Thermochemistry of Alkali Fluorides with LnF,
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 2589
Thermochemistry of Binary Liquid Mixtures of Alkali Fluorides with LnF, K. C. Hongt and 0. J. Kleppa” The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637 (Received February 28, 1979) Publication costs assisted by the National Science Foundation
The liquid mixtures of YF3, LaF,, and YbF3 with LiF, NaF, and KF have been studied by solid-liquid mixing calorimetry at 1360 K. The experiments cover concentrations up to 60-70 mol % LnF3, and allow reliable determinations of the liquid-liquid enthalpies of mixing and of the enthalpy interaction parameters AM = AHM/NlN2at this temperature. The results are compared with data previously reported for AF-AlF3 and AC1-LnC13 mixtures. The concentration dependence of the interaction parameter is somewhat similar to that found for the latter systems and varies from simple in LiF-LnF3 to quite complex in the KF-LnF3 systems. In the mixtures of NaF and KF with YF3and YbF3the interaction parameters show well-defined minima between 20 and 30 mol % LnF,. This suggests that YF2- and YbF:- are important species in these systems in analogy with the cryolite anion in AF-A1F3. The results show reasonable agreement with the linear dependence of AM on 612 = (d, - d z ) / d l d 2predicted by conformal ionic solution theory. We again find an empirical linear relation between AM and the relative ionic potential of the two cations, AIP = I(Zl/rl) - (Zz/r2)l(2;is the charge on the cation of radius r J . It is suggested that this parameter may be useful for predicting the enthalpy of mixing in previously unexplored systems.
Introduction Recently we have reported new data on the enthalpies of mixing in the liquid mixtures of alkali fluorides with the alkaline earth fluorides (hereafter referred to as 1:2 binary fluorides)., In this work we found significant deviations from the linear dependence of the enthalpy interaction on the size parameter a12 parameter AM (=AHM/NINz) (=(d, - d2)/dld2)predicted by conformal solution theorya2l3 We also demonstrated an empirical linear relation between AM and the relative ionic potential of the two cations in the mixture, AIP = I(Zl/rl) - (Z2/rz)l,where Zi is the charge of the cation with ionic radius, ri. A relation of this type was found for systems of the type AX-BX2 with X = F, C1, or Br, and even for simple binary alkali fluoride mixtures AF-A’F. In the present communication we extend our study of charge-unsymmetrical fluoride mixtures to systems of the type AF-LnF3 (A = Li, Na, or K; Ln = Y, La, or Yb; hereafter referred to as 1:3 binary fluorides). On the basis of enthalpy of mixing data for these systems, we shall again test the applicability of conformal solution theory and the empirical relation between AM and AIP. We shall also compare our results with corresponding enthalpy data for the systems AF-All?: and for some AC1-LnC13 mixture^."^ Experimental Section The chemicals used in the present work were (1)LiF, Fisher Certified Reagent; (2) NaF, Baker Analyzed Reagent; (3) KF, Baker and Adamson, Anhydrous Granular Reagent (min 99.0% KF); (4) LaF3, Ventron Alfa Products, 99.9% LaF,; ( 5 ) YF3, Apache Chemicals, 99.9% YF3; (6) YbF3, Apache Chemicals, 99.9% YbF3. Before their use in the calorimeter the alkali fluorides were purified and treated as described in ref 1. The other salts were used as received after drying in vacuo at 140 O C for 24 h. The purity of the salts was checked by an ion-exchange method and by atomic absorption and/or emission spectroscopy. The results of these tests are summarized in Table I. Department of Energy and Environment,Brookhaven National Laboratory, Upton, L.I., N.Y. 11973. 0022-3654/79/2083-2589$0 1.OO/O
TABLE I: Overall Purity and Metallic Impurities of Salts Used detected metallic salt purity: % impuritiesb LiF 99.8 Ca, Mg < 0.02%; Na, Al, Fe, Ti < 0.001% NaF 99.9 La, Si, Mg, Ba, Mn, Sr < 0.001% KF 99.3 Na, Nb, Ru, Te < 0.001% LaF , 99.5 Y 0.3%, Fe ~~~
~
-
YF,
99.7
YbF,
99.8
--
0.09%, A1 0.03% Mn, Mg, Cu < 0.001%
-
Si 0.05%; Lu, Pb, Cu < 0.001% a Overall purity was determined by an ion-exchange method. The impurities in each compound used were detected by atomic absorption and/or emission spectroscopy.
All calorimetric measurements were of the solid-liquid type and were carried out a t 1360 K. The calorimetric apparatus, the mixing devices used, and the experimental methods adopted have all been described in some detail e l ~ e w h e r e .In ~ ~evaluating ~ the results of our measurements, we have neglected all experimental uncertainties which might arise from impurities in the salts (particularly in KF) and from evaporation of the salts. The latter errors were estimated to be less than 0.5%. Results and Discussion A total of nine binaries of the type AF-LnF3 were studied, i.e., three yttrium fluoride systems, three lanthanum fluoride systems, and three ytterbium fluoride systems. (Since yttrium and lanthanum are chemically very similar to the rare earths, we shall for convenience refer to their fluorides as “rare earth fluorides’’ (LnF3).) Our experimental results are presented in graphical form in Figures 1-3. In these figures the quantity AHsLM/Nz is plotted against N z = 1- N,, the mole fraction of LnF,; MSLM is the molar enthalpy change associated with the process NzLnF3(s) + NIAF(l) = liquid mixture 0 1979 American Chemical Society
2590
K. C. Hong and 0. J.
The Journal of Physical Chemistty, Vol. 83, No. 20, 1979
TABLE 11: Summary of the Solid-Liquid Enthalpies of Mixing for the AF-LnF, Systems at 1 3 6 0 Ka system a’ b’ C’ d’ LaF,-LiF 10.499 2.818 -NaF 2.886 11.290 -0.195 -KF -2.706 13.743 2.681 ~~
a
~
Kleppa
~
e’
YF,-LiF -NaF -KF
- 0.836 - 10.893 - 16.83
7.164 0.516 - 60.81
94.332 402.92
- 151.57 -704.84
74.462 426.96
YbF,-LiF -NaF -KF
-1.935 -11.976 - 14.86
9.023 1.184 -96.96
92.232 493.32
- 141.33 -721.25
66.127 361.28
A H s L M I N , = a’ t b‘N, t ciNZ2 t d’N,, t e’NZ4 kcal mol, N , is the mole fraction of LnF,, 0 < N , < 0.65. I61
I
l
l
I
i
l
4
0.2
0.4 0.6 N2 ( L a F3 1
0.8
Flgure 1. Plots of A H ~ ~ against ~ I N N2 ~ (LaF,). to AH,, for LaF, at N , = 1.
I
1.0 Curves extrapolate
0.2
0.4 0.6 Nz(YbF31
0.8
Figure 3. Plots of AHsLMIN,against N, (YbF,). to AH,,, for YbF, at N2 = 1.
AF-YF3,1360K
1.0
Curves extrapolate
c
i -20.0
KF-YF3
f i
-24,00
0.2
04 0.6 Nz(YFj)
0.8
Figure 2. Plots of AHsLMIN,against N, (YF,). for YF, at N, = 1.
1.0
Curves extrapolate
to AH,
The solid curves in Figures 1-3 are based on leastsquares fittings of the data to polynomials of the type AHsLM/N2= a’+ b’N2 + c ‘ N ~+~... The values of the coefficients a’, b’, c’, etc., are listed in Table 11. Note that for the three systems which contain LiF, the results are particularly simple since the data may be fitted by means of a linear relation. For the other systems second- and higher-order terms are necessary. Figures 1-3 show that these 1:3 binary fluorides are considerably more complex than the corresponding 1:2 mixtures covered by ref 1. For this reason it is also more
difficult to extrapolate the solid-liquid enthalpy data to N 2 = 1 so as to obtain the enthalpy of fusion of the solid fluoride. Clearly, the most reliable extrapolations to N2 = 1 are obtained for the LiF-LnF3 systems. We have adopted the enthalpies of fusion calculated from the data for these three binaries to get the liquid-liquid enthalpies of mixing for all the considered systems at 1360 K. In Table I11 we give all the values of AHfusionderived from our solid-liquid enthalpy measurements. This table also contains enthalpies of fusion at the melting points of LnF3 which were taken from the literature, as well as values at 1360 K obtained by taking into account the heat capacity difference between solid and liquid LnF3 Liquid-Liquid Enthalpies of Mixing. We adopted the values 13.31, 6.33, and 7.09 kcal mol-l for the heats of fusion of LaF3, YF3, and YbF3 at 1360 K in order to calculate ’the liquid-liquid enthalpies of mixing. This yields the values of the interaction parameter, AM = AHM/N1N2which are plotted against composition in Figures 4-6. Clearly, a major part of the uncertainty in these values of AM must be attributed to possible errors in the adopted enthalpies of fusion. If this error is h0.3 kcal mol-’ (see Table 111), the corresponding error in AM at the 50-50 composition may be as large as *0.6 kcal mol-l. Fortunately, an error of this order does not change either the sign or the magnitude of AM. The solid curves drawn through the experimental points in Figures 4-6 are based on a least-squares fitting of the data to polynomials in N,; the dashed curves represent our “best curves”. Interaction parameter data are summarized in Table IV in terms of the orthogonal Legendre poly-
Thermochemistry of Alkali Fluorides with LnF,
The Journal of Physical Chemistry, Vol, 83, No. 20, 1979 2591
TABLE 111: Enthalpies of Fusion of LnF, Compounds at 1360 K AHf,,(LnF,), kcal/mol system LaF,-LiF -NaF -KF
at 1360 K, obsd 13.31 13.98 13.72 av 13.67 i 0.24
YF -LiF -NaF
6.33 6.88 av 6.59
YbF,-LiF -NaF -KF
* 0.25
at mp
13.64 ?: 0.4a
6.48
?
12.01b
0.20
6.69 r O . l b
7.09 7.12 av 7.10
Reference 12.
at 1360 K, calcd
Reference 10.
?:
0.02
7.07 c 0.30
7.11 ?: O . l O c
Reference 11.
TABLE IV: Summary of Liquid-Liquid Enthalpies of Mixing for the AF-LnF, Mixtures at 1360 Ka system Li F-LaF , -YF, -YbF,
41
40
- 2.813 - 7.063
-8.967
NaF-LaF, -YF, -YbF,
-8.724
4AHo.s -2.816 -7.063 - 8.968
q3
2.507 -4.199 - 2.770
1.004 -6.719 -4.870
- 3.618 -4.242 - 10.536
2.426 -4.142 -11.10
- 18.634 - 20.37
KF- LaF , -YF, -YbF,
q,
0.002 0.183 0.080
- 14.50
-30.33 -34.73
- 9.226 -15.276 - 17.890
-4.716 - 3.650
-15.711 -5.303 -12.36
- 28.251
-29.183
A H M = h M N 2 ( 1- N,), kcal mol-' Cq,P,(N,);P, = Legendre polynomials Po(N2 = 1 P,(N,) = 2N, - 1 P2(N2)= 6NZ2- 6N2 t 1 P,(N,) = 20N23- 30N,' t 12N2- 1 hM =
(2m - 1)(2N2- 1) P,.-,(N2)m N, is the mole fraction of LnF,, 0 < N, < 0.65.
p , (N, 1 =
a
m-1
-Prn-2(N2) m O
' i A F - Y F3, I 3 6 0K
1
I
4
-40 1
i
z4 - i 2 . 0 1 c
- 16.0
4
I
-
w+##k#c;'K F - L o F3
-20.0 1
I
,
u 0
-I 6.0
s-
I rc
1
-20.0
t
-
~
1
-24.0 -
I
,
l
---
-28.0
4 i
-I
-32 0 1
0
1
I
02
04
06 N2IY F3)
08
IO
Figure 5. Liquid-liquid enthalpy interaction parameters (AM = AHM/ N , N P ) plotted against N, (YF,). Solid curves based on Legendre polynomial expansion and data in Table IV. Broken lines are "best curves".
LnF3 While these minima are somewhat less well defined than those observed in KF-A1F3 and NaF-AlF,, their presence strongly suggest the importance in these systems of the complex anions YF,% and YbFe3-. These ions would be analogous to the cryolite anion AlF,3-. Figure 4 shows that the corresponding minimum in KF-LaF3 is very
2592
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 I
I
K. C. Hong and 0. J. Kleppa 0,
'
'
,
- 6 0 1 AF-YbF3, 1360K
1
-14.01
Flgure 8. Plot of enthalpy interaction parameter at NkF, = 0 (loM) against a,, = ( d , - d2)/did2:solid lines, common alkali fluorlde; broken lines, common trivalent fluoride.
'K F - Y bF3
-38.0
I
0
l
l
0.2
,
I
0.4 0.6 NZ(YbF3)
0.8
1
1.0
Flgure 6. Liquid-liquid enthalpy interaction parameters (AM = AHM/ N I N z ) plotted against N2 (YbF,). Solid curves based on Legendre polynomlal expansion and data in Table IV. Broken lines are "best curves".
11
to 0.85 i% (Yb3'). We believe this expression may represent a reasonable approximation to AM and the enthalpy of mixing for any AF-LnF3 mixture. In fact, since we now have demonstrated the nearly linear dependence of XoM on AIP for several different families of fused salt mixtures, we propose that this parameter may well be quite useful in attempts to predict the solution properties of previously unexplored fused salt mixtures which have a common anion. In general, we would expect that each family of such mixtures should follow a relation of the type XoM = a
-24
-32 -4Ot - 4 8 k
0
1.0
I
1
I
3.0 AI.? = 1
2.0
,
1
4.0 3
IT;-Tj 1
1
l ' h l
5.0
6.0
Flgure 7. Plot of enthalpy interaction parameter at NLnF3= 0 (A,,"') against the relative ionic potential of cations (AIP = l ( l / r i )- (3/r3)1) for 1:3 fluorlde mixtures ( r , is ionic radius of a monovalent cation, r 3 of a trivalent cation).
poorly defined. This suggests that LaFt- probably is not a very stable anion in this system at 1360 K. Dependence of AM on the Ionic Potential. We previously demonstrated the nearly linear empirical relation between AM and the relative ionic potential, AIP, of the two cations for the AX-MX, and AF-A'F binary mixtures.l The larger the relative ionic potential, the more exothermic the enthalpies of mixing. Let us now examine the applicability of this relation for mixtures of the type AF-BFB. For this purpose we have plotted in Figure 7 hM (AM at N2 = 0) against the relative ionic potential both for the AF-LnF3 systems studied in the present work and for the AF-A1F3 systems. It is quite evident from this figure that an approximately linear relation exists between XoM and AIP for all the considered mixtures (see dashed line in Figure 7). The linear relationship is particularly convincing and clearcut for the AF-LnF, mixtures, for which the following relation was derived by the leastsquares method (solid line in Figure 7): hoM(AF-LnF3)= 14.0 - 13.5AIP (f1.2) kcal mol-l
(1)
Note that the experiments on which this relation is based involve trivalent ions with radii ranging from 1.04 (La3+)
+ pAIP
(2)
In this expression, a will always be positive, while /3 is negative. Note that for AIP = 0 the radius ratio of the two cations is rA,/rA= 1, rM/rA = 2, and rB/rA = 3 for AF-A'F, AF-MF2, and AF-BF, mixtures, respectively. From what is generally known about the thermodynamic properties of fused salt solutions, we would predict that a should be due in part to van der Waals-London dispersion interaction between second nearest neighbor cations and in part to steric effects associated with the mixing of two cations of different size and charge. Thus one would expect to find a rather small positive value of a for AF-A'F mixtures, and otherwise increasing values in the sequence AF-A'F C AF-MF, C AF-BF3. This is consistent with our experimental results. On the other hand, the negative terms in eq 2, pAIP, should arise mainly from the contributions of the Coulomb and polarization energy to the enthalpy of mixing. For systems with quite small values of AIP, these negative terms might be overshadowed by the positive terms due to dispersion energy and/or steric effects to yield a net positive enthalpy of mixing. Among the AF-A'F mixtures, this is the case, e.g., for KF-RbF and KF-CsF. However, in most other cases the larger negative terms dominate and give rise to negative enthalpies of mixing. Finally, it should be noted that the complex formation which occurs in many systems with large values of AIP may also give rise to an additional exothermic effect. For example, this might perhaps explain why the slope B is somewhat more negative for the AF-A1F3 systems as a group than for the AF-LnF, systems. Conformal Solution Theory. We present in Figure 8 plots of XoM against the size parameter aI2 (= (l/dl) ( l f d , ) ; di is the interionic distance in each of the component salts) for the AF-LnF3 and AF-A1F3 mixtures. In this graph we have drawn solid lines to connect points for mixtures with AF as a common component and broken lines for mixtures which have BF3 in common. It is evident
Thermochemistry of Alkali Fluorides with LnF,
that for the LnF3 systems we have an approximately linear relation in either case. Thus we conclude that for these systems the first-order approximation of the conformal ionic solution theory of Davis2i3is consistent with the experimental data. Note, in particular, the close similarity between the data for the YF3-AF and YbF3-AF families. This similarity again underlines the importance of the ionic radius of the trivalent cation in determining the thermodynamic properties of the mixture. On the other hand, as already noted in our earlier work on the AlF3 systems, significant deviations from the linear Davis plot is found for this family of mixtures. Comparison with AC1-LnC13 Mixtures. During recent years reliable calorimetric data have become available for a few alkali chloride-rare earth chloride mixtures. Thus the AC1-CeC1, systems were studied by Papatheodorou and K l e ~ p athe , ~ AC1-LaCl3 systems by Papatheodorou and 0stv0ld,~and the AC1-GdC13 systems by Dienstbach and Blachnik.’ The last named authors also carried out measurements on several other rare earth chloride mixtures of the type NaC1-LnC13. We want to compare our own results for the fluorides with these data for the rare earth chloride systems. (1)The earlier investigators found that the enthalpy of mixing tends to become more negative with increasing size of the alkali metal cation. For example, for the liquid mixtures of LaC13 with LiC1, NaC1, and KC1 at 1173 K Papatheodorou and ICgtvold reported AoM to be -2.4, -9.3, and -15.7 kcal mol-l, respectively. Our own values for the correspondingfluoride mixtures at 1360 K are very similar: -2.8, -10.2, and -15.7 kcal mol-’. The somewhat more negative values found for the fluoride systems suggest that the Coulomb energy is more important than polarization energy in determining the enthalpies of mixing the these systems. In this respect these systems are quite analogous to the previously discussed AF-MF2 and AC1-MC12
mixture^.'?^ (2) The earlier investigators noted that the composition dependence of the interaction parameter AM changes from very simple in the LiC1-LnC13 systems to quite complex in the mixtures formed by KC1, RbC1, and CsC1. In the latter systems they also found well-defined minima in AM near N 2 = 0.25. This was interpreted to indicate the importance in these mixtures of the “complex” anion LnClB3-. In some of the NaC1-LnC13 systems the minima in AM are quite shallow @e3+,Gd3+)or even absent (La3+). This may indicate that in these systems the anion LaC12is relatively unstable and has a fairly large degree of dissociation. As already noted above, very similar behavior of AM is found in the corresponding fluoride mixtures. Even so, it is of interest to take note of the difference between KC1-LaC13, for which Papatheodorou and ICgtvold found a well-defined minimum in AM at 1173 K, and KF-LaF,, for which our own work shows at most a very shallow minimum at 1360 K. Since these two systems have very we would expect the tendency toward similar values of hM, complex formation to be quite comparable. Therefore, we believe that the difference between KC1-LaC13 at 1173 K and KF-LaF3 at 1360 K in large measure may reflect the temperature dependence of the dissociation of the complex ion LaXG3-. It would be very interesting to explore this problem further by spectroscopic methods.
The Journal of Pbysical Chemistry, Vol. 83, No. 20, 1979 2593
(3) The earlier investigations of AC1-LaC13 mixtures noted that these systems show considerable energetic asymmetry, i.e., they found much more negative values of AM in the alkali chloride-rich than in the LnCl,-rich regions of the binaries. The asymmetry increases with increasing size of the alkali metal cation. In addition, for the mixtures of LaC13 and GdC13 with KC1, RbC1, and CsC1, Papatheodorou et al. found a rather sharp rise in AM from the minimum at N2 = 0.25 to much less negative values at higher mole fractions of LnC13. In contrast to this, our own data for the fluoride mixtures show little or no evidence of energetic asymmetry. It should be noted, however, that while the chloride data covered the complete range of liquid composition from 100% AC1 to 100% LnC13, the fluoride data do not extend beyond 60-70 mol % LnF3. The difference between the curves for AM against N2 for AF-LnF3 and AC1-LnC13 may in part be due to the influence of temperature already referred to above. However, it possibly may also reflect a basic difference between fluoride and chloride mixtures; while there is no evidence for the existence of the complex anion LnC14- in the thermodynamic data for the AC1-LnC13 systems,5@ it seems likely that the AlF4- anion may exist along with AlFt- in AF-A1F3 m e l t ~ . ~Since J ~ the dependence of AHMand AM on concentration in the AF-LnF3 systems is very similar to that found in AF-A1F3, it is quite possible that YF2and YbF2- dissociate to form LnF,- complex anions at fairly high mole fractions of LnF3. It might prove worthwhile to explore this problem by spectroscopic methods. (4) Papatheodorou et al. showed that for the AC1-LnC13 systems the values of AM do not vary linearly with the size parameter aI2, but more nearly linearly with 6122. Unfortunately, since we do not have enthalpy of mixing data for RbF-LnF3 and CsF-LnF3, we are unable to make any detailed comparisons on this point. On the other hand, as we already noted above, we found a nearly linear dependence of AM on aI2 for the mixtures of LnF3 with LiF, NaF, and KF.
Acknowledgment. We acknowledge that the chemical analyses were carried out by the late Dr. Jun Ito. This work has been supported by NSF Grants CHE75-13936 and DMR78-11657. It has also benefited from the support of materials science at The University of Chicago provided by the National Science Foundation-Materials Research Laboratory. References and Notes (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
K. C. Hong and 0. J. Kleppa, J. Pbys. Cbem., 82, 1596 (1978). H. T. Davis, J. Cbem. Pbys., 41, 2761 (1964). H. T. Davis, J. Pbys. Cbem., 78, 1629 (1972). K. C. Hong and 0. J. Kleppa, J. Pbys. Cbem., 81, 176 (1978). G. N. Papatheodorou and 0. J. Kleppa, J . Pbys. Cbem., 78, 178 (1974). G. N. Papatheodorouand T. Dtvokl, J. Pbys. Cbem., 78, 181 (1974). F. Denstbachand R. Blachnik, Z. Anorg. A/b.Cbem., 412, 97 (1975). 0. J. Kleppa and K. C. Hong, J. Phys. Chem., 78, 1478 (1974). K. C. Hong, unpublished Ph.D. Dlssertatlon,The Unhrersityof Chicago, 1975. F. H. Spedding and D. C. Henderson, J. & e m . Pbys., 54,2476 (1971). F. H. Spedding et al., J. Chem. Pbys., 60, 1578 (1974). Based on C (I) = 30.7 cal mol-’ K-’ for LaF,, the average heat capacity of &IF,, LuF PrF, CeF,, and YbF,. Spedding’s reported valuei0 (80.7 cal mOT’k‘) prkumably is the resuk of a printlng error. C. W. Bale and A. D. Pelton, Mefall. Trans., 5, 2323 (1974). B. Gilbert, G. Mamantov, and G. M. Begun, J. Chem. Pbys., 62, 950 (1975).
