3708
J. Phys. Chern. 1981, 85, 3708-3712
Refractlve Indexes of Ionic Melts Y. Iwadate,+ J. Mochinaga,' and K. Kawamura" Research Laboratory for Nuclear Reactors. Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152, Japan, and Department of Synthetic Chemistry, Facutty of Engineering, Chlba University, Yayoi-cho, Chlba 280, Japan (Received: h4ay 4, 198 1; In Flnal Form: July 15, 1981)
Refractive indexes of some pure nitrate, chloride, bromide, and sulfate melts were measured by a goniometer method using visible light at nine wavelengths. The refractive indexes of these melts were represented as functions of both temperatureand wavelength. According to the obtained formulas, the refractive indexes were extrapolated to infinite wavelength, from which the electronic polarizabilities of ions in the melts were estimated by use of the Clausius-Mossotti equation. From the obtained correlation between the electronic polarizabilities of ions and the ionic radii, the effective ionic radii of NO3- and Sod2-were estimated to be 1.89-1.94 and 2.11-2.16 A, respectively.
Introduction Numerous works on the refractive indexes of materials have been performed by various methods. For molten ionic liquids, the results have already been summarized.l Since the refractive index has yielded valuable information on electronic polarization, there have been considerable efforts to obtain the refractive indexes as well as a fundamental understanding of polarization of ions in ionic melts during the past several years. However, there are few data available to estimate the electronic polarizabilities of ions in melts, since the electronic polarizability is determined by extrapolating the refractive indexes measured with light at several wavelengths to infinite wavelength. Highly accurate measurements of the refractive indexes of molten salts with wave-front-shearing interferometry have recently been carried out by Gustafsson et a1.,24 and the molar refractivity of molten AgN03 extrapolated to infinite wavelength was reported by Aronsson and KarawackiS6 The correlation between the polarizability of an ion and the ionic radius has been clarified by Bottcher,6 and his expression was extended successfully to aqueous solutions'~~ and organic solvent^.^ However, this remained inapplicable to molten ionic liquids as described by Karawacki.1° The purpose of the present paper is to obtain the refractive indexes of molten salts, to evaluate the electronic polarizabilities of ions in melts, to make clear the correlation between the electronic polarizability and the ionic radius, and to learn the factors governing it. Experimental Section The chemicals used were of analytical reagent grade. They were prepared the same way as previously rep0rted.l' The rare-earth chlorides were made synthetically by the reactions of corresponding rare-earth oxides and ammonium chloride, and these crude chlorides were purified to the pure crystals by sublimation in vacuo in order to remove impurities such as oxides, NH4C1,and water.12 The purities of these crystals and the sublimation apparatus have been fully described el~ewhere.'~The experimental method and the schematic diagram of the apparatus have been reported in detail previ~usly.'~J~ The volume of a melt needed for one experimental run was only 2 cm3,and 'Tokyo Institute of Technology. -. t Chiba University. *Address correspondence to this author at the Tokyo Institute of Technology. 0022-365418112085-3708$01.25/0
it took a few hours to perform one run. In order to estimate the refractive indexes of melts, the angles of minimum deviations were measured with a goniometer, which were read with a precision of 1 min. The relation between the refractive index and the angle of minimum deviation is expressed in the form n,, = sin [(ax A)/2]/sin (A/2) (1) where nk uA,and A are the refractive index at wavelength A, the angle of minimum deviation, and the apex angle of the prism, respectively. The apex angle of the prism was calibrated by use of the reference material of which refractive indexes have been accurately measured by Gustafsson and K a r a ~ a c k i .The ~ temperature of the melt was automatically controlled and measured by directly inserting a sheathed chromel-alumel thermocouple into the melt and recorded with a precision of 0.1 "C during the experiment. The refractive-index measurements of the melts were carried out at nine wavelengths, namely, 434.1,460,486.2, 510,530,560,589.3,620, and 656.3 nm. Since a PrC13melt has absorption bands in the visible wavelength region, the refractive indexes of the PrC13melt were measured similarly, but excluding 460 and 486.2 nm.
+
Results The refractive indexes of 24 kinds of ionic melts measured with light of fixed wavelengths decreased linearly with increasing temperature in the same manner as described before.11-13 Gustafsson and Karawacki? Wendelov et a1.,2 and Karawacki et al.436have reported that the refractive indexes of ionic melts at a given wavelength slightly decrease curvilinearly with a rise of temperature and concluded that they are better fitted by quadratic (1) G. J. Janz, "Molten Salts Handbook", Academic Press, New York, 1967. D 89. (2) 'L.-W. Wendelov, S. E. Gustafsson, N. Halling, and R. A. Kjellander, Z. Naturforsch. A , 22, 1363 (1967). (3) S. E. Gustafsson and E. Karawacki, Appl. Opt., 14, 1105 (1975). (4) E. Karawacki and S. E. Gustafsson, Z. Naturforsch. A, 31, 956 (197fil. ~ - -- . (5fR. Aronsson and E. Karawacki, 2.Naturforsch. A, 35,694 (1980). (6) C. J. F. Bottcher, Physica, 9, 945 (1942). (7) C. J. F. Bottcher, Recl. Trau. Chirn. Pays-Bus, 62,325,503 (1943); 65, 19, 91 (1946). (8) H. R. Petty, J. A. Crumb, V. E. Anderson, E. T. Arakawa, and J. K. Baird, J . Phys. Chern., 81, 696 (1977). (9) J. D. Olson and F. H. Horne. J . Chern. Phrs., - . 58,. 2321 (1973). . . (IO) E. Karawacki, Thesis, Goteborg, 1977. (11) Y. Iwadate, K. Kawamura, and J. Mochinaga, J. Phys. Chern., 86, 1947 (1981). (12) J. Mochinaga and Y. Iwadate, Denki Kugaku, 47, 345 (1979). (13) J. Mochinaga and Y. Iwadate, J. Fac. Eng., Chiba Uniu., 30,213 (1979). ~~
0 1981 American Chemical Society
Refractive Indexes of Ionic Melts
The Journal of Physical Chemistty, Vol.
85, No. 24, 198 1 3709
TABLE I : Refractive Index Equations on the Basis of Cauchy's Relation
n ( t , h )= (P t Q/h2 + R/h4) t (Pt t Qt/hz + Rt/h4)t
P io-4~ 10-9~ 1 0 4 ~ ~ 10-'Qt 10-6Rt 1 0 3 ~
temp range/"(=
-
LiNO,
NaNO,
KNO,
RbNO,
CsNO,
1.4728 1.0255 - 0.2749 - 1.0269 -1.2487 1.4504 0.50 280-420
1.4617 -0.4318 1.7704 -1.5531 2.2077 -3.6761 0.69 340-436
1.4405 1.0720 -0.6219 -1.2712 -1.5981 2.1499 0.53 370-460
1.4595 0.2520 0.4040 - 1.5644 0.4367 -0.4312 0.77 330-420
1.4879 0.4723 0.3006 -1.6462 -0.1707 -0.0279 0.49 440-530
LiCl
NaCl
1.5680 0.1012 1.0351 -1.3280 0.5855 -1.1244 1.54 639-860
1.4502 2.9392 -3.2756 -0.6278 -2.7041 3.9008 0.51 830-9 3 8
-
P
*
io-'^
10-9~ 1 0 4 ~ ~ 1O-'Qt 10-6Rt 1 0 3 ~
temp range/"(=
P
io-'^ 10-9~ 1 04pt lO-'Qt 10-6Rt 1 0 3 ~
temp range/"C
P 10-4~ 10-9~ 1 o4pt 1O-'Qt 10-'Rt 1 0 3 ~
temp range/"C
P 10-49 10-9~ 1 04pt 10-'Qt 10-'Rt 1 0 3 ~
temp range/"C
KCI 1.4656 3.2262 - 3.7149 -1.1366 - 3.1045 4.4117 0.27 804-896
RbCl
CSCl
1.4576 2.6914 -3.0256 -0.8885 - 2.8429 4.0930 0.60 755-850
1.4847 3.7102 -4.0633 -0.7705 - 4.4697 5.9373 0.53 680-770
LiBr
NaBr
KBr
RbBr
CsBr
1.6441 1.7031 -1.1696 - 1.3977 -1.2669 2.237 1 0.67 590-650
1.5516 2.8929 -2.3809 -0.9807 - 2.7954 3.7506 0.34 780-850
1.5453 1.5997 -1.9626 - 1.4705 - 1.2042 2.9226 0.46 780-850
1.5362 1.9079 -1.8237 - 1.3446 - 1.6599 2.8575 0.45 740-810
1.5446 3.2348 - 2.8005 - 1.1437 - 3.3661 4.1102 0.39 700-780
MgC4
CaCl,
Li,SO,
Na,SO,
1.5449 - 1.0961 2.1797 -0.9533 1.9798 - 2.4293 0.43 823-898
1.5603 5.8635 - 5.9429 9.3908 6.1627 7.3976 0.45 821-912
1.5264 -0.4833 0.7037 -0.9139 0.9447 - 0.7882 0.41 901-1002
1.4163 2.3204 -2.2176 -0.3435 -2.0612 2.3478 0.44 929-1011
YCl, 1.6726 1.4042 - 0.2039 - 0.8009 -0.8336 0.7594 0.47 771-903
LaC1, 1.8194 1.0469 0.6784 -1.4861 0.1019 -0.5288 0.27 893-971
functions of temperature. In the present work, however, the standard deviations for the linear functions were nearly equal to those for the quadratic ones; that is, the temperature coefficients of the quadratic terms were too small to affect the refractive indexes above experimental errors. In addition, the accuracy of the refractive index was sufficiently high to determine the electronic polarizability of an ion, as will be described in the Discussion section, since the refractive index and the density have been measured up to five and four significant figures, respectively. On the other hand, it is well-known that the refractive indexes curvilinearly decrease with increasing wavelength at fixed temperature, a process called normal di~persi0n.l~ In order to analyze this phenomenon for inert gases such as Ar, Kr, and Xe, M ~ ~ C Ohas Umade X ~ ~use of the following equation: nh2 = A
(h/nm and t/"C)
+ B / X 2 + C/X4
(2)
(14) M. Born and E. Wolf, "Principles of Optics", Pergamon Press, Elmsford, NY, 1974, Chapter 2. (15) J. E. Marcoux, Can. J. Phys., 48, 1947 (1970).
,
PrCl 1.8447 -0.0030 1.7545 -1.7932 1.2559 -1.5678 0.44 856-954
GdCl, 1.7223 2.5190 - 1.3236 -0.8340 -2.1070 2.2293 0.52 649-803
dyc13 1.7116 1.6368 -0.2747 -0.9241 -0.7660 0.5542 0.37 708-808
where X is the wavelength used. However, we have ascertained experimentally that eq 3 is best applicable to the nh = A + B / X 2 + C/X4 (3) refractive indexes of ionic melts.'l When the temperature and wavelength dependencies of the refractive index were taken into account, eq 4 was obtained.16 The constants n(X,t) = (P + Q/X2 + R/X4) + (Pt + Qt/X2 + R t / h 4 ) t (4) from P to Rt for the ionic melts were determined by a least-squares method. The results are shown in Table I, where is the standard deviation on fitting. The values for the rare-earth chlorides were recalculated from the original data previously reported,13 and those for the alkaline-earth chlorides were taken from the literature16for convenience and comparison. It is worth noting that, with the aid of eq 4, the refractive index extrapolated to infinite wavelength is reduced to P + Ptt, which is invariably (16) Y. Iwadate, K. Igarashi, and J. Mochinaga, Denki Kagaku, 48,97 (1980).
3710
Iwadate et al.
The Journal of Physical Chemistry, Vol. 85, No. 24, 1981
needed to evaluate the electronic polarizability. The refractive index or its temperature coefficient at an arbitrary temperature and wavelength is also obtainable from eq 4. In the application of eq 4 to the original data, attention must be paid to the anomalous dispersion, namely, the drastic changes of refractive indexes near the absorption bands.
TABLE 11: Electronic Polarizabilities of Ions in the Molten State (a_/A3) 420 "C
(5)
where N is Avogadro's number, M is the molar weight, d is the density, and the subscript 00 refers to the infinite wavelength. An alternative expression has been introduced for the purpose of further interpretation of the polarization phenomenon (nm2- l)/(nm2+ 2) = (47r/3)(CNiai)
Na*
4.13
0.36
K+
Rb'
cs+
1.06
1.70
2.82a
820 "C
Discussion Estimation of the Electronic Polarizability of an Ion. The polarizability is known to be one of the most fundamental parameters that describe the polarization phenomenon. As indicated previously,ll it is noted that the polarizability discussed here is the electronic one. The electronic polarizabilities of ions contained in the melts are defined by the semiclassical Clausius-Mossotti equation analogous to the Lorentz-Lorenz equation am= 3/((47rN)[(nm2- l)/(nm2+ 2)1(M/d))
NO;
c1-
Na+
K+
Rb+
CS+
3.23
0.41
1.23
1.98
3.17
820 "C Br-
Na'
K+
Rb+
cs+
4.54
0.49
1.35 '
2.04
3.33
900 "C
so,= 5.71 a
Extrapolated. 6
...e
I
O
A
5t
B
(6)
where Ni and aiare the number and the electronic polarizability of the ith ion in unit volume, respectively. By use of eq 4-6, the electronic polarizabilities of ions in the molten state were determined. In the present case, the electronic polarizability of a Li+ ion, which is the smallest one among those of the series of ions, Le., 0.03 A3, is taken as a reference. There are two reasons for selecting the Li+ ion: (a) Since it has been found that the error caused by determining the electronic polarizability of the Li+ ion is negligibly small1' and the absolute value of electronic polarizability for the Li+ ion is also small, the errors for calculating the electronic polarizabilities of other ions will remain small. (b) If the temperature coefficient of electronic polarizability for the Li+ ion is considered to be small, the small temperature coefficients for other ions which are usually observed e~perimentally'~ are obtained. The process for calculating the electronic polarizabilities of ions is as follows: the electronic polarizabilities of LiN03, LiC1, LiBr, and Li2S04are determined, from which that of the Li+ ion is subtracted, and then those of anions are estimated. Finally, the values for anions are used to evaluate the electronic polarizabilities of cations such as Na+, K+,Rb+, Cs+,Ca2+,Mg2+,Y3+,and Ln3+(Ln3+refers to the lanthanoid ions.). The numerical results were tabulated in Table 11, in which the density data were taken from the literature,I8indicating the following facts: (i) The electronic polarizability of an ion slightly increases with a rise of temperature. (ii) The electronic polarizabilities of alkali cations generally increase with increasing ionic radius. (iii) The electronic polarizabilities of anions are much larger than those of alkali cations. Facts i and ii imply that the factors governing the electronic polarizabilities of ions are the temperature and the ionic radius. It should be naturally noted that electron-electron interactions as well as nuclear-electron attraction determine the "radius" of an ion. Fact iii is mainly determined by (17)L. Pauling, Proc. R. SOC.London, Ser. A , 114,181 (1927). (18)G.J. Janz, F. W. Dampier, G. R. Lakshminarayanan,P. K. Lorenz, and R. P. T. Tomkins, Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.), 15 (1968). J. Mochinaga, K. Igarashi, H. Kuroda, and H. Iwasaki, Bull. Chem. SOC.Jpn., 49,2625(1976);K. Cho, K. Irisawa, J. Mochinaga, and T. Kuroda, Electrochim. Acta, 17, 1821 (1972).
2 1 -
01
'
300
700
500
900
tC '/
Flgure 1. Temperatwedependence of electronic polarizabilities of ions: (A) SO:-, (B) Br-, (C)NO
