThe reason for this is not clear. It would seem, knowledge the partial financial support of this however, that whatever factors affect reactivity research by the Office of Ordnance Research under caused by exposure to radiation are operating Project T B 1-0004. 7.5 MIN
1’HE EXCHANGE OF Li+, Naf AND K + WITH Hi- O S ZIRCOI1’IUICI PHOSPHATE’ BY EDWIN M. LARSENAND DOXALD R. VISSERS ?’he Departnient of Chemistry, the Universiy of Wzscmszn, Madison, ll’zsroti~cn Recetved M a y 18, 1950
The equilibrium exchange of Li+, Na+, K + with the hydrogen form of zirconium phosphate in 0.1005 N HCl W:Mstudied over the temperature range 1.17 to 44.5’. The following data were obtained for Li+, Naf and K+, respectively: AFO +2.0, 3-1.1, +0.56kcal./mole; AHO0.0, -2.7, -5.7kcal./moleandAS0, -6.7, -13, -21e.u.
The use of zirconium phosphate as an ion-ex- tative studies of the equilibria have been reported, change material has been reported by Kraus2-6 an examination of the exchange of Li+, lis+ and and Am~hlett.’-~ Since no systematic quanti- K+, with hydrogen ion was undertaken. (1) Baaed on a thesia submitted by Donald R. Viasers in partial fulExperimental fillment of the requirements of the degree of Doctor of Philosophy. Preparation of Zirconium Phosphate.-In general, the phosphates were prepared by the slow addition of 0.015 to 0.2 M sodium dihydrogen phosphate solution or phosphoric (4) K. A. Kraus and F. Nelson, “Proc. Intern. Conf. on Peaceful acid to a 0.01 to 0.1 M zirconium oxychloride solution with Uses of Atomic Energy,” Vol. 7, 113, 131 United Nations (19.56). (5) K. A. Kraus, T. A. Carlson and J. S. Johnson, Nature (London) rapid stirring, both solutions being 0.1 M in hydrochloric ( 2 ) K. A. Kraus, Chem. Eng. N e w s , 34, 4760 (1956). (3) K. A. Kraus, J . Am. Chem. Soc., 78, 694 (1956).
177, 1128 (1956). (6) K. A. Kraus, H. 0. Philips, T. A. Carlson and J. S. Johnson, Abstracts, Boston Meeting, Bm. Chem. Soo., 1959. (7) C. B. Amphlett, L. A. McDonald and M. J. Redman, Chemistry and Industry, 1314 (1956).
(8) C. B. Amphlett, L. A. McDonald and hf. 3. Redman, ibid., 6, 220 (1958). (9) C. R. Amphlett, L. A. hlcDonald, J. S. Burgess and J. C. Maynard, %bid., 10,69 (1969).
EXCHANGE OF Li+, Na+ AND K + WITH H + ON ZIRCONIUM PHOSPHATE
Nov., 1960
acid. The gelatinous precipitate was washed by decantation with distilled water to a pH of about 3.4, filtered and air dried. The glassy material, when replaced in water, broke u p into particles about 10 mesh in size. The roperties and compositions of the roducts are given in Tagle I. Hydrolysis Studies.-&mplea of the five preparations were studied with respect to their stability toward hydrolysis. An apparatus was assembled in which the agitated sample was washed continuously with conductivity water (pH 7.0 to 6.85). The system was under slight pressure of nitrogen, and protected from the carbon dioxlde of the atmosphere by drying tubes containing Ascarite. The pH of the effluent was recorded and the washing was continued until the pH approached the value of the pure water. The effluent waa collected in a large storage bottle and the phosphate and hydroden-ion concentrations determined. Determination of the Capacity and Equilibrium Data.Two-tenths gram samples of 10 mesh zirconium phosphate in the h drogen form were packaged in Visking tubing (l/Rth inc& to prevent loss during handling A presoaked 2.0 inch section of Visking tubing was tiedoff at one end, the sample introduced by means of a small long-stemmed funnel, rinsed down with a few drops of water and the remaining end tied off The sample occupied about onefifth of the total volume of the sack. Blank runs with 0.1 M KMnO, in the Visking sack showed that the electrolyte e ui librated with the external solution within 15 minutes. %he same batch of phosphate (D) was used throughout, and a new portion was used for each equilibration. I n one set of experiments, the sodium form of the phos hate was preared by equilibration in sodium acetate soktion a t pH 5. &his sample was used to approach equilibrium from the other direction. The samples for the equilibrium constant data were equilibrated with 200 ml. of lithium, sodium and potassium chloride solutions ranging from 0.1 to 0.8 molal all in 0.1005 N HCl. The ion-exchange studies were carried out over the temperature range 1.17 to 44.5 i 0.1". Equilibration time varied from a month at 0" to four days at 44". To determine the cation capacity, samples were equilibrated a t 25" for one week with 200 ml. of 1 M lithium, sodium and potassium acetateacetic acid mixtures. At least two samples were run for each system and the average taken. In all cases, the sample was removed from the mother liquor, washed to remove absorbed ions (negative chloride test), and then the alkali metal in the solid phase was completely displaced by the addition of a copper(I1) salt solution. The copper form of the zirconium phosphate was separated, washed, and the combined filtrate and washings, which now contained the alkali metal, were prepared for analysis by electrodeposition of the copper. Analytical Methods.-The alkali metals were determined flamephotometrically using a Perkin-Elmer Flame Photometer. Standard solutionsusing the same amounts of nitric acid and sulfuric acid as contained in the unknown solutions were used as references. The readings were checked with standard solutions just below and above that of the un known. The errors in the metal ion analyses were judged to be Li, i 3 % ; Na, +4%; K, *4%. The analysis of zirconium phos hate was based on the factlo that zirconium com ounds &solve completely in an alkaline hydrogen perox& mixture, which u on digestion a t an elevated temperature, yields an acid-soyuble peroxyzirconium precipitate. In the case of the zirconium phosphate, the phosphate is in solution, and may be quantitatively separated from the zirconium-containing precipitate. The zirconium and phosphate may then both be determined by standard methods. The determination of phosphate a t very low concentrations was accomplished using the photometric method based on the absorption a t 315 mfi of a molybdovanadophosphoric acid complex.11
Results and Discussion Stumper and Metlocki2 studied the composition of zirconium phosphate as a function of the composition of the reagents used. When an excess of phosphate relative to that required for the normal phosphate, (ZrOz/Pz06mole ratio = 1) was used, the product was the normal phosphate. (10) P. Hurst. Doctoral Thesis, TJniversity of Wisconsin, 1956. (11) 0. B. Michelson, A n d . Clien., as, 633 (1957). (12) R. Stumper and Metlock, Bull. am. chim., 1, 674 (1947).
P.
1733
When 100% or greater excess of zirconium(1V) was used, the product had a ZrOz/PzOa ratio of 2.0. Products of intermediate composition could be obtained by varying the initial solution compositions. Amphlett prepared the phosphates from solutions which had initial ZrOz/Pz06 mole ratios in the range 0.8 to 4 in an accompanying 1 N acid. The products were not analyzed. Kraus,6 on the assumption that an excess of the phosphoric acid anhydride was necessary for the product to exhibit cation-exchange properties, precipitated zirconium phosphate from solutions con6aining an excess of phosphoric acid. The products were not analyzed. We have observed (Table I) that the ZrOz/Pz06 mole ratio of the product is higher than the ZrOz/PzOsmole ratio of the solutions from which the product is precipitated. We have also observed that cation-exchange properties are exhibited by products with a ZrO2:PzO6ratio of more than one. TABLE I Mole ratio
Sample
A B C
D E
ZrO%/PrOa Soh. Product
0.50 1.00 1.16 1.16 1.33
0.98 1.35 1.30 1.28 1.55
Lowest equil. pH
3.7 5.85 5.40 6.3 6.55
+:
Total Cu capacity meq. ration pe? Meq. G. air PnOs dried
Mm. ZrOr
..
..
..
1.35 1.36
6.98 6.02
2.32 2.10
..
..
1.37
5.46
1.98
..
Zirconium phosphate precipitation can be used for the quantitative determination of phosphate; therefore a product of known and reproducible composition can be produced. However, it is a well known factla that the freshly precipitated material is subject to loss of phosphate by hydrolysis and this must be repressed. The dry, normal phosphate also shows a tendency toward hydrolysis and therefore is undesirable for the quantitative study of its ion-exchange properties. It was thus necessary for our purpose to produce a phosphate of a composition which was a t least kinetically stable with respect to hydrolysis. The normal phosphate (A, Table I) hydrolyzed to give a product of a ZrOz/PzOSmole ratio of 1.16. A mass balance was made to substantiate the phosphate loss. From the eleven liters of wash water of pH 4.8, the calculated total phosphate associated with this hydrogen-ion concentration was 1.59 X mole. The experimentally determined phosphate content of the wash water was 2.08 X mole which agreed with the calculated value within experimental error. From the original composition of product A, and the phosphate loss, the residue should have had the ZrO2/PzO6mole ratio of 1.16. The experimentally determined mole ratio was identical with this. This hydrolysis explains the low pH of 3.7 recorded for sample A. Amphlett,' who made a similar observation, remarks that "the hydrogen form of the zirconium phosphate imparts an acid reaction to distilled water when equilibrated with it due to the ionization of the more acid groups.'' However, this idea is not reasonable for it would require a charged solid (13) I. M. Rolthoff and E. B. Sandell. "Textbook of Quantitative Inorganic Analysis," The Maamillan Co.. New York, N. Y., 1953.
1734
EDRINM. LARSENAND
0.0
DOSALD
4 0.4 bD 0
0.6
0.8 0.6 1.o
0.8
TABLEI11 CAPACITY OF ZIRCONIUMPHOSPHATE D
b
5
-1
w
-
1.9 I
1
1
I
I
I
1
0.00 0.050 0.100 0.150 0.200 0.250 0.300 l\’M Zr
Fig. 1.-Solid
.
line, data 1.17O; dashed lime, data 14.5’.
residue a t the bottom of the beaker. Samples of composition H, C, D and E were subjected to the same hydrolysis experiment (Table I). Only a small drop in pH was noted and the test for phosphate in the wash water was negative. It was concluded that for our purposes preparations of ZrOz/P20smole ratio 1.16 and higher were kinetically stable with respect to hydrolysis. However, when samples were equilibrated in conductivity water for a period (Table 11) of a week rather than hours, some slight phosphate loss was observed for sample D even at low pH’s, but this was not considered significant. At higher pH’s however, the sample was largely decomposed, and it is clear that zirconiuin phosphate is not stable in basic solution.
pHofsoln. % PaOa lost in 1 wk.at25’
1 0
3.0
5 0
6 0
8 0
9.0 10 0
11.0 1 3 . 0
0 ?
0 d
0 B
0 8
3 95
7 9
19.3 43 0
15 8
that the actual metal-ion concentration on the phosphate was determined, rather than measuring the difference in the alkali-metal concentration of the solution. The strong affinity of the zirconium phosphate for copper ion provided an excellent means of removing the exchanged sodium, lithium and potassium from the sample. I n this way the average capacity of 0.315 f 0.002 meq. H+/meq. of Pz06was determined. The capacity was determined with the alkali-metal ions rather than by exchange of copper. The total capacity by copper exchange was much greater than that determined by the alkali-metal ions which was interpreted to mean that the copper exchanged with the less-acid sites as well as the strong acid sites. The copper data, however, did originally provide evidence of the fact that the exchange sites are related to the phosphate content of the sample, for the only correlation of capacity was with the phosphate content (Table I). For the exchange of a univalent ion with the hydrogen form of the zirconium phosphate the following equation and associated equilibrium constant expression may be written MS,+ HZrw _J MZrw Ha,+
+
TABLE I1 A FUNCTION OF PH
PHOSPHATE Loss AS
From titration data it would appear that the zirconium phosphate exchange sites are multifunctional.? In view of the degradation of the phosphate a t pH’s above 6 one might question the interpretation of Amphlett’s curves, nevertheless it is reasonable to expect multifunctional cationexchange sites. To make possible the interpretation of the equilibrium data it was necessary to study the exchanger in a pH range in which it was behaving unifunctionally. It was also necessary to choose a pH a t which the phosphate loss was negligible. For this reason pH 1 was chosen. The choice of solution volume and sample size was such that the absorption of solvent by the solid sample had a negligible effect on the solution concentration, and so that the hydrogen-ion and metal-ion concentrations of the solution remained essentially constant during equilibration. The
K+ 0.313 ,310 316
0.316 .a15 ,320
0.315 .316 ,313
1.2
G 1.7
Meq. M +/yeq. PnOr Na
Li +
0
1
1.5
Vol. 64
combined effects resulted in a maximum change of one per cent. Owing to the unfavorable equilibrium constant for this reaction, it was impossible to saturate the phosphate with univalent metal ion at pH 1 to determine the capacity. Since the titration curves show a straight portion up to pH 6, it was assumed that the exchanger was unifunctional up to p H 5, and the capacity was determined in a buffer solution of the alkali-metal ion acetates at this pH (Table 111). It should be pointed out
. 0.2
1.0
R. VISSERS
+
The concentrations of the species in the solid phase are expressed in terms of their respective mole fractions (Table IV). The solution species are expressed in molalities corrected by the mean activity coefficient for the solute in a binary solution. The mean activity coefficients were calculated by the method and from data given by Harned and Owen.14 The assumption has been made that tJhe activity coefficient ratio is little changed with temperature and the data at 25’ were used a t all temperatures. It was necessary also to consider the activity of the ions in the solid phase. Our calculations of equilibrium constant showed, that like the organic exchangers, the activities of the ions in the solid phase were changing appreciably wit,h changes in (14) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” Reinhold Publ. Corp., New York, N. Y.,1958, p. 593
ff.
1735
EXCHIKGE OF Li+, Xa+ AND K+ with H+ ON ZIRCONIUM PHOSPHATE
Nov., 1960
0.4
TABLE IV EQUILIBRIUM DATA
0.6 i
Li + M,,+(m) ( r*sY/(Y*SY
x 102 1.17" 14.5' 25.0" 44.5"
0.1005 1.008
0,2010 1.032
0.4040 1.023
2.54 2.86 2.54 2.54
4.45 4.13 4.45 4.13
6.67 6.98 6.98 6.66
0,1010 1.039
0.2015 1.085
0.4050 1.122
0.8160 1.044
AT1m
-
0.8
0
1.o
10.2 10.5 10.5 10.2
0.8
1.2 1.0
Na +
1.2
Mag+(m) ("f*S)'J/(Y*2
x 102 1.17" 14.5" 25.0°b 44.5"
0.8160' 1.263 1.5
NMZr
11.1 10.5 9.43 7.30
17.1 15.9 14.0 10.8
22.9 20.1 19.4 15.9
29.5 26.7 24.8 20.6
IC + M,,+(m) (Y*a)'J/(
?,**)e
0.1005 1.068
0.2020 1.143
x 10' 18.7 23.8 1.17" 15.9 20.6 14.5' 13.3 19.4 25.0' 44.5O 11.4 14.0 HC1 0.1015 rather than 0.1005 zirconium phosphate used.
0.4060" 1.173
0.8230" 1.328
.
2"
*8 Ld
c
4 1.4
,$ 1.7
-3
1.9
1
I
I
I
I
I
I
1
0.0 0.050 0.100 0.150 0.200 0.250 0.300 NMZ~. Fig. 2.-Solid line, data 25.0'; dashed line data, 44.5'.
NMZr
5
29.8 33.0 27.0 31.1 24.4 28.9 20.0 25.4 IN. * Sodium form of
0.0 0.2 0.4
5
0.6 concentration. With organic exchangers the prob0 lem of the activities of the ions in the solid phase 0.8 has been studied by Argersinger15 and SillBn,'6 both of whom arrived a t the expression for the true 1.0 1.6 equilibrium constant as In K =Jolln Ka dNm 1.5 where Ka is, the apparent equilibrium constant, and Nm is the mole fraction of the ion exchanger 3.0 3.2 3.4 3.6 3.8 in the metal form. The evaluation requires graphI/T x 103. ical integration over the mole fraction of the metal Fig. 3. form from zero to 1. In this treatment the standard state of each ion in the solid phase is the From the equilibrium constants thus detercorresponding pure form of the exchanger. In the present work we do not make any observations mined, AFO was calculated and along with the ar-fo on systems in which the fraction of the sites oc- from the 1/'T plots of the equilibrium constants cupied by the metal ion exceeds the mole fraction (Fig. 3), AXo was calculated. The entropy changes 0.35, thus it is not possible to use this procedure are strikingly close to the relative entropies for to obtain a thermodynamic equilibrium constant the aqueous ions tabulated by Latimer," which for the exchange reaction. However, by extrap- are Li+, 4.7; Na+, 14 and K+, 24.2. One can conolating the apparent equilibrium constants to the clude that upon exchange of cations the entropy pure hydrogen form, (Figs. 1 and 2 ) . we obtain an change of the solid phase is small. The trend in equilibrium constant based on one state for the AFO with ion size is in agreement with the elution hydrogen ion in the solid phase, the pure hydrogen- experiments of Kraus and Amphlett. The organic, ion form of the solid phase, and a different standard strong-acid, cation exchangers have equilibrium state for the alkali-metal ions in the solid phase. constants greater than one for the alkali metals. This state is the hypothetical pure alkali-metal form of the solid phase which has the properties TABLE V extrapolated from the hydrogen ion containing ASO, e.u. Ion Fa, kcal./mole AHO, kcal./mole solid phase in which the alkali-metal ion is infinitely Li 4-2.0 0.0 - 6.7 dilute. Na +l.l -2.7 - 13 I
I!
115) W. J. Argersinger, A. W. Da\ldson and 0 D Bonrier, Trans k'ans. Acad. Sa.,63,404 (1950). (16) E. Hogfeldt. E Ekedahl and L. G. SillCn, Acta Chem. Scnnd4,4,
556 (1950).
K
4-0.56
-5.7
(17) W. M. Latimer, "Oxidation Potentials," New York, N: Y . , 195%
- 21
Preotice-Hall,Inc.,
L.
1736
w. DILLER,R. L. ORR A N D RALPHHULTGREN
Acknowledgment.-The authors wish to thank Professor E. L. King for helpful discussions concerning this work. This work was supported in
Vol. 64
part by the Research Committee of the Graduate School from funds supplied by the Wisconsin Alumni Research Foundation.
THERMODYNAMICS OF THE LEAD-ANTIMOXY SYSTEM' BY LINDAWARNERDILLER,RAYMOND L. ORRAND RALPHHULTGREN Department of Mineral Technolopg, University of California, Berkeley, California Received M o y $1, 1960
Heats of formation of solid a-phase Pb-Sb alloys have been measured by solution calorimetry. These data have been combined with previously known data in the liquid state and the phase diagram to complete the thermodynam.i!iq description of the a-phase. The thermodynamic data for both solid and liquid alloys and the phase dlagram have been critically evaluated and discussed, and selected thermodynamic properties have been tabulated. An attempt is made to interpret the unusually large positive values found for the excess partial molar entropy of Sb in the a phase.
Introduction Although a considerable number of thermodynamic measurements have been made on liquid Pb-Sb alloys, there exist none a t all on the alloys in the solid state. Thermodynamic properties of the I'b-rich solid phase are calculable from the phase diagram and the liquid data, but entropies of formation so derived seem imdausiblv high (e.g., AS;;; = 10.8 e.u. a t ZSb '= O.O& a i d 525OK.). _-_ I n o&er to establish better the thermodynamic properties of the solid phases, it was decided to measure directly heats of formation within the Pb-rich (a) solid solution. These data, together with a critical analysis of the liquid data and the phase diagram, are presented in this paper. Experimental Materials.-Antimony in the form of rods was obtained from Johnson-Matthey and Go., Ltd., Toronto, Canada, who stated it to be 99.9+% pure. Lead rods specified to be 99.998% pure were obtained from the American Smelting and Refining Co. Preparation of Alloys.-Four 10-g. ingots, containing 2.00, 3.00,4.00 and 5.00 at. .% Sb, all in thea-solid solution range, were prepared by melting together at 500" the weighed components in evacuated, sealed Vycor tubes. The tubes were shaken briskly for five minutes while in the furnace, then quenched rapidly in ice-water to minimize segregation. Weight losses on fusion were less than 0.03%; the weighed compositions of the alloys were therefore taken to be correct. The ingots were cold worked, resealed in evacuated Pyrex tubes, and homogenized for seven weeks a t 252", the eutectic temperature. They were again quenched in ice-water and stored in a refrigerator until used. Filings taken from both ends of each ingot mere strain annealed at 250" and quenched in ice-water. The sharp X-ray diffraction lines obtained from the filings indicated the alloys to be homogeneous. Measured lattice constants were in excellent agreement with the measurements of Tyzack and Raynor,* while disagreeing with the older measurements of Ageev and K r ~ t o v . ~ Apparatus and Methods.-Heats of solution in liquid P b of pure Sb and the alloys were measured using the ralorimetric apparatus and methods described previously.4 Samples were dropped from an initial temperature, Ti, near 52OCK., into the lead-bath at temperature Tt, near
-
( I f Based on a thesis by Linda Warner submitted in partial satis-
faction of the requirements for the degree of Master of Science in Engineering Science to the University of California, 1959. This work was supported in part by grants from the Office of Ordnance Research, U. S. Army, and the U. S. Atomic Energy Commission. (2) C . Tyaack and G. V. Raynor. Acta Cryst., 7, 505 (1954). (3) N. V. Ageev and I. V. Krotov, J . Inst. Metals, 69, 301 (1936). (4) R . L. Orr, A, Goldberg and R . Hultgren, Reu. Sci. Instr., 28, 767 (1957).
677°K. The heat capacity of the calorimeter was determined by dropping specimens of pure Pb from room temperature, using the heat content values of Kelley.6 From these data heats of formation a t temperature Ti were calculated in the usual way.' During the runs the concentra tion of Sb in the liquid Pb-bath never exceeded 0.4 at. 3. Within this dilute range the heat of solution of Sb was mdependent of Sb concentration within the experimental uncertainty.
Results The experimental results are given in Table I. The heats of formation have been referred to a common temperature, 525" K. , assuming Kopp's law of additivity of heat capacities in correcting the results for the small deviations of Ti from that temperature. The heats of formation (Fig. 1) appear to be best represented by the straight line, AH = 6300xsb, with an average deviation of 14 cal./g.-atom. The relative partial molar heat .b = contents thus obtained are M P b = 0 and A& 6300 cal./g.-atom. TABLE I EXPERIMENTAL RESULTS AHtam.,
Sample comp., at. % Sb
100.00
2.00
3.00 4.00 5.00
OK.
Tt,
no.
OK.
A Hao~n. cal./g.atom
64-3 64-15 65-3 65-15 64-5 65-13 647 65-11 6411 65-7 64-13 65-5
523.7 519.1 523.5 514.9 523.6 515.6 526.5 519.7 522.3 526.0 522.5 522.4
676.6 677.3 676.5 677.2 677.5 677.5 677.6 677.3 677.8 677.3 677.8 677.3
5652 5713 5729 5692 2190 2264 2130 2203 2195 2151 2130 2117
I
Run
Ti,
525'K.. cal./g.atom
138 124 220 188 211 234 310 321
Selecting from published data the value (HWK 1000 cal./g.-atom for Sb, the relative partial molar heat of solution of Sb(,, at infinite dilution in Pba, at 677°K. may also be evaluated from the data yielding
- H 6 r 6 0 ~=)
ARSb. 677OK. m b - 1 = 4670 Cd./g.-atOm (5) K. K. Kelley, U. S. Bur. Mines Bull. 584, 1960.
