Calcium ruthenates: Determination of Gibbs energies of formation using electrochemical cells

Article abstract of DOI:10.1149/1.1557082

Metallic Ru has been found to coexist separately with CaO, RuO₂, and the interoxide phases, Ca₂RuO₄, Ca₃Ru₂O₇, and CaRuO₃, present along the pseudobinary system CaO-RuO₂. The standard Gibbs energies of formation (Δ_f(ox)G°) of the three calcium ruthenates from their component oxides have been measured in the temperature range 925-1350 K using solid-state cells with yttria-stabilized zirconia as the electrolyte and Ru + RuO₂ as the reference electrode. The standard Gibbs energies of formation (Δ_f(ox)G°) of the compounds can be represented by Ca₂RuO₄: Δ_f(ox)G°/J mol^-1 = -38,340 - 6.611 T (±120), Ca₃Ru₂O₇: Δ_f(ox)G°/J mol^-1 = 75,910 - 11.26 T (±180), and CaRuO₃: Δ_f(ox)G°/J mol^-1 = -35,480-3,844 T (±70). The data for Ca₂RuO₄ corresponds to the stoichiometric composition, which has an orthorhombic structure, space group Pbca, with short c axis ( S form). The structural features of the ternary oxides responsible for their mild entropy stabilization are discussed. A three-dimensional oxygen potential diagram for the system Ca-Ru-O is developed as a function of composition and temperature from the results obtained. Using the Neumann-Kopp rule to estimate the heat capacity of the ternary oxides relative to their constituent binary oxides, the standard enthalpies of formation of the three calcium ruthenates from the elements and their standard entropies at 298.15 K are evaluated.

Full text of DOI:10.1149/1.1557082

Journal of The Electrochemical Society, 150 ͑4͒ E227-E232 ͑2003͒
E227
0013-4651/2003/150͑4͒/E227/6/$7.00 © The Electrochemical Society, Inc.
Calcium Ruthenates: Determination of Gibbs Energies
of Formation Using Electrochemical Cells
K. Thomas Jacob,a,z Kay Thi Lwin,a and Yoshio Wasedab
aDepartment of Metallurgy, Indian Institute of Science, Bangalore 560012, India
bInstitute for Multidisciplinary Research on Advanced Materials, Tohoku University, Sendai 980-8577, Japan
Metallic Ru has been found to coexist separately with CaO, RuO2 , and the interoxide phases, Ca2RuO4 , Ca3Ru2O7 , and
CaRuO3 , present along the pseudobinary system CaO-RuO2 . The standard Gibbs energies of formation (⌬f͑ox)G°) of the three
calcium ruthenates from their component oxides have been measured in the temperature range 925-1350 K using solid-state cells
with yttria-stabilized zirconia as the electrolyte and Ru ϩ RuO2 as the reference electrode. The standard Gibbs energies of
formation (⌬f͑ox)G°) of the compounds can be represented by Ca2RuO4 : ⌬f͑ox)G°/J molϪ1 ϭ Ϫ38,340 Ϫ 6.611 T ͑Ϯ120͒,
Ca3Ru2O7 : ⌬f͑ox͒G°/J molϪ1 ϭ Ϫ75,910 Ϫ 11.26 T ͑Ϯ180͒, and CaRuO3 : ⌬f͑ox͒G°/J molϪ1 ϭ Ϫ35,480Ϫ3.844 T ͑Ϯ70͒.
The data for Ca2RuO4 corresponds to the stoichiometric composition, which has an orthorhombic structure, space group Pbca,
with short c axis ͑‘‘S’’ form͒. The structural features of the ternary oxides responsible for their mild entropy stabilization are
discussed. A three-dimensional oxygen potential diagram for the system Ca-Ru-O is developed as a function of composition and
temperature from the results obtained. Using the Neumann-Kopp rule to estimate the heat capacity of the ternary oxides relative
to their constituent binary oxides, the standard enthalpies of formation of the three calcium ruthenates from the elements and their
standard entropies at 298.15 K are evaluated.
© 2003 The Electrochemical Society. ͓DOI: 10.1149/1.1557082͔ All rights reserved.
Manuscript submitted July 22, 2002; revised manuscript received October 16, 2002. Available electronically February 28, 2003.
Crystal, magnetic, and electronic structures of the three calcium
ruthenates, CaRuO3 , Ca2RuO4 , and Ca3Ru2O7 , have been studied
extensively.1-17 The compounds ARuO3 (A ϭ Ca, Sr, and Ba͒ are
good electrical conductors with Ru4ϩ ion in low-spin t24geog
configuration.1 The compound CaRuO3 exhibits metallic behavior
with low resistivities of the order of 10Ϫ3 ⍀ cm at room
temperature.2 Recent studies show that CaRuO3 has the orthorhom-
bic perovskite structure, space group Pnma, with a ϭ 0.5519 nm,
b ϭ 0.5364 nm, and c ϭ 0.7665 nm.1 To maintain consistency with
extensive literature on transition metal oxides, the long axis has
been reassigned as the c direction. Earlier crystallographic data2-5
are consistent with this description. Although the compound
CaRuO3 had been characterized earlier by Longo et al.6 as being
shorter Ru-O in-plane distances.13 The structure changes from ortho-
rhombic to tetragonal at the insulator to near-metal transition at 357
K.12 The S phase is stoichiometric and thermodynamically stable in
air at temperatures above ϳ1623 K, while the L phase probably
contains excess oxygen and is stable in air at much lower
temperatures.13-15 Although the single S phase can be obtained eas-
ily by heating the component oxides in the temperature range from
1633 to 1653 K, the single L phase was not always easy to synthe-
size because of the frequent presence of the S phase. Annealing the
powder or pellets of the S phase in air at 673 K for 50 h reliably
made single-phase L.13-15
The structure of Ca3Ru2O7 has been reported to be isostructural
with both Sr3Ru2O7 and Ca3Ti2O7 , having a body-centered tetrag-
onal unit cell with the symmetry of I4/mmm with a ϭ 0.3841 nm
and c ϭ 1.9609 nm.16 Single-crystal Ca3Ru2O7 shows a metallic
antiferromagnetic phase intermediate between first-order metal to
nonmetal transition at TM ϭ 48 K and the antiferromagnetic order-
´
antiferromagnetic with a Neel temperature of TN ϭ 110 (Ϯ10) K,
Ru Mossbauer spectroscopy7,8 has shown conclusively that there is
99
¨
no magnetic ordering even at 4.2 K. The compound CaRuO3 is a
paramagnetic metal following the Curie-Wiess law at high tempera-
tures. It is used as a metallic barrier layer in making superconductor-
normal metal-superconductor ͑SNS͒ type Josephson junctions.9 The
ing ͑Neel͒ temperature TN ϭ 56 K.16 Guertin et al.17 observed very
´
unusual nonohmic dc current-voltage characteristics, including
17
Ͻ
negative differential resistivity ͑NDR͒ for T
TM .
Mallika and Sreedharan18 have reported high-temperature ther-
modynamic studies on CaRuO3 . Their measurements were based on
an incorrect assumption that CaRuO3 is the only ternary oxide in the
pseudobinary system CaO-RuO2 . No information is available in the
literature on enthalpy and Gibbs energy of formation of the com-
pounds Ca2RuO4 and Ca3Ru2O7 . In this study, the thermodynamic
data on all three calcium ruthenates were determined using solid-
state electrochemical cells. These data are useful for assessing the
compatibility of CaRuO3 with other materials in device applications.
conducting oxide CaRuO3 grows epitaxially on YBa2Cu3O7Ϫ␦
.
SNS-type high-TC step-edge junction dc superconducting quantum
interference devices ͑SQUIDs͒ with CaRuO3 as the normal metal
have been fabricated by Lee et al.10
Ͻ
Ca2RuO4 compound shows nonmetallic behavior for T
357
K.11,12 An antiferromagnetic transition has been identified at TN
ϭ 110 K.11 Nakatsuji et al.13 have reported that the two distinct
phases of Ca2RuO4 , denoted as ‘‘S’’ and ‘‘L’’ phases characterized
by shorter and longer c axis parameters, behave as Mott insulators.
A recent neutron powder diffraction pattern of S is indexed for
orthorhombic structure, consistent with space group Pbca with
a ϭ 0.54097 nm, b ϭ 0.54924 nm, and c ϭ 1.19613 nm.14 The
pattern of L is also indexed for orthorhombic structure, but with
space group P21 /c with a ϭ 0.53292 nm, b ϭ 0.53194 nm, and
c ϭ 1.23719 nm at 295 K.14 Both structures are derived from the
ideal K2NiF4 structure type by rotation of the RuO6 octahedra
around the long axis, combined with a tilt around an axis lying in the
RuO2 plane. The orientation of the tilt axis seems to distinguish the
two room-temperature symmetries; the L phase is characterized by
significantly smaller tilt angle, slightly higher rotation angle, and
Experimental
Materials.—Calcium oxide was prepared by the decomposition
of 99.99% pure CaCO3 at 1100 K under vacuum. Ruthenium pow-
der was produced from 99.99% RuO2 by reducing the fine oxide
powder in dry hydrogen at 1073 K for 3 h. Samples of the three
calcium ruthenates were prepared by the solid-state reaction be-
tween CaO and RuO2 . The three ternary oxides, CaRuO3 ,
Ca2RuO4 , and Ca3Ru2O7 , were prepared by heating pellets con-
taining CaO and RuO2 powders in the appropriate stoichiometric
ratio at 1300, 1640, and 1700 K, respectively, for 6 days in dry
oxygen with six intermediate grindings. The pellets were prepared
from an intimate mixture of the component oxides by compaction at
100 MPa using a steel die. The pellets were contained in a closed
z E-mail: katob@metalrg.iisc.ernet.in
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Journal of The Electrochemical Society, 150 ͑4͒ E227-E232 ͑2003͒
platinum crucible and supported on a sacrificial pellet of the same
composition. CaRuO3 forms first at lower temperatures and pro-
longed heating at higher temperatures are necessary to obtain
Ca2RuO4 and Ca3Ru2O7 . The Ca2RuO4 phase from synthesis at
1640 K was a mixture of S and L phases. The sample was annealed
at 773 K for 3 days in pure dry oxygen to convert phase S into phase
L. The pure L phase contains excess oxygen and can be represented
as Ca2RuO4.08 . The S phase is almost stoichiometric. The oxygen
content was determined from mass loss on hydrogen reduction.
The formation of the three ternary compounds was confirmed by
X-ray powder diffraction ͑XRPD͒. The XRPD pattern for Ca3Ru2O7
obtained in this study indicates that the structure is orthorhombic
rather than tetragonal as reported earlier.16 The lattice parameters of
Ca3Ru2O7 are a ϭ 0.5523 nm, b ϭ 0.5379 nm, and c ϭ 1.9568
nm. The lattice parameters for black-colored CaRuO3 obtained in
this study are a ϭ 0.5526 nm, b ϭ 0.5359 nm, and c ϭ 0.76619
nm, in fair agreement with data available in the literature.1-5 The
lattice parameters of S and L phases of Ca2RuO4ϩ␦ obtained in this
study are fully compatible with the crystal parameters given
by Braden et al.14 Yttria-stabilized zirconia solid-electrolyte tubes
used in this study were obtained from a commercial source.
Figure 1. Isothermal section of the phase diagram for the Ca-Ru-O system
at 1300 K.
Phase relations.—Each of the three ternary oxides was equili-
brated with Ru metal separately at 1300 K in evacuated quartz am-
poules. Intimate mixtures of the oxides and Ru powders in the molar
ratio 1:1 were pelletized. The pellets were contained in zirconia
crucibles, each placed and sealed individually in evacuated quartz
ampoules. The samples were equilibrated for 6 days. The phase-
composition of the samples was investigated after quenching to
room temperature by XRPD and scanning electron microscopy
͑SEM͒ equipped with an energy-dispersive system ͑EDS͒. The
phase composition of the samples after equilibration was found to be
the same as in the starting material. Each of the ternary oxides was
found to coexist with Ru metal. However, the starting L form of
Ca2RuO4 had changed to the S form after equilibration with Ru.
This suggests that both S and L forms are stable, the L form in
oxygen-rich atmospheres and the S form at low oxygen chemical
potentials. The S form is almost stoichiometric. Since the space
group P21 /c characterizing the L form is a subgroup of Pbca cor-
responding to the S form, there is probably a continuous solid solu-
tion between the two forms, at least at the higher temperatures. Pure
CaO and RuO2 were also found to coexist separately with metallic
Ru. A tentative phase diagram for the system Ca-Ru-O based on
these results is shown in Fig. 1.
reference electrode. In this arrangement, the cell emf and hence the
driving force for oxygen transport are significantly reduced. More-
over, the standard Gibbs energy of formation of calcium ruthenates
from their component binary oxides CaO and RuO2 can be directly
obtained from the emf by using Ru ϩ RuO2 as the reference elec-
trode. In all the cells, the partial pressures of oxygen at both elec-
trodes were quite appreciable, especially at the higher temperatures.
Therefore, the static-sealed design used by Charette and Flengas23
was found more appropriate than other designs that employ either
dynamic vacuum or inert gas flow over the electrodes.24,25 The cell
design used for high-temperature emf measurements is shown in
Fig. 2. It consisted of two distinct compartments, separated by an
impervious yttria-stabilized zirconia ͑YSZ͒ tube. The working elec-
trode was contained inside the zirconia tube. The electrodes were
sealed under vacuum in separate compartments. The equilibrium
oxygen partial pressure is established at each electrode by decom-
position of an oxide phase.
The working electrode consisted of an intimate mixture of CaO
ϩ Ca2RuO4 ϩ Ru in the molar ratio 1:1.5:1 in cell 1, a mixture of
Ca2RuO4 ϩ Ca3Ru2O7 ϩ Ru in the same ratio in cell 2, and a mix-
ture of Ca3Ru2O7 ϩ CaRuO3 ϩ Ru in the same ratio in cell 3. The
Measurement of Gibbs energies of formation of ternary ox-
ides.—The reversible electromotive force ͑emf͒ of the following
solid-state cells was measured as a function of temperature in the
range 925–1350 K:
1. Pt, CaO ϩ Ca2RuO4 ϩ Ru//͑Y2O3)ZrO2 //Ru ϩ RuO2 , Pt
2. Pt, Ca2RuO4 ϩ Ca3Ru2O7 ϩ Ru//͑Y2O3)ZrO2 //Ru ϩ RuO2 , Pt
3. Pt, Ca3Ru2O7 ϩ CaRuO3 ϩ Ru//͑Y2O3)ZrO2 //Ru ϩ RuO2 , Pt
The cells were designed based on phase relations depicted in Fig.
1. All the cells are written such that electrodes on the right are
positive. (Y2O3)ZrO2 is an oxygen ion conductor with ionic trans-
port number greater than 0.99 at the temperatures and oxygen partial
pressures encountered in this study. Two experiments were con-
ducted on each cell.
In earlier studies,19-22 an advanced version of the solid-state cell
incorporating a buffer electrode was used along with pure oxygen
gas as a reference electrode to prevent polarization of the three-
phase electrode. The polarization is caused by the electrochemical
flux of oxygen through the solid electrolyte from the electrode with
the higher oxygen potential to the electrode with the lower oxygen
potential. The oxygen transport occurs by coupled migration of oxy-
gen ions and trace concentration of electrons or holes. In this study,
the polarization effect was minimized by using Ru ϩ RuO2 as the
Figure 2. A schematic diagram of the apparatus for high-temperature emf
measurements.
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Journal of The Electrochemical Society, 150 ͑4͒ E227-E232 ͑2003͒
reference electrode consisted of an intimate mixture of Ru
E229
ϩ RuO2 in the molar ratio 1:1.5. In each case, an excess of the
component that decomposed to establish the oxygen pressure in the
closed system was taken. The phase mixture was rammed against
the closed end of a stabilized zirconia tube with a short Ru wire
embedded in the mixture. The Ru wire was spot-welded to a Pt lead,
ϳ10 mm above the electrode. An alumina sheath was used to insu-
late the metallic lead and to press the working electrode against the
flat end of the zirconia tube. The top of the zirconia tube was closed
with a tight-fitting bell-shaped Pyrex tube, which supported a tung-
sten electrode connection sealed into the glass. The joint between
the bell and the zirconia tube was sealed with De Khotinsky cement.
A spring placed between the bell and the alumina sheath applied
pressure on the working electrode. The assembled working electrode
half-cell was first evacuated using a sidearm tube shown in the dia-
gram, then heated to ϳ600 K, and finally the tube was flame sealed
under vacuum.
The cell was assembled inside a fused quartz enclosure. The
zirconia crucible containing the reference electrode was placed on
the zirconia beads. The working electrode assembly was then loaded
into the crucible. The annular space between the zirconia tube and
crucible was filled with the reference electrode mixture. The work-
ing electrode assembly was pressed down by means of a second
metal spring placed between the bell and the top Pyrex cover. The
top cover supported two tungsten-glass seals through which electri-
cal connections were made. All electrode connections were silver-
soldered. Finally, the top cover was cemented in place by melting
the De Khotinsky cement in the ring container shown in the dia-
gram. The cement was allowed to solidify while pressing the top
cover against the spring. Then the outer quartz enclosure was also
evacuated from a sidearm tube and flame sealed under vacuum. The
cell assembly, shown in Fig. 2, was essentially identical to that
developed by Charette and Flengas.23
Figure 3. The reversible emf of cells 1, 2, and 3 as a function of tempera-
ture.
The entire assembly shown in Fig. 2 was placed inside a vertical
resistance furnace with the electrodes located in the even-
temperature zone ͑Ϯ1 K͒. The oxygen partial pressure in the evacu-
ated and sealed enclosures around the working and reference elec-
trodes was established by the dissociation of the oxides. Because the
joints between Ru and Pt leads were located in the even-temperature
zone, there was no significant thermoelectric contribution to the emf
from this source. The cell assembly, where cement seals were lo-
cated, remained at room temperature during measurements. A Fara-
day cage made from thick stainless steel foil was placed between the
furnace and the cell assembly. The foil was grounded to minimize
induced emf on cell leads. The temperature of the furnace was con-
trolled to ͑Ϯ1 K͒. The temperature was measured by a Pt/Pt-13% Rh
thermocouple, checked against the melting point of gold. The cell
potentials were measured with a high-impedance digital voltmeter
with a sensitivity of ͑Ϯ0.1 mV͒. The potential readings were cor-
rected for small thermal emfs, measured separately using a symmet-
ric cell with identical electrodes. At the end of each experiment, the
electrodes were cooled to room temperature and examined by opti-
cal microscopy, SEM, and XRPD. Although small changes in the
relative concentration of the constituents were observed in each
case, the number and nature of the phases remained unaltered. The
change in relative concentration was consistent with the expected
decomposition of one of the oxides at high temperature to generate
the equilibrium oxygen pressures in sections of the apparatus.
at each electrode was displaced from equilibrium by an essentially
infinitesimal amount. Since the electrodes returned to the same po-
tential after such displacements in opposite directions, equilibrium
was experimentally verified. The emfs of all the cells were also
found reproducible on repeated temperature cycling. Within experi-
mental uncertainty, the emfs show a slight linear increase with tem-
perature. The linear least-squares regression analysis of the emf of
cell 1 gives
EI ϭ 99.33 ϩ 0.01713 T Ϯ0.31͒ mV
͓1͔
͑
The uncertainty limit corresponds to twice the standard error esti-
mate. The emf of cell 1 is related to the standard Gibbs energy
change for the overall cell reaction
2CaO ϩ RuO2 → Ca2RuO4 S form͒
͓2͔
͑
⌬
G° ϭ ⌬f͑ox)G° Ca RuO ͒ ϭ Ϫ4FE ϭ Ϫ38,340
͑
2 4 I
r͑2͒
Ϫ 6.611 T Ϯ120͒ J molϪ1
͓3͔
͑
where F is the Faraday constant and ⌬r(2)G° represents the standard
Gibbs energy change for Reaction 2. The temperature-independent
term on the right side of Eq. 3 is the enthalpy of formation of
Ca2RuO4 ͑S form͒ from component oxides at an average tempera-
ture of ϳ1140 K. The temperature-dependent term is related to the
corresponding entropy of formation. The oxygen chemical potential
over the three-phase electrode of cell 1 is established by the reaction
Results and Discussion
High-temperature thermodynamic properties of ternary ox-
ides.—The reversible emfs of cells 1, 2, and 3 in the temperature
range 925–1350 K are plotted as a function of temperature in Fig. 3.
Reversibility of the emf was established by microcoulometric titra-
tion in both directions. A small current ͑ϳ50 ␮A͒ was passed
through the cell using an external potential source for ϳ3 min, and
the open-circuit emf was subsequently monitored as a function of
time. The emf was found to return to the steady value before each
perturbation. During the titration, the chemical potential of oxygen
2CaO ϩ Ru ϩ O2 → Ca2RuO4
͓4͔
The oxygen potential can be computed using the emf of cell 1 and
refined values for the Gibbs energy of formation of RuO2 reported
recently26
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E230
Journal of The Electrochemical Society, 150 ͑4͒ E227-E232 ͑2003͒
⌬␮ CaO ϩ Ca RuO ϩ Ru͒
͑
O
2
4
2
ϭ Ϫ363,060 ϩ 347.60 T
Ϫ 23.49 T ln T Ϯ150͒ J molϪ1
͓5͔
͑
The least-square regression analysis of the emf of cell 2 gives
E2 ϭ 95.38 ϩ 0.00695 T Ϯ0.12͒ mV ͓6͔
͑
The emf of cell 2 is related to the standard Gibbs energy change for
the net cell reaction
3Ca2RuO4 ϩ RuO2 → 2Ca3Ru2O7
͓7͔
⌬
G° ϭ Ϫ4FE2 ϭ Ϫ36,810 Ϫ 2.682 T Ϯ50͒ J molϪ1
͑
r͑7͒
͓8͔
By combining Reactions 2 and 7, one obtains the reaction represent-
ing the formation of Ca3Ru2O7 from its component oxides
3CaO ϩ 2RuO2 → Ca3Ru2O7
͓9͔
⌬
G° Ca Ru O ͒ ϭ Ϫ75,910 Ϫ 11.26 T Ϯ180͒ J molϪ1
͑
͑
f͑ox)
3
2
7
͓10͔
The oxygen chemical potential over the three-phase electrode of cell
2 is established by the reaction
3Ca2RuO4 ϩ Ru ϩ O2 → 2Ca3Ru2O7
͓11͔
The oxygen potential can be computed using the emf of cell 2 and
26
the Gibbs energy of formation of RuO2
Figure 4. Comparison of the Gibbs energy of formation of CaRuO3 from
their component binary oxides obtained in this study with data reported in
the literature.18
⌬␮ Ca RuO ϩ Ca Ru O ϩ Ru͒ ϭ Ϫ361,530 ϩ 351.53 T
͑
O
2
4
3
2
7
2
Ϫ 23.49 T ln T Ϯ100͒ J molϪ1
͓12͔
͑
ϭ Ϫ35.48 kJ molϪ1͒, whereas the results of Mallika and
The measured emf of cell 3 can be expressed by the equation
E3 ϭ 79.09 ϩ 0.000706 T Ϯ0.07͒ mV ͓13͔
Sreedharan18 suggest that the reaction is endothermic (⌬f͑ox)
H
͑
ϭ 14.4 kJ molϪ1͒. According to the data of Mallika and
Sreedharan,18 the compound CaRuO3 is mainly entropy stabilized.
From a theoretical point of view, it is difficult to understand the
large positive entropy of formation suggested by Mallika and
Sreedharan.18 This discrepancy is caused by the unstable nature of
their working electrode. They mixed CaO, CaRuO3 , and Ru in the
The emf of cell 3 is related to the standard Gibbs energy change for
the cell reaction
Ca3Ru2O7 ϩ RuO2 → 3CaRuO3
͓14͔
⌬
G° ϭ Ϫ4FE3 ϭ Ϫ30,530 Ϫ 0.273 T Ϯ30͒ J molϪ1
͑
r͑14͒
mass ratio 3:4:2. This corresponds to XRuO Ϸ 0.36 in the pseudo-
2
͓15͔
binary system CaO-RuO2 , and at equilibrium a mixture of Ca2RuO4
and Ca3Ru2O7 should be stable. Hence, during their high-
temperature electrochemical measurements, the starting compounds
CaO and CaRuO3 would have gradually reacted to form a mixture
of Ca2RuO4 and Ca3Ru2O7 , causing spurious effects.
The standard Gibbs energy of formation of CaRuO3 from its com-
ponent oxides can be computed by combining the standard Gibbs
energy changes associated with Eq. 9 and 14
CaO ϩ RuO2 → CaRuO3
͓16͔
The oxygen chemical potential over the three-phase electrode of
cell 3 is established by the reaction
⌬
G° CaRuO ͒ ϭ Ϫ35,480 Ϫ 3.844 T Ϯ70͒ J molϪ1
͑
͑
f͑ox)
3
͓17͔
Ca3Ru2O7 ϩ Ru ϩ O2 → 3CaRuO3
͓19͔
Assuming that CaRuO3 is the only ternary oxide present in the
system Ca-Ru-O, Mallika and Sreedharan18 have evaluated
The oxygen potential can be computed using the emf of cell 3 and
refined values for the Gibbs energy of formation of RuO2
26
⌬
f͑ox)G°(CaRuO3) from its component oxides as
⌬␮ Ca Ru O ϩ CaRuO ϩ Ru͒ ϭ Ϫ355,250 ϩ 353.94 T
͑
O
3
2
7
3
2
⌬
G° CaRuO ͒ ϭ 14,396 Ϫ 44.221 T Ϯ1905͒ J molϪ1
͑
͑
f͑ox)
3
Ϫ 23.49 T ln T Ϯ90͒ J molϪ1
͓20͔
͓18͔
͑
They used a solid oxide cell with CaO ϩ CaRuO3 ϩ Ru as the
working electrode and air at the reference. Three ternary oxides are
found to be stable in this study. The phases CaO and CaRuO3 cannot
coexist with Ru metal under equilibrium conditions. Figure 4 com-
pares ⌬f͑ox)G° (CaRuO3) obtained in this study with the data of
Mallika and Sreedharan.18 The reported uncertainty limits are also
shown in the figure. The results of this study indicate that the for-
The enthalpy and Gibbs energy of mixing at 1100 K for the
system CaO-RuO2 is shown in Fig. 5 as a function of composition.
The value of the Gibbs energy of mixing for each compound is
obtained by dividing its standard Gibbs energy of formation from
binary oxides by the number of molecules of the binary oxides
present in the compound. The minimum in the Gibbs energy of
mixing occurs at the 1:1 composition corresponding to the com-
pound CaRuO3 . The enthalpy of mixing also has a similar shape.
mation of CaRuO3 from component oxides is exothermic (⌬f͑ox)
H
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Journal of The Electrochemical Society, 150 ͑4͒ E227-E232 ͑2003͒
E231
Table I. Thermodynamic properties of Ca2RuO4 , Ca3Ru2O7 ,
and CaRuO3 at 298.15 K.
⌬
f͑ox)Hؠ298.15 ⌬fH2ؠ 98.15
(kJ molϪ1 (kJ molϪ1
⌬
f͑ox)Sؠ298.15
Sؠ298.15
(J molϪ1 KϪ1
)
Compound
Ca2RuO4
Ca3Ru2O7
CaRuO3
)
)
(J molϪ1 KϪ1
)
Ϫ38.34
͑Ϯ0.25͒
Ϫ75.91
͑Ϯ0.37͒
Ϫ35.48
͑Ϯ0.13͒
Ϫ1622.034
͑Ϯ1.78͒
Ϫ2608.215
͑Ϯ2.67͒
Ϫ984.090
͑Ϯ0.89͒
6.611
͑Ϯ0.22͒
11.260
͑Ϯ0.50͒
3.844
128.91
͑Ϯ0.34͒
217.78
͑Ϯ0.64͒
88.07
͑Ϯ0.17͒
͑Ϯ0.22͒
in small Jahn-Teller distortion. The flattening of the RuO6 octahedra
along the c axis of S-Ca2RuO4 is indicative of the Jahn-Teller effect.
The three calcium ruthenates can be considered as members of
the Ruddelsdon-Popper series, Canϩ1RunO3nϩ1 (n ϭ 1, 2, and ϱ͒.
The structure is composed of planes of corner-sharing RuO6 octa-
hedra separated by CaO rock-salt layers. The number of RuO6
planes between two adjacent rock-salt layers is determined by the
number n. Half a unit cell offsets the RuO6 planes on opposite sides
of a rock-salt layer relative to one another. Tilting and rotation of the
RuO6 octahedra away from the idealized structure results in ortho-
rhombic distortions. The amount of distortion within the planes ap-
´
preciably decreases with n. It is interesting to note that the Neel
temperature of the compounds varies inversely with the number of
planes n. Reduction in RuO6 planar distortion probably increases the
degree of overlap Ru-4d and O-2p orbitals, resulting in stronger
magnetic interactions between neighboring ions.
The small positive entropy of formation of calcium ruthenates
may be related to ͑a͒ excess entropy associated with rotation and
tilting of RuO6 octahedra, and/or ͑b͒ randomization of the direction
of the small Jahn-Teller distortion associated with Ru4ϩ ion at high
temperatures. The volume change in forming the ternary oxide from
their component binary oxides at 298 K calculated from unit cell
parameters is mildly negative for CaRuO3 (⌬V ϭ Ϫ1.53 cm3
molϪ1͒ and Ca3Ru2O7 (⌬V ϭ Ϫ0.61 cm3 molϪ1͒ and slightly posi-
tive for Ca2RuO4 (⌬V ϭ 1.064 cm3 molϪ1 for the S form and
⌬V ϭ 0.36 cm3 molϪ1 for the L form͒.
Figure 5. The Gibbs energy and enthalpy of mixing as a function of com-
position for the pseudobinary system CaO-RuO2 .
There is little entropy stabilization of all the three interoxide com-
pounds. However, the shape of the curves indicates that all the com-
pounds are stable at low temperatures.
To understand the origin of the small positive entropy of forma-
tion of calcium ruthenates from component oxides, it is useful to
review the structural features associated with these compounds.
CaRuO3 has GdFeO3-type orthorhombic perovskite structure con-
sisting of a framework of corner-sharing RuO6 octahedra linked to
zig-zag chains. In the ideal perovskite structure ABO3 , the BO6
octahedra are set at corners of a cubic unit cell with their axis ori-
ented along the cell edges. In the center, there is space for A ion
which will fit perfectly with 12-fold coordination if dAO
The strong misfit between Ca2ϩ and Ru4ϩ ionic sizes, which
drives the structural deformation in Ca2RuO4 , favors the insertion
of interstitial oxygen. The additional oxygen relaxes the pressure
caused by the misfit, because it oversaturates the Ca coordination,
and the charge transfer toward the RuO2 planes results in smaller
Ru-O distances. This is reflected by the volume change associated
with the formation of the two forms of Ca2RuO4 .
ͱ
ϭ
2dBO . When A is too small to satisfy this criterion, BO6 octa-
hedra are rotated and tilted to fill the extra space around the A ion.
These rotations cause the unit cell to be smaller and distorted from
the ideal cubic cell. The A-O bond lengths split into two groups of
eight short and four long. The distortion is discussed in terms of the
Room-temperature thermodynamic properties of ternary ox-
ides.—By invoking the Neumann-Kopp rule to estimate the heat
capacity of the ternary oxides relative to their constituent binary
oxides, standard enthalpies and entropies of formation of the three
calcium ruthenates from their component binary oxides at 298.15 K
ͱ
Goldschmidt tolerance factor, t ϭ dAO /( 2dBO). The factor for
can be estimated from the measured high-temperature data. Using
CaRuO3 is 0.88. There are no significant distortions in the RuO6
octahedra. The rigid character of RuO6 octahedra is related to the
strong overlap between Ru-4d and O-2p orbitals and the pro-
nounced covalent character of the Ru-O bond. The density of states
͑DOS͒ at the Fermi level (EF) of CaRuO3 consists primarily of
Ru-4d states with a small contribution from O-2p states. The con-
tribution of Ca to the DOS at EF is negligibly small.1
26,28
auxiliary thermodynamic data for CaO27 and RuO2
from the
literature, the standard enthalpy of formation of the ternary com-
pounds from elements and their standard entropies at 298.15 K can
be assessed. The thermodynamic data for CaO (Sؠ298.15/J molϪ1
KϪ1 ϭ 38.0744; ⌬fH2ؠ 98.15/kJ mol Ϫ 1 ϭ Ϫ635.089)27 and RuO2
(Sؠ298.15/J
molϪ1
K Ϫ 1 ϭ 46.15;28
⌬fHؠ298.15/kJ
molϪ1
ϭ Ϫ313.52)26 are used in the evaluation. The derived data for the
ternary oxides are summarized in Table I. Calorimetric measure-
ments on low and high-temperature heat capacities and enthalpies of
formation can provide independent confirmation of the values given
in the table.
Because of the larger radial extent of the 4d shell compared to
the 3d shell, it should be more strongly affected by the crystal-field
interaction of surrounding ions. This in turn should cause the
t
2g-eg splitting to be quite large, so that the filling of the lower-lying
triplet t2g should precede the filling of the much more highly excited
doublet eg level. Thus, low spin state (S ϭ 1) is expected for the
Ru4ϩ(4d4) ion. The asymmetric filling of the t2g orbitals can result
Three-dimensional oxygen potential diagram.—The oxygen po-
tential diagram for the Ca-Ru-O system as a function of composition
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E232
Journal of The Electrochemical Society, 150 ͑4͒ E227-E232 ͑2003͒
on the phase relations, three solid-state cells were designed to mea-
sure the chemical potential of oxygen corresponding to three-phase
fields in the ternary, each involving three condensed phases. The
measurements were conducted from 925 to 1350 K with Ru/RuO2 as
the reference electrode. The Gibbs energy changes corresponding to
the following reactions were directly measured
2CaO ϩ RuO2 → Ca2RuO4
⌬rG° ϭ Ϫ38,340 Ϫ 6.611 T Ϯ120͒ J molϪ1
͑
3Ca2RuO4 ϩ RuO2 → 2Ca3Ru2O7
⌬rG° ϭ Ϫ36,810 Ϫ 2.682 T Ϯ50͒ J molϪ1
͑
Ca3Ru2O7 ϩ RuO2 → 3CaRuO3
⌬rG° ϭ Ϫ30,530 Ϫ 0.273 T Ϯ30͒ J molϪ1
͑
Gibbs energies, enthalpies, and entropies of formation of three cal-
cium ruthenates from their component binary oxides were deduced.
The standard enthalpies of formation of these oxides from elements
and their standard entropies at 298.15 K were also evaluated for the
first time. Correlations between electronic and crystallographic
structure and thermodynamic properties of the ternary oxides are
outlined. The chemical potential diagram for the Ca-Ru-O system is
developed as a function of composition and temperature based on
the thermodynamic data obtained in this study and auxiliary infor-
mation on RuO2 from the literature.
Figure 6. Three-dimensional representation of oxygen potential diagram for
the Ca-Ru-O system as a function of composition and temperature, where P°
is the standard pressure ͑0.1 MPa͒.
Acknowledgment
and temperature, computed from the results of this study, is shown
One of the authors ͑K.T.L.͒ is grateful to the Indian Council for
Cultural Relations ͑ICCR͒ for financial assistance.
in Fig. 6. The composition variable is cationic fraction, ␩Ru /(␩
Ca
ϩ ␩Ru), where ␩i represents moles of component i. Since oxygen is
not included in the composition parameter, information on oxygen
stoichiometry cannot be displayed on the diagram. Nevertheless, the
diagram provides useful information on the oxygen potential range
for the stability of various phases. The diagram is complementary to
the conventional Gibbs triangle representation of phase relations in
ternary systems, where the composition of each phase can be unam-
biguously displayed. All the topological rules of construction for
conventional temperature-composition phase diagrams are appli-
cable to an isothermal section of the oxygen potential diagram
shown in Fig. 6.
When three condensed phases coexist with a gas phase at equi-
librium in a ternary system such as Ca-Ru-O, the system is mono-
variant; the logarithm of the oxygen partial pressure varies linearly
with the reciprocal of absolute temperature. At constant temperature,
the three condensed phases coexist only at a unique partial pressure
of oxygen. Therefore, horizontal lines on isothermal sections of the
diagram represent three-phase equilibria. Each shaded plane repre-
sents the variation of oxygen partial pressure for a three-phase equi-
librium in the temperature range 925-1350 K. Each vertical line
represents the composition of a compound expressed as cationic
fraction of Ru. On reducing the oxygen partial pressure, RuO2 dis-
sociates first followed by the ternary oxides in order of decreasing
cationic fraction of Ru. The phase equilibria at very low oxygen
potentials between Ca-Ru alloys and CaO are not shown in the
figure, since accurate data on Gibbs energies for the binary system
Ca-Ru required for the calculation are not available. The oxygen
potentials corresponding to Ca-Ru alloy/CaO equilibria are too low
to be measured directly by any technique currently available.24 Iso-
baric sections of the diagram in Fig. 6 give information on phase
relations as a function of temperature.
Tohoku University assisted in meeting the publication costs of this ar-
ticle.
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Conclusions
A partial phase diagram of the system Ca-Ru-O has been delin-
eated by equilibration of metallic Ru with the three ternary oxides,
Ca2RuO4 , Ca3Ru2O7 , and CaRuO3 , separately at 1300 K. Based
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