A. J READ
3656 approach to investigate oxygen reduction in acid solution. A suitjable system for study is the carbon-iron phthalocyanine system, which closely resembles the graphite/ cObslt-iron Oxide system in its mode Of Oxygen reduction.
Acknowledgment. This work was supported by the Science Research Council on Grant No. B/SR 4334. (26) H. Jahnke and M , Sc+jn,erg, proc. J . I&. Etudes pilesCombust,, Brussels, 1060, 60 (1969).
Dissolution of Copper in Weakly Acidic Solutions by A. J. Read Chemistry Division, Department of Scientific and Industrial Research, Gracefield, N e w Zealand
(Received Pebruary 7 , 1978)
The dissolution of copper in weakly acidic perchlorate solutions was measured over a range of pI3 (4.0-5.5), PO, (0.05-1.0 bar), and cupric ion concentrations (1 X 10-4-16 X M) a t constant ionic strength (0.05 M ) ~The method used allowed several measurements to be made under pseudo-zero-order conditions on a and PO$was found to be 1.0 and 0.25, respecsingle piece of copper in situ. The order dependence on (H+) tively. Increasing the temperature from 16.9 to 45.0' increased the rate by a factor of 6.2. Addition of C1-- and Br- ions enhanced the dissolution rate while added F-, NOS-, S042-, and Zn2+ had a negligible effect. These results are discussed in terms of a solid-state mechanism involving the formation, transport, and destruction of cation vacancies and positive holes.
Introduction Numerous publications have appeared dealing with the corrosior. of copper under a wide variety of conditions. l - I G However, few authors studied dissolution under conditions allied to natural mater systems.6b16l7 The reaction mechanism was not fully elucidated under acidic and is even less well understood in solutions conhaining low concentrations of complexing ions. The present work seeks t o improve the understanding of the dissolution reaction in weakly acidic media (pH range 4.0-5.5). The oxjde films, formed initially on copper single crystals in water, were shown to consist of cuprous oxide@-*O even though thermodynamic considerations indicated cupric oxide was the stable phasesz1 At room temperature, Lhese films grew more rapidly in water than in air.lR It seemed likely, therefore, that cuprous oxide would be an intermediate in the dissolution of copper in the present study. It Is often difieult to control all the variables for a heterogeneous reaction, to a suitable level of precision. I n the present P ; O I ' ~ a technique was used which allowed the precise control of reaction variables (e.y., PO,,pH, (Cu2+),m d ionic strength) and minimized the problem of .aeprodiicing characteristic metal surfaces. Further, ns relai,jve rate measurements are sufficient for a mechanistic ttud.y, no great importance ivas attached to thcb variation of rate with surface preparation. The Journal of Physical Chemistry, Vol. 76, N o . $4, 1072
Experimental Section The samples of copper used in the present investigation were of Analar copper foil for which an emission spectrographic analysis is given. (1) B. C. Y. Lu and W.F. Graydon, Can. J. Chem., 32, 153 (1954). (2) 5. R . Weeks and G. R . Hill, J. Electrochem. Soc., 103,203 (1956). (3) R. P.Russel and A. White, I n d . Eng. Chem., 19, 116 (1927). (4) G. H. Damon and R. C. Cross, ibid., 28, 231 (1936). (5) I. Cornet, E . A. Barrington, and G. U . Behrsing, J . Electrochem. SOC.,108, 947 (1961). (6) A. I. Kinevski, J . A p p l . Chem. U S S R , 28, 1088 (1955). (7) W. D. Robertson, V. F. Nole, W. H . Davenport, and F. P. Talboom, Jr., J . Electrochem. Soc., 105, 569 (1958). (8) 2. Zembura and TV. Glodzinska, Rocz. Chem., 42, 1525 (1968). (9) R . Glauner, 2 . Phys. Chem., Abt. A, 142, 67 (1929). (10) T. Hurlen, Acta Chem. Scand., 15, 1239 (1961). (11) 6. R.Hill, J . Electrochem. SOC.,100, 345 (1953). (12) J. Halpern, ibid., 100, 421 (1953). (13) 2. Bzabo, J . Amer. Chem. Soc., 7'1, 1511 (1949). (14) W. Kats, Werkst. Korros. (Weinheim), 1, 393 (1950). (15) T. Hurlen, Acta Chem. Scand., 15, 1246 (1961). (16) D . J. G. Ives and A . E. Rawson, J . Electrochem. Xoc., 109, 452 (1962). (17) 2 . Zembura and W. Glodzinska, Rocz. Chem., 40, 911 (1966). (18) ,J. Kruger, J . Electrochem. Soc., 106, 847 (1959). (19) J. Kruger, ibid., 108, 503 (1961). (20) A . Goswami, I n d i a n J . P u r e A p p l . Phya., 7, 211 (1969). (21) M. Pourbaix, "Atlas of Electrochemical Equilibria," Pergamon Press, London, 1966.
DISSOLUTION 3~ COPPER IN WEAKLY ACIDICSOLUTIONS
The dissolution rate is defined by the equation
99.99+%
Copper Lead Bismuth Antimony Arsenic Manganese Tin Zinc
PPm
, Le., ( 2 ) describes the equilibrium between cuprous oxide and an aqueous solution containing cupric ions where PO,is that existing a t the CuzO-CuO interface. The PO, value for the CuzOCuO stability boundary is about 10-37.6bar.27 Values calculated from stationary state experiments deviate from this probc,bly as a result of the nonstoichiometric nature of the cuprous oxide, an incomplete coverage of the Cu2Q by a CuO film, and the system not being a t equilibrium. At the stationary state there would be a slow growth of the cuprous and cupric oxide layers with a corresponding utilization of oxygen. Once the cuprous oxide was covered with a layer of cupric oxide no change in pH would be expected. In view of the interest in the corrosion of copper in natural. waters it is ueefiil to consider the possible role CUO
Cu2+
Figure 3. Effect of cupric ion concentration on tho rate of dissolution of copper a t pH 5.50 with different amounts of cupric oxide deposited on the surface (see text).
of cupric oxide in this process. Copper is usually passivated when coated with an impervious layer of corrosion product.28 There are instances when this does not happenz1and the presence of cupric oxide may be relevant. Some related data are now given. After determining the curve in Figure 2 for pM 5.50 (curve a in Figure 3) the sample was allowed t o corrode with the pH titrator disconnected, until a stationary state was attained. As indicated above, material is deposited on the sample surface. Curves b, c, and d of Figure 3 show the rate dependence on (Cu2+) after successive increments of material had been deposited from solution. The increase in rate a t zero (Cu2+j for curves a-d might be the result of increased surface area, the deposited material being rather loosely adherent.I3 The increased sensitivity of the rate to iiicreasing (Cu2+) for a-d may indicate how corrosion is rapidly stifled when growth of mixed oxide film has occurred under certain conditions. Effect of Oxygen. The rate dependence on PO,was determined a t different (Cu2+) and pH values and in the presence of chloride (Table IV). PO,was varied using 02-Nz mixtures and without removing the copper sample a serieR of measurements at constant p B . (Cu2+),I , and stirring conditions but a i different PO, values was made. To ascertain whether the copper surface had changed during the series a rede termination of the dissolution rate under the initial conditions of PO,was made. A typical plot of log R (mol min-' cm+) us. log P O , (bar) is shown in Figure 4 while Table IV records the range of conditions for which the oxygen dependence was measured. The slopes o i these plots are approximately 0.25. (26) Nat. BUT.Stand. ( U . S.), Circ. 500 (1952). (27) ,R. M. Carrels and C. L. Christ, "Solutions, IClinerals, slid Equlllbria," Harper and Row, Kew York, N. Y . , 1965, p 155. (28) L. Giulianl, A. Tamba, and 6. Modenzt, Coiros. Sci., 11, 486 (1971).
The Journal of Physical Chemistry, Vol. 76, No. 84, 1978
A. J. READ
3660 log R = log ic - plx -
1
E
]
I
slope = O 24
.-
Effect of Added Ions. The effects produced by the addition of fluoride, chloride, bromide, sulfate, nitrate, or zinc ions on the dissolution rate are plotted in Figure 6 as R/R, where R, was the rate without added ions present. After measuring R, (usually a t pH 5.5, (Cu2+) = 2.3 X M ) successive rate measurements were made with additions of C02-free solutions (at correct
log(102Po2 /bar)
Figure 4. Effect of oxygen on the dissolution of copper.
Table V : Range of Conditions for Which the Rate Dependence on pH Was Determineda 104(~1-),
104(~112+),
M
M
17.0 17.0 17.0 11;4 11.4 2.22 2.27 1.48 0.75 a
Figure 5 . Effect of pI3 on the dissolution of copper.
Table PV. Range of Conditions for Which the Rate Dependence on Oxygen Concentration Was Determined
lO'(CU2 +),
M
2.22 4.93 17.1 17.1
PH
Slope of order plot
5.51 5.32 5.58 4.33
0.24 0.26 0.27 0.25
10"C1-),
34
100
Eflect of p t l . 'The effect of pH on the dissolution reaction was! studied over the range 4.0-5.5 at varying (Cu2+)anti in the presence of chloride (Table V). Following additims of HG10, solution a series of rate measurements was made a t constant PO,, (Cuz+), and I but at, vnqying plI. To check whether the surface had altered during the series, the rate was occasionally remeasured after the OHhad been increased by the addition of carbonate-free Ba(OM)2 solution. A sample plot of log R (mol n4n-I us. pH is shown in Figure 5. The dependence on pH (Table V) appears to vary with cupric ion concentration and only at the higher concer~traticins~~ used was the dependence typical of a simple linear relationship of the type R = k(H+) giving The Jouriutl of Phyrvical Chemistry, Vol. 76, No. 8.4, 1979
10.0 50.0
Slope of order plot
-1.07 -1.07 - 1.07 -1.02 -1.05 -0.77 -0.66 -0.54 -0.68
p H range
4.0-4.9
4.4-4.8 4.5-5.2 4.1-5.3 4.5-5.3 4.5-5.5 4.4-5.5 4.5-5.5 4.6-5.5
Air was the aerating gas.
pH, (Cuz+), and ionic strength) of the various ions. The anions were added as their sodium or potassium salts and the zinc ions as zinc sulfate. Chloride and bromide ions which complex strongly wj th cuprous greatly enhanced the dissolution rate, while the ions En2+, F-, Sod2-,and NO3- had no appreciable , ~ observed a positive effect. Robertson, et ~ l . similarly catalytic effect for chloride additions and a minor effect for sulfate additions a t pH 6.
1-
I I
I
I
1
1
n 3 m / m i 1-1
Figure 6. Catalytic effect of added ions on the rate of dissolution of copper. (29) Although the results in Table V appear seli-consistent it is apparent from Figure 2 that under certain condltions one may obtain a much lower dependence on pH a t relatively high cupric ion concentrations. (30) (a) L. G. Sillen, C'hem. SOC.,Spec. Publ., NO. 17, (1964); (b) "International Critical Tables," Vol. 111, McGrawHill, Xew York, N. Y., 1928, p 257.
DISSOLUTION OF COPPERIN WEAKLY ACIDICSOLUTIONS
IC".'):
2.28 x TI-3
rrm
1-1
Mi = 4 . 5 7 Air \
Figure 7. 1hso;ution rste of copper as a function of reciprocal temperature.
Efect of 'Temperal'ure. The data showing the effect of temperature (16.9-45.0') on the dissolution rate (Figure 7) were obtained as follows. After the rate was measured at 25" the temperature was raised to 45" and the rate remeasured. The other points were obtained after cooling the bath by various amounts. The glass electrode assembly was calibrated before and after the run at each temperature and a minor correction has been made for the change in oxygen solubility with temperatureaobin terms of the dependence given in Table IV. Ah the measurements at 25' indicated that the sample surface mey have altered during the temperature cycling, t l e activation energy cannot be accurate. The value obtained Tvtas in the range 12 3 kcal mol-'.
*
Discussion The rate of dissolution of metals and compounds in aqueous reagents has been discussed in terms of a diffusion layer theory.75 The elementary model describes the formation of an extremely thin layer of saturated solution a t Lhc solid Burface, the rate being determined by drffusion from this layer. The corresponding model for the disscllu?ior, of copper covered with cuprous oxide would be
l/,C1,0 4- H+
c u 'surfsce
CU+
+ H + -k
-
eCU+ + '/zH20
'/402
CU'bulk Cu2+
+ '/2H,O
(6)
(7) (8)
Equation 6 describes the reaction occurring a t the Cu20-H20 inr erfaoe while (8) describes the overall reaction in thc. buik solution. If (7) is the slow step, reactions 6 and 8 must be rapid. Yet if (8) is rapid, the cuprous ions d l be oxidized before they rnove from the surface. The rate dependence on PO,eliminates (6) as the rate-determining step, suggesting that the oxidalion of Cu+ m:ty be 3 ow. This is considered later. On the other hand, control by solution diffusion of 0 2 , H", or Cu.'' was untenable in view of the observed
366 i rate dependence on Po2,(H+), (Cu2+),(Cl-), and (Br-). This conclusion was supported by the relatively minor effect of increased stirring, although such evidence must be treated with caution. While the dependence of a diffusion-controlled reaction generally weakens with more violent agitation, this is not necessarily synonymous with a transition into a region of kinetic control. In fact, lack of a stirring effect was shown to occur in the diffusional range,31 due to a slipping effect with the stirrer failing to carry the liquid along with it a t the higher rotational rates. Therefore, additional information must be available to enable a distinction between a chemical reaction and a solution diffusion process to be made unequivocally. We conclude that the dissolution is not controlled by a simple diffusion process in solution. A solid-state mechanism is now proposed. The oxidation of a metal in a gaseom environment has been described in terms of reactions at the metal-oxide and oxide-gas interfaces and the transport of material through the oxide film.32 The slowest of these steps will control film growth. In an aqueous environment film growth is opposed by dissolution and for films of constant thickness we expect the rate of oxide growth to equal the rate of dissolution. In the present investigation, when steady-state rates were observed (pseudozero-order conditions) we consider the film thickness to be constant. The oxidation and dissolution of copper will now be considered in terms of the production of cation vacancies and positive holes at the Cu20-N20 interface, their migration across the oxide film with their consequent destruction at the Cu-GuzO interface. The following reactions may take place a t the CuzOHzOinterface. (i) The transfer of a cuprous ion to the aqueous phase33 Cucu
-
A
Cu+,g
c v-cu
(9)
(ii) The oxidation of cuprous ions in oxygenated aqueous solution at the surface for which the overall reaction is described by (8). (iii) The formation of a "positive hole" in the CunO structure by a cupric ion occupying a cation vacancy. Cu2+aq
+ v-cu
A T'-
p+
(10)
In these equations CucUrepresents a curpous ion on a normal site of Cu20 with an apparent charge of zero; V-cu is a cuprous ion vacancy with an apparent charge of - 1;pi- is a cupric ion ( a cuprous ion with an electron removed, a "positive hole") with an apparent charge of +i. Whereas a positive hole may migrate by electron transfers4& (31) D . A. Frank-Kamenetskii, "Diffusion and Heat Exchange in Chemical Kinetics," translated by K. Thon, Princeton University Press, Princeton, N. J., 1955, p 66. (32) T . B. Grimley, "Chemistry of the Solid State," W. E. Garner, Ed., Butterworths, London, 1955, Chapter 14. (33) R. F. North and M. J. Pryor, Corros. Sci., 10, 297 (1970).
The Journal of Phy8iCd Chemistry, Val. 76, N o . 24, 1972
A. J. READ
3662 cucu A p+ 4p+cucu the movement of vacancies is by migration of cuprous ions into a vacant structural site.a4a At the Cu--CueO interface the defects are removed by an overall reaction of the type c:u 4- p +
+ v-cu
A
2cucu
(11)
The sum of 2 X (8), 2 X (9), (lo), and (11) gives the familiar eq I , describing the overall process, viz. CU
+ 2H-' -b
--+ Cu2+.,
'/202
+ HzO
(a) It does not appear possible to explain the rate ) , PO,in terms of dependence on (I%+), ( C U ~ + ~ ,and (9) being rate determining and this suggestion is not considered further. (b) The mechanism for the oxidation of the cuprous ion in aqueoutr solution (8) has not been resolved. Following P;iord3& we consider the following steps @US
+
cu02+
0 2
(12)
+ H+ Cu2faq+ HOz w'Os + %if+ + 3Cu+ --+ products CuOa+
(13) (14)
Kord regarded (13) to be rate determining giving
R
r'cl~(CuO~'-)(N+) = kl?,Kl2(Cu+)(H+)(02)
trical neutrality in both the solid and aqueous phases so that (p+) = (V-c,). This is strictly true only in the bulk phases and not in the space charge regions in the vicinity of each interface.32 Hence (V-cu) = K170.5(02)0*26(W+)/ (CU2 fa,)0*6
(19)
To maintain electrical neutrality, cation vacancies and positive holes migrate at equal rates across the bulk oxide and, for a process governed by the diffusion of these, vacancy migration is considered to be the slow ~tep.34~This will take place under an electrochemical potential gradient due to the concentration gradient of V-cU across the film and to the electric field in the film. I n simple terms
R
=
km(V-~u)
where km is a function describing charged particle migration in an electric field.34c Utilizing (19)
R
==
kmK17'.'(02)
6za'
(H +)/ (CU' +aq)0,5
(20)
This rate equation also correctly describes .the observed dependence on PO,and (H+) (Tables IV and V) and predicts an order of -0.5 with respect to (CuZfa,). (e) Suppose a reaction a t the Cu-Cu20 interface is rate controlling. The slow step might be the diffusion of copper atoms on to a vacant structural siteas
+
-
cu v-cu cuocu (21) This fails to account for the rate dependence on PO,. Similarly (1.2) is rejected as the slow step. The simple followed by a rapid transfer of electrons steps of (14) are unknown and will not be considered. p+ CUOC" +2cucu Henceforth the oxidation of cuprous ion in aqueous where Cuocuis a copper atom on a normal site with an solution is considered to be rapid compared with the apparent charge of - 1. In this case dissolution process (e) If (143) is rate determining then R = kzi(V-cu) R == klO(CU2+,,) (V-c,) (15) where (V-0,) will be described by eq 19, the production and transport of cation vacancies being rapid. Thus which upon subst;itution using (8) and (9) gives
+
R
=:
klo.KaKg(0Z)0*26(H+)
(16)
This equation correctly describes the observed dependence on Po,and (15 +) (Tables IV and V) and predicts a zero-order dependence on ( C U ~ + ~ (cf. , ) Figure 2). (d) For control by a slow diffusion process across the oxide layer the reactions a t the two interfaces may be regarded as rapid. At the stationary state the distribution of cation vacancies and positive holes within the bulk oxide will be Hence the rates of production of cation vacancies and positive holes will also be equal and their formation36is derived from (9), (IO), and ( I l j as 2CUcu
+ 2N-'i. '/202
_A
+ p + + V-cu + HzO
CU'+,~
(17)
Thus K17
(p +) ('V-c,) (CU' +aq)/(02)0.5( H +)
(18)
An essential requirement is the maintenance of elecThe Journal
of
Physical Chemistry, Vol. 76, N o .
1973
R
= k2iK17°.6(02)0.26(H+)/ (Cu2+,q)o.6
(22)
(34) 0. Kubaschewski and B. E. Hoplrins, "Oxidation of Metals and Alloys," Butterworths, London, 1962: (a) p 22; (b) p 82; (e) Chapter 2. (35) H. Nord, Acta Chem. Scand., 9 , 430 (1955). (36) An alternative set of rapid interfacial equilibria87 for the formation of positive holes and vacancies may be written as follows 0 2
-
+ 4H+ +4Cucu ---cu
p+ E cu2+ p+ V-cu
+ +
4p+
+ v-cu
--
A
+ 2H20
2Cucu
From these, the equations describing the overall rapid equilibrium a t the Cu-HtO interface and the overall reaction may be found identical with (17) and (l), respectively. These reactions suggest a n alternative path for the formation of positive holes and vacancies, though the dissolution of cuprous oxide in aqueous media is known t o be rapid.88 (37) P. C. A. Bailey and G. A. Wright, private communication. (38) W. Feitknecht and P. Schindler, Pure App2. Chem., 6 , 130 (1963). (39) T. B. Grimley and B. M. W. Trapnell, Proc. Roy. Soc., Ser. A, 234, 405 (1956).
IN WEAKLY ACIDIC SOLUTIONS
DISSOLUTION OF’C ~ P P E R
This formulation satisfies the PO,and (H+) dependence found experimentally (Tables IV and V) and predicts an order of -8.5 with respect to ( C U ~ + ~ , ) . A distinction between (lo), (21), and cation vacancy migration (all of which predict the observed rate dependence on Po2 and @+)) as the rate-determining step cannot he made in terms of the measured rate dependence on (Cui+) (see Figure 2). The significance of the ordor dependence (-0.2) as compared with --0.5 ((21) or vacancy migration rate dctermining) and zero ((10) rate determining) is not clear. However, the energy of activation provides additional information. In the present work this was 12 kcal mol -I. From high-temperature oxidation experiments using radioactive copper, Moore and S e l i l r ~ o ncalcu~~ lated the activation energy for the self-diffusion of Cu 111 CuzQ to be 36.1 kcal mol-’. The activation energy €or the self-diifusior, process represents the sum of the activation entqies for the formation and diffusion of ration v a ~ a n c ~ eThus, s ~ ~ ~using the enthalpy of formation derived by 0”Keeffe and (21.7 kcal mol-l), the enthalpy of rnigration is calculated as 14.4 kcal mol -l. This compares well with that obtained in the present work (12 kcal mol-’). However, in a recent p u b l i e a t i ~ n ,the ~ ~ eathalpy for the self-diffusion has been found to be 24.0 kcal mol-l. Further, some of was indicated to be of inferior the earlier quality. In view of the large discrepancy between the enthalpies reported for self-diffusion, it cannot be concluded without reservation that the slow step in the current study i s a cation vacancy migration. As noted earlier added CI- and Br- ions enhance the rate with Br- having the greater effect (Figure 6). In contrast, added F-, S042-, and NO3- ions have a negligible effert. This behavior parallels the ability of these ions to complex with cuprous ions in aqueous solution.2g However, let us consider complexing reactions of the tylie CU
‘aq
$- nC1-,,
-~
* . .
euCl(-l)--
aq
(23)
Incorporatiyg this type of complexing in equations corresponding to (9) and (8), we find that the sum of these with (IO) its identical with (12), demonstrating that the dependence of the rates on PO,and H+ would be unchanged (Table IV and V) but also that there would be no chtalysis by chloride. On the other hand, the effect of chloride has been described in terms of the substitution of C1 for 0 in the crystal lat t i ~ a : . ~This ~ substitution would create a charge imbalance leading to the formation of cation vacancies to maintain electrical neutrality, i.e. A
0 0
7
02-aq
+ Vo2+
3663
c1-
+ + VoZ+
cucu
cu
02--,q 2H+
Cu+aq
+ Hi+
‘/402
H20 ClC1
+v
-C-- Cu2+aq + l/J&Q
where Oo represents an oxygen ion on a normal lattice site with an apparent charge of zero; CICIis a chloride ion occupying a normal lattice site with an apparent charge of +1, Vo2+ is an anion vacancy with an apparent charge of + 2 . The overall equation satisfying electroneutrality requirements in both the aqueous and solid phases is
+ + 3H+ + Cl-aq +
CUC~
0 0
CU2+aq
+ ’//z€IzO + V-cu -i- C ~ C I(26)
giving (V-cu)
=
Kz6(H +) ’( Cl-,,) (Q2)o.25/ (Cu2+aq)
On this basis, the observed rate dependence on (?I+) is not satisfactorily explained. Furthermore, increased substitution of oxygen ions of the lattice by bromide ions to account for the increased effect of the latter would not be expected from simple ion size considerations. Thus while some substitution may take place, it does not appear to be the dominant mechanism. In addition, the negligible effect of added fluoride ions (Figure 6) would indicate only minor substitution in the structure. Neither suggestion for the catalytic effect of chloride fits the data well. It is worth noting that the substitution model describing the effect of (H+) on the corrosion of alumin i ~ m also * ~ does not appear to apply in the present case. To summarize, each solid-state model predicts the same dependence on PO,and (H+) and the data showing i,he rate dependence on (Cu2+)does not clarify the situation. Hence the conclusion that the slow step is a slow cation vacancy migration rests on the available evidence concerning the enthalpy of migration,
Aclcnotvledyments. The author is most grateful to Professor G. A. Wright and to Drs. A. J. Ellis, K. J. D. MacKenzie, W. H. Robinson, and T. M. Seward for their useful comments on this work. The oxygen analyses were performed by W. J. Harrison, and Miss J. Beanland helped with some of the measurements. (40) W. J. Moore and B. Selikson, J. Chem. Phys., 19, 1539 (1951). (41) P. G. Shewmon, “Diffusion in Solids,” McGraw-Bill, New York, N. Y., 1963. (42) M. O’Keeffe and W. J. Moore, .J. Chem. Phys., 36, 3009 (1962). (43) S. Mrowec and A. Stolrloss, Bull. Acad. Pol. Sci., Ser. Sei. Chim., 18, 523 (1970). (44) M. A. Heine and M . J. Prior, J. Electrochem. floc., 119,1205 (1963).
The Journal of Physical Chemistry, Vol. r6,No. 24, 1972
