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Chronopotentiometric determination of interdiffusion coefficients and heats of interdiffusion in molten salts
J. Inorg. Nucl, Chem,, 1964, Vol. 26, pp. 347 to 357. Pergamon Press Ltd. Printed in Northern Ireland
CHRONOPOTENTIOMETRIC DETERMINATION OF I N T E R D I F F U S I O N COEFFICIENTS A N D HEATS OF I N T E R D I F F U S I O N IN MOLTEN SALTS* C. E. THALMAYER, S. BRUCKENSTEIN~" and D. M. GRUEN Argonne National Laboratory, Argonne, Illinois (Received 17 June 1963; in revised form 3 July 1963)
Abstraet--Chronopotentiometry has been used to determine the interdiffusion coefficients and heats of activation for Ag e, Cd s÷, Pb ~÷, BP ÷ and U 4+ in lithium chloride-potassium chloride eutectic and for Ag+ in molten sodium nitrate and in molten cesium nitrate. In LiCI-KCI, the diffusion coefficients in cm~/sec × 106 at 400°C, and the heats of activation for diffusion in kcal/mole are given after the ionic species with errors indicated: Ag+: 24" i 7., 5-8 ___0.2; Cd2+: 12.1 4- 2", 6.5 + 0.3; Pb2~: 8.9 4- 2., 7.9 4- 0.1; BP+: 6.3 5: 1., 9.8 4- 1., U~÷: 4.9, 7.7. The temperature range studied was approximately 365-750°C. The diffusion coefficient and heat of activation for diffusion for Ag+ in sodium nitrate (in the same form as above) is 32.5 ± 0.2, 4'52 ~ 0.1, and in cesium nitrate is 24-8 5: 2" and 5.06 5: 0-1. These data indicate interdiffusion proceeds by a mechanism other than viscous flow, and are consistent with transport by "ion-diameter jumps into ion-sized holes". "~) Significant transport via a paired vacancy mechanism is not supported for interdiffusion in these melts. THE purpose of this work was to determine the interdiffusion coefficients o f various ions in several molten salts over a sufficiently large temperature range to calculate the heats o f activation for interdiffusion (AH). It was felt that the study o f several ions in the same melt, and o f the same ion in different melts over a large temperature range would yield valuable information, and perhaps shed some light on the mechanism o f interdiffusion in molten salts. After considering the various experimental techniques, it was decided that an electrochemical technique would prove most versatile. Since melts were to be studied at temperatures as high as 800°C, the use of the dropping mercury electrode, as illustrated by the work o f STEINBERG and NACHTRIEB,(1) was not considered. The use o f higher melting metals as substitutes for mercury was rejected because of the experimental problems. STEIN(2) reported the application o f linear scan voltammetry in the N a C 1 - K C I eutectic as a means o f determining the interdiffusion coefficient o f lead ion. This m e t h o d was not considered since it contains a very serious drawback, i.e., the peak current depends on whether the reaction is reversible or irreversible; in the latter case a knowledge o f the transfer coefficient is necessary to calculate the interdiffusion coefficient. The chronopotentiometric m e t h o d appeared to be the best choice for this investigation, since considerable development in the m e t h o d as applied to all phases o f electrochemistry has occurred in recent years. In particular, LAITINEN and coworkers(a, 4) have successfully applied chronopotentiometry to the determination o f interdiffusion coefficients o f A g +, T1+, Cu +, Pb 2+, Co z+, Cd ~+, and * Based on work performed under the auspices of the U.S. Atomic Energy Commission. t Department of Chemistry, University of Minnesota, Minneapolis, Minnesota. H) M. STEINBERGand N. H. NACHTRIEB, J. Amer. Chem. Soc. 72, 3558 (1950). ~t) R. B. STEIN,d. Electrochem. Soc. 106, 528 (1959). ~*) H. A. LAmNENand W. S. FERGUSON,Analyt. Chem. 29, 4 (1957). *() H. A. LAITINENand H. C. GAUR,Analyt. Chim. Acta. 18, I (1958). 347
348
C.E. THALMAYER,S. BRUCKENSTE1Nand D. M. G R u ~
Bi~ in LiCI-KCI eutectic at 450°C using platinum electrodes sealed in Corning 0120 glass. In that work, electrodes of various geometries were investigated and it was found that two different physical geometries yielded results which were a good approximation to semi-infinite linear diffusion. The first of these electrodes was a platinum wire, while the other was a 9 mm ~ platinum plate welded to a short piece of platinum wire; both electrode wires were sealed to a glass tube, thus providing electrodes of known area. Because no method for producing a platinum to glass seal which would be usable at the temperatures involved in this work is known, a modified version of Laitinen's plate electrode which avoids this difficulty was used. This is described below in the Experimental section. Recently INMAN and BOCKRIS(5) have used platinum sphere and hanging mercury drop electrodes in various molten salts. EXPERIMENTAL Materials Solutes. AgCI, CdClz and PbCI~ were Analytical Reagent grade, not further purified. BiCIB was Analytical Reagent grade, purified by fourfold vacuum sublimation. AgNO, was Analytical Reagent grade, purified by vacuum melting and filtering through a
Pyrex frit. CszUCI6 was prepared as follows: 0.05 mole UO~(NOa)~was dissolved in 1.5 1.4 M HCI and 4 oz silver powder added. Argon was bubbled through the solution at 80°C for 15 hr. (The solution turned green after 3 hr.) After filtering under an argon atmosphere to remove excess silver and silver chloride, 0-11 mole CsCl was added. The solution was cooled to -20°C for 4 hr and resaturated with HCI gas. The precipitate was then collected on a fritted glass filter, washed with 100 ml chilled, concentrated HCI, and air pulled through the precipitate to remove surface hydrochloric acid. The product was dried for 60 hr at 70°C in vacuum. It was a light green microcrystalline material. Analysis on the basis of U(IV) content was 100.2% CszUCI6 and the yield was 87 per cent on the basis of U. Gases. HCI was purified by passing over coconut charcoal to remove organic matter, and over magnesium perchlorate to remove water. Argon was purified by passing over molecular sieve to remove water, and over hot copper dispersed in kieselguhr to remove oxygen. Solvents. The LiC1-KC1 eutectic was prepared from Analytical Reagent grade salts by a method similar to that of L~Tr~N et al. (e) The weighed salt mixture (140 g) was supported by a fritted disk in a quartz tube mounted vertically above the electrolysis cell bottom and connected to the cell by a water-cooled ball-joint. A resistance furnace was placed around the tube, vacuum was applied through the cell, and the salt was dried overnight at elevated temperature under vacuum. HCI was then passed through the salt from below, while the temperature was raised over several hours to the melting point of the salt. HCI bubbling through the melt was continued for 1 hr to ensure removal of water. The HCI was then swept from the melt by bubbling with argon. Magnesium shavings were poured into the melt to reduce heavy metals, and the argon bubbling continued for several hours. Vacuum was then suddenly applied, causing the melt to filter into the cell. The salt tube was then removed from the cell, and the cell head put in its place. The NaNOs and CsNOa were prepared from Analytical Reagent grade materials in a way similar to the above. The weighed salt (160 g NaNOs or 240 g CsNO,) was dried overnight under vacuum at elevated temperature. Argon was then passed through the salt as the temperature was raised over several hours to the melting point of the salt. Argon bubbling through the melt was continued for 2 hr to digest the precipitate which was present. The melt was then filtered into the cell. Apparatus The electrolysis cell consisted of a quartz bottom, a Pyrex top, electrodes, and quartz electrode compartments. ts) D. It,~AN and J. O'M. Boc~ras, J. Electroanalyt. Chem. 3, 126 (1962). (6) H. A. L~nm,~N, W. S. FEROUSONand R. A. OS~RYOt~G, J. Electrochem. Soc. 104, 516 (1957).
Interdiffusion coefficients and heats of interdiffusion in molten salts
349
The cell bottom was a quartz tube, 5 cm diameter by 25 cm height, closed at the bottom, with a 65]40 water-cooled inner ball-joint at the top, just below which was a sidearm leading to the vacuum andthegas supplies. The cell top consisted o f a n o u t e r 65/40 water-cooled ball-joint andsix standard taper joints. Experience dictated the use of water-cooled ball-joints to prevent sticking after the cell had been subjected to high temperature and vacuum for a considerable length of time. In the taper joints rested the three electrode tubes, a closed thermocouple tube and, when necessary, tubes for admission or removal of gas. Solutes were generally introduced through a funnel inserted through one of the taper joints. The above joints were sealed with silicone stopcock grease. Each of the electrodes was sealed into the top of its tube with Apiezon W wax. The reference electrode in the LiCI-KCI runs was a tungsten or platinum -10 per cent rhodium wire, generally in direct contact with the melt, its short tube serving only to support it in the cell head. The auxiliary electrode was a tungsten or platinum-10 per cent rhodium wire enclosed in a quartz tube which ended in a fritted disk and had a small hole near the top for pressure equalization; melt was forced into the auxiliary compartment by temporarily closing the small hole and then applying and releasing vacuum, or simply by applying argon pressure to the cell through the sidearm. The polarized indicator electrode, made of platinum-10 per cent rhodium, was a rectangular plate welded to a wire; the total area of the faces and edges of the plate plus the immersed portion of the wire was about 3 cm ~. A new polarized indicator electrode was used for nearly every run in LiCI--KCI, while the other two electrodes were merely cleaned before each run. In the nitrate melt experiments reported in this paper, the reference electrode was a silver wire and the auxiliary electrode was platinum-10 per cent rhodium; new reference and polarized indicator electrodes were used for each run. In order for the electrode compartments to fill with molten salt readily it was necessary to increase the porosity of the electrode frits by immersion in dilute hydrofluoric acid. The furnace was nichrome wound and had a massive stainless steel liner, closed at the bottom, to reduce temperature gradients in the melt. Being mounted on a jack, it could be lowered smoothly to permit examination of the cell. Power was supplied to the furnace through a constant-voltage transformer and an autotransformer. The resulting voltage stability enabled the temperature of the cell, as measured by a potentiometer and a calibrated chromel-alumel thermocouple, to be known to better than I°C during a chronopotentiogram. The degassing cell and furnace were essentially identical to the cell and furnace described above. The vacuum line consisted of a mechanical pump, mercury diffusion pump and liquid nitrogen trap. A conventional three-electrode chronopotentiometric circuit was used. The constant current regulator was capable of delivering cathodic or anodic currents in the range 1-100 mA constant to ~0.1 per cent. The voltage compliance of this device was ~60 V. The voltmeter used to measure the e.m.f, difference between the polarized indicator electrode and the reference electrode was an a.c. line operated device with an input impedance of 10TM ~). Its frequency response was adequate for the transition times measured. The output of this voltmeter was used to drive a Tektronix Type 502 oscilloscope and the resulting voltage-time curves were recorded with a Polaroid camera. In order to obtain the maximum accuracy in time measurement, the sweep frequency of the oscilloscope x-axis was adjusted to yield 2--4 sweeps during a chronopotentiogram. The potential-time curve was recorded by opening the camera shutter, turning the current on, and closing the camera shutter after the transition time had been observed. Since an appreciable interval exists between the time the beam disappears from the extreme right side of the screen and the time the beam starts to sweep across the screen again, a time scale independent of the oscilloscope was required. This was provided by a time-mark generator consisting of three decimal counting units and a 1 kc tuning-fork oscillator. This generator produced pulses at intervals of 1 msec, 10 msec or 0-I sec, depending upon the range selected. These pulses were used to intensity modulate the oscilloscope beam. Every tenth pulse was of higher voltage, thereby producing a more intense spot of light on the oscilloscope screen. Fig. 1 (see below) shows a typical result.
Procedure a. Preliminary. The cell and solvent-preparation tube were cleaned with nitric and hydrofluoric acids; the frit of the solvent tube was heated to incandescence to oxidize any remaining impurities. Solvent preparation, as described above, was begun two days before each run. Electrodes were prepared as follows: Tungsten wires were cleaned with emery cloth; silver wires were cleaned by dilute nitric acid; the platinum-lO per cent rhodium electrodes were cleaned by
350
C . E . THALMAYER,S. I~IRUCKENSTE1Nand D. M. GgUEN
boiling in nitric acid. The electrodes were assembled in their previously prepared compartments. For the LiCI-KCI runs, the electrodes and thermocouple tube were dried overnight under vacuum and high temperature (,~ 750°C). For the nitrate runs, drying was accomplished by heating with a hand torch, before and after assembly. Chronopotentiograms of the pure solvent were obtained as described below, before several of the LiCI-KCI runs and before all nitrate runs. The weighed solute was dropped into the melt and the cell bottom heated with a hand torch to speed dissolution and mixing. b. Conduct of the run. (1) The electronic equipment was connected to the electrode wires by shielded cables terminating in alligator clips. (2) The current regulator, voltmeter, oscilloscope and time-marker generator were checked and set for the desired characteristics. The oscilloscope was set to give a recurrent sweep at a rate which spread the transition time over several sweeps. (3) The desired melt temperature was attained by manipulation of the furnace autotransformer. (4) The chronopotentiogram was obtained: while observing the oscilloscope, the camera shutter was opened, the switch closed to pass current between the electrodes, the shutter closed and the constant current interrupted at the end of the transition time. Visual observation at the oscilloscope ordinarily made it possible to start the electrolysis while the beam was on the oscilloscope face and to terminate the experiment at the desired e.m.f. However, at sweep rates faster than 50 msec/cm, it was not possible to co-ordinate the opening and closing of the shutter manually with the position of the oscilloscope beam, and it was sometimes necessary to perform several experiments before satisfactory pictures could be obtained. (5) The bulk concentration of solute was re-established in the vicinity of the polarized indicator electrode by gas bubbling, agitation of the electrode or simply waiting for several minutes; only the latter was done in the nitrate runs. (6) In the chloride runs, the polarized indicator electrode was stripped periodically to restore the solute concentration: reversed (oxidizing) current was passed through the cell just long enough to remove the deposited metal from the electrode, as indicated by the e.m.f, displayed on the oscilloscope. The electrode was then plated with a thin coat of the metal. In the nitrate runs, the polarized indicator electrode was removed from the melt after each picture, washed in hot water, soaked several minutes in hot nitric acid, washed again with water and heated to incandescence with a torch. This removal of silver from the electrode was found necessary because of the otherwise rapid increase in transition time, presumably due to dendrite growth increasing the electrode area. Oxidizing current was not passed through the cell. (7) Samples of the melt were taken; except in the earliest runs, this was done by inserting a quartz tube terminating in a fritted quartz disk, drawing up the sample, removing the tube from the cell, manipulating the salt to the center of the tube, and sealing off the sample with a torch. In the chloride runs, electrode compartments were used as sampling tubes; in the case of the volatile solutes, BiCIs and PbCI~, samples were taken at the end of each temperature series; the total number of samples varied from one to twelve. In the nitrate runs, the sampling tubes were large Pyrex tubes; because of the large amount of melt removed, samples could be taken only before and after the run; the total number per run varied from seven to nine; the need for such multiplicity of samples will be made clear later. c. Temperature measurements. Temperatures in the melt were measured with a calibrated chromelalumel thermocouple to an accuracy of better than 1°C. d. Electrode area. The area, A, of each plate electrode was measured with a micrometer; it comprised the area of the sides and edges of the plate, plus the area of the immersed portion of the wire. A was calculated at every temperature in order to take into account the variation in wire immersion depth due to the change in volume of the melt. To determine the effective chronopotentiometric area of the electrodes, experiments were performed with thallous ion in aqueous potassium nitrate as supporting electroyte at 25°C. A small Pyrex cell with fritted compartments was used, hut in all other respects the aqueous chronopotentiometry was identical to that of the fused salt work. The usual precautions such as deoxygenation by argon bubbling were observed. About a dozen observations were made on each of ten electrodes, the current being varied as usual to produce transition times in the range 1-10 sec. The area was then calculated from the Sand Equation (Equation I below), using the value of the diffusion coefficient for
lnterdiffusion coe~cients and heats of interdiffusion in molten salts
351
thallous ion which had been independently determined by chronopotentiometry under conditions of ideal semi-infinite linear diffusion, tT~ It was found that this area for all electrodes agreed within 1 per cent with the area measured with a micrometer, provided the edges were taken into account. These results verify the previous observations of LAmNEN and FEaOUSON~3~ who concluded that a plate electrode can yield results in substantial agreement with those obtained under conditions of semi-infinite linear diffusion. e. Transition time measurement. The transition time, r, is defined as the time interval between the beginning of electrolysis and the time at which the surface concentration of the electroactive species becomes zero. Experimentally, we have located the beginning and the end of the transition time as follows. The beginning of electrolysis was generally taken as the point on a chronopotentiogram where the oscilloscope trace left the rest potential. In all experiments there was a visible potential change when a current was applied. In the few cases where there was a large potential difference ( ~ 0.2 V) between the rest potential and the slowly rising portion of the potential-time curve, doublelayer charging was taken into consideration ; the beginning of electrolysis was taken as the point of intersection of the lines drawn tangent to the initial potential-jump and to the slowly rising portion of the potential-time curve. The end of the transition time was arbitrarily taken as the point of intersection of lines drawn tangent to the slowly rising portion of the curve, near its end, and to the subsequent sharply rising portion at its highest slope. In the case of well defined potential-time curves, this procedure is capable of yielding results in agreement with previously suggested methods for evaluating 7. When drawn-out or distorted curves were obtained, this method yielded consistent results when used by different individuals. An example of this graphical procedure is shown in Fig. 1. f. Analytiealprocedures. A g - - A solution of the sample was treated with H2S. The precipitated Ag2S was filtered, washed and dissolved with a mixture of sulphuric and nitric acids. Silver was determined in this solution by the Volhard method. For each LiCI-KC1 run only one sample was taken; these analyses are estimated to be accurate to 5 per cent. For each nitrate run, three to five samples were taken both before and after each run; the relative mean deviations of the analyses performed on these samples ranged from 0.6 to 5.4 per cent. C d - - F o r the first run, the sample was dissolved in water, fumed with sulphuric acid and the cadmium precipitated as the sulphide. Cadmium sulphide was separated and dissolved. Cadmium was then plated out by electrolysis from an alkaline cyanide solution. For the remaining runs, a solution of the sample was treated with H~S, the precipitated CdS filtered, washed and dissolved in HCI. This solution was evaporated to dryness, the residue dissolved in H2SO4, evaporated and converted to CdSO4, which was heated to constant weight at 500°C. The accuracy of the analyses on the single samples is estimated to be 2 per cent. P b - - A colorimetric determination with dithizone was performed. For each run, replicate analyses were performed on samples taken during the course of the run. The relative mean deviation of these analyses was 1.1 per cent. Bi--A colorimetric determination with iodide in the presence of hypophosphorous acid was performed. 3/9/61: Analyses performed on seven samples taken in the course of the run were considered 60 per cent low and were rejected. 4/27/61,5/4[61,6/6/61: Duplicate analyses ofduplicate samples taken during the course of the run had relative mean deviations (within each group of four) of about 2 per cent. The over-all accuracy of the analyses, however, is estimated to be about 5 per cent. U---U(IV) was volumetrically determined by addition of excess ceric sulphate to a solution of the sample and back titration with ferrous sulphate. Total U was volumetrically determined by passing a solution of the sample through a lead reductor, adding an excess of eerie sulphate, then backtitrating with ferrous sulphate. Cs was determined by direct flame photometric analysis on a solution of the sample, using the emission line at 852 m/a. The agreement between these analyses indicated an accuracy of 2 per cent. EXPERIMENTAL
RESULTS
T h e diffusion coefficient w a s c a l c u l a t e d for e a c h o b s e r v a t i o n f r o m the S a n d E q u a t i o n in t h e f o r m i%" D r = k~n~d~N~A2 (1) c~ T. O. RousE. Ph.D. Thesis, University of Minnesota (1960). 10
6/20/61
3/9/61 4]27/61 5/4/61 6/6/61
9/20/60t 12/15]60
19
43 24 36 32
30 55
51 19 19 28
23 19 12 16
420--621
364-564 372-657 364-617 367-517
513-735 381-705
395-809 403-664 533-660 426--670
374-677 502-746 432-535 378-645
Temperature range (°C)
5- 35
++ 1"9§ 0"24§ 1 "9§
0"86 1"26
0.76 0-60 + +
1-75 1-45 1-46 2.32
N (mmole/g) × 10= 25.1 18"3 31"1 21 '7 24. -4- 7. 10-1 14.1 --12.1 4- 2. 10'2 7"6 8.9 4- 2-5"27 6'35 7"20 6.3 4- 14.89
D4oo. (cm=/sec) x l 0 s*
0.03
2"0 0"06 0"03 0"03
0"3 0"I
0.2 0-I 1-2 0"4
0"2 0"6 0"3 0"1
~rD (cm=/sec) x 10e 5-84 6"04 5.68 5"61 5.8 4- 0.2 6-62 6.69 6.18 6.57 6.5 4- 0.3 7"98 7"81 7-9 4- 0.I 10"64 9"03 10"86 8"68 9.8 4- 1. 7.72
AH (kcal/mole)
0.07
0"25 0"08 0"06 0"07
0"16 0"09
0-10 0.04 0.13 0.05
0"08 0"21 0"11 0"03
Cr~H (kcal/mole)
* Calculated from Equations (1) and (2) using d = 1"8851--0-0005275 t. t"~ The value o f n used in Equation (I) corresponded to the oxidation state of the ion except in the case of U(IV) where a value of unity was used. I" The timing technique used in these experiments differed from that described in Experimental. The transition time was calculated from the length of the trace as estimated from the grid and the sweep rates. To this value the n u m b e r of "off times" was added. (The "off time" is the time interval between the end of one trace and the beginning of the next.) The accuracy of the time base of the oscilloscope and the "off time" were determined using a Tektronix Time Mark Generator Model No. 180 A. This timing technique was abandoned since the method described under Experimental is more convenient and accurate. .+ Analysis rejected because it differed excessively from the approximate concentration calculated from the starting weights of salt and the amount of solute added. § The actual concentration varied during the experiment because of the volatility of the solute. Samples were taken and analysed during the run as described under Experimental. lSI E. R. VAN ARTSDALEN and I. S. Y A r ~ , .L Phys. Chem. 59, 118 (1955).
Mean U 4+
Mean BP ÷
Mean Pb ~÷
9/12160t 7/31/61 8/2/61 8/7/61
6/28161 7/28/61 8/11/61 917161
Ag +
Mean Cd =+
Date
System
Number of observations
TABLE 1 .--INTERDIFFUSION IN L i C I - K C I E t r r E c a a c
t~q Z
v
I=l ta.
ml
m
.m ,-1
""N,
1
"'" ;" 2 L.:_:_. . . . . .
~J
t
1
V.
T-
I --,-----TIME
FiG. I . - - C h r o n o p o t e n t i o g m m of U(IV) in LiCI KC1 eutectic. N~.,n; =0.0535 mmole/g.* T = 560 C. 'rime axis intensity modulated at 10 msec intervals, with every 100 msec accented, tiach major vertical division 0"2 V. Electrode area 4'52 cm 2. Currcnt ~ 100-0 mA, r 1"56 sec. *0"0850 M at this tcmperalurc.
352
Interdiffusion coefficientsand heats of interdiffusion in molten salts
353
where D r is the interdiffusion coefficient at temperature T, -r the transition time, in seconds, i the current, in mA, k = zrt F]2 = 8"552 x 104, n the number of electrons involved in the electrode process, d the density of the solvent, in g/ml, N the concentration, in mmole/g, and A the electrode area, in cm ~. The heat of activation for interdiffusion, AH, is given by AH log D r ---- A -- R---T "
(2)
The method of least squares was used to obtain the best values of D4o0 and A H for each run. Data which gave evidence of having been affected by convection or double layer charging were rejected. Generally, it was possible to measure transition times as short as 0.3 see with the solute concentration we used without encountering double layer charging. Transition times as long as 2 or 3 sec usually showed no evidence of convection, and in some cases transition times as long as 8 sec appeared to be satisfactory. Table 1 presents a summary of the results obtained with Ag(I), Cd(II), Pb(II) Bi(IH) and U(IV) in lithium chloride-potassium chloride eutectic, while Table 2 presents the results obtained for Ag(I) in sodium and cesium nitrates. Considering the data in Table 1 it is seen that the standard deviations, tr, within each run are quite small, whereas the differences between runs of the same system are quite large; this seems to indicate that the largest experimental error is in a quantity which is constant within each run, probably the analytical concentration, N. Further support for this view is that A H values obtained in different runs for the same ion are usually in better agreement with each other than are the diffusion coefficients. Our estimates of the relative error in the analytical determination of the concentrations of the various electroactive species are indicated above under Analytical
procedures. The other principal source of error is the measurement of ~-. The good fit of the data to the least squares line of Equation (2) indicates that the random error in measuring r is small. Systematic errors in determining r are not ruled out. One source of systematic error occurs when the final sharply rising portion of a potential-time curve is distorted by the presence of reducible trace impurities. This distortion is difficult to eliminate because the prior reduction of the ion under study enhances the transition times for all trace impurities which are subsequently reduced. DISCUSSION Table 3 presents a comparison between the results obtained in this work and previously reported values of interdiffusion coefficients. There is excellent agreement between our value for the diffusion coefficient of Ag + in sodium nitrate at 310 ° and the value found by LAITY and MILLER.(1°)* Good agreement is also found between the value of the diffusion coefficient of Cd ~+ at 450 ° in molten lithium chloride-potassium chloride eutectic and that reported by LAITINEN and FERGUSON,(a) HEUS and * These workers used a diaphragm cell technique, inserting silver electrodes into each compartment to follow the concentration changes. tx0~R. W. LArrYand M. P. MILLER. Private communication 0962).
25 27
24 31 411-466 414-520
314-430 313-425
Temperature range (°C)
1.6 1.5
1.9 1-9
N (mmole/g) × 102t 32-3 32-6 32.5 4- 0.2 26-2 23.4 24.8 4- 2"
D400o (cm=/sec) x 10e*
0.2 0.1
0.1 0.2
o"D (cm=/sec) × 106 4-50 4-55 4.52 4- 0.1 5-00 5.11 5"06 4- 0.1
AH kcal/mole
OAIt
0-16 0.03
0.07 0.08
kcal/mole
cg~F. M. JAEG~a, Z. Anorg. Chem. 101, 16 (1917) quoted in "International Critical Tables," Vol. 3, p. 24. McGraw-Hill, New York (1928).
* Calculated from Equations (1) and (2) using dN-a~Oa = 2-114-0"00067 t c°~ and dcs~o, = 3-270-0.001115 t cs~. I" As a result of the technique used to clean the polarized indicator electrode, each electrolysis resulted in a decrease in silver ion concentration. Therefore, the value of N used for each observation was arrived at by interpolating between the various analytical results. In addition to the electrolytic loss of silver, there was a slight loss of silver on long standing in the cell due to unknown causes. The interpolations correct for these losses also.
Mean
2/14/62 3/21/62
2]2/62 3/8/62
NaNO~
Mean CsNOs
Date
System
N u m b e r of observations
TABLE 2.--INTERDIFFUSION OF Ag ~" IN SODIUM AND CESIUM NITRATES
Z
I=
¢3
¢0
>=
Interdiffusion coefficientsand heats of interdiffusion in molten salts
355
EGAN,(u) and ANGELL and TOMLINSON.(t~)* However, the values we find for the interdiffusion coefficients of silver, lead, and bismuth at 450 ° in molten lithiumpotassium chloride eutectic are in much poorer agreement with previously published literature values. ~3'4'1ma~ In the case of silver and lead, the experimental errors in our results are large enough to include at least one of the previously reported literature values, all of which exhibit a large spread of values. It should be noted that in all TABLE3.--COMPARISONOF PREVIOUSLY PUBLISHED INTERDIFFUSION COEFFICIENT DATA IN MOLTEN SALTS WITH THIS WORK
Molten salt Li-KCI eut.
NaNOs
D x 105 (cmg/sec)
Temp. (°C)
This work++
Ag +
450
3.2 :I: 0.5
Cd2+
450
1.7 -6 0"3
1"7,'3~ 1"8'11~ !'4 Im
P b ~+ BP +
450 450
1"3 -6 0"2 I'0 -t- 0"I
2"18, "~ 1"7 Im 0'C 8~
Ag+
310
1"93 -6 0"01
Ion
Literature values 2.6/s~ 2.08, "~ 1.85 'la~
2.09 + 0-12(t°)
**Calculated from the individual values of D,0o and AH given in Tables ! and 2. the quoted literature rather good precision is obtained by each set of workers, generally better than 5 per cent. The only conclusion that can be drawn is that the experimental problems involved in making diffusion coefficient measurements in fused salts are considerable and, often, unsuspected systematic errors occur. A comparison of A H values with other workers is possible only for Ag ÷ and Cd 2+ dissolved in lithium-potassium chloride. SENDEROFFet al.tm t report A H = 6.95 kcal/mole for Ag + compared to our value of 5"8 ~ 0.2 kal/mole (average of four independent experiments), while ANGELL and TOMLINSONt12) report 6.7 kcal/mole for Cd e÷ compared to our mean value of 6,5 Jz 0.3 kcal/mole. A plot of ln[D/T] gave straight lines for Ag ÷, Cd ~÷, Pb ~+ and U 4÷ in LiCI-KCI with slopes which in all cases were significantly less than 7.04 kcal/mole calculated from the viscosity data of KARPACHEV et ak (m When plotted this way Bia+ yielded 8.2 ± 1 kcal/mole. (Over the temperature range studied, plotting log D / T instead of log D vs. 1/T decreases the slope by an amount equivalent to ~ 1 . 6 kcal/mole.) Stokes-Einstein behavior is ruled out in all cases, except that of Bia+. It seems unlikely a paired vacancy mechanism, such as that suggested by BOCKRIS and HOOFER(m to explain their self-diffusion data for NaCl, RbCl, CsCl and NaI, is operable in Li-KC1 eutectic. This mechanism would require that solute ions diffuse according to the Stokes-Einstein equation, and that the observed deviations represent diffusion of paired vacancies. BOCKRIS and HOOPER'St15) results yield a heat of activation for this process considerably larger than that for viscous flow. Since our heats of activation for iaterdiffusion are less than for viscous flow, paired vacancy interdiffusion cannot be an important mechanism in LiCI-KCI. * These authors used 11sCdwith the capillary reservoir technique. t A radioactive tracer method with 11lAgwas used. m) R. J. HEus and J. J. EGAN,Y. Electrochem. Soc. 107, 824 (1960). (is) C. A. ANGELLand J. W. TOMUNSON.Private communication 0963). (18)S. SENDEROVF,E. M. KLOPand M. L. KRO~ERC~. Private communication 0962). '~') AEC-TR-1923. Original reference: S.V. KARPACHEV,A. G. STROMBERGand V. N. PODCnAINOVA, Zh. Obshch. KMm. 5, 1517 (1935).
356
C.E. T~x,~,
S. BRUCKENmmm and D. M. GRtmN
Interpretation of the results obtained in LiCI-KCI in fight of current theories of diffusion in molten salts is difficult. It is significant that solute ions have substantially lower heats of activation for diffusion than for viscous flow, indicating that the mechanisms for these two processes are quite different. It is possible to rationalize our experimental results in terms of a hole theory by assuming that the AH values reflect the different amounts of work involved in creating the proper sized hole for a solute ion and the work involved in the elementary jump process. (As has been indicated previously,(15) the heat of activation for the jump process is probably quite small.) Since each solute ion interacts with the melt to an unknown extent, e.g., by complex ion formation with unknown coordination number, the different diffusion coefficients and AH values are explained by the "effective radius" of the solute ion in the melt. It is interesting to compare the heats of interdiffusion for Ag + with those of selfdiffusion of the cation in sodium and cesium nitrates. In NaNO3, Ag+ requires a heat of activation 0.5 kcal/mole less than does Na +, and 0-6 kcal/mole less than Cs + in CsNOs. (le) This result is hard to interpret in terms of a simple hole model. The radius of Ag+ lies between the radii of Na + and Cs+ and a simple model would predict that AH for hole formation of silver ion in sodium nitrate should be larger than of Na + in sodium nitrate. It is possible that the presence of Ag+ significantly disrupts the local structure of the nitrate melt around the silver ion, making the formation of a hole easier than in the bulk of the melt. In sodium and cesium nitrates the heat of interdiffusion of Ag+ is significantly larger than for self-diffusion in silver nitrate, 3.7 kcal/mole. (le) No temperature-independent relation involving masses or radii can exist between the measured interdiffusion coefficient of Ag + and the self-diffusion coefficients of the solvent cations in sodium and cesium nitrates since there is a significant difference in AH values for these ions. If our data are presented in the form DAg+ = A e x p ( - - A H / R T ) , the pre-exponential factor, A, is found to be 1"34 × 10-s in sodium nitrate and 1.09 x 10-3 in cesium nitrate. These values are indistinguishable from the preexponential factors found for the self-diffusion of the melt cation, ~1~) 1"29 × 10-s for Na + and 1"13 × 10-3 for Cs+. This result suggests that the experimental pre-exponential factors are independent of solute cation-solvent cation mass ratios and radius ratios. DWOR~N et al. (~e) have objected to YANG'S(x7) use of the method of BoRucr,~ et al. (Is) in separating the observed self-diffusion coefficients of Na + and NO 3- into diffusion coefficients of Na +, NOa-and NaNO3 (paired vacancy diffusion). YANG found excellent agreement between the self-diffusion coefficient of Na + and NO 3calculated from the observed data, the Nernst-Einstein equation and equivalent conductance data with that calculated from the Stokes-Einstein equation. Their (x°) objection has been conclusively refuted by BocKms. (15) YANG'Sresult of 4.3 kcal/mole for the AH of self-diffusion is experimentally indistinguishable from our observed value of 4-5 keal/mole for Ag+ in sodium nitrate. This agreement at first seems to indicate that the Stokes-Einstein equation also holds for Ag+ diffusing in sodium nitrate, assuming paired vacancy diffusion plays no part in the interdiffusion process. tx6) A. S. DWORKI~, R. B. ESCUE and E. R. VAN ARTSDALEN, Y. Phys. Chem. 64, 872 (1960). (xT) L. YANG, d. Chem. Phys. 27, 601 (1957). (ls) A. Z. BORUCKA, J. O'M. BOCKRIS and J. A. KITCHENER, Proe. Roy. Soe. A 241,554 (1957).
Interdiffusion coefficientsand heats of interdiffusion in molten salts
357
This is not the case as can be shown by calculating the pre-exponential factor for Ag + in NaNOa. The pre-exponential factor for Na + becomes 0.60 x I0 -s using YANO'S calculated self-diffusion data corrected for paired vacancy diffusion. Since the radius of Ag + is approximately 33 per cent larger than that of sodium, the preexponential factor for Ag + in sodium nitrate is calculated to be 0.45 x 10-a assuming the Stokes-Einstein equation, a result which is only 25 % of the observed experimental value. It must be concluded that agreement between A H for interdiffusion in sodium nitrate and that predicted from viscous flow is fortuitous. In summary, the chronopotentiometric results indicate that interdiffusion does not obey the Stokes-Einstein relation in lithium chloride-potassium chloride eutectic, molten sodium nitrate or molten cesium nitrate. In addition, while there is strong evidence that paired vacancy diffusion is a significant transport process in the selfdiffusion of solvent cation and anion in some alkali metal halides and sodium nitrate, such a mechanism for interdiffusion seems unlikely in the solvents we have studied. Note added hi proof: Using oscillographic polarography, SCHMIDT(le) found the following values of D × 10~at 450°C in LiCI-KCI: Ag+: 3"3; Cd2+: 2"1; Pb2÷: 2"2; Bi3÷: 2"8. Acknowledgements--We thank W. K. BROOKSrn~Rof the Argonne National Laboratory Electronics
Division for the design and construction of the current regulator and high impedance voltmeter, W. C. BENTLEYof the Argonne National Laboratory Chemistry Division for design and construction of the time-mark generator, and the Analytical Chemistry Group for performance of the analyses. cx,~E. SCHMIDT,Electrochim. Acta 8, 23 (1963).
CHRONOPOTENTIOMETRIC DETERMINATION OF I N T E R D I F F U S I O N COEFFICIENTS A N D HEATS OF I N T E R D I F F U S I O N IN MOLTEN SALTS* C. E. THALMAYER, S. BRUCKENSTEIN~" and D. M. GRUEN Argonne National Laboratory, Argonne, Illinois (Received 17 June 1963; in revised form 3 July 1963)
Abstraet--Chronopotentiometry has been used to determine the interdiffusion coefficients and heats of activation for Ag e, Cd s÷, Pb ~÷, BP ÷ and U 4+ in lithium chloride-potassium chloride eutectic and for Ag+ in molten sodium nitrate and in molten cesium nitrate. In LiCI-KCI, the diffusion coefficients in cm~/sec × 106 at 400°C, and the heats of activation for diffusion in kcal/mole are given after the ionic species with errors indicated: Ag+: 24" i 7., 5-8 ___0.2; Cd2+: 12.1 4- 2", 6.5 + 0.3; Pb2~: 8.9 4- 2., 7.9 4- 0.1; BP+: 6.3 5: 1., 9.8 4- 1., U~÷: 4.9, 7.7. The temperature range studied was approximately 365-750°C. The diffusion coefficient and heat of activation for diffusion for Ag+ in sodium nitrate (in the same form as above) is 32.5 ± 0.2, 4'52 ~ 0.1, and in cesium nitrate is 24-8 5: 2" and 5.06 5: 0-1. These data indicate interdiffusion proceeds by a mechanism other than viscous flow, and are consistent with transport by "ion-diameter jumps into ion-sized holes". "~) Significant transport via a paired vacancy mechanism is not supported for interdiffusion in these melts. THE purpose of this work was to determine the interdiffusion coefficients o f various ions in several molten salts over a sufficiently large temperature range to calculate the heats o f activation for interdiffusion (AH). It was felt that the study o f several ions in the same melt, and o f the same ion in different melts over a large temperature range would yield valuable information, and perhaps shed some light on the mechanism o f interdiffusion in molten salts. After considering the various experimental techniques, it was decided that an electrochemical technique would prove most versatile. Since melts were to be studied at temperatures as high as 800°C, the use of the dropping mercury electrode, as illustrated by the work o f STEINBERG and NACHTRIEB,(1) was not considered. The use o f higher melting metals as substitutes for mercury was rejected because of the experimental problems. STEIN(2) reported the application o f linear scan voltammetry in the N a C 1 - K C I eutectic as a means o f determining the interdiffusion coefficient o f lead ion. This m e t h o d was not considered since it contains a very serious drawback, i.e., the peak current depends on whether the reaction is reversible or irreversible; in the latter case a knowledge o f the transfer coefficient is necessary to calculate the interdiffusion coefficient. The chronopotentiometric m e t h o d appeared to be the best choice for this investigation, since considerable development in the m e t h o d as applied to all phases o f electrochemistry has occurred in recent years. In particular, LAITINEN and coworkers(a, 4) have successfully applied chronopotentiometry to the determination o f interdiffusion coefficients o f A g +, T1+, Cu +, Pb 2+, Co z+, Cd ~+, and * Based on work performed under the auspices of the U.S. Atomic Energy Commission. t Department of Chemistry, University of Minnesota, Minneapolis, Minnesota. H) M. STEINBERGand N. H. NACHTRIEB, J. Amer. Chem. Soc. 72, 3558 (1950). ~t) R. B. STEIN,d. Electrochem. Soc. 106, 528 (1959). ~*) H. A. LAmNENand W. S. FERGUSON,Analyt. Chem. 29, 4 (1957). *() H. A. LAITINENand H. C. GAUR,Analyt. Chim. Acta. 18, I (1958). 347
348
C.E. THALMAYER,S. BRUCKENSTE1Nand D. M. G R u ~
Bi~ in LiCI-KCI eutectic at 450°C using platinum electrodes sealed in Corning 0120 glass. In that work, electrodes of various geometries were investigated and it was found that two different physical geometries yielded results which were a good approximation to semi-infinite linear diffusion. The first of these electrodes was a platinum wire, while the other was a 9 mm ~ platinum plate welded to a short piece of platinum wire; both electrode wires were sealed to a glass tube, thus providing electrodes of known area. Because no method for producing a platinum to glass seal which would be usable at the temperatures involved in this work is known, a modified version of Laitinen's plate electrode which avoids this difficulty was used. This is described below in the Experimental section. Recently INMAN and BOCKRIS(5) have used platinum sphere and hanging mercury drop electrodes in various molten salts. EXPERIMENTAL Materials Solutes. AgCI, CdClz and PbCI~ were Analytical Reagent grade, not further purified. BiCIB was Analytical Reagent grade, purified by fourfold vacuum sublimation. AgNO, was Analytical Reagent grade, purified by vacuum melting and filtering through a
Pyrex frit. CszUCI6 was prepared as follows: 0.05 mole UO~(NOa)~was dissolved in 1.5 1.4 M HCI and 4 oz silver powder added. Argon was bubbled through the solution at 80°C for 15 hr. (The solution turned green after 3 hr.) After filtering under an argon atmosphere to remove excess silver and silver chloride, 0-11 mole CsCl was added. The solution was cooled to -20°C for 4 hr and resaturated with HCI gas. The precipitate was then collected on a fritted glass filter, washed with 100 ml chilled, concentrated HCI, and air pulled through the precipitate to remove surface hydrochloric acid. The product was dried for 60 hr at 70°C in vacuum. It was a light green microcrystalline material. Analysis on the basis of U(IV) content was 100.2% CszUCI6 and the yield was 87 per cent on the basis of U. Gases. HCI was purified by passing over coconut charcoal to remove organic matter, and over magnesium perchlorate to remove water. Argon was purified by passing over molecular sieve to remove water, and over hot copper dispersed in kieselguhr to remove oxygen. Solvents. The LiC1-KC1 eutectic was prepared from Analytical Reagent grade salts by a method similar to that of L~Tr~N et al. (e) The weighed salt mixture (140 g) was supported by a fritted disk in a quartz tube mounted vertically above the electrolysis cell bottom and connected to the cell by a water-cooled ball-joint. A resistance furnace was placed around the tube, vacuum was applied through the cell, and the salt was dried overnight at elevated temperature under vacuum. HCI was then passed through the salt from below, while the temperature was raised over several hours to the melting point of the salt. HCI bubbling through the melt was continued for 1 hr to ensure removal of water. The HCI was then swept from the melt by bubbling with argon. Magnesium shavings were poured into the melt to reduce heavy metals, and the argon bubbling continued for several hours. Vacuum was then suddenly applied, causing the melt to filter into the cell. The salt tube was then removed from the cell, and the cell head put in its place. The NaNOs and CsNOa were prepared from Analytical Reagent grade materials in a way similar to the above. The weighed salt (160 g NaNOs or 240 g CsNO,) was dried overnight under vacuum at elevated temperature. Argon was then passed through the salt as the temperature was raised over several hours to the melting point of the salt. Argon bubbling through the melt was continued for 2 hr to digest the precipitate which was present. The melt was then filtered into the cell. Apparatus The electrolysis cell consisted of a quartz bottom, a Pyrex top, electrodes, and quartz electrode compartments. ts) D. It,~AN and J. O'M. Boc~ras, J. Electroanalyt. Chem. 3, 126 (1962). (6) H. A. L~nm,~N, W. S. FEROUSONand R. A. OS~RYOt~G, J. Electrochem. Soc. 104, 516 (1957).
Interdiffusion coefficients and heats of interdiffusion in molten salts
349
The cell bottom was a quartz tube, 5 cm diameter by 25 cm height, closed at the bottom, with a 65]40 water-cooled inner ball-joint at the top, just below which was a sidearm leading to the vacuum andthegas supplies. The cell top consisted o f a n o u t e r 65/40 water-cooled ball-joint andsix standard taper joints. Experience dictated the use of water-cooled ball-joints to prevent sticking after the cell had been subjected to high temperature and vacuum for a considerable length of time. In the taper joints rested the three electrode tubes, a closed thermocouple tube and, when necessary, tubes for admission or removal of gas. Solutes were generally introduced through a funnel inserted through one of the taper joints. The above joints were sealed with silicone stopcock grease. Each of the electrodes was sealed into the top of its tube with Apiezon W wax. The reference electrode in the LiCI-KCI runs was a tungsten or platinum -10 per cent rhodium wire, generally in direct contact with the melt, its short tube serving only to support it in the cell head. The auxiliary electrode was a tungsten or platinum-10 per cent rhodium wire enclosed in a quartz tube which ended in a fritted disk and had a small hole near the top for pressure equalization; melt was forced into the auxiliary compartment by temporarily closing the small hole and then applying and releasing vacuum, or simply by applying argon pressure to the cell through the sidearm. The polarized indicator electrode, made of platinum-10 per cent rhodium, was a rectangular plate welded to a wire; the total area of the faces and edges of the plate plus the immersed portion of the wire was about 3 cm ~. A new polarized indicator electrode was used for nearly every run in LiCI--KCI, while the other two electrodes were merely cleaned before each run. In the nitrate melt experiments reported in this paper, the reference electrode was a silver wire and the auxiliary electrode was platinum-10 per cent rhodium; new reference and polarized indicator electrodes were used for each run. In order for the electrode compartments to fill with molten salt readily it was necessary to increase the porosity of the electrode frits by immersion in dilute hydrofluoric acid. The furnace was nichrome wound and had a massive stainless steel liner, closed at the bottom, to reduce temperature gradients in the melt. Being mounted on a jack, it could be lowered smoothly to permit examination of the cell. Power was supplied to the furnace through a constant-voltage transformer and an autotransformer. The resulting voltage stability enabled the temperature of the cell, as measured by a potentiometer and a calibrated chromel-alumel thermocouple, to be known to better than I°C during a chronopotentiogram. The degassing cell and furnace were essentially identical to the cell and furnace described above. The vacuum line consisted of a mechanical pump, mercury diffusion pump and liquid nitrogen trap. A conventional three-electrode chronopotentiometric circuit was used. The constant current regulator was capable of delivering cathodic or anodic currents in the range 1-100 mA constant to ~0.1 per cent. The voltage compliance of this device was ~60 V. The voltmeter used to measure the e.m.f, difference between the polarized indicator electrode and the reference electrode was an a.c. line operated device with an input impedance of 10TM ~). Its frequency response was adequate for the transition times measured. The output of this voltmeter was used to drive a Tektronix Type 502 oscilloscope and the resulting voltage-time curves were recorded with a Polaroid camera. In order to obtain the maximum accuracy in time measurement, the sweep frequency of the oscilloscope x-axis was adjusted to yield 2--4 sweeps during a chronopotentiogram. The potential-time curve was recorded by opening the camera shutter, turning the current on, and closing the camera shutter after the transition time had been observed. Since an appreciable interval exists between the time the beam disappears from the extreme right side of the screen and the time the beam starts to sweep across the screen again, a time scale independent of the oscilloscope was required. This was provided by a time-mark generator consisting of three decimal counting units and a 1 kc tuning-fork oscillator. This generator produced pulses at intervals of 1 msec, 10 msec or 0-I sec, depending upon the range selected. These pulses were used to intensity modulate the oscilloscope beam. Every tenth pulse was of higher voltage, thereby producing a more intense spot of light on the oscilloscope screen. Fig. 1 (see below) shows a typical result.
Procedure a. Preliminary. The cell and solvent-preparation tube were cleaned with nitric and hydrofluoric acids; the frit of the solvent tube was heated to incandescence to oxidize any remaining impurities. Solvent preparation, as described above, was begun two days before each run. Electrodes were prepared as follows: Tungsten wires were cleaned with emery cloth; silver wires were cleaned by dilute nitric acid; the platinum-lO per cent rhodium electrodes were cleaned by
350
C . E . THALMAYER,S. I~IRUCKENSTE1Nand D. M. GgUEN
boiling in nitric acid. The electrodes were assembled in their previously prepared compartments. For the LiCI-KCI runs, the electrodes and thermocouple tube were dried overnight under vacuum and high temperature (,~ 750°C). For the nitrate runs, drying was accomplished by heating with a hand torch, before and after assembly. Chronopotentiograms of the pure solvent were obtained as described below, before several of the LiCI-KCI runs and before all nitrate runs. The weighed solute was dropped into the melt and the cell bottom heated with a hand torch to speed dissolution and mixing. b. Conduct of the run. (1) The electronic equipment was connected to the electrode wires by shielded cables terminating in alligator clips. (2) The current regulator, voltmeter, oscilloscope and time-marker generator were checked and set for the desired characteristics. The oscilloscope was set to give a recurrent sweep at a rate which spread the transition time over several sweeps. (3) The desired melt temperature was attained by manipulation of the furnace autotransformer. (4) The chronopotentiogram was obtained: while observing the oscilloscope, the camera shutter was opened, the switch closed to pass current between the electrodes, the shutter closed and the constant current interrupted at the end of the transition time. Visual observation at the oscilloscope ordinarily made it possible to start the electrolysis while the beam was on the oscilloscope face and to terminate the experiment at the desired e.m.f. However, at sweep rates faster than 50 msec/cm, it was not possible to co-ordinate the opening and closing of the shutter manually with the position of the oscilloscope beam, and it was sometimes necessary to perform several experiments before satisfactory pictures could be obtained. (5) The bulk concentration of solute was re-established in the vicinity of the polarized indicator electrode by gas bubbling, agitation of the electrode or simply waiting for several minutes; only the latter was done in the nitrate runs. (6) In the chloride runs, the polarized indicator electrode was stripped periodically to restore the solute concentration: reversed (oxidizing) current was passed through the cell just long enough to remove the deposited metal from the electrode, as indicated by the e.m.f, displayed on the oscilloscope. The electrode was then plated with a thin coat of the metal. In the nitrate runs, the polarized indicator electrode was removed from the melt after each picture, washed in hot water, soaked several minutes in hot nitric acid, washed again with water and heated to incandescence with a torch. This removal of silver from the electrode was found necessary because of the otherwise rapid increase in transition time, presumably due to dendrite growth increasing the electrode area. Oxidizing current was not passed through the cell. (7) Samples of the melt were taken; except in the earliest runs, this was done by inserting a quartz tube terminating in a fritted quartz disk, drawing up the sample, removing the tube from the cell, manipulating the salt to the center of the tube, and sealing off the sample with a torch. In the chloride runs, electrode compartments were used as sampling tubes; in the case of the volatile solutes, BiCIs and PbCI~, samples were taken at the end of each temperature series; the total number of samples varied from one to twelve. In the nitrate runs, the sampling tubes were large Pyrex tubes; because of the large amount of melt removed, samples could be taken only before and after the run; the total number per run varied from seven to nine; the need for such multiplicity of samples will be made clear later. c. Temperature measurements. Temperatures in the melt were measured with a calibrated chromelalumel thermocouple to an accuracy of better than 1°C. d. Electrode area. The area, A, of each plate electrode was measured with a micrometer; it comprised the area of the sides and edges of the plate, plus the area of the immersed portion of the wire. A was calculated at every temperature in order to take into account the variation in wire immersion depth due to the change in volume of the melt. To determine the effective chronopotentiometric area of the electrodes, experiments were performed with thallous ion in aqueous potassium nitrate as supporting electroyte at 25°C. A small Pyrex cell with fritted compartments was used, hut in all other respects the aqueous chronopotentiometry was identical to that of the fused salt work. The usual precautions such as deoxygenation by argon bubbling were observed. About a dozen observations were made on each of ten electrodes, the current being varied as usual to produce transition times in the range 1-10 sec. The area was then calculated from the Sand Equation (Equation I below), using the value of the diffusion coefficient for
lnterdiffusion coe~cients and heats of interdiffusion in molten salts
351
thallous ion which had been independently determined by chronopotentiometry under conditions of ideal semi-infinite linear diffusion, tT~ It was found that this area for all electrodes agreed within 1 per cent with the area measured with a micrometer, provided the edges were taken into account. These results verify the previous observations of LAmNEN and FEaOUSON~3~ who concluded that a plate electrode can yield results in substantial agreement with those obtained under conditions of semi-infinite linear diffusion. e. Transition time measurement. The transition time, r, is defined as the time interval between the beginning of electrolysis and the time at which the surface concentration of the electroactive species becomes zero. Experimentally, we have located the beginning and the end of the transition time as follows. The beginning of electrolysis was generally taken as the point on a chronopotentiogram where the oscilloscope trace left the rest potential. In all experiments there was a visible potential change when a current was applied. In the few cases where there was a large potential difference ( ~ 0.2 V) between the rest potential and the slowly rising portion of the potential-time curve, doublelayer charging was taken into consideration ; the beginning of electrolysis was taken as the point of intersection of the lines drawn tangent to the initial potential-jump and to the slowly rising portion of the potential-time curve. The end of the transition time was arbitrarily taken as the point of intersection of lines drawn tangent to the slowly rising portion of the curve, near its end, and to the subsequent sharply rising portion at its highest slope. In the case of well defined potential-time curves, this procedure is capable of yielding results in agreement with previously suggested methods for evaluating 7. When drawn-out or distorted curves were obtained, this method yielded consistent results when used by different individuals. An example of this graphical procedure is shown in Fig. 1. f. Analytiealprocedures. A g - - A solution of the sample was treated with H2S. The precipitated Ag2S was filtered, washed and dissolved with a mixture of sulphuric and nitric acids. Silver was determined in this solution by the Volhard method. For each LiCI-KC1 run only one sample was taken; these analyses are estimated to be accurate to 5 per cent. For each nitrate run, three to five samples were taken both before and after each run; the relative mean deviations of the analyses performed on these samples ranged from 0.6 to 5.4 per cent. C d - - F o r the first run, the sample was dissolved in water, fumed with sulphuric acid and the cadmium precipitated as the sulphide. Cadmium sulphide was separated and dissolved. Cadmium was then plated out by electrolysis from an alkaline cyanide solution. For the remaining runs, a solution of the sample was treated with H~S, the precipitated CdS filtered, washed and dissolved in HCI. This solution was evaporated to dryness, the residue dissolved in H2SO4, evaporated and converted to CdSO4, which was heated to constant weight at 500°C. The accuracy of the analyses on the single samples is estimated to be 2 per cent. P b - - A colorimetric determination with dithizone was performed. For each run, replicate analyses were performed on samples taken during the course of the run. The relative mean deviation of these analyses was 1.1 per cent. Bi--A colorimetric determination with iodide in the presence of hypophosphorous acid was performed. 3/9/61: Analyses performed on seven samples taken in the course of the run were considered 60 per cent low and were rejected. 4/27/61,5/4[61,6/6/61: Duplicate analyses ofduplicate samples taken during the course of the run had relative mean deviations (within each group of four) of about 2 per cent. The over-all accuracy of the analyses, however, is estimated to be about 5 per cent. U---U(IV) was volumetrically determined by addition of excess ceric sulphate to a solution of the sample and back titration with ferrous sulphate. Total U was volumetrically determined by passing a solution of the sample through a lead reductor, adding an excess of eerie sulphate, then backtitrating with ferrous sulphate. Cs was determined by direct flame photometric analysis on a solution of the sample, using the emission line at 852 m/a. The agreement between these analyses indicated an accuracy of 2 per cent. EXPERIMENTAL
RESULTS
T h e diffusion coefficient w a s c a l c u l a t e d for e a c h o b s e r v a t i o n f r o m the S a n d E q u a t i o n in t h e f o r m i%" D r = k~n~d~N~A2 (1) c~ T. O. RousE. Ph.D. Thesis, University of Minnesota (1960). 10
6/20/61
3/9/61 4]27/61 5/4/61 6/6/61
9/20/60t 12/15]60
19
43 24 36 32
30 55
51 19 19 28
23 19 12 16
420--621
364-564 372-657 364-617 367-517
513-735 381-705
395-809 403-664 533-660 426--670
374-677 502-746 432-535 378-645
Temperature range (°C)
5- 35
++ 1"9§ 0"24§ 1 "9§
0"86 1"26
0.76 0-60 + +
1-75 1-45 1-46 2.32
N (mmole/g) × 10= 25.1 18"3 31"1 21 '7 24. -4- 7. 10-1 14.1 --12.1 4- 2. 10'2 7"6 8.9 4- 2-5"27 6'35 7"20 6.3 4- 14.89
D4oo. (cm=/sec) x l 0 s*
0.03
2"0 0"06 0"03 0"03
0"3 0"I
0.2 0-I 1-2 0"4
0"2 0"6 0"3 0"1
~rD (cm=/sec) x 10e 5-84 6"04 5.68 5"61 5.8 4- 0.2 6-62 6.69 6.18 6.57 6.5 4- 0.3 7"98 7"81 7-9 4- 0.I 10"64 9"03 10"86 8"68 9.8 4- 1. 7.72
AH (kcal/mole)
0.07
0"25 0"08 0"06 0"07
0"16 0"09
0-10 0.04 0.13 0.05
0"08 0"21 0"11 0"03
Cr~H (kcal/mole)
* Calculated from Equations (1) and (2) using d = 1"8851--0-0005275 t. t"~ The value o f n used in Equation (I) corresponded to the oxidation state of the ion except in the case of U(IV) where a value of unity was used. I" The timing technique used in these experiments differed from that described in Experimental. The transition time was calculated from the length of the trace as estimated from the grid and the sweep rates. To this value the n u m b e r of "off times" was added. (The "off time" is the time interval between the end of one trace and the beginning of the next.) The accuracy of the time base of the oscilloscope and the "off time" were determined using a Tektronix Time Mark Generator Model No. 180 A. This timing technique was abandoned since the method described under Experimental is more convenient and accurate. .+ Analysis rejected because it differed excessively from the approximate concentration calculated from the starting weights of salt and the amount of solute added. § The actual concentration varied during the experiment because of the volatility of the solute. Samples were taken and analysed during the run as described under Experimental. lSI E. R. VAN ARTSDALEN and I. S. Y A r ~ , .L Phys. Chem. 59, 118 (1955).
Mean U 4+
Mean BP ÷
Mean Pb ~÷
9/12160t 7/31/61 8/2/61 8/7/61
6/28161 7/28/61 8/11/61 917161
Ag +
Mean Cd =+
Date
System
Number of observations
TABLE 1 .--INTERDIFFUSION IN L i C I - K C I E t r r E c a a c
t~q Z
v
I=l ta.
ml
m
.m ,-1
""N,
1
"'" ;" 2 L.:_:_. . . . . .
~J
t
1
V.
T-
I --,-----TIME
FiG. I . - - C h r o n o p o t e n t i o g m m of U(IV) in LiCI KC1 eutectic. N~.,n; =0.0535 mmole/g.* T = 560 C. 'rime axis intensity modulated at 10 msec intervals, with every 100 msec accented, tiach major vertical division 0"2 V. Electrode area 4'52 cm 2. Currcnt ~ 100-0 mA, r 1"56 sec. *0"0850 M at this tcmperalurc.
352
Interdiffusion coefficientsand heats of interdiffusion in molten salts
353
where D r is the interdiffusion coefficient at temperature T, -r the transition time, in seconds, i the current, in mA, k = zrt F]2 = 8"552 x 104, n the number of electrons involved in the electrode process, d the density of the solvent, in g/ml, N the concentration, in mmole/g, and A the electrode area, in cm ~. The heat of activation for interdiffusion, AH, is given by AH log D r ---- A -- R---T "
(2)
The method of least squares was used to obtain the best values of D4o0 and A H for each run. Data which gave evidence of having been affected by convection or double layer charging were rejected. Generally, it was possible to measure transition times as short as 0.3 see with the solute concentration we used without encountering double layer charging. Transition times as long as 2 or 3 sec usually showed no evidence of convection, and in some cases transition times as long as 8 sec appeared to be satisfactory. Table 1 presents a summary of the results obtained with Ag(I), Cd(II), Pb(II) Bi(IH) and U(IV) in lithium chloride-potassium chloride eutectic, while Table 2 presents the results obtained for Ag(I) in sodium and cesium nitrates. Considering the data in Table 1 it is seen that the standard deviations, tr, within each run are quite small, whereas the differences between runs of the same system are quite large; this seems to indicate that the largest experimental error is in a quantity which is constant within each run, probably the analytical concentration, N. Further support for this view is that A H values obtained in different runs for the same ion are usually in better agreement with each other than are the diffusion coefficients. Our estimates of the relative error in the analytical determination of the concentrations of the various electroactive species are indicated above under Analytical
procedures. The other principal source of error is the measurement of ~-. The good fit of the data to the least squares line of Equation (2) indicates that the random error in measuring r is small. Systematic errors in determining r are not ruled out. One source of systematic error occurs when the final sharply rising portion of a potential-time curve is distorted by the presence of reducible trace impurities. This distortion is difficult to eliminate because the prior reduction of the ion under study enhances the transition times for all trace impurities which are subsequently reduced. DISCUSSION Table 3 presents a comparison between the results obtained in this work and previously reported values of interdiffusion coefficients. There is excellent agreement between our value for the diffusion coefficient of Ag + in sodium nitrate at 310 ° and the value found by LAITY and MILLER.(1°)* Good agreement is also found between the value of the diffusion coefficient of Cd ~+ at 450 ° in molten lithium chloride-potassium chloride eutectic and that reported by LAITINEN and FERGUSON,(a) HEUS and * These workers used a diaphragm cell technique, inserting silver electrodes into each compartment to follow the concentration changes. tx0~R. W. LArrYand M. P. MILLER. Private communication 0962).
25 27
24 31 411-466 414-520
314-430 313-425
Temperature range (°C)
1.6 1.5
1.9 1-9
N (mmole/g) × 102t 32-3 32-6 32.5 4- 0.2 26-2 23.4 24.8 4- 2"
D400o (cm=/sec) x 10e*
0.2 0.1
0.1 0.2
o"D (cm=/sec) × 106 4-50 4-55 4.52 4- 0.1 5-00 5.11 5"06 4- 0.1
AH kcal/mole
OAIt
0-16 0.03
0.07 0.08
kcal/mole
cg~F. M. JAEG~a, Z. Anorg. Chem. 101, 16 (1917) quoted in "International Critical Tables," Vol. 3, p. 24. McGraw-Hill, New York (1928).
* Calculated from Equations (1) and (2) using dN-a~Oa = 2-114-0"00067 t c°~ and dcs~o, = 3-270-0.001115 t cs~. I" As a result of the technique used to clean the polarized indicator electrode, each electrolysis resulted in a decrease in silver ion concentration. Therefore, the value of N used for each observation was arrived at by interpolating between the various analytical results. In addition to the electrolytic loss of silver, there was a slight loss of silver on long standing in the cell due to unknown causes. The interpolations correct for these losses also.
Mean
2/14/62 3/21/62
2]2/62 3/8/62
NaNO~
Mean CsNOs
Date
System
N u m b e r of observations
TABLE 2.--INTERDIFFUSION OF Ag ~" IN SODIUM AND CESIUM NITRATES
Z
I=
¢3
¢0
>=
Interdiffusion coefficientsand heats of interdiffusion in molten salts
355
EGAN,(u) and ANGELL and TOMLINSON.(t~)* However, the values we find for the interdiffusion coefficients of silver, lead, and bismuth at 450 ° in molten lithiumpotassium chloride eutectic are in much poorer agreement with previously published literature values. ~3'4'1ma~ In the case of silver and lead, the experimental errors in our results are large enough to include at least one of the previously reported literature values, all of which exhibit a large spread of values. It should be noted that in all TABLE3.--COMPARISONOF PREVIOUSLY PUBLISHED INTERDIFFUSION COEFFICIENT DATA IN MOLTEN SALTS WITH THIS WORK
Molten salt Li-KCI eut.
NaNOs
D x 105 (cmg/sec)
Temp. (°C)
This work++
Ag +
450
3.2 :I: 0.5
Cd2+
450
1.7 -6 0"3
1"7,'3~ 1"8'11~ !'4 Im
P b ~+ BP +
450 450
1"3 -6 0"2 I'0 -t- 0"I
2"18, "~ 1"7 Im 0'C 8~
Ag+
310
1"93 -6 0"01
Ion
Literature values 2.6/s~ 2.08, "~ 1.85 'la~
2.09 + 0-12(t°)
**Calculated from the individual values of D,0o and AH given in Tables ! and 2. the quoted literature rather good precision is obtained by each set of workers, generally better than 5 per cent. The only conclusion that can be drawn is that the experimental problems involved in making diffusion coefficient measurements in fused salts are considerable and, often, unsuspected systematic errors occur. A comparison of A H values with other workers is possible only for Ag ÷ and Cd 2+ dissolved in lithium-potassium chloride. SENDEROFFet al.tm t report A H = 6.95 kcal/mole for Ag + compared to our value of 5"8 ~ 0.2 kal/mole (average of four independent experiments), while ANGELL and TOMLINSONt12) report 6.7 kcal/mole for Cd e÷ compared to our mean value of 6,5 Jz 0.3 kcal/mole. A plot of ln[D/T] gave straight lines for Ag ÷, Cd ~÷, Pb ~+ and U 4÷ in LiCI-KCI with slopes which in all cases were significantly less than 7.04 kcal/mole calculated from the viscosity data of KARPACHEV et ak (m When plotted this way Bia+ yielded 8.2 ± 1 kcal/mole. (Over the temperature range studied, plotting log D / T instead of log D vs. 1/T decreases the slope by an amount equivalent to ~ 1 . 6 kcal/mole.) Stokes-Einstein behavior is ruled out in all cases, except that of Bia+. It seems unlikely a paired vacancy mechanism, such as that suggested by BOCKRIS and HOOFER(m to explain their self-diffusion data for NaCl, RbCl, CsCl and NaI, is operable in Li-KC1 eutectic. This mechanism would require that solute ions diffuse according to the Stokes-Einstein equation, and that the observed deviations represent diffusion of paired vacancies. BOCKRIS and HOOPER'St15) results yield a heat of activation for this process considerably larger than that for viscous flow. Since our heats of activation for iaterdiffusion are less than for viscous flow, paired vacancy interdiffusion cannot be an important mechanism in LiCI-KCI. * These authors used 11sCdwith the capillary reservoir technique. t A radioactive tracer method with 11lAgwas used. m) R. J. HEus and J. J. EGAN,Y. Electrochem. Soc. 107, 824 (1960). (is) C. A. ANGELLand J. W. TOMUNSON.Private communication 0963). (18)S. SENDEROVF,E. M. KLOPand M. L. KRO~ERC~. Private communication 0962). '~') AEC-TR-1923. Original reference: S.V. KARPACHEV,A. G. STROMBERGand V. N. PODCnAINOVA, Zh. Obshch. KMm. 5, 1517 (1935).
356
C.E. T~x,~,
S. BRUCKENmmm and D. M. GRtmN
Interpretation of the results obtained in LiCI-KCI in fight of current theories of diffusion in molten salts is difficult. It is significant that solute ions have substantially lower heats of activation for diffusion than for viscous flow, indicating that the mechanisms for these two processes are quite different. It is possible to rationalize our experimental results in terms of a hole theory by assuming that the AH values reflect the different amounts of work involved in creating the proper sized hole for a solute ion and the work involved in the elementary jump process. (As has been indicated previously,(15) the heat of activation for the jump process is probably quite small.) Since each solute ion interacts with the melt to an unknown extent, e.g., by complex ion formation with unknown coordination number, the different diffusion coefficients and AH values are explained by the "effective radius" of the solute ion in the melt. It is interesting to compare the heats of interdiffusion for Ag + with those of selfdiffusion of the cation in sodium and cesium nitrates. In NaNO3, Ag+ requires a heat of activation 0.5 kcal/mole less than does Na +, and 0-6 kcal/mole less than Cs + in CsNOs. (le) This result is hard to interpret in terms of a simple hole model. The radius of Ag+ lies between the radii of Na + and Cs+ and a simple model would predict that AH for hole formation of silver ion in sodium nitrate should be larger than of Na + in sodium nitrate. It is possible that the presence of Ag+ significantly disrupts the local structure of the nitrate melt around the silver ion, making the formation of a hole easier than in the bulk of the melt. In sodium and cesium nitrates the heat of interdiffusion of Ag+ is significantly larger than for self-diffusion in silver nitrate, 3.7 kcal/mole. (le) No temperature-independent relation involving masses or radii can exist between the measured interdiffusion coefficient of Ag + and the self-diffusion coefficients of the solvent cations in sodium and cesium nitrates since there is a significant difference in AH values for these ions. If our data are presented in the form DAg+ = A e x p ( - - A H / R T ) , the pre-exponential factor, A, is found to be 1"34 × 10-s in sodium nitrate and 1.09 x 10-3 in cesium nitrate. These values are indistinguishable from the preexponential factors found for the self-diffusion of the melt cation, ~1~) 1"29 × 10-s for Na + and 1"13 × 10-3 for Cs+. This result suggests that the experimental pre-exponential factors are independent of solute cation-solvent cation mass ratios and radius ratios. DWOR~N et al. (~e) have objected to YANG'S(x7) use of the method of BoRucr,~ et al. (Is) in separating the observed self-diffusion coefficients of Na + and NO 3- into diffusion coefficients of Na +, NOa-and NaNO3 (paired vacancy diffusion). YANG found excellent agreement between the self-diffusion coefficient of Na + and NO 3calculated from the observed data, the Nernst-Einstein equation and equivalent conductance data with that calculated from the Stokes-Einstein equation. Their (x°) objection has been conclusively refuted by BocKms. (15) YANG'Sresult of 4.3 kcal/mole for the AH of self-diffusion is experimentally indistinguishable from our observed value of 4-5 keal/mole for Ag+ in sodium nitrate. This agreement at first seems to indicate that the Stokes-Einstein equation also holds for Ag+ diffusing in sodium nitrate, assuming paired vacancy diffusion plays no part in the interdiffusion process. tx6) A. S. DWORKI~, R. B. ESCUE and E. R. VAN ARTSDALEN, Y. Phys. Chem. 64, 872 (1960). (xT) L. YANG, d. Chem. Phys. 27, 601 (1957). (ls) A. Z. BORUCKA, J. O'M. BOCKRIS and J. A. KITCHENER, Proe. Roy. Soe. A 241,554 (1957).
Interdiffusion coefficientsand heats of interdiffusion in molten salts
357
This is not the case as can be shown by calculating the pre-exponential factor for Ag + in NaNOa. The pre-exponential factor for Na + becomes 0.60 x I0 -s using YANO'S calculated self-diffusion data corrected for paired vacancy diffusion. Since the radius of Ag + is approximately 33 per cent larger than that of sodium, the preexponential factor for Ag + in sodium nitrate is calculated to be 0.45 x 10-a assuming the Stokes-Einstein equation, a result which is only 25 % of the observed experimental value. It must be concluded that agreement between A H for interdiffusion in sodium nitrate and that predicted from viscous flow is fortuitous. In summary, the chronopotentiometric results indicate that interdiffusion does not obey the Stokes-Einstein relation in lithium chloride-potassium chloride eutectic, molten sodium nitrate or molten cesium nitrate. In addition, while there is strong evidence that paired vacancy diffusion is a significant transport process in the selfdiffusion of solvent cation and anion in some alkali metal halides and sodium nitrate, such a mechanism for interdiffusion seems unlikely in the solvents we have studied. Note added hi proof: Using oscillographic polarography, SCHMIDT(le) found the following values of D × 10~at 450°C in LiCI-KCI: Ag+: 3"3; Cd2+: 2"1; Pb2÷: 2"2; Bi3÷: 2"8. Acknowledgements--We thank W. K. BROOKSrn~Rof the Argonne National Laboratory Electronics
Division for the design and construction of the current regulator and high impedance voltmeter, W. C. BENTLEYof the Argonne National Laboratory Chemistry Division for design and construction of the time-mark generator, and the Analytical Chemistry Group for performance of the analyses. cx,~E. SCHMIDT,Electrochim. Acta 8, 23 (1963).