Nov., 1959
RADIOTRACER STUDIESOF CADMIUM-CADMIUM IONEXCHANGE
1819
RADIOTRACER STUDIES OF CADMIUM-CADMIUM ION EXCHANGE BY CECILV. KINGAND ROBERT SHOMOROSHI Department of Chemistry, New York University, New York, N . Y . Received February 97, I969
Measurements have been made of the rate and extent of acquisition of radioactivity by cadmium specimens when immersed in cadmium perchlorate solutions containing Cd"6 as tracer. Good reproducibility of measurement was obtained with electropolished coupons in deaerated solutions. It is shown that the continuing activity picku is due to self-diffusion within the metal, most of it presumably along grain boundaries. The diffusion coefficient calculatecffrom pickup as a function of time is higher than expected from values in the literature unless adsorption of cadmium salt on the metal is assumed. The distribution of activity in depth in the specimens has been measured, to calculate diffusion coefficients a t room temperature and at 98".
We have found no quantitative studies reported in the literature, of exchange between cadmium metal and its ions in solution. Exchange with cadmium amalgam has been studied by the radiotracer method by Fronaeus,' who found exchange to be so rapid from ordinary cadmium salts as to deplete the surface layer of solution of the tracer ions; the loss of activity from solution is then controlled by convection and diffusion. This indicates that the actual exchange is very rapid, and the "exchange current" is high. Measurements of exchange current with the amalgam have been made by a non-tracer method12and found to be as large as 0.12 amp./cm.2 for M Cd(NO& in 1 M KNOI. The purpose of the present study was to see what could be learned about the metal-solution interface, by measuring the rate and extent of radioactivity pickup on cadmium specimens when immersed in a solution containing active cadmium ions. It was necessary to study the effects of corrosion in the presence and absence of air and the effect of surface preparation. It was expected that internal diffusion would be a rate-controlling factor, and i t was hoped that diffusion coefficients could be estimated. Experimental
vessel was placed in boiling water and equipped with a condenser.
Results Table I shows the activity pickup in air-saturated solution; these results are of interest because comparison with the deaerated solution shows that the corrosion film blocks the surface and acts as an inhibitor. After the 13-hr, and 17-hr. immersions the coupons were covered with a colorless, gelatinous film, which was largely removed on rubbing with cleansing tissue and water. Activity in the film need not all represent exchange. TABLE I Air-saturated 0.01 M Cd(C104)2, 23'. each immersion. Time immersed, hr.
5
1 1 2 3 4 5 13 17 Wt. gain.
Wt. loss, mg.
0.3 .1
... ... -
.2 .2 .3 .25
A new coupon for
C,p.m. side 1
C.p.m. side 2
Gram atoms per cm.2 x 108
187 124 91 167 240 346 2720 920
253 340 74 152 196 914 3140 1350
87 91 32 62 84 240 1120 410
Cadmium sheet, 0.07 cm. thick and of 99.99% purity, was cut into 2.54 cm. square coupons, and a 2 mm. hole was drilled in a corner of each in order to suspend it on a glass hook or a lslatinum wire. The actual area was 6.60 cm.* on each side. Radiocadmium, CdllSm with half-life of 43 days, was obsolution. Since the experitained as the nitrate in "03 ments .were to be carried out with Cd(C104)~in the hope of minimizing corrosion, HC1O4 was added and the HNOa expelled by evaporation. Inactive Cd( ClO& was prepared from reagent grade CdCOs and HC104, and the stock solution was standardized by the sulfide method.3 Small amounts of tracer were addkd on diluting. Counting and conversion to gram atomic amounts have been d e ~ c r i b e d . ~The coupons were thick enough to absorb nearly all radiation from the side away from the G.M. tube. Tests showed that about 4% of the radiation is absorbed in passing through 1.75 X 10-8 om. of the metal (about 65,000 atomic layers). The counting time was chosen so that the counting error ordinarily was less than 2% a t the nine-tenths probability level. Immersion experiments usually were carried out with 250 ml. of 0.01 M active Cd(C104)~in a 500-ml. bottle. Purified nitrogen was used for deaeration. The temperature was 23 f 3"; for a few experiments at 98 f 2" the immersion
The counts per minute columns of Table I give an idea of the divergence in counts between the two sides of a coupon in air-saturated and even in deaerated solutions when the surfaces were prepared by abrasion with fine paper. In deaerated solutions the coupons corroded slowly, the greatest weight loss noted corresponding to about 10 atomic layers per hour. No visible solid films were formed, and the pH of the solutions (about 5.7) did not change appreciably. The activity pickup was much greater than with air present and increased regularly with time. With abraded coupons the reproducibility was no better than the values given in Table I, and various methods of polishing and etching were tried. The best results were obtained by electropolishing the coupons as described below.6 Table I1 shows some results for comparison. Not only was there usually (though not always) good agreement in counting, but the pickup was much smaller, no (1) 8. Fronaeus, Acta Chem. Scand., 7,764(1953); 8,412 (1954). doubt due to a much smaller roughness factor. (2) J. E. E. Randles and K. W. Somerton, Trone. Faraday Sac., 48, The polishing solution was made with 20 g. of 951 (1952). Cd(OH)2 and 120 g. of KCN per liter. The (3) W. W. Scott, "Standard Methods of Chemical Analysis," D. Van Nostrand Co., Inc., New York, N . Y., 1946,p. 203. (4) C. V. King and S. Evans, THIS JOURNAL, 63, 1816 (1959).
(5) C. J. Smithells, "Metals Referenoe Book," Interscience Publishers, Inc., New York, N. Y., 1949, p. 240.
CECILV. KINGAND ROBERTSROMOROSKI
1820
Vol. 63
TABLE I1
TABLEI11
Deaerated 0.01 M Cd(C10& at 23'. A new coupon for each immersion. A, polished with No. 600 silicon carbide paper; B, electropolished. Time A B, B, B,
Coupons immersed in deaerated 0.01 M Cd( ClO& etched in 0.02 M HC!, 0.06 M KNO,. A, etched immediately after immersion. B, etched 67 days after immersion.
immersed, hr.
30 min. 1 2 2 4 4
c,.p.m. aide 1
c.p.m. side 2
Wt. diss.,
..
..
200 324 336 380
332 523 540 551
g. atdms/ g. atoms/ cm.2 X l o 9 cm.2 X 10s
720 1430 1840 1460 2680 2820
..
..
A
Wt. diss.,
mg.
..
..
C.p.m.
329 554 522 707
61 182
3080 684 63
139 430
6480 223 46
171 608
..
cadmium coupon was suspended between 2 iron sheet cathodes in a 400-ml. beaker. After a number of experiments a current of 1 amp. (on 13.2 cm.2) for 5 minutes was chosen for all further work. This reduces the thickness of the coupons by about 0.01 cm. Exchange as a Function of The.-Three groups of coupons were prepared as follows: (a) abraded and electropolished; (b) stored in deaerated inactive Cd(C104)2solution for several days, electropolished; (c) annealed in vu.cuo at 110" and electropolished. In all, 22 coupons were then immersed in deaerated, active 0.01 M Cd(C10& for periods from 15 minutes to 24 hours. On plotting the amount of exchange vs. the square root of time, all of the points could be represented within experimental error by a single straight line of gram atoms cm.-2 sec.-'/z. slope 4.2 X The plot is in accordance with the theory of diffusion from an interface of constant composition into a homogeneous medium. The best straight line does not pass through the origin, however. The behavior is like that of zinc4 and silver.6 There is a very rapid pickup corresponding to complete exchange in 2 or 3 apparent atomic layers, followed by slow exchange with continual upward curvature of the plot vs. t'12, when this is examined in detail. Several coupons were immersed in active 0.1 M Cd(C10J2; the corresponding plot showed upward curvature with apparent linearity in the range 16-250 hours, the slope being 1.8 X lo-* gram atoms cm.-2 sec.-'/p. Depth of Penetration.-The extent of penetration of activity can be studied by etching the metal with a reagent which dissolves it uniformly and measuring the remaining activity as well as the weight lost. The reagent chosen was a solution of 0.02 M HC1, 0.06 M "Oat which is known to dissolve several metals at a maximum, diffusion (or transport) controlled rate.' This does not ensure uniform dissolution, but our experience has shown that the softer metals remain quite smooth. Table 111gives the results of preliminary experiments to determine the extent of penetration. The A and B coupons had undergone about the same amount of exchange, although the counts per minute are not the same. The B coupons show that inward diffusion continues on storage. The weight of cadmium dissolved can be expressed in distance cm. on these coupons of since 1 mg. = 8.74 X 13.2 cm.2 area. If more than 200 mg. were dissolved in a quantitative experiment, it should be (6) H. Gerischer and R. P. Tischer, 2.Elektrochem., 68, 819 (1954). (7) C. V. King and P. Howard, Ind. Eng. Chem., 29,75 (1937).
.. 170 280
B
mg.
C.p.m.
..
2220 490 75
..
3240 377 48
remembered that radiation from greater depths was originally subject to more than 4y0 self-absorption. (Calibration coupons were never stored so long that self-absorption of radiation was appreciable.) Quantitative measurements were made with 14 coupons which were immersed until the activity had penetrated to a suitable depth and then were dissolved down a few milligrams at a time until 75-90% of the activity had been removed. Grainboundary diffusion theory predicts that the logarithm of the activity, per unit volume at each penetration depth, should be a linear function of depth. Plots of log activity remaining on some of the coupons, in c.p.m., us. milligrams dissolved, are shown in Fig. 1. About 9 of the 14 curves showed a reasonably linear portion; the other straight lines were drawn as seemed best. It was expected that the first points would be high, because there must be appreciable diffusion into the surface grains, which is slower and follows a different law; however, this behavior was not shown uniformly. The last points on each plot become uncertain because the number of counts is small, self-absorption of the deeper radiation diminishes, and the assumption of uniform dissolution becomes uncertain. Self-diffusion in Cadmium.-Lattice and grainboundary self-diffusion in cadmium have been studied by Wajda, Shirn and Huntington,8 the latter in the temperature range 56-146". Thin layers of active cadmium were electrodeposited on inactive specimens and, after storage at various temperatures, thin sections were milled off and dissolved to measure the activity. Single crystals were used in measuring lattice diffusion, and grainboundary diffusion coefficients were derived from experiments with polycrystalline specimens, using the method of analysis developed by F i ~ h e r . ~The equations (1) to (3) summarize their results Lattice diffusion parallel to hexagonal axis D, = 0.05 exp( - 18,20O/RT)
(1)
Lattice diffusion perpendicular t o hexagonal axis D , = 0.10 exp( -19,10O/RT)
(2)
Grain-boundary diffusion Db = 1.0 exp( - 13,000/RT)
(3)
The units of D are cm.B/sec., and the numbers in the exponentials are calories per gram atom. From equation 3, Db = 2.4 X 10-lo cm.2/sec. at (8) E. S. Wejda, G . A. Shirn and H. B. Huntington, Acta MetalZurgica. 3, 39 (1955). (9) J. C. Fisher, J . AppE. Phve., 22,74 (1951).
Y
RADIOTRACER STUDIESOF CADMIUM-CADMIUM IONEXCHANGE
Nov., 1959
1821
23", 2.2 X cm.2/sec. a t 98", values about lo6 times as large as D,. The Fisher equations relates grain-boundary and lattice diffusion coefficients and is based on the analogy with heat conduction down thin sheets of a good conductor imbedded in a semi-insulating body. The relation may be put in the form Db
= 20,'/2 (log e)2
S-1(?rt)-1/2
(d log a,/dz)-z
(4)
where e is the log base, 6 is the grain boundary thickness, a, is the activity per unit volume a t penetration depth x after the time t. From equations 1 and 2, average values of D,are 1.27 X cm.2/sec. a t 23" and 7.4 X a t 98". Fisher suggested that 6 be taken as 5 X lo-* cm., and in the absence of better information other workers have used this value.8 Inserting numerical values in equation 4 we obtain Db = 0.152t-% (slope)-2 at 23" Db = 3.671-'/1 (slope)-z at 98"
(5) (6)
where the slopes (A log a/Ax) can be taken from plots like Fig. 1 with a in c.p.m. and x in cm. ( = mg. X 8.74 X loe6). Table IV gives details of the treatment of the 14 coupons used in these experiments and summarizes the calculated Db values. All the coupons were electropolished except No. 8 and 9, and it was shown previously that abraded coupons acquire activity faster than electropolished ones. Coupon 7 probably was immersed too long in the more concentrated Cd(C10& so that diffusion into the surface grains was exceptionally large. In expt. 1 and 2, only the immersion time was used; the values are included to show that the calculation is rather insensitive. TABLE IV GRAIN-BOUNDARY DIFFUSION COEFFICIENTS 23 =t 3" Immersion time, hr.
Db,
cm.Vsec.
98 =t 2' Immersion Db time, crn.2/sec.
40 60 80 Wt. dissolved, mg. Fig. 1.-Coupons 1, 2, 3, 4 of Table IV. 20
from the literature, but in that case the numerical values are lo7 times smaller and D, is obtained by extrapolation from much higher temperatures. Cold-rolled silver sheet, which presumably consists of very fine, distorted grains, gave linear plots of log a vs. x,while annealed silver, with much larger grains and a rough surface, did not. There is no independent theory of grain-boundary diffusion, since the relative area and volume of grain boundaries is not known and varies with grain size. The Fisher relation assumes that diffusion takes place into the crystals from grain boundaries, but that lattice diffusion can be neglected a t the specimen surface. The relation is independent of grain size, since only the ratio of activity a t different depths is needed. Exchange vs. Time.-When the slopes of the square root plots given above are inserted in the equation
X 1010 Expt. hr. x 108 4OU 1.8 10 2 2.12 40" 1.8 11 2 0.37 3 40 1.52 12 1 1.06 at = 2 a o ( D t / ~ ) V ~ 4 40 1.47 13 2 0.50 5 160.5 1.46 14 3 0.71 with a0 = and mole~/cm.~, respectively 6 185 1.42 (the solution concentrations), apparent values of 7b 258 0.34 the diffusion coefficient become 1.4 X lo-' and 8c 12 16 2.5 X cm.P/sec. These are much larger than 90 14 28 the values in Table IV; but if the surface concentraand 1.3 X 10-3 a Etched 22 days after immersion. In 0.1 M Cd(C104)2. tion a0 were taken as 3 X All others in 0.01 M Cd(C104)~. Abraded coupons. All mole~/cm.~, corresponding to adsorption of a small others electropolished. fraction of a monolayer, the discrepancy would
Expt.
1 2
Discussion The values of Db in expt. 3-6 and 10-14 of Table IV are in satisfactory agreement with equation 3, considering the extrapolations and approximations made, the neglect of corrosion, etc. Similar experiments with silverlodid not agree as well with values (10) C. V. King and N. E . McKinney, Can. J . Chem., 87, 205 (1959).
disappear. Since this is not a homogeneous diffusion, further speculation is unwarranted. We are continuing the exchange studies with cadmium single crystals, since the homogeneous diffusion should be more amenable to simple interpretation. The authors wish to thank the U. S. Army Office of Ordnance Research for its support of this investigation.
