Refractive indexes and electronic polarizabilities of molten HoCl3-NaCl and HoCl3-KCl mixtures

Article abstract of DOI:10.1016/S0925-8388(98)00805-6

The refractive indexes of molten HoCl₃-NaCl and HoCl₃-KCl mixtures were measured by goniometry using visible light at eight wavelengths and expressed as functions of both temperature and wavelength into empirical formulas by a least-squares method. The electronic polarizabilities of ions in the mixture melts were obtained from the data of refractive indexes and molar volumes, and the polarizability of a Ho³⁺ ion was evaluated to be about 0.98 × 10^-30 m³ according to the Clausius-Mossotti equation. The isotherms of these properties show little deviation from their additivity line.

Full text of DOI:10.1016/S0925-8388(98)00805-6

Journal of Alloys and Compounds 281 (1998) 163–168
L
Refractive indexes and electronic polarizabilities of molten HoCl –NaCl
3
and HoCl –KCl mixtures
3
*
Kazuya Shirao, Takuma Iida, Kazuko Fukushima, Yasuhiko Iwadate
Department of Materials Technology, Faculty of Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba 263-8522, Japan
Received 13 June 1998; received in revised form 11 August 1998
Abstract
The refractive indexes of molten HoCl –NaCl and HoCl –KCl mixtures were measured by goniometry using visible light at eight
3
3
wavelengths and expressed as functions of both temperature and wavelength into empirical formulas by a least-squares method. The
electronic polarizabilities of ions in the mixture melts were obtained from the data of refractive indexes and molar volumes, and the
3
1
230
3
polarizability of a Ho ion was evaluated to be about 0.98310
m according to the Clausius–Mossotti equation. The isotherms of
these properties show little deviation from their additivity line.

1998 Elsevier Science S.A. All rights reserved.
Keywords: Refractive index; Electronic polarizability; Molar volume; Ionic melt; HoCl3 mixtures
1
. Introduction
alkali ions and halide ions have already been reported
5–10] and well known to be closely related to the
[
Refractive index is one of the useful optical properties
effective volumes of ions [8,11,12]. The main purpose of
the present work is to obtain the refractive index and the
electronic polarizabilities for molten salt mixtures and ions
in order to acquire the information concerning the mutual
influence of ions in the mixture on structure and the other
physicochemical properties.
reflecting ionic or molecular behaviors in the melts.
Furthermore, the index data are necessary for the measure-
ment of hypersonic velocity in melt by Brillouin scattering
[
1] to characterize the high temperature relaxation process,
in particular, having been indispensable for the estimation
of thermal conductivity by wave-front shearing inter-
ferometry [2,3]. Comparison of the molar volume data
between crystal and melt is capable of a simple evaluation
for structural change on melting, in particular being of a
potential use in well understanding the nearest neighbour
coordination of unlike ionic pair. The electronic
polarizabilities of ions or molecules in molten salts are
generally estimated from the refractive indexes extrapo-
lated to infinite wavelength and the molar volumes on the
basis of evaluation of the effective local field around the
species. It has been so far considered for molten salt
system that refractivity should give information concerning
the structure of these ionic melts, but strictly speaking, the
polarizability data are fundamental parameters describing
the dispersion force term in pair potentials as was used in
the analysis of structure in condensed matter such as
molten salts by computer simulation [4].
2
. Experimental
2
.1. Chemicals and melt preparation
The chemicals NaCl and KCl were of analytical reagent
grade, which separately dehydrated under reduced pressure
22
of about 6.7310 Pa for 8 h just below the respective
melting points, melted and rapidly quenched.
The hygroscopic chemical HoCl was synthesized ac-
3
cording to the reaction [13,14] at 623K for 2.5 h,
Ho O 1 6NH Cl → 2HoCl 1 6NH 1 3H O
(1)
2
3
4
3
3
2
The obtained crude HoCl was purified by sublimation at
3
1273 K for 8 h under reduced pressure in order to remove
The electronic polarizabilities of the lanthanide ions,
impurities such as unreacted oxides, excess NH Cl, oxy-
4
chloride by-products and water. The sublimation apparatus
has been fully described elsewhere [15]. The mole ratio of
the mixtures was determined by accurately weighing out
*
Corresponding author.
0
925-8388/98/$ – see front matter
 1998 Elsevier Science S.A. All rights reserved.
PII: S0925-8388(98)00805-6

1
64
K. Shirao et al. / Journal of Alloys and Compounds 281 (1998) 163–168
each component in a glove box filled with dry N gas,
2
melted for well mixing, rapidly quenched, and stored in
ampoules.
2
.2. Method
A hollow prismatic cell made of fused silica was used
for the goniometric measurement of refractive index and
experiments were made in the temperature range of 1073–
1
4
173 K using visible light at eight wavelengths, namely
40, 470, 500, 530, 560, 590, 620 and 650 nm. The angle
of minimum deviation u was practically measured with a
l
goniometer. The relation between refractive index n and
l
the angle u is expressed by the following formula,
l
n 5 sinh(u 1 A)/2j/sin(A/2)
(2)
l
l
where A is the apex angle of the prismatic cell, which was
calibrated beforehand with the aid of a reference material
KNO [16]. The molar volumes of the melts were mea-
3
sured by dilatometry, the data of which were employed in
calculation of the electronic polarizabilities of ions. The
apparatus and procedures were described in detail else-
where [6,7].
3
. Results and discussion
3
.1. Molar volume
The molar volumes Vm values of molten HoCl –NaCl
3
and HoCl –KCl mixtures were illustrated in Fig. 1. The
3
molar volumes increased linearly with increasing tempera-
ture in the whole compositions. By simply comparing
molten HoCl with solid state HoCl , the volume expan-
3
3
sion on melting V was estimated to be 1.3%, which was
m
quite small in comparison with 19–26% for light lantha-
nide chlorides (see Table 1). The V values are expressed
m
as functions of mole fraction of HoCl , X, and temperature,
3
T, by the least-squares fitted empirical equation,
3
3
i
i
Vm(X,T) 5
O
(a ? X ) 1
H
O
(b ? X )
J
? T
(3)
i
i
i50
i50
2
6
3
21
where a and b are the constants, V in 10 m mol
i
i
m
and T in K. The values of a and b for molten HoCl –
i
i
3
Fig. 1. (a) Molar volume of molten HoCl
(a) 100; (b) 87.5; (c) 75.0; (d) 62.5; (e) 50.0; (f) 37.5; (g) 25.0; (h) 12.5;
i) 0.0%: (b) Molar volume of molten HoCl –KCl system. HoCl
3
3
–NaCl system. HoCl (mol%):
3
NaCl and HoCl –KCl systems are given in Table 2. Fig. 2
3
(
shows the molar volume variations with composition in
molten HoCl –NaCl and HoCl –KCl mixtures at 1113 K.
3
(mol%): (a) 100; (b) 87.5; (c) 75.0; (d) 62.5; (e) 50.0; (f) 37.5; (g) 25.0;
3
3
(
h) 12.5; (i) 0.0.
A straight line in Fig. 2 indicates the additivity,
Vmix 5 X V 1 X V
(4)
and V refer to the molar fraction and molar volume of the
1
1
2
2
i
i-th component, respectively. It was demonstrated that the
where Vmix is the molar volume of the mixture melt, and Xi
deviations from additivity were within the range of 5%.

K. Shirao et al. / Journal of Alloys and Compounds 281 (1998) 163–168
165
Table 1
Classification of pure Lanthanide trichloride melts on the basis of structural information
a
Salt
Symmetry and structure type of crystal
m.p (K)
DV (%)
Molecular weight
Cationic radius (nm)
LaCl3
PrCl3
NdCl3
SmCl3
GdCl3
YCl3
HoCl3
ErCl3
NaCl
KCl
Hexagonal UCl3
Hexagonal UCl3
Hexagonal UCl3
Hexagonal UCl3
Hexagonal UCl3
Monoclinic AlCl3
Monoclinic AlCl3
Monoclinic AlCl3
Cubic NaCl
1150
1059
1041
935
875
987
19.1
21.0
21.8
24.5
26.4
0.5
1.3
5.3
38.0
28.5
0.4b
18.5
245.26
247.27
250.60
256.72
263.63
195.26
271.29
273.56
58.45
0.103
0.099
0.098
0.096
0.094
0.090
0.090
0.089
0.099
0.137
0.100
0.060
993
1049
1073
1043
1055
591
Cubic NaCl
Orthorhombic CaCl2
Tetragonal
74.56
110.99
136.30
CaCl2
ZnCl2
a
Tm
Tm
l
DV5100(V l 2V )/V , where V
DV517.4% in case of monoclinic crystal.
is the molar volume of liquid at melting point, V the molar volume of solid (crystal).
s
s
s
b
3
.2. Refractive index
2
2
2
2i
22i
n(l,T) 5
O
(P ? l ) 1
H
O
(Q ? l
)
J
? T
(6)
i
i
i50
i5o
The refractive indexes of molten HoCl –NaCl and
3
HoCl –KCl measured with visible light at fixed wave-
3
where P and Q were the constants determined by the
i
i
lengths decreased linearly with increasing temperature in
the same manner previously reported [8,10,16]. Since the
refraction phenomenon occurred by light scattering on and
around the atom or ion, namely, the electron clouds, the
magnitude of refractive index should originally be propor-
tional to the number density of the species in the melt, and
in consequence the refractive indexes decreased linearly
with increasing temperature (see Figs. 3 and 4). The same
nonlinear least-squares method and l is the wavelength.
The results for molten HoCl –NaCl and HoCl –KCl
3
3
mixtures are tabulated in Table 3, where d is the standard
error on fitting.
3.3. Electronic polarizability
tendency was recognized in the molten HoCl –KCl sys-
The electronic polarizability a of an ‘apparent’ mole-
3
`
tem. On the other hand, the refractive indexes decreased
curvilinearly with increasing wavelengths at a given
temperature (see Fig. 4), and this phenomenon was found
to correspond to normal dispersion of refraction [8,17],
which could be expressed by the Cauchy’s dispersion
formula,
cule in a melt is defined by the semiclassical Clausius–
2
4
n(l) 5 p 1 q/l 1 r/l
(5)
Furthermore, a series of phenomena were well reproduced
by the so-called modified Cauchy’s relation [7,12,18],
Table 2
Parameters in empirical equations of molar volumes for molten HoCl3 –
NaCl and HoCl –KCl systems
3
System
HoCl –NaCl
HoCl –KCl
3
3
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
d
0
0
0
0
0
0
0
0
a0
a1
a2
a3
1.991
28.797
1.060
26.601
1.602
4.207
21.062
6.317
2.797
4.391
23.275
1.985
1.956
21.097
2.534
b0
2
b1
b2
b3
2
2
21.886
0.742
0.861
Fig. 2. Molar volume variation with composition in molten HoCl –NaCl
3
2
6
3
21
mol ).
d, standard error (310
m
and HoCl –KCl systems at 1113 K.
3

1
66
K. Shirao et al. / Journal of Alloys and Compounds 281 (1998) 163–168
Fig. 3. Refractive indexes of molten HoCl –NaCl system at 560 nm.
3
HoCl (mol%): (a) 100; (b) 87.5; (c) 75.0; (d) 62.5; (e) 50.0; (f) 37.5; (g)
3
2
5.0; (h) 12.5; (i) 0.0.
Mossotti equation (similar to the Lorentz–Lorentz equa-
tion),
2
`
2
`
a 5 h3/(4pN )jh(n 2 1)/(n 1 2)j ?V
(7)
`
A
m
where the subscript ` refers to infinite wavelength, N is
A
Avogadro constant and n` the value of n at l5`. With
l
the aid of Eq. (6), n can be quite easily evaluated to be
`
P 1Q T. The temperature dependence of a obtained for
0
0
`
a HoCl –NaCl stoichiometric unit in melt and the iso-
3
therms of a for the mixtures are shown in Figs. 5 and 6,
`
respectively. According to the Clausius–Mossotti equation,
the electronic polarizability should be independent of
temperature because of cancellation between the dispersion
2
2
term of (n 21)/(n 12) and the molar volume V in Eq.
`
`
m
(
7), but a` slightly decreased or increased linearly with
increasing temperature in the present work. This phenom-
enon may be caused by the fact that experimental error in
V was larger than that in n , that is, being much larger
m
`
2
`
2
`
than that in (n 21)/(n 12). If additivity is assumed to
apply to a as well as Eq. (4), the following relation holds
`
good,
amix 5 X a 1 X a
2
(8)
1
1
2
Fig. 4. Refractive index variation of molten HoCl –NaCl with tempera-
3
ture and wavelength. (a) HoCl :NaCl5100:0 (mol%); (b) HoCl :NaCl5
where a refers to the electronic polarizability of the i-th
3
3
i
7
5:25 (mol%).
component. The deviations from additivity are turned out
to be within a few percent (see Fig. 6).
In case of molten salts which are composed of several
different chemical particles, additivity is expressed as
follows,
where N and a are the number of j-th particles (ions) per
j
j
unit volume and the electronic polarizability of the j-th
particles, respectively. For example, in the fully ionic
description of the molten salt with a stoichiometry CA3,
2
`
2
`
(
n 2 1)/(n 1 2) 5 (4p/3)
O
N a
j j
(9)

K. Shirao et al. / Journal of Alloys and Compounds 281 (1998) 163–168
167
Table 3
Parameters in empirical equations of refractive index for molten HoCl –NaCl and HoCl –KCl systems
3
3
2
5
29
10 P2
4
22
10 Q1
27
10 Q2
X
P0
10 P1
10 Q0
d
HoCl -NaCl
3
1
00.0
1.686
1.946
1.746
1.824
1.712
1.683
1.635
1.520
1.786
2.096
21.213
24.339
29.735
7.820
24.008
22.640
3.060
21.606
1.707
1.095
1.585
26.348
9.837
5.057
21.312
2.750
25.385
24.335
21.911
23.073
22.193
22.292
22.030
28.948
23.900
29.674
1.709
5.536
1.391
27.750
6.405
5.115
21.455
2.089
1.476
22.285
21.245
22.105
6.657
21.232
27.720
24.078
23.071
0.390
0.620
0.592
0.497
0.950
0.815
0.543
0.620
0.520
87.5
75.0
62.5
50.0
37.5
25.0
12.5
0
.0
21.801
HoCl 2KCl
3
1
00.0
1.686
1.883
1.628
1.565
1.641
1.713
1.622
1.890
1.752
2.096
21.230
0.786
4.793
2.720
25.313
23.504
2.091
21.606
2.606
20.666
22.080
23.357
9.162
6.507
2.091
21.593
25.385
23.088
21.013
20.716
21.567
22.668
21.994
24.659
23.665
29.674
1.600
20.896
24.326
22.589
7.018
5.219
2.023
21.713
1.476
23.184
0.866
1.474
3.936
21.090
28.159
22.595
1.871
0.390
0.435
0.494
0.697
0.822
0.815
0.256
1.520
1.359
87.5
75.0
62.5
50.0
37.5
25.0
12.5
0
.0
1.463
2
3
X, HoCl3 (mol%); d, standard error (310 ); temperature range, 1073–1173 K.
the a is divided into the two contributions of cation, a ,
hypothesis [12,19,20] was introduced for the ion with less
1 1
`
C
and anion, a , in the following manner,
electron such as Li ion. The value of a (Li ) has already
`
230 3
A
been calculated in Ref. [21] to be 0.029310
m .
a 5 a 1 3a
A
(10)
`
C
According to the calculation process and the assumption
As for molten HoCl , a and a correspond to the
for a as mentioned above, the electronic polarizability of
3
C
A
`
3
1
2
2
2
electronic polarizabilities of a Ho ion and a Cl ion,
the Cl ion, a (Cl ), was computed from a of LiCl
`
`
3
1
230
3
respectively. The electronic polarizability of a Ho ion,
[7,12] unit to be 3.17310
m , therefore, the a values
were equal to 0.33, 1.10 and
`
3
1
1
1
31
a`(Ho ), was estimated by subtracting the contributions
of Na , K and Ho
2
230
3
of three Cl ions from the value of a for a HoCl unit.
0.98310
m , respectively.
`
3
However, the electronic polarizability of the individual
The electronic polarizabilities of alkali, alkaline earth
ions cannot be calculated from a` until the specific
Fig. 5. Temperature dependence of electronic polarizability for molten
HoCl –NaCl system. HoCl (mol%): (a) 100; (b) 87.5; (c) 75.0; (d) 62.5;
Fig. 6. The electronic polarizability variation with composition in molten
3
3
(e) 50.0; (f) 37.5; (g) 25.0; (h) 12.5; (i) 0.0.
HoCl –NaCl (s) and HoCl –KCl (d) systems at 1073 K.
3
3

1
68
K. Shirao et al. / Journal of Alloys and Compounds 281 (1998) 163–168
3
ion and halide ions are well known to be closely related to
the volumes of ions [22,23], as was also demonstrated in
a` 5 2 1.375 1 3.176r
(11)
where r refers to the effective ionic radius of trivalent
lanthanide ions with six-fold coordination. Taking into
account the trends in Eq. (11), behaviors similar to that
observed in the lanthanide ions might appear at the
ionization of the other inner transition elements.
Fig. 7. a values were approximately proportional to the
`
3
value r , where r was the effective ionic radius rec-
ommended by Shannon [24], but the correlation between
3
a and r in lanthanide ions shifted from that in alkali and
`
halide ions, the reason of which has been described in
3
1
detail elsewhere [12]. The a (Ho ) was well along the
`
straight line which was best fitted for the other lanthanide
References
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3
tals. The correlation between a and r for lanthanide ions
`
[
[
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[
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Fig. 7. Correlation between the electronic polarizability of an ion (a ) and
`
3
1
the effective ionic radius (r). (h) Ho
.