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SOLUBILITY OF Mn AND Cd IONS IN NaCl
J. Chapman, E. Lilley
To cite this version:
J. Chapman, E. Lilley. SOLUBILITY OF Mn AND Cd IONS IN NaCl. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-455-C9-464. �10.1051/jphyscol:1973975�. �jpa-00215451�
JOURNAL D E P H Y S I Q U E Colloque C9, supplkment au no 11-12, Tome 34, Nouetnbre-DPcembre 1973, page C9-455
SOLUBILITY OF Mn AND Cd IONS IN NaCl
J. A. C H A P M A N (*) a n d E. LILLEY
School o f Applied Sciences, University o f Sussex, Falmer, Sussex, UK
RksumC. - Une etude de la solubilite a ete effectuke sur NaCI/MnC12 et NaCI/CdCI2 a faibles teneurs en cations divalents. Dans les deux cas la phase precipitee a la mSme stcechiornetrie (6 NaCI, MnC12) et la meme structure cristalline. La solubilite totale de ces phases dans NaCl a ete deterrninee en fonction de la temperature et interpretee en termes de cations divalents libres, de paires associees et de trinieres. Les enthalpies et entropies de solution pour les ions libres en solution sont 0,82 eV et 0,99 eV et ASllk - 2,5 et l , l pour 6 NaCI, MnC12 et 6 NaCI, CdC12 respectivement. La tendance a former des agglomerations superieures, ii I'equilibre, semble beau- coup plus grande dans NaCI/CdClr que dans NaCI/MnC12. L'entlialpie de solution du systerne NaCI/CdC12 est notablement differente des resultats de Cappelletti et Fieschi (1969).
Abstract. - A solubility study has been made of NaCI/MnCI? and NaCIICdC12 at low concen- trations of the divalent cation. In both cases the precipitating phase had the same stoichiometry (6 NaCI. MnC12) and crystal structure. The total solubility of these phases i l l NaCl was determined as a function of temperature arid accounted for in terms of free divalent cations, associated pairs and trimers. The enthalpies and entropies of solution for the free ions in solution are 0.82 eV and 0.99 eV and ASl/lc - - 2.5 and 1.1 for 6 NaCI.MnCI? and 6 NaCI.CdCI2 respectively. The tendency to form higher order clusters, at equilibriu~ii, appears to be much greater in NaCI/CdCI2 than in the NaCI/MnCIz system. The enthalpy of solution for tlie N a c l / C d C l ~ system is markedly different to the results of Cappelletti and Fiesclii (1969).
I . Introduction. - Alkali lialide crystals have for m a n y years been a fruitful field o f study f o r the understanding o f point defects. F r o m an experimental point o f view it is tlie charged n a t u r e o f tlie defects that has m a d e t h e m accessible t o study by a variety o f techniques such a s ionic conductivity. dielectric loss, I T C . etc. In n u m e r o u s experimeiits the alkali lialide crystals have been d o p e d with divalent cation impurities t o introduce a controlled concentration o f extrinsic vacancies. These include studies o f c o l o u r centres, tliermoluminescence, clustering kinetics, mechanical properties, etc.
I n a solid solution the divalent impurity ions can be free, o r exist a s associated pairs. o r a s higher o r d e r clusters, possibly a s dimers a n d [rimers. What has n o t generally been recognised is tliat in s t ~ ~ d i e s per- formed at root11 temperature, a n d even u p t o a few h u n d r e d degrees centigrade, it is not unconirnon t o exceed tlie solubility limit of the divnlent cations.
Consequently, if a second phase nucleates, divalent cations a n d extrinsic vacancies will be removed f r o m solid solution. In m a n y cases precipitation has been avoided by working at Iiigii t e m p e r a t u r e s ; however, i n the lower temperature regions a know- ledge of t h e solubility lirnit a n d the mechanisms o f precipitation is i m p o r t a n t .
F o r a n y detailed understanding of solubility in a system it is necessary t o identify the precipitating phase, i. e. its stoichiometry a n d crystal structure.
(*) J. A. Chapman is now ill the h4ullaril Rcsca~ch Labol'i- tories, Redhill. Surrey.
Suzuki (1961), using X-ray diffraction t o study NaCI/CdC12, discovered the first o f a family of precipitate structures based o n t h e stoichiometry 6 M X . N X 2 . where M represents the alkali ion.
X the halogen ion a n d N the divalent cation. Subse- quently Lilley atid Newkirk (1967) found a n analogous structure in LiF/MgF,. a n d others have been found by Lilley a n d coworkers. It appears tliat all of these phases a r e metastable.
A number o f ionic conductivity studies have generated information :tboilt tlie solubility of divalent cations, yet the results have rarely been analysed into meaningful enthalpies atid entropies of solution.
The original \YO[-k o f Haven (1950) demonslrated tliat the total solubility limit could be derived f r o m the break in the ionic conductivity plot at tlie end of tlie precipitation region, i. e. this is the temperature of the solubility limit o f a given composition crystal.
Such d a t a taken o n several crystals o f different diva- lent cation concentration would correspond t o the phase diagram solvus curve. Several studies have attempted t o obtain tlie impurity free solubility limit using ionic conductivity, e. g. Brown a n d Hoodless
( 1967). Cappelletti a n d Fieschi ( 1969) have used I T C t o determine the solubility of associated pairs a s a function o f temperature, but they found unu- sually low enthalpies of solution. In these studies the precipitating phase was never identified. altliougli sometinlcs it \\.;IS assumed tliat tlie stable prccipitatilig phases. a s indicated by their phase di:~grams. nrerc fbrriied. This is a hazardou: assumption, considering the tendency t o form metastable phases in thesc
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973975
C9-456 J . A . CHAPMAN A N D E. LILLEY
systems. Only in tlie LiF/MgF, system have the precipitating phases been identified and their solu- bilities determined with any degree of accuracy (Lilley, 1966, 1973).
Given the dearth of solubility data in alkali halide/
divalent cation systems, it was decided to investigate two systems in detail :
a) The NaCl/CdCI, system : this system is known to have a relatively high solubility and to precipitate the metastable 6 NaCI. CdCl, phase.
6) The NaCI/MnCI, system : of all systems, this is probably tlie most thoroughly studied (Watkins 1959, Symmonds 197 I).
2. Theory. - 2.1 S O L U B I L I T Y . - Let us consider tlie case of precipitation of MX, from solid solution.
A divalent halide precipitate phase in equilibrium with an alkali halide matrix of the same halogen type makes tlie treatment of solubility more compli- cated than for metallic systenis, because the divalent ions in solid solution must be compensated by an equal number of extrinsic vacancies. It is necessary to take the extrinsic vacancies into account in calcu- lating the configurational entropy term. I f tlie assump- tion is made that all the M f + ions and extrinsic vacancies are free, as opposed to being associated, then, using elementary thermodynamics, it can readily be shown that the expression for solubility is
- AHl A S l
C, = exp -
2 kT exp -
2 k
where C, is the equilibrium mole fraction of free M + + ions and of extrinsic vacancies in solid solution ' at temperature T ; A H , is the enthalpy of solution of a molecule of M + + X 2 ; A S , is the entropy of solution of a molecule of M+'X;.
Alternatively, if it is assumed that all the M + + ions in solid solution are associated with extrinsic vacancies as associated pairs, Lidiard (1962) lias shown that the solubility is given by
and extrinsic vacancies can exist in even higher order states of association than pairs, for example as trimers.
If all the M + + ions and extrinsic vacancies in solid solution are in the form of trimers, then, using asso- ciation theory, an expression for the solubility of trimers can be obtained in the same way as that for associated pairs
(3 AH2 - E , ) 3 A S , C, = 3 2, exp -
I< T exp -
k (4)
where C, is the equilibrium mole fraction of M + + ions present as trirners in solid solution, A H , is the enthalpy of solution of an associated pair, i. e.
AH, = A H , - E., ; E, is the enthalpy of formation of a trimer from 3 associated pairs. Tlie entropy of formation is again assumed to be zero. Z, is a geo- metrical entropy factor which is equal to 8.
Up to this point only the precipitation of M + + ions in a particular state of association lias been considered.
Tlie situation in alkali halide crystals doped witli divalent cations is niore complicated than this, for tlie M + + ions can exist in different states of asso- ciation. Moreover, these different species can co- exist in a solid solution, in equilibrium witli a preci- pitated phase. The problem then arises how to describe analytically the total solubility C, = C, + C, + C,, of M + + ions in solid solution in an alkali halide crystal.
The three forms of the M + + ions, free, associated pairs, and trimers can be considered as distinct che- mical species. If they do not interact with one another and A H and AS are independent of concentration, which is reasonable at low concentrations, then it may be seen that the expression for total solubility can be made up of the sum of the eq. ( I ) , (3) and (4).
This is in fact the case because the equilibrium is still being maintained between free ions, associated pairs and trimers in solution according to the law of mass action. It is evident, therefore, that the total solubility can be described in terms of A H , , A S , , E., and E,.
A H A S , AG
C, = Z, exp exp --- exp 2 (2) 2 . 2 El-FECT OF D E B Y E - H ~ ~ C K E L INTERACTIONS. -
kT k It T Debye-Hiickel theory, as formulated by Lidiard (1954), should also be applied to the solubility of free divalent where C, is the equilibrium mole fraction of asso-
ions and vacancies. When such interactions occur ciated pairs in solid solution at temperature T,
eq. (I) is incorrect and we must use activities instead AG, is the binding free energy of an associated pair,
of concentrations, i. e.
2, is a geometric entropy term which is 12 for nearest
neighbours and 18 if next nearest neighbour pairs - A H , A S ,
a , = exp- exp -
are included and considered to possess the same AG.,. 2 kT 2 k (5)
For simplicity tlie entropy of formation of an
where a , is the activity and is related to the concen- associated pair will be considered negligible in compa-
tration of free M + + ions and extrinsic vacancies C, rison with tlie enthalpy of association. Thus AG:,
through the activity coefficient j;, can be replaced by E:,, the enthalpy of association,
and eq. ( 2 ) becomes 01 = C I . f 1 . (6)
SOLUBILITY OF Mn AND Cd IONS I N NaCl C9-457
and the Debye-Hijckel screening factor 1 is given by
where C, is the mole fraction of cation vacancies, R is the separation distance below which we regard a divalent atom and a cation vacancy to be associated, V is the volume per molecule of pure salt, q is the charge, E is the dielectric constant.
The solubility equation for free M t i ions should then be written as
where A H , - ' is now the effective free
~ ( 1 + XR)
enthalpy of solution where the divalent ions and the cation vacancies are free, whereas AH, is the enthalpy of solution when there is no Debye-Hiickel effect, i. e. at very low concentrations, and eq. (1) becomes valid.
The analysis just described can be most simply applied in a graphical plot of log, C , versus 1/T.
A schematic plot is shown in figure 1 . The total solubility line C , is obtained experimentally. Lines C , , C,, C, represent the concentration of M + + ions existing as free M + + ions, associated pairs, and trimers respectively in equilibrium with the preci- pitated phase. They should add up to give the expe- rimental solvus line. Line a , is the Debye-Huckel corrected line. Line C , can be obtained from ionic conductivity results in the precipitation region.
Line C, can be obtained from Q meter measurements and C, can be drawn to a best fit so that C , + C, + C, gives good agreement witli experimentally determined solvus line. E., may be obtained from ionic conduc- tivity, then, using this value witli the slopes of C, and C,, the entlialpy and entropy of solution and the binding energy of a trimer are inimediately found.
If the Debye-Huckel theory is adequate for alkali halide crystals the line a , should be related to the line C,. I n the plot of log, C versus [ I T , the total solubility line C , is likely to be curved rather than straight and n o physical meaning can normally be attached to its slope.
2 . 3 TONIC CONDUCTIVITY. - The theory of ionic conductivity ltas been described by Lidiard (1957).
In the extrinsic region, where the anion vacancy contribution is negligible, tlie conductivity is given by :
I I 1 I
As, AH4 4
a = e x p - e r p - -
2 k Z k
FIG. I. -Schematic solubility plot as a function of temperature in which C 1 is the concentration of free divalent cations, C2 is the concentration of associated pairs, C3 is the concentration of trimers and ideally C1 + C2 + C3 should equal CL , the total solubility. a1 is the activity of the free divalent cations.
mobility enthalpy, and a is the anion-cation lattice spacing.
The Debye-Hiickel drag term, g , is given by
In the extrinsic temperature range, where higher order clusters are negligible, the concentration of free vacancies, C,, is related to the doping concentration of tlie crystal, C,, through the mass action equation :
where C , is the mole fraction of free cation vacancies, q is the electronic charge, 17, is tlie lattice vibrational frequency, AS,,, is the liiobility entropy. Atl,, the
This equation includes Debye-Hiickel interactions.
By applying eq. (10) and ( I q ) to a set of experimental ionic conductivity curves, it is possible to relate the
C9 458 J. A. CHAPMAN AND E. LILLEY measured ionic conductivity to the number of free
cation vacancies as a function of temperature. As the number of cation vacancies and divalent cations are equal at temperatures below the intrinsic region, we can obtain the concentration of free divalent ions in equilibrium with a precipitated phase as a function of temperature. Tonic conductivity measurements may also be used t o determine the solubility limit.
For a crystal of given composition, the solubility limit occurs at that temperature where the precipi- tation region on the conducting plot branches into the association region. Thus conductivity curves for a variety of crystal doping levels can be used to obtain total solubility C, as a function of temperature.
2 . 4 DIELECTRIC LOSS. - In order to perform the solubility analysis, as described above, it is necessary to measure the concentration of associated pairs, in equilibrium with the precipitated phases, as a function of temperature. According t o the theory formulated by Lidiard (1955) there are two contri- butions t o the dielectric loss in alkali halides doped with divalent cations : a ) that due to the free vacancies, which is given by :
where v is the jump frequency and (0 is the applied angular frequency ; b) that due to nearest neighbour associated pairs given by
where the relaxation time z is given by I/T = 2(w1 + o?),
o, is the nn + nnn jump frequency and w, is the vacancy + divalent ion interchange frequency.
It is possible t o separate out these two contributions (as they are additive) in a plot of log tan 6 versus log w. Plotted in this way, eq. (13) yields a slope of - 1, whereas eq. (14) yields the familiar shape of a Debye peak. A further complication to analysing the loss peaks arises from the presence of nnn pairs which give rise to a broadening of the Debye peak (Dreyfus (1961) has shown that this broadening can be resolved into two overlapping Debye peaks).
This effect can be accounted for by the following equation :
8 nq2 C 2 tan dFnaEairs =
3 ckTa (1 5)
where
a n d f = w,/w, = exp(- AGl/kT), w, is the nn -+ nnn jump frequency, w, is the nnn + nn jump frequency, AG, is the difference in binding free energy between a nn and a nnn pair and t = w, z. It is t o be expected that w, will be similar t o o, but reduced slightly because of the difference in energy, AE,. O n the assumption that the saddle point is reduced by AEl/2, then w, can be approximated to w, exp(AE1/2 k T ) . Consequently 5 is given by
1 AEl
iJ I. ,exp -
2 k T for w, - a , ,
and
1 AE,
< = -exp-
2 2 k T for w, % w , .
3. Experimental. - 3 . 1 CRYSTAL GROWTH. -
Single crystals of NaCl/MnC12 and NaCI/CdC12 over the concentration range 40 to 10.000 ppm were grown in a Stockbarger furnace. The starting material was composed of single crystals of NaCI, obtained from the Harshaw Chemical Company, anhydrous MnCI,, from ROC/RIC (USA) and anhydrous CdCl,, from Hopkins and Williams Ltd. These materials were encapsulated in quartz tubes which had previously been baked out under vacuum a t 950 OC. The tubes were finally sealed under a low pressure of chlorine.
A typical crystal growth rate was 3 mm/li. Crystals adjacent to those used for ionic conductivity arid dielectric loss were chemically analysed using flame absorption spectroscopy.
3 . 2 IONIC CONDUCTIVITY. - Ionic conductivity measurements were performed using a nickel elec- trode assembly in a nitrogen gas atmosphere. The system was maintained at uniform temperature by means of a molten Pb/Bi eutectic bath which sur- rounded the rig. This arrangement produced a uniform temperature across the electrode assembly for a wide range of control temperatures. The conductance measurements were taken using a Wayne Kerr Uni- versal bridge ( B 221) operating at 1.592 Hz. Electrical contact between the nickel electrodes and the crystal was improved either by painted carbon Alca dag o r by the deposition of evaporated carbon on the crystal surface. In order to achieve a fully precipitated state, the crystals studied were either as grown o r progranime cooled at 3 "C per hour. The conductivity data were taken by heating the crystals in steps from
150 OC up to the intrinsic region.
3 . 3 DIELECTRIC LOSS. - The dielectric loss cell consisted of a copper heating block within a stainless steel cylinder and a spring loaded centre electrode insulated by PTFE and the whole system operated under a vacuum. A Marconi Q meter was employed to measure tan 6 over a range of frequencies (10' -, lo9 Hz) at various temperatures. and measu-
SOLUBILITY O F Mn A N D Cd IONS I N NaCl C9-459
250 2i)o "C rements of tan 6, at frequencies below the range of
the Q meter, were made with the Wayne Kerr bridge.
- - 4. Results. - 4.1 IONIC CONDUCTIVITY. - A - detailed study of ionic conductivity from the preci- pitation region through to the intrinsic region has
- -
- -
- been performed on NaCI/MnCI, and NaCI/CdCI,.
- - These results will be described elsewhere (Chapman
- and Lilley, 1973).
- For the solubility analysis it is necessary to produce
- - ionic conductivity data in the precipitation region, and the results for NaCI/MnCI, and NaCI/CdCI, are shown in figures 2 and 3 respectively. We have established by means of X-ray diffraction that the precipitating phase in the system NaCI/MnCI, is 6 NaCI. MnC1, and confirmed Suzuki's (1961) finding that 6 NaCI.CdCI, precipitates in the NaCIICdCI, system. The ionic conductivity plots for the different composition crystals superimpose in the precipitation region and the breaks, indicating the limits of solu- bility, are clearly defined. The total solubility so derived is presented in figures 4 and 5.
In order to obtain the free cation vacancy (and hence divalent cation) concentration in the precipi- tation region, it is necessary to relate it to the ionic
3 conductivity. This can be done, as mentioned earlier,
I O O O / T (I< - ' ) by an analysis of the ionic conductivity curves in the
FIG. 2. - Ionic conductivity plot of various composition extrinsic region. For NaCl it was found that the crystals of NaCl doped with MnC12.
i r X - r a y s
FIG. 3. - Ionic conductivity plot of various con~position FIG. 4. - Total solubility of 6 !\laCl.MnCl~ in NaCl plotted crystals of NaCl doped with CdC12. as a function of temperature.
C9-460 J. A. CHAPMAN AND E. LILLEY
FIG. 6 . - Dielectric loss curves for a NaCl crystal doped with 100 ppm MnC12 a t various temperatures.
F ~(n:) ~ ~ ~ ~ ~ - ~ ~
FIG. 5. - Total solubility of 6 NaCl.CdC12 in NaCl plotted
as a function of temperature. FIG. 7. - Dielectric loss curves for a NaCl crystal doped with 232 pprn CdC12 at various temperatures.
ionic conductivity is related to the free divalent cation concentration by the following equation
0.7 1 a T = 1.2 x 10' gC, exp - -- .
kT (17)
This equation applies to both NaCIIMnCI, and NaCl/CdCI, and should apply to other NaCl systems.
Eq. (17) can then be used to determine the equilibrium free divalent ion concentration in the precipitation region as a function of temperature for both systems.
4.2 DIELECTRIC LOSS. - The results of the tan 6 measurements at different temperatures for a crystal containing 100 ppm MnC1, are plotted in figure 6 and for 232 ppm CdC1, in figure 7. An ideal Debye peak has been subtracted out (dotted lines) so that the continuous lines represent the summation of the free vacancy line, having a 45" slope, and the Debye peak. In the precipitation region the Debye peak increases in height with temperature as the precipitates dissolve. Above the limit of solubility the peaks should decrease in height slowly as dissociation into free ions and vacancies occurs. Plots of tan (j;;',:, versus
1/T in figures 8 and 9 indicate that there is superpo- sition of results in the precipitation region (except for the highly doped Mn crystal), followed by a well defined break, at the limit of solubility.
The frequency at which the Debye peakis a maximum is also plotted as a function of temperature in figures 8 and 9. The slopes of these plots, which represent the activation energy for rotation of a dipole, are 0.73 and 0.61 eV for NaCl/Mn and NaCI/Cd respectively.
The correction to the peak niaxima due to the dis- placement caused by next nearest neighbour pairs makes little difference to the measured slope, since the peaks are found to be sli~fted to higher frequencies by a constant factor of about 10 %.
The tan 5 values of the Debye peaks in figures 6 and 7 can be converted into dipole concentrations using eq. (15). In the case of the NaCIIMn crystals.
where the work of Watkins ( 1959) and Symmonds ( 1 971) indicates the existence of next nearest neighbour pairs, we have made use of Symmonds' value of AE, = 0.039 eV to find f ; i. e. f = exp - AE,/liT.
Similarly we have taken < = 1 exp (0,03912 AT). Using these values of J and ( i t is possible to calculate
SOLUBILITY O F Mn AND Cd IONS IN NaCl C9-461
Manganese concentration 1 0 0 m p p m
1 2 9 mppm
1 0 2 5 0 0 m p p m '-1
FIG. 8. - Tan 65,"i:s and wmsx plotted as a function of tempe- rature for NaCI/Mn crystals.
, o - Z 3 5 0 S O 0 ? 5 0 Z o o OC
I I -
- -
_&d-(? -
Co
0 Z 3 2 m p p m A 4 3 0 mppm
FIG. 9. - Tan S,"d& and plotted as a function of tempe- rature for NaCl/Cd crystals.
L(to,,, 7 ) and calculate, by means of eq. (15), the concentration of nn pairs. The concentration of nnn pairs may then be calculated from the value 0f.f.
This was done for the measurements taken in the
precipitation region and used in the solubility plot.
In calculating < it would have been preferable to use the Symmonds (1971) o , and o, values, rather than use the approximation for <. However, these values of w , and o, together with the experimental a,,, values, determined in this study, or by Watkins (1957), give values for a,,, 7 which are less than unity. This is physically impossible. Presumably these o, and o, values are in error. Fortunately, the error in 5 is not serious because L ( o s ) is quite insensitive t o < : the concentration of nn pairs and nnn pairs is reduced by 10 "/,hen o, and o, deter- mined by Symmonds are used to calculate /.
Unlike the Mn case there is no information in the literature regarding nnn pair formation in NaCI/Cd.
Consequently the Debye peaks were analysed on the assumption that the nn pairs greatly exceed the number of nnn pairs. In this case eq. (15) is used with L ( o r ) = 0.25.
4 . 3 SOLUBILITY. - The results of our measurements on the solubility of 6 NaCI. MnCI, and 6 NaCI.CdC1, in NaCl are shown in figures 10 and 1 1 . These figures also show the activity of the free divalent ions a , calculated from the free ion concentration (C,).
The line C, has been drawn t o give the << best fit )) between C, and C, + C, + C,. It is assumed in this analysis that the higher order clusters exist as trimers.
The solubility data has been analysed in terms of
FIG. 10. - Composite solubility plot as a function of ternpe- raticre for NaCII6 NaCI . MnC12.
C9-462 J. A. CHAPMAN AND E. LILLEY
FIG. 11. - Composite solubility plot as a function of tempe- rature for NaC1/6 NaCI.CdC12.
I I I I I
- - -
- - - - - - - - - -
- - - -
- - - -
D Cl Free [~d"]
- o C,N* [cd*' J Ln n e o r c s ~ necqhbo-v paLrs \,, lo-' = - - C 3 [cdi2] ~n t r r m e r s
- A PC; = C , * c 2 * * * C 3
- - 0 a, A c t l v ~ t ~
eq. (I), (3), (4) and (5), in order to determine the thermodynamic parameters listed in tables I and 11.
- -
TABLE I
Solubility of 6 NaCI. MnCI, in NaCl ,
-7
-
AH (eV) AS1 -
k Implication
a -- - - 0.408
2 - 2.92 AH1 = 0.816 eV i 0.02
cTN AH2 = 0.430 - 2.48 EFN = 0.386 eV 5 0.02
cTNN AH; = 0.469 - 2.42 EFNN = 0.347 eV & 0.02 C3 AH3 = 0.306 - 2.34 Et = 0.984 eV f 0.05
Av. - 2.54
TABLE I1
Solubilify of 6 NaCI. CdC12 in NaCl
AH (eV) AS
- Implication
k
a - - AH' - 0.496
2 + 0.81 A H ! = 0.992 eV & 0.03 CFN h H 2 = 0 . 6 1 5 + 1.56 E2s = 0.378 eV 0.02
C3 AH3 = 0.650 + 0.95 Et - 1.195 eV 1 0.08
Av. + 1.1 1
It is evident from these results that a far higher fraction of higher order clusters, presumed here to be trimers, is to be found in NaCI/Cd than in NaCl/Mn.
5. Discussion. - 5.1 IONIC CONDUCTIVITY. -
The ionic conductivity plotted in figures 2 and 3 is notable for two reasons. Firstly, the conductivity data superimpose in tlie precipitation region, as expected, but this has not always been found by other workers, e. g. Kirk and Pratt (1967), studying NaCI/
MnCI,, and Stoebe and Pratt (1967) studying LiF/
MgF,. Secondly, the precipitation region in both systems is clearly curved, which is a consequence of the Debye-Hiickel interactions discussed in 2.2. In previous studies of ionic conductivity in the precipi- tation region (see Barr and Lidiard, 1970), Debye- Hiickel interactions have been ignored, and the slope a ton of the ionic conductivity curve in the precipit t.
region taken to be
This will only be true when extremely low concen- trations of free ions are in solution. In this present study, tlie ionic conductivity in the precipitation region has been used to derive tlie free vacancy and hence, the free divalent ion concentration, which are in equilibrium with [lie precipitated phase. The procedure, which is described in more detail elsewhere (Chapman and Lilley, 1973). includes Debye-Hiickel theory (which may not be strictly applicable to alkali halide crystals), and also ~nvolves curve fitting. The error in C, could easily be I0 ';/, at low concen- trations, and even more at higher concentrations when Debye-Hiickel theory is more likely to break down. Nevertheless, the errors in C, slope and a, slope should be much less.
The ionic conductivity data have also been used to determine the total solubility as a function of temperature. Cappelletti and Fiesclii comment that there are difficulties i n deciding at which point the branching occurs at the top of the precipitation region.
Looking at the results in tile literature this is frequently true ; however there are no ambiguities in figures 2 and 3. The major ert-or in the total solubility plots in figures 4 and 5 stem from the chemical analysis, and should be no more than + 5 "/,.
5.2 DIELECTRIC LOSS. - The activation enthalpy for the reorientation of associated pairs of 0.73 eV found for Mn i n NaCl is considerably higher than the 0.63 eV found by Watkins. However, various dielectric loss, ESR and ITC experiments have given higher values. (See Barr and Lidiard, 1970.)
Fewer studies have been performed on NaCI/Cd.
However, the ITC results of Dansas (1971) of 0.65 eV, Bucci rt a/. (1966) of 0.68, and the relaxation results of Dreyfus (1961) of 0.69 eV are all 11iglier than tlie 0.61 eV activation energy found here. In order to convert the tan 0 measut-ements to the concentration of associated pairs, it is necessary to use the procedure described in section 2.4. Inaccuracies will arise from tlie subtraction of the fl-ee vacancy curve, and
SOLUBILITY O F M n A N D Cd IONS I N NaCl CY-463
from the fact that ideal Debye peaks are not always found. The correction for nnn pairs, as stated earlier, involves approximations. Tlie errors in C, could easily be f: 10 "/, ; however the slope of C, is expected to be much more accurate.
5 . 3 SOLUBILITY ANALYSIS. - The binding energies of nn pairs found in this study are slightly lower than those found by Chapman and Lilley (1973) who analysed the non-precipitation region of the ionic conductivity plot and found 0.415 + 0.010 eV for NaCI/Mn and 0.425 0.010 eV for NaCl/Cd.
Nevertheless they agree with tlie theoretical calcu- lations of Bassani and Ferrni (1954) for NaCI/Cd.
Even with tlie higher binding energies, the AH, values calculated from C , using Debye-Huckel theory should not differ by more than 0.05 eV from that calculated from C,. The overall accuracy of tlie enthalpy and entropy of solution depend on the accuracy of tlie free ion and associated pair concen- trations determined experimentally and on the assump- tion that tlie entropies of formation of associated pairs are negligible.
It is possible that the trimer binding energy may have no meaning since the existence of trimers has not yet been proven conclusively in alkali halide crystals. However, if trimers do exist and have much higher binding energies than other possible clusters,
such as dimers, which are believed to have a binding energy of 0.37 eV in NaCI/Mn, according to Strutt and Lilley, 1973, then this analysis may be satisfac- tory. Tlie trimer binding energies determined here are considerably higher than those found for other systems, e. g. Cook and Dryden (IY62), which are typically 0.7 eV.
While discussing enthalpies and entropies of solu- tion it is worth commenting on some of the methods described in the literature to derive these parameters.
As mentioned earlier, the slope of the ionic conduc- tivity plot in the precipitation region cannot normally be used to determine AH, and A S , . Brown and Hoodless (1967) have used a method to determine tlie inipurity free solubility which involves extrapo- lating the ionic conductivity curve from the upper part of the extrinsic region down to the precipitation region, tlie intercept giving the solubility limit. This procedure would be satisfactory if it took into account Debye-Hiickel interactions and the fact that there is some association even at high temperatures. This we have done in this study.
The other commonly used method of obtaining entlialpies and entropies of solulion is based on plots of tlie total solubility as a function of temperature.
The theory in 2 . 1 and 2 . 2 shows that this procedure is incorrect, for the plots will in general be curved, giving meaningless AH and A S values (see Allnatt
FIG. 12. - Comparative total solubility plot for NaCI/Mn. FIG. 13. - Comparative total snlaabilit~ plot for NaCI Cd.
C9-464 J. A. CHAPMAN A N D E. LILLEY
and Jacobs, 1962, Haven, 1950, and Benveniste et nl., 1965). Not surprisingly the entropies of solution quoted in Barr and Lidiard (1970) show no agreement between the so-called free impurity and total solu- bility results.
Let us now compare the solubility results found for NaCl/Mn and NaCl/Cd. It is surprising tliat both systems have virtually the same total solubility as a function of temperature, even though NaCl/Cd has a considerably higher free divalent ion entlialpy of solution. This can be understood, liowever, fro111 the observation tliat 6 NaCI. CdCI2 has a positive entropy of solution ( A S , / k = 1 .I) compared with that of 6 NaCI. MnCI2 ( A S , l k = - 2.5). 111 addition the relative concentration of liiglier order clusters (trimers) in equilibrium with the precipitated phase is significant at all temperatures in NaC1/6 NaC1. CdCl,, but negligible except at low temperatures in NaCI/
NaCI.MnC1,. In both systems the free ion solubility increases rapidly at high concentrations due to Debye- Huckel interactions, thereby increasing the total solubility. Both figures 10 and 1 1 indicate greater total solubility than is expected from the sum of C1 + C, + C,. This probably arises from the inade- quacy of Debye-Hiickel theory at high concentrations.
In both systems the activity data depart from the ideal linear activity line at free divalent ion concen-
trations of about 30 ppm. A similar observation has been made by Lilley (1973) in LiF/MgF,.
Finally, let us compare the total solubility data in this study with those of other authors. This is presented in figures 12 and 13. Errors in the work of Kirk and Pratt (1967) and Trnovcova (1968) and Haven (1950), using ionic conductivity, are expected to arise primarily from the interpretation of knees in the ionic conductivity plot, and chemical analysis. Kahn (1967) used a volunle fraction method in which he quenched crystals from within the preci- pitation region to room temperature and then observed the amount of precipitate present by means of electron microscopy. This method is limited by tlie efficiency of quenching from high temperatures. The same problem of rapid quenching arises in the work of Cappelletti and Fiesclii (1969). I t is not possible directly t o present their results in figure 13. They are, liowever, completely at variance with our results.
We have found that tlie entlialpy of solution for an associated pair in NaCl/Cd is 0.614 eV compared with their value of 0.235 eV.
Acknowledgments. - J. A . C. gratefully acknow- ledges tlie support and facilities provided by Prof.
R. W. Calin and E. L. similarly acknowledges the financial support for this work froni UKAEA Harwell.
References
ALLNATT, A. R. and JACOBS, P. W. M., Trnrrs. Furcrcloy Soc. 58 (1962) 116.
BARR, L. W. and LIDIARD, A. B., PI~ysicoI Clr~ttiistq., An Advanced Treat~se (Academic Press, New York) 1970 152.
BASSANI, F. and F U M I , F. G., NIIOVU Cit?~etrto 11 (1954) 274.
BENVENISTE, M., LAREDO, E., BERGE, P. and TOURNARIE, M., J. Physiqlre 26 (1 965) 189.
BROWN, N. and HOODLESS, I. M., J. P11j.s. & Clrcnr. Solids 28 (1967) 2297.
Buccr, C., FIESCHI, R. and G U I D I , G., Plrys. Rev. 148 (1966) 816.
CAPPELLETTI, R. and FIESCHI, R., Crist~iI Lottice Defects 1 (1969) 69.
CHAPMAN, J. A. and LILLEY, E., to be published (1973).
COOK, J. S. and DRYDEN, J. S., Proc. PItys. SOC. (London) 80 (1962) 479.
DANSAS, P., J. Phj's. & Cherlr. So1id.s 32 (1971) 2699.
DREYFUS, R. W., Pl~j*s. Rev. 121 (1961) 1675.
DREYFUS, R. W. and NOWICK, A. S., PIrjv. Rev. 126 (1962) 1367.
HARRISON, R. P., Ph. D. thesis, Imperial College, London (1965).
HAVEN, Y., Rec. Trrnl. Clritrl. Poys-Bus 69 (1950) 1505.
KAHN, A. R., Ph. D. thesis, Imperial College, London (1967).
K I R K , D. L. and PRATT, P. L., Proc. Brit. Cernt~t. Soc. 9 (1967) 215.
LIDIARD, A. B., P1r.1.s. Rev. 94 (1954) 29.
LIDIARD, A. B., Report on Conference on Defects in Crystallin Solids, Pliys. Soc. London (1955) 283.
LIDIARD, A. B., Hut~db~rch der Plr)..sik, ed. S. Flugge (Springer- Verlag, Berlin), 1957, Vol. 20, 246.
LIDIARD, A. B., J. Appl. Phys 33 (1962) 414.
LILLEY, E., Ph. D. thesis, Cornell University (1966).
LILLEY, E. and N E W K I R K , J. B., J. Mrrt. Sci. 2 (1967) 567.
LILLEY, E., Proc~ec1itig.s of tlit Sixth Irrtrrtmtionnl Corlfererrce otr the Recrcrivity of Solirls, edited by J . W. Mitchell, R. C. de Vries, R . W. Roberts and P. Cannon (J.
Wiley) 1969, 63 1.
LILLEY, E., Proc~~~r1it1g.s of the Sevortlt Itr~er.t~otiorral Sytlrpo.sirotr otr t / ~ c Reactivifj~ of Solirk, edited by J. S. Anderson and
M. W. Roberts (Chapman & Hall) 1973, 56.
OWSTON, C . N., Proc. PII~Js. SO(.. 88 (1966) 205.
STOEBE, T. G . and PRATT P. L., Proc. Brit. Cerut?~. Soc. 9 ( 1 967) 181.
STI~UTT, J . E. and LILLEY, E., Proc.~orIirrg.s of the Srverrt/r Itrter- rrntiot~ol Syr?r/)o.si~~rii orr the Rcrrctivity of Solirls, edited by J. S. Anderson and M. W. Roberts (Chapman
& Hall) 1973, 84.
S U Z U K I , K., J. P11j's. SOC. Joprrtr 16 (1961) 67.
SYMMONS, H . F., J. Phy.s. C. 4 (1971) 1945.
TRNOVCOVA, V., Fj'ziknltrj' Crrso/~is 18 (1968) 21 1.
WATKINS, G. D., Plrj~s. Rev. 113 (1959) 79 ; and 113 (1959) 91.
DISCUSSION
E. LAREDO. - The high concentration of trimers on the same system. We studied by this method quen- deduced by you in the dissolution process of the ched crystals and the reproducible intensity scattered Suzuki phase in NaCI does not agree with the low could only be interpreted in terms of free Cadniiunl angle X-rays scattering experiments we performed ions and dimers.
