Heats of solution/substitution of Tl+, Rb+, K+, Br-, I- in crystalline CsCl from heats of solid phase transition by differential scanning calorimetry

Article abstract of DOI:10.1016/S0022-3697(01)00251-7

Measurements of the change in heat (enthalpy) of transition in crystalline CsCl effected by the presence of guest ions K⁺, Rb⁺, Tl⁺, Br^-, I^- using differential scanning calorimetry are reported. The n

Full text of DOI:10.1016/S0022-3697(01)00251-7

Journal of Physics and Chemistry of Solids 63 +2002) 1669±1675
www.elsevier.com/locate/jpcs
Heats of solution/substitution of Tl1, Rb1, K1, Br2, I2
in crystalline CsCl from heats of solid phase transition
by differential scanning calorimetry
a,
E.A. Secco , R.A. Secco
b
*
aDepartment of Chemistry, St. Francis Xavier University, P.O. Box 5000, Antigonish, NS, Canada B2G 2W5
bDepartment of Earth Sciences, The University of Western Ontario, London, ON, Canada N6A 5B7
Received 13 August 2001; accepted 5 October 2001
Abstract
Measurements of the change in heat +enthalpy) of transition in crystalline CsCl effected by the presence of guest ions K1,
Rb1, Tl1, Br2, I2 using differential scanning calorimetry are reported. The nature of each mixed-ion solid, `mixed crystal' or
`crystalline solid solution' is discussed. The limits of solubility of each guest ion are found to be consistent with the subsolidus
region described in its respective phase diagram. The quantitative heat of transition values are used to calculate some funda-
mental solution quantities, viz. slope DHt=x or DHsolute; x, DHS0; DHL0 Ðapparent partial molar heat of solution, partial molar
ꢀ
heat of solution at in®nite dilution, the heat of solution, recovered lattice energy, respectively. q 2002 Elsevier Science Ltd. All
rights reserved.
Keywords: D. Phase transitions; C. Differential scanning calorimetry +DSC); C. X-ray diffraction
1. Introduction
i and j, r0 ˆ ri 1 rj; e the electronic charge, rij the distance
separating the ions, l is the coef®cient and r a measure of
the fall-off of the repulsive potential as a function of the
interionic distance. In ionic compounds the dominant inter-
action is the cation±anion attractive one represented by the
®rst term within the brackets of Eq. +1) while the secondary
interactions +cation±cation and anion±anion) are small, of
roughly equal importance and are repulsive in nature whose
contributions are attributed to the second summation term
in Eq. +1). To a ®rst approximation for a M1X2 type
compound hosting a similar guest ion in amounts 0 , x !
1:0 mole fraction Eq. +1) contains the net additional
contribution
The nature of ion±ion interactions in the solid and their
effects on the physico-chemical properties of mixed-ion
compositions in polymorphic systems involving isostruc-
tural compounds is a relatively unexplored area. The exis-
tence of a polymorphic substance indicates that the
minimum internal energy or cohesive/binding energy of
the crystal U0 does not differ greatly from one structure to
another. The enthalpy DHt accompanying the structural
transition represents the difference between the cohesive
energies of the two structural states, i.e. U0ꢀ2† 2 U0ꢀ1†
DHt: The cohesive energy is given by the general expression
ˆ
!
0
1
A
2
2
X
1
MZM ZX
e
MZiZje2
2 u=r
X
xN 2
1
lM
e2ur
1X2
1
X
M
U0 ˆ N 2
1
lij e2ur u=r
ꢀ1†
ij
@
1
rM 1 rX
2
M1X2
r0
ij
in both structures. The presence of a guest in the host would
be re¯ected in the difference in the transition enthalpy
between the pure crystal transition and the `mixed crystal'
transition, viz. DHtꢀpure† 2 DHtꢀmixed† ˆ dꢀDHt†: This latter
quantity can lead to the partial molar heat of solution in a
crystal at in®nite dilution, i.e. x.
where N is the Avogadro number, M the Madelung constant
for the lattice type, ZiZj the number of charges on given ions
* Corresponding author. Tel.: 11-902-8672250; fax: 11-902-
8632645.
E-mail address: secco@uwo.ca +E.A. Secco).
As a continuation of our program on the studies of the
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
PII: S0022-3697+01)00251-7

1670
E.A. Secco, R.A. Secco / Journal of Physics and Chemistry of Solids 63 82002) 1669±1675
nature of ion±ion interactions in the solid and their effects
on the physico-chemical properties of mixed-ion composi-
tions of polymorphic systems involving isostructural
compounds [1±6] we include an investigation on CsCl host-
ing systems, viz. CsCl±KCl, CsCl±RbCl, CsCl±TlCl,
CsCl±CsBr and CsCl±CsI. Two of the relevant factors
cited in the solubility/substitution of a guest ion in the
host lattice to form a mixed crystal are the similarity in
structure of the host and guest compounds, ion property
similarity [7] and the effective radius of the guest ion rela-
tive to the substituted host ion. All the guest compounds
along with CsCl exist only in the cubic structure, space
group Pm3m or Fm3m. The aim of this study is to measure
the relative cohesive energy effect in the CsCl structure by
replacing the Cs1 ion with guest cations of decreasing ionic
for In and Cd were used as internal references. Repetitive
DSC traces of the same pan sample gave DHt values within
0.4% error whereas different pan samples of the same
composition gave DHt values within 4% of each other.
The transition temperature Tt values of DSC traces agreed
within 2 8C for duplicate samples of each composition.
The X-ray diffraction patterns of samples, suspended in
methanol using Cu Ka1 radiation and dry unsuspended using
Co Ka1 radiation, obtained at room temperature as described
earlier [4,6] gave identical patterns of cubic structure of b-
CsCl, Pm3m. Samples of CsCl±KCl, CsCl±TlCl and CsCl±
CsI showed trace peaks of KCl, TlCl and CsI, respectively,
along with the dominant pattern characteristic of the room
temperature phase b-CsCl. The patterns of CsCl±RbCl and
CsCl±CsBr showed only the b-CsCl pattern at room
temperature.
radius, viz. Rb1, Tl1, K1 where rCs ˆ 188 pm; rRb
ˆ
1
1
1
1
rTl ˆ 174 pm and rK ˆ 165 pm for C.N. +coordination
number) ˆ 8 with a monoatomic Cl2 sublattice relative to
that of a polyatomic NO23 sublattice where rCl ˆ rNO
ˆ
2
2
3
3. Results and discussion
171 pm for C.N. ˆ 8. Also we set out to compare the relative
effect on the cohesive energy of the CsCl structure by
replacing the Cl2 ion with guest anions of increasing ionic
The mixed composition diffraction patterns con®rm that
the host CsCl crystal retains its structure, indicating a
straightforward ion substitution on their respective sub-
lattice to form a `mixed crystal' or `crystalline solid solu-
tion'. In other words, an ideal substitutional solid solution
results, permitting the determination of the heat of solution/
substitution of the speci®c guest +solute) ion in the host
+solvent) CsCl crystal.
radius, viz. Br2, I2 where rBr ˆ 190 pm and rI ˆ 216 pm:
2
The differences in the electropositivity and electronegativity
of the guest ions may also have an impact on the lattice
cohesive energy. The method of analysis of the experi-
mental data from these measurements has already been
detailed in earlier reports [4±6].
This report therefore presents the heat of solution/substi-
tution of K1, Rb1, Tl1, Br2, and I2 in crystalline CsCl
along with their recovered lattice energies obtained from
heats of transition using differential scanning calorimetry
+DSC).
Cesium chloride transforms from the low-temperature
Pm3m structure +b) structure to the high-temperature struc-
ture Fm3m +a) +NaCl structure). There is no observable
transition in DSC trace for Cs0.896K0.104Cl up to 520 8C
while the transition for Cs0.935K0.065Cl occurs at 365 8C. If
there is no transition up to 500 8C as suggested for xKCl
.
0:10 then this fact indicates that KCl stabilizes the high-
temperature CsCl-Fm3m structure compatible with Fm3m
for KCl over the entire T-range of the experiments. In
other words the CsCl-Fm3m structure is stabilized with no
evidence of the Pm3m±Fm3m transition. No transition is
reported in the 1 atm phase diagram [8] of CsCl between
520 8C and the melting temperature at 645 8C. Therefore the
stabilized CsCl-Fm3m structure is stable up to the fusion
temperature consistent with its phase diagram and the
Condon±Morse potential energy curve [9]. It is interesting
to note that Cs0.896K0.104Cl sample after 12 months storage
in an air-®lled capped glass bottle gave a broad endo-
therm peak at 464 8C characteristic of pure CsCl. Electrical
conductivity measurements showed a transition at ,460 8C
paralleling the conductivity behavior in pure CsCl. These
facts suggest that the `mixed crystal' Cs0.896K0.104Cl freshly
prepared as fused mass in this study and as single crystal by
Weijma and Arends [10] is in a metastable high energy state
where slow kinetics operate to effect unmixing/separation.
The kinetics for unmixing can be accelerated by X-radiation
which can explain the b-CsCl Pm3m structure pattern with
KCl peaks where only the a-CsCl Fm3m structure pattern
2. Experimental
The compounds used in this study were from the follow-
ing suppliers with their stated purities: CsCl, Analar +BDH
Chemicals), .99.9%; KCl, Alfa Ventron, .99.9%; RbCl,
Alfa Ventron, .99.9%; TlCl, Aldrich Chemical, 99%;
CsBr, Alfa Ventron, 99%; CsI, Aldrich Chemical, 99.9%.
All compositions were prepared by mixing followed by
fusing ,50 K above melting in a covered porcelain crucible
for ,30 min with slow cooling to room temperature in the
furnace over 12 h with power OFF. Each composition of the
fused mass was thoroughly ground manually and an aliquot
sample was taken for thermal analysis. Random checks after
fusion showed no weight loss within limits of weighing
error.
Thermal analysis was done with DSC accessory to the
DuPont Instrument 9900 Computer/Thermal Analyzer unit
for process monitoring, data acquisition and data analysis.
The samples encapsulated in copper pans were bathed
in ¯owing N2 +ultrapure) atmosphere and heated at
10 8C min21. The melting temperatures and heats of fusion

E.A. Secco, R.A. Secco / Journal of Physics and Chemistry of Solids 63 82002) 1669±1675
1671
phase diagrams [23±25] which are in marked disagreement
with the results for K1 and Rb1 reported by Rao et al.
[14,15]. Furthermore, the latter results are also inconsistent
on the extent of solubility in the subsolidus region of their
respective phase diagrams, viz. CsCl±KCl [24] and CsCl±
RbCl [25].
The Tt behavior of I2 in CsCl transition represents a
special case where Tt decreases to a constant value at xCsI
ˆ
0:10 and remains constant to xCsI ˆ 0:80 and the transition
disappears at xCsI ˆ 0:90: The limits 0:10 , xCsI , 0:80 are
consistent with the reported phase diagram. Fig. 2 gives
DSC traces A and B of CsCl12xIx at x ˆ 0:097 and 0.509,
respectively. Fig. 2A shows the effect of heating 30 min
after earlier heat±cool cycle representative of behavior for
x , 0:25 and Fig. 2B shows the appearance of a distinct
doublet representative of behavior for 0:33 , x , 0:80:
The constant Tt values at 393 and 415 8C are consistent
with the reported limits of conjugate solid solution presence,
CsCl-rich S1 and CsI-rich S2 in CsCl±CsI phase diagram
[26] and labeled CsI1 and CsI2 in Fig. 1. We attribute the
endotherm at 415 8C to interaction of S1 and S2 to form the
1:1 complex S1S2 where the maximum DH value occurs at
S1=S2 ù 0:5: with increasing S2.
Fig. 1. Plot of transition temperature Tt vs. guest ion mole fraction,
xMX, CsCl±MX system; CsI1 and CsI2 are described in text.
was expected in the diffraction patterns of Cs0.896K0.104Cl.
Similarly, the existence of the metastable state and the
accelerated effect of X-radiation on the kinetics of unmixing
in CsCl±TlCl and CsCl±CsI mixed crystals can account for
the trace TlCl and CsI peaks in their diffraction patterns.
3.2. Enthalpy of transition DHt dependence on composition
of guest 8solute) ion
3.1. Transition temperature Tt dependence on composition
of guest 8solute) ion
The dependence of DHt of the CsCl b $ a phase transi-
tion on mole fraction x of guest ions K1, Rb1, Tl1, Br2 and
I2 is plotted in Fig. 3. The slope of each plot represents the
dependence of DHt on mole fraction of guest ion in CsCl
lattice, that is, the apparent partial molar heat of solution,
The transition temperature Tt values cited in the literature
range from 445 8C [11,12] to 470±480 8C [12±14] and the
transition enthalpy DHt values spread is between 2:43 ^
0:10 kJ mol21 and 3.8 kJ mol21 [10,11,12±18]. Our
measured values of Tt and DHt for pure CsCl are 460 ^
2 8C and 2:93 ^ 0:08 kJ mol21; respectively, reproducible
on six traces of samples on different pans. Our DHt values
are in excellent agreement with those reported by Weijma
and Arends [10], Poyhonen and Mansikka [11], Arell et al.
[17] and by Clark [18].
ꢀ
DHsolute; i.e. slope DHt/x. From these molar DHt values we
calculate the partial molar heat of solution d+DHt)/x, where
dꢀDHt† ˆ DHtꢀCsCl† 2 DHtꢀCsCl1guest† with plots of +dDHt/x)
vs. x, mole fraction of guests, Rb1, Tl1 and Br2, K1 and I2
given in Figs. 4±7, respectively. The aberrant datum at x ˆ
0:1 in Fig. 4 is disregarded but it is purposely included to
illustrate the limit of the mixed crystal composition required
for heat of solution determination. The intercepts of these
plots yield the values for the partial molar heat of solution at
in®nite dilution, x, of the respective guest ion in CsCl as
expressed in
Fig. 1 presents the dependence of the transition tempera-
ture Tt as a function of the guest ion mole fraction, xMX, in
the CsCl±MX system. Tt approaches linear behavior with
increasing Tl1 and Br2 in the host CsCl while maintaining
the cubic b-CsCl structure, Pm3m, undergoing the b ! a,
Pm3m ! Fm3m, transformation. This observation is consis-
tent with the earlier reported phase diagrams by independent
workers on CsCl±TlCl [19±22] and CsCl±CsBr [23] along
with the differential thermal analysis +DTA) by Weijma and
Arends [10]. Our subsolidus temperature behavior for
composition region 0 , xTlCl , 0:14 conforms to the dia-
gram of Ref. [21] but is in contrast to Ref. [22]. On the other
hand Tt decreases linearly with increasing KCl and RbCl
consistent with earlier reports [24,25]. The subsolidus
region of CsI±CsCl diagram is unknown to us. It is relevant
to note that our Tt values and limits of solution/substitution
of K1, Rb1 and Br2 compare very well with those observed
by Weijma and Arends [10] using single crystals and their
ꢀ
ꢁ
2ꢀDH†
2x
DH
ˆ lim
; x
x!0
x
xˆ0
which leads to DHS0 from DHS0 ˆ x 2 ‰DHf0ꢀCsCl† 2
DHf0ꢀguest†Š: It is understood that the DHf0 quantities are
heat/enthalpies of formation from the elements in their stan-
dard thermodynamic states. The x value can also be
obtained from the xguest value at the intercept dꢀDHt†=x ˆ 0
divided into DHt of pure host, viz. CsCl. This xguest value
represents the theoretical amount of solute/guest to com-
pletely stabilize the high-temperature CsCl a-structure
thus eliminating its natural b ! a transition. The con-
sistency between the x values from the two intercepts, i.e.

1672
E.A. Secco, R.A. Secco / Journal of Physics and Chemistry of Solids 63 82002) 1669±1675
Fig. 2. DSC traces for CsCl0.903I0.097, trace A, on second heating and CsCl0.491I0.509, trace B, illustrate effect of increasing CsI composition.
x ˆ 0 and dꢀDHt†=x ˆ 0; appears only with Rb1 in CsCl
paralleling earlier consistencies for Rb1 and Cs1 in TlI
[1,2] and Tl1 in RbNO3 and Rb1 in TlNO3 [4,5]. The ener-
can obtain virtual x values of 6:8 ^ 0:3 kJ mol21 for Tl1
and 0:60 ^ 0:05 kJ mol21 for Br2. The positive slope for
Br2 parallels I2, Fig. 7, indicating an exothermic contribu-
tion in the solution process which counters the negative
slope observed in all our cation solution/substitution studies
[2±6]. The solution of K1 in CsCl is interpreted as stabiliza-
tion of the high-temperature a-structure in accordance with
its phase diagram [8]. Fig. 6 yields x ˆ 41:5 ^ 3:0 kJ mol21
and its calculated value from the intercept mole fraction
xKCl ˆ 0:10 at dꢀDHt†=x ˆ 0 is 29:3 ^ 7:0 kJ mol21: These
values are within the range of x ˆ 32:8 kJ mol21 calculated
from Ref. [10] and shown in Table 1.
getics of Rb1 solubility in CsCl is in strong contrast with
Rb1 solubility in CsNO3 where HRb and xRb are zero
since DHmix ˆ 0:
ꢀ
1
1
The plots of d+DHt)/x vs. x for K1, Tl1, Br2 and I2 reveal
a distinct pattern of solution energetics from Rb1 in CsCl
which is attributed to the speci®c manner that the CsCl
structure responds to accommodating these guest ions. As
evident in Fig. 5 the amounts xTlCl ˆ 0:01 and xCsBr ˆ 0:054
have no impact on DHt of CsCl. This fact is interpreted in
terms of ideal solution behavior, i.e. DHmix ˆ 0 for these
compositions. DHmix ˆ 0 for Tl1 in CsCl parallels the result
for Tl1 in CsNO3 with different composition limits [6].
Passing over the very limited ideal solution regime one
The plot of DHt vs. mole fraction CsI, Fig. 3, is consistent
with the Tt dependence on xCsI, Fig. 1, and our data extend
the region of subsolidus conjugate solutions, S1 and S2, in
the CsCl±CsI phase diagram [26]. The noteworthy feature is

E.A. Secco, R.A. Secco / Journal of Physics and Chemistry of Solids 63 82002) 1669±1675
1673
Fig. 3. Plot of transition enthalpy DHt vs. guest ion mole fraction,
xMX, in CsCl±MX systems.
Fig. 5. Plot of partial molar heat of solution d+DHt/x) vs. mole
fraction x of Tl1 in CsCl and of Br2 in CsCl crystal.
the change of slope from positive, 0 , xCsI , 0:18; to nega-
tive 0:18 , xCsI , 0:80; for DHt vs. xCsI. The positive slope
is for the single phase CsCl-rich whereas the negative slope
is for the conjugate solution region, S1 1 S2, attaining
DHt ˆ 0 for the single phase CsI-rich. Plotted along with
the experimentally measured DHt values in the S1 1 S2
region of Fig. 3 are calculated DHt values for the fraction
S1 phase, open symbols W identi®ed by CsI2, undergoing the
b ! a CsCl transformation using the lever principle. The
excellent agreement between the measured and calculated
DHt is evident and af®rms our identi®cation of conju-
gate solid solutions S1 and S2 at xCsI ˆ 0:18 and 0.80,
respectively.
Values of x, DHS0 and recovered lattice energy DHL0;
understood as the destruction of 1 mol of M'X guest lattice
and the creation of a new imperfect lattice M'MX, calcu-
lated from DHL0 ˆ x 2 ‰DHf0LꢀCsCl† 2 DHf0Lꢀguest†Š in this
study along with some mixed thallium and alkali related
compounds for comparison purpose are tabulated in Table
1 where DHf0L represents heat of formation of the lattice
from ions in their standard states, i.e. UL ˆ DHf0L: Also
included in Table 1 are the DHf0 and DHf0L values taken
from the literature, [12,27±29] except TlCl which was
calculated from the Kapustinskii equation, [30] corrected
to the transition temperature of the solvent, i.e. 460 8C for
CsCl, using the heat capacities of the components [12]. We
repeat that only CsCl undergoes a phase transition, viz.
CsCl, Pm3m ! Fm3m, while the remaining compounds
maintain their standard state structures to melting
temperature.
Attempts to correlate DHS0 values with ionic radius of the
guest ion incorporated in a speci®c lattice-type have not
been successful. It has been suggested that when a larger
ion replaces a smaller one the value of DHS0 is positive [31]
as in Rb1 ! K1, Br2 ! Cl2, Cs1 ! Tl1 but positive DHS0
is also observed for smaller ion replacing larger ion, viz.
Fig. 4. Plot of partial molar heat of solution d+DHt/x) vs. mole
fraction x of Rb1 in CsCl crystal.
Fig. 6. Plot of partial molar heat of solution d+DHt/x) vs. mole
fraction x of K1 in CsCl crystal.

1674
E.A. Secco, R.A. Secco / Journal of Physics and Chemistry of Solids 63 82002) 1669±1675
considers the interplay of various factors affecting the lattice
energy of a given solid composition, viz. dipole±dipole and
dipole±quadrapole interactions, attractive and repulsive
potentials, relative polarizability, etc. in addition to ionic
radius.
In summary, this paper contains additional examples
of `mixed crystal' formation of cations and anions
substituted in crystalline CsCl. That is, it provides
useful data relevant to ion±ion interaction energies in
a common cubic environment to carry out a theoretical
analysis of static properties in mixed crystals using the
Monte Carlo technique or an approximate quantum
ꢀ
approach. The heats of solution terms, viz. DHsolute; x,
DHS0 and DHL0 were calculated from quantitative heat of
transition measurements using DSC. DSC has been
shown once again to be a simple, straightforward and
non-destructive solid-state method for reproducible
measurements to obtain fundamental enthalpic solution
quantities.
Fig. 7. Plot of partial molar heat of solution d+DHt/x) vs. mole
fraction x of I2 in CsCl crystal.
K1 ! Cs1, Rb1 ! Cs1, Tl1 ! Cs1 as evident in Table 1.
A trend between positive DHL0 values for host ion replace-
ment by a larger guest ion appears in all cases in Table 1. A
corollary of this trend is of increasing negative DHL0
for smaller cations replacing Cs1 in CsCl from
Acknowledgements
K1 ! Rb1 ! Tl1. Since rRb ˆ rTl the large difference
in DHS0 cannot be attributed to size factor alone. The values
of DHS0 and DHL0 and their signs +1 or 2) do, however, show
their interdependence on the DHf0 and DHf0L values, respec-
tively, of the solute and solvent compounds evident in the
equation DHS0 ˆ x 2 ‰DHf0ꢀsolvent† 2 DHf0ꢀsolute†Š: It would be
naive to visualize a simple relationship between relative
host±guest ionic size and x, or HS0; or DHL0 when one
This study received ®nancial support from Natural
Sciences and Engineering Research Council of Canada
grants to each author and from the Shell Oil Company
of Canada to EAS. EAS is grateful to Prof. M. Steinitz,
Physics Department, St. Francis Xavier University for
providing laboratory space and facilities in the later
stage of this study and to Michael Lewis for technical
assistance.
1
1
Table 1
Comparison of heats of solution +kJ mol21) of K1, Rb1, Tl1, Br2, I2 in CsCl with related metal compoundsa
DHS0
DHL0
2DHf0L a +solvent)
Reference
a
a
Solvent +host)
Solute +guest)
x +solute)
Intercept at x ˆ 0
dꢀDHt=x† ˆ 0 .
CsCl
KCl
41.5
32.8
11.8
9.5
0, 6.8b
0, 0.6b
1.7
29.3
±
37.5
15.0
28.5
675
±
This study
[10]
CsCl
CsCl
KCl
±
±
±
RbCl
RbCl
TlCl
12.5
±
221.2
±
675
±
This study
[10]
CsCl
CsCl
CsCl
±
257.0
38.4
297.0
20.8
±
675
675
±
This study
This study
[10]
CsBr
±
CsCl
CsBr
±
±
CsCl
CsI
21.0
6.3
±
22.2
210
16.3
49.6
39.6
233
44
675
759
726
759
726
759
759
This study
[5]
[5]
RbNO3
CsNO3
TlNO3
CsNO3
TlNO3
RbNO3
CsNO3
RbNO3
CsNO3
TlNO3
RbNO3
TlNO3
24.2
±
0
9.4
19.4
±
2252
263
[5]
0
233
11.4
14.7
[5]
11.4
14.7
12.7
16.0
2258.4
261.7
[4]
[4]
a
All values of DHf and DHfL used to calculate DHS0 and DHL0 for mixed compositions were corrected to the Tt of the host compound, using
R
their Cp values, i.e. 733 DCp dT:
b
298
Virtual values.

E.A. Secco, R.A. Secco / Journal of Physics and Chemistry of Solids 63 82002) 1669±1675
1675
[17] A. Arell, M. Roiha, M. Aaltonen, Phys. Kondens. Materie 6
+1967) 140.
References
[18] S.P. Clark Jr, J. Chem. Phys. 31 +1959) 1526.
[19] C. Sandonnini, Gazz. Chim. Ital. 441 +1914) 323 also in
Phase Diagrams for Ceramists, The Amer. Ceramic Soc.
No. 1230.
[1] P.-N. Huang, E.A. Secco, J. Solid State Chem. 103 +1993)
314.
[2] E.A. Secco, A. Sharma, J. Phys. Chem. Solids 56 +1995) 251.
[3] E.A. Secco, J. Phys. Chem. B 101 +1997) 1641.
[4] E.A. Secco, R.A. Secco, Phys. Chem. Chem. Phys. 1 +1999)
5011.
[20] V.A. Isaenko, A.N. Kirgintsev, Zh. Neorg. Khim. 21 +1976)
2493.
[21] V.A. Isaenko, A.N. Kirgintsev, Russ. J. Inorg. Chem. +Engl.
Transl.) 21 +1976) 1370 also in Phase Diagrams for Ceramists,
The Amer. Ceramic Soc. No 7240.
[5] E.A. Secco, R.A. Secco, Phys. Chem. Chem. Phys. 2 +2000)
417.
[6] E.A. Secco, R.A. Secco, J. Phys. Chem. Solids 63 +2002) 433.
[7] C.W. Bunn, Chemical Crystallography, Oxford University
Press, London, 1958 p. 59.
[22] A. Schiraldi, E. Pezzati, G. Chiodelli, Z. Phys. Chem. +Wies-
baden) 113 +1978) 189 also in Phase Diagrams for Ceramists,
The Amer. Ceramic Soc. No. 7241.
[8] L.P. Cook, H.F. McMurdie +Eds.), Phase Diagrams for Cera-
mists Amer. Ceramic Soc., Inc, Westerville, OH, 1989 No.
7235 and references therein.
[23] J. Sangster, A.D. Pelton, J. Phys. Chem. Ref. Data 16 +3)
+1987) 509 also in Phase Diagrams for Ceramists, The
Amer. Ceramic Soc. No. 7767+B).
[9] J.C. Anderson, K.K. Leaver, R.D. Rawlings, J.M. Alexander,
Materials Science, Fourth ed., Chapman and Hall, New York,
1990 p. 132.
[24] J. Sangster, A.D. Pelton, J. Phys. Chem. Ref. Data 16 +3)
+1987) 509 also in Phase Diagrams for Ceramists, The
Amer. Ceramic Soc. Nos. 7235 and 7239.
[10] H. Weijma, J. Arends, Phys. Status Solidi 35 +1969) 205.
[11] J. Poyhonen, K. Mansikka, Phys. Kondens. Materie 3 +1965)
218.
[25] N.B. Chanh, B. DeLuzy de Pelissac, Bull. Soc. Fr. Mineral.
Cristallogr. 91 +1968) 13 also in Phase Diagrams for Cera-
mists, The Amer. Ceramic Soc. Nos. 7238 and 7239.
[26] J.D. Weyand, Diss. Abstr. Int. B 32 +1972) 7014 also in Phase
Diagrams for Ceramists, The Amer. Ceramic Soc. No 7801.
[27] J.E. Huheey, Inorganic Chemistry, Third ed., Harper and Row,
New York, 1983 p. 67.
[12] Selected Values of Chemical Thermodynamic Properties,
NBSCircular 500, National Bureau of Standards, Gaithers-
burg, 1952.
È
[13] I. Barin, O. Knacke, O. Kubaschewski, Thermochemical
Properties of Inorganic Substances, Springer, Berlin, 1977
p. 250.
[28] D. Cubicciotti, J. Chem. Phys. 31 +1959) 1646.
[29] D. Cubicciotti, J. Chem. Phys. 34 +1961) 2189.
[30] A.F. Kapustinskii, Q. Rev. Chem. Soc. 20 +1956) 203.
[31] D.S. McClure, in: N.B. Hannay +Ed.), Treatise on Solid State
Chemistry, 2, Plenum Press, New York, 1975, pp. 5±17.
[14] M. Natarajan, K.J. Rao, C.N.R. Rao, Trans. Faraday Soc. 66
+1970) 2497.
[15] A.K. Shukla, J.C. Ahluwahlia, C.N.R. Rao, J. Chem. Soc.,
Faraday Trans. 1 72 +1976) 1288.
[16] C.E. Kaylor, G.E. Walden, D.F. Smith, J. Phys. Chem. 64
+1970) 1960.