Phase Equilibria in Ca-Co-O System D. Sedmidubsk´ y a,∗ , V. Jakeˇs a , O. Jankovsk´ y a , J. Leitner a , Z. Sofer a , J. Hejtm´anek b , a Institute b Institute
of Chemical Technology, Technick´ a 5, 166 28 Prague, Czech Republic of Physics of ASCR, v.v.i, Na Slovance 2, 182 21 Prague, Czech Republic
Abstract The phase equilibria in the ternary Ca-Co-O system have been studied by thermal analysis (DSC/DTA, TGA), Xray diffraction of quenched samples and low temperature heat capacity measurements. These experimental data were combined with the data available in literature and used to assess the thermodynamic quantities of the involved phases. A particular focus was put on the misfit cobaltite Ca3 Co3.93 O9.36 as a potential candidate for high temperature thermoelectric conversion whose observed nonstoichiometry was described in terms of compound energy formalism. The phase diagram was mapped using FactSage program. Key words: Ca-Co-O system, misfit cobaltites, thermodynamic data, phase diagrams
1. Introduction Due to the lack of fossil fuels and risks connected with nuclear energy recently manifested by the accident in the Japanese nuclear power plant, energy recovery is becoming extremely important. Electrical energy consumption alongside with the rate of heat loss is increasing every year. Thermoelectric energy recovery from waste heat is recognized as a promising technology suitable for direct electric power generation. This is possible thanks to the Seebeck effect, where electric power is generated as a consequence of a thermal gradient applied on a conductor. The misfit layer cobaltites recently attracted a considerable attention in the search for new thermoelectric materials which can be applied in thermoelectric conversion devices operated at elevated temperatures. Their structures are based on the [CoO2 ] hexagonal layers formed by the edge sharing CoO6 octahedra, interleaved between rock-salt type slabs. Since at least one lattice parameter is ∗ Corresponding author, tel: +420 220 444 122 Email address:
[email protected] (D. Sedmidubsk´ y ). Preprint submitted to Elsevier
different in these two types of structural units, the resulting stoichiometric coefficients are nonintegers even though the structures are perfectly ordered. The typical representatives Ca3 Co3.93 O9.36 and Bi2 Sr2 Co1.82 O7.64 can thus be expressed in terms of crystal chemical formulas [Ca2 CoO3 ][CoO2 ]1.62 and [Bi2 Sr2 O3 ][CoO2 ]1.82 , respectively. All misfit cobaltites exhibit a positive Seebeck coefficient exceedeng 100 µV/K and can thus constitute one pole of thermoelectric couples which are series-connected to form a thermoelectric battery. Nowadays these materials could be used in car industry. The exhaust pipe near car catalyst is warmed up to 700◦ C and this extremely large thermal gradient dramatically increases the amount of electric power which could be recovered and reduce already very large loads of the current auto-batteries. In far future these materials could be used in space industry as an energy source for missions beyond the solar system. The primary aim in the development of new thermoelectric devices is to fabricate materials with a figure of merit approaching unity. To achieve this goal the material should simultaneously exhibit high 13 January 2012
thermopower, low electrical resistivity and low thermal conductivity. The Seebeck coefficient is largely predetermined by the electronic structure and character of charge carriers and can be modified, for instance, by tuning Fermi level through chemical substitutions (forming solid solutions). That is the reason why a number of studies has been devoted to homovalent and heterovalent substitutions or chemical dopant additions. The electrical resistivity and thermal conductivity, on the other hand, are much more influenced by material microstructure. Nevertheless for high temperature thermoelectric conversion the stability of the thermoelectric material with respect to partial or complete decomposition as well as to corrosion represents an equally important issue. It follows that the knowledge of the respective phase diagram describing the pertinent phase stoichiometry and stability is crucial for proper optimization and tailoring of a given thermoelectic material, as well as for its safe operation. In this study we focus on the assessment of the CaCo-O phase diagram based on both our and literature experimental data. Since the system under study should be considered as closed for Ca and Co while open for oxygen which is exchanged with the surrounding atmosphere and whose content is determined and controlled by the oxygen activity in surroundings, the phase diagram is represented by means of three experimentally adjustable predictors - temperature, cation composition and oxygen activity (partial pressure).
ter in Bragg-Brentano parafocusing geometry using CuKα radiation. The JANA program [1] for Rietveld refinement of incommensurate structures was employed to determine the lattice parameters including the misfit ratio, atomic positions and site occupancies of the Ca3 Co3.93±x O9+δ structure using the structure model as proposed and confirmed by Lambert at al.[2]. The low temperature heat capacity of the misfit cobaltite was measured on the Physical Properies Measurement System (PPMS ) using a two relaxation time method on a ceramic sample with a mass of 30 mg. An adenda associated with the sample holder and the Apiezon grease applied to attach the sample was determined over the entire temperature range (2–300 K) prior to the respective sample run. The differential scanning calorimetry (DSC) measurements were performed on Netzsch DSC 404 C Pegasus calorimeter at a heating rate 10 K/min in the dynamic oxygen and purified air atmosphere within the temperature range 20-1130◦ C. The measured temperature was calibrated on the melting points of pure metal standards and the apparatus sensitivity was obtained as a function of temperature by measuring the sapphire standard (NIST, ref. N◦ 720) under the same experimental conditions. The oxygen stoichiometry of the misfit cobaltite was studied by thermogravimetric analysis (TGA) performed on Setaram STA instrument, model Setsys Evolution with a heating rate 10 K/min in air atmosphere. The calculations of phase equilibria and the construction of phase diagrams were carried out by means of the FactSage thermochemical software and databases [3], version 6.1.
2. Experiment and Calculation Samples with different Ca/Co stoichiometries used for DSC measurements were prepared by standard ceramic route starting from CaCO3 and Co2 O3 powders mixed in appropriate stoichiometric rates (7/3, 3/2, 1/1, 1/2, 1/4, and five compositions in a close vicinity of the ideal stoichiometry 3/3.93 of the misfit phase, namely 3/3.7, 3/3.8, 3/3.9, 3/3.95, 3/4 and 3/4.1), homogenized and calcined in air atmosphere at 850◦ C and 900◦ C for 24 hours at each temperature. The calcined powders were pressed into pellets and sintered at 940◦ C in O2 atmosphere for 100 hours. The phase composition of the multiphase samples and the structure parameters of misfit structure obtained in a form of single phase samples were evaluated from powder XRD patterns recorded within the range 2θ = 2 - 80◦ on X’Pert PRO diffractome-
3. Thermodynamic Models The thermodynamic models of stoichiometric phases (Ca3 Co2 O6 , Co3 O4 and Ca3 Co4 O9.2 considered as a stoichiometric misfit phase in the first approximation) and end-members of solution phases (CaO(s,l), CoO(s,l), Co(l) and Ca3 Co3.9 O9.3 ) are based on standard enthalpies of formation and entropies referred to ambient temperature T = 298 K, and on the temperature dependence of heat capacity in a polynomial form, which are stored in FactSage Compound database format and serve as source data for calculation of Gibbs free energies. In the case of high temperature polymorphs the enthalpies and temperatures of phase transitions 2
from the low temperature forms are used in place of enthalpies of formation and entropies. The Gibbs energy of all solution phases is expressed in a standard way, ∑ Gϕ = (yi G◦i ) − T ∆S id + ∆Gex , (1)
lower (∼3) in [Ca2 CoO3 ] slabs and higher (∼3.5) in [CoO2 ] layers. Furthermore, the variable oxygen sub-stoichiometry in [Ca2 CoO3−δ ] is not assumed to fall below δ = 0.8 and it can be compensated either by Ca2+ substitution for Co3+ in the rocksalt blocks or by reducing the Co states in [CoO2 ] located at Fermi level. Hence, the general crystal chemical formula describing the misfit cobaltite solid solution reads
i
as a sum of Gibs energies of the involved species G◦i , the ideal mixing entropy term and the excess Gibbs energy considered in the Redlich-Kister (RK) polynomial form ∑ ∆Gex = yM yN (2) Lj(M,N ) (yM − yN )j ,
[Ca2+ ,Co2+ ]10 [Co3+ ,Ca2+ ]5 [Co3+ ,Co4+ ]8 [O,Va]4 O27 where the 27 fully occupied oxygen positions belong to both blocks (11 and 16, respectively) while the four partly vacant oxygen sites inhere in the [Ca2 CoO3−δ ] block. We apply the compound energy formalism (CEF) in order to transform the outlined crystal chemical model into a thermodynamic description. As a result we obtain 16 end-members which are listed in Table 1 as sets of species occupying the respective sublattices along with the particular terms forming the Gibbs energy of a given end-member. These involve the Gibbs energy of the ideal composition Ca10 Co13 O31 = 10 3 × Ca3 Co3.9 O9.3 , the ideal mixing term −RT [5/8ln(5/8) + 3/8ln(3/8)], Gibbs energies of O2 (g), CaO(s) and CoO(s), as well as the enthalpies of the pertinent point defect formation ∆HC4 (Co3+ →Co4+ ), ∆HC3 (Co3+ →Ca2+ ), ∆HC2 (Ca2+ →Co2+ ) and ∆HO (Va→O2− ). Only the ideal mixing on the respective sublattices without any excess terms is considered. The Gibbs energy of the misfit phase is thus obtained as a linear combination of Gibbs energies of the respective end-members plus the ideal mixing entropy terms, formally equivalent to Eq. 1 (with ∆Gex = 0), where the constitution coefficients yi must satisfy, for a given set of predictors (xCo , pO2 , T ), the conditions of charge and mass balance and Gibbs energy minimum.
j
for the liquid phase and the rock-salt type solid solution Ca1−x Cox O with CaO(l,s), CoO(l,s) and Co(l) representing the respective end-members. The model for Ca1−x Cox O solid solution can be in fact considered as two-sublattice model with a Ca2+ Co2+ mixing on cation sublattice, while the liquid is described as a mixture of phenomenological components CaO-CoO-Co or, as seen from the model parameters given in Table 3, rather as a pseudobinary mixture CaO-CoOx with CoOx covering the whole composition range from liquid Co-metal to CoO-oxide melt. As shown hereinafter (Section 5), the misfit phase reveals a variable Ca/Co ratio and an oxygen substoichiometry due to formation of oxygen vacancies. Since the misfit ratio is preserved at nearly constant value q ∼ 1.618 over the whole homogeneity range, the variable composition of stable components should be due to formation of substitutional defects Ca→Co and Co→Ca on the respective sides from the ideal stoichiometry. Regarding the relative structural rigidity of the [CoO2 ] block all considered defects are supposed to be merely confined to the [Ca2 CoO3 ] block. Moreover, the invariable misfit ratio makes it possible to approximate the incommensurate stoichiometric coefficient by a commensurate one being selected as close as possible to the actual value. In our case the misfit parameter exactly corresponds to the ”Golden ratio ”and can be thus approximated by a fraction of two successive members of the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, ...}. In this study we consider the ratio 8/5 = 1.6 which results in the crystal chemical formula [Ca2 CoO3 ]5 [CoO2 ]8 and the net formula Ca3 Co3.9 O9.3 (differing by 0.03 in Co stoichiometry from the real value). The ideal stoichiometry of the misfit cobaltite corresponds to an average valency Co3.23 , however, according to bond valence sum analysis it is
4. Thermodynamic Data SGTE values from SGPS (pure substances) database comprised in FactSage 6.1 [3], were used for binary oxides in solid and liquid state, CaO(s,l), CoO(s,l), as well as for Co(l). Our description of cobalt spinel Co3 O4 stems from the assessment by ◦ Jung et al. [4]. We adopt the values of ∆f H298 ◦ and S298 as they are reported, however, we rectify the apparently erroneous values of heat capacity in three different temperature intervals. The corrected data used in the present study are given in Table 2. 3
Table 1 The end-members in the CEF model of misfit cobaltite. Net charge Z, species on the respective sublattices originally occupied by Ca2+ (RSCa ), Co3+ (RSCo ), O2− (RSO ), all in rock-salt block, and Co3+/4+ (HCo ) in [CoO2 ] block, followed by coefficients of the respective terms occurring in the Gibbs energy formula for a given end-member.
1
Z
RSCa
RSCo
HCo
RSO
G◦CC
mix
-3
Ca2+
Co3+
Co3+
O2−
1
-8
Co3+
Co4+
O2−
G◦O
2
G◦CaO
G◦CoO
∆HO
∆HC4
∆HC3
∆HC2
0
0
0
0
-3
0
0
2
5
Ca2+
1
-8
0
0
0
0
5
0
0
3
-3
Co2+
Co3+
Co3+
O2−
1
-8
0
-10
10
0
-3
0
10
4
5
Co2+
Co3+
Co3+
Va
1
-8
-2
-10
10
-4
-3
0
10
5
0
Ca2+
Ca2+
Co3+
Va
1
-8
-2
5
-5
-4
-3
5
0
6
5
Ca2+
Co3+
Co3+
Va
1
-8
-2
0
0
-4
-3
0
0
5
Co2+
Co3+
Co4+
O2−
1
-8
0
-10
10
0
5
0
10
13
Co2+
Co3+
Co4+
Va
1
-8
-2
-10
10
-4
5
0
10
Ca2+
Co4+
7 8 9
8
Ca2+
Va
1
-8
-2
5
-5
-4
5
5
0
10
13
Ca2+
Co3+
Co4+
Va
1
-8
-2
0
0
-4
5
0
0
11
-8
Co2+
Ca2+
Co3+
O2−
1
-8
0
-5
5
0
-3
5
10
0
Co2+
Ca2+
Co4+
O2−
1
-8
0
-5
5
0
5
5
10
Ca2+
Co3+
12 13
0
Co2+
Va
1
-8
-2
-5
5
-4
-3
5
10
14
8
Co2+
Ca2+
Co4+
Va
1
-8
-2
-5
5
-4
5
5
10
15
-8
Ca2+
Ca2+
Co3+
O2−
1
-8
0
5
-5
0
-3
5
0
0
Ca2+
Ca2+
Co4+
O2−
1
-8
0
5
-5
0
5
5
0
16
The entropy of the stoichiometric compound ◦ , was derived from the low temperCa3 Co2 O6 , S298 ature heat capacity data reported by Hardy et al. [5] and the temperature dependency of the heat capacity above room temperature was approximated by a modified Neumann-Kopp rule Cp = 3Cp (CaO) + Cp (Co3 O4 ) − Cp (CoO)
reveals two distinct peaks. While the sharp effect at 400 K has been reported to be associated with an ordering (cooperative displacement) of oxygen atoms in the [Ca2 CoO3−δ ] block [7], the origin of the second broad peak centered at ∼830 K is not yet completely clear. However, we recently proposed a possible scenario of spin state crossover of Co3+ in rock-salt blocks from intemediate spin (S=1) to high spin state (S=2) [8]. Indeed, if we compare the associated entropy change evaluated by integrating the corresponding ∆Cp /T , we get a remarkably nice agreement of the obtained value ∆S = 6.7 J·mol−1 ·K−1 with the theoretical value ∆S = 1.5Rln(5/3) = 6.37 J·mol−1 ·K−1 . In any case, since both effects occur well below our interval of interest, we simply consider them as phase transitions between different polymorphs of a given compound whose enthalpies and entropies are determined from transition temperatures and enthalpies corresponding, respectively, to peak maxima and areas. The enthalpy of formation at 298 K is evaluated from the temperature of phase decomposition into Ca3 Co2 O6 and rock-salt solution Ca1−x Cox O identified by DSC in air and oxygen atmosphere (see Table 4). In the next step the misfit phase was modeled as
(3)
and fitted simultaneously with the experimental Cp data from the temperature interval 250-300 K [5]. ◦ Finally, the enthalpy of formation ∆f H298 , was assessed taking into account the temperatures of decomposition of Ca3 Co2 O6 into rock-salt solid solution Ca1−x Cox O in air and oxygen as identified by our DSC measurements (see Fig. 3(a)). A similar approach was applied for the misfit phase which has been considered as a stoichiometric compound Ca3 Co4 O9.2 in the first approximation. The heat capacity data obtained by two independent methods, relaxation time technique below the room temperature and DSC in dynamical regime above, is plotted in Fig. 1. The low temperature heat capacity used for the evaluation of entropy at 298 K exhibits a small bump at ∼30 K which has been attributed to a magnetic ordering transition [6]. Above the ambient temperature the Cp curve 4
Table 2 ◦ (a), or Assessed values of enthalpies of formation, ∆f H298 heats of transformation, ∆Htr (b) (in kJ·mol−1 ), entropies, ◦ S298 (a) (in J·mol−1 ·K−1 ), or transition temperatures Ttr (b), and coefficients of temperature dependence of heat capacity (in J·mol−1 ·K−1 ) for solid stoichiometric compounds. A shortcut notation denoting only the cation stoichiometry (C stands for both Ca and Co) is used for ternary oxides.
500 Ca Co O 3
4
9.2
300
◦ ∆f H298
∆Htr
200
C
p
-1
-1
(J.mol .K )
400
100
0
200
400
600
800
(a)
Ttr /K
(b)
Cp = a + bT + cT −2 b×103 c/106
a
-3206
297.2
408.1
5.52
7.074
C3 C4 IT,(b)
2.18
397
408.1
5.52
7.074
6.59
840
408.1
5.52
7.074
-3205
300.1
404.6
5.47
7.013
-2524
228.4
268.8
26.6
4.408
-914
109.3
HT,(b)
C3 C3.9
T (K)
(b)
◦ S298
C3 C4 LT,(a)
C3 C4 0
(a)
C3 C2
(a)
(a)
Co3 O4
(a)
see below
Cp = 321.5 - 0.01184T - 3742T −1/2
Fig. 1. Heat capacity of Ca3 Co4 O9.2 measured by relaxation method (PPMS) below ambient temperature and by continuous DSC (Netzsch) at elevated temperatures. The solid line reperesents a polynomial fit with parameters given in Table 2.
+2074450 T −2
298−900K
Cp = -764.8 + 4.453T - 0.006769T 2 +3.331×10−6 T 3
900−1200K
Cp = -9138 + 4.151T
a solid solution in terms of CEF model described above. The thermodynamic data of Ca3 Co3.9 O9.3 (C3 C3.9 in Table 2) from which the Gibbs energies of all end-members are derived, were assessed from the low temperature form of Ca3 Co4 O9.2 (C3 C4 LT ) by modifying the entropy and heat capacity with respect to different stoichiometry of Co and fitting the enthalpy in order to reproduce the decomposition temperature much like in the stoichiometric case. However, the existence of high temperature forms (IT and HT) was disregarded due to limitations in FactSage implementation of CEF (three separate solutions phases would have to be considered). From the four additional parameters representing the enthalpies of defect formation only three are independent, namely, ∆HC2 associated with a homovalent substitution and two of the remaining three, ∆HC4 , ∆HC3 , and ∆HO representing heterovalent processes which must compensate each other. Hence, in addition to ∆HC2 , the enthalpy changes of two independent reactions are given in Table 2), the oxygen incorporation and Ca2+ for Co3+ substitution in RS-blocks, both compensated by Co3+ to Co4+ oxidation in hexagonal layers. These parameters were optimized to achieve the best possible fit with the experimentally determined homogeneity range (this work) and oxygen stoichiometry (our TGA data and those from Shimoyama et al. [9]). The thermodynamic behavior of high temperature rock-salt type Ca1−x Cox O solid solution has
1200−1360K
+227.2T −1/2 + 6.843×109 T −2
Cp = 269.4 - 0.015 T - 2500 T −1/2 1360−2500K
+1.0×10−5 T 2
been studied by several authors by direct determination of miscibility limits by phase equilibration studies [10–12] and by measuring the respective component activities in solid electrolyte galvanic cells [13,14]. Although only the data reported by Jakob et al. [11] and Mukhopadhyay and Jakob [12] were used to evaluate the temperature dependent R-K parameters for excess Gibbs energy (Eq. 2, Table 3), the agreement between the other experiments and the miscibility gap calculated using the optimized parameter values shown in Fig.2 is quite satisfactory. The calculated activities of CoO at the miscibility gap boundary are also consistent with the experimental values [13,14]. As identified by Woermann and Muan [10] the two-phase compositions within the miscibility gap of Ca1−x Cox O solid solution melt at the eutectic temperature ∼1350◦ C to a CaO-CoO liquid with an eutectic composition xCoO ∼ 0.65 located close to the solubility limit of CaO(s) in CoO(s) (xCoO ∼ 0.68). To describe this equilibrium behavior of high temperature liquid we use a single regular solution parameter between CaO(l) and both Co involving species, Co(l) and CoO(l), which was optimized to 5
metal liquid are indeed reproduced.
1700
1600
5. Phase diagram
T (K)
1500
1400
To our knowledge, the only phase diagram of CaO-CoOx system available in literature in a graphical form is that reported by Woermann and Muan [10]. Their assessment is purely based on experimental results obtained by microscopic and XRD examination of samples equilibrated at different temperatures in air atmosphere and rapidly quenched. Considering the misfit cobaltite as a stoichiometric phase with thermodynamic data as given in Table 2, our phase diagram calculated for pO2 = 0.21 appears to be in satisfactory agreement with both the experimental diagram [10] and our DSC results (see Fig. 3a and Table 4). Moreover the temperatures of invariant points calculated for pO2 = 1.0 correspond likewise to the respective effects observed on our DSC curves acquired in oxygen atmosphere (Table 4). However, the most significant difference resulting from our model is the low temperature behavior of the Ca3 Co2 O6 phase (below 1000 K) which turns out to be unstable with respect to a Ca3 Co4 O9.2 - Ca1−x Cox O mixture. The decomposition of Ca3 Co2 O6 on cooling is quite understandable given its lower relative oxygen content compared to the misfit phase. Indeed, the long term annealing of a phase pure Ca3 Co2 O6 sample at 650◦ C led to a formation of the misfit cobaltite and CaO, although the conversion was not complete presumably due to kinetic reasons. Similarly, as a result of different oxygen content, the eutectics in Co-rich part, the decomposition of Ca3 Co4 O9.2 into Ca3 Co2 O6 and Ca1−x Cox O solid solution, as well as the decomposition of Ca3 Co2 O6 into Ca-rich and Co-rich Ca1−x Cox O are all shifted to higher temperatures in oxygen compared to air atmosphere, namely by 54, 56 and 73 K, respectively.
1300
1200
1100
1000 0.0
0.2
0.4
x
0.6
0.8
1.0
CoO(ss)
Fig. 2. A comparison of the miscibility gap of rock-salt type Ca1−x Cox O solid solution calculated using the assessed model parameters (Eq.2, Table 3) with various experimental data ( - [11], ◦ - [12], ▽ - [10], △ - [15], I - [13], J - [14]). Table 3 Assessed interaction parameters Lj(M,N ) (Eq.2) and enthalpies of defect formation (in J·mol−1 ) for solution phases. Liquid L0(CaO,CoO) =L0(CaO,Co) = -51000 L0(CoO,Co) = 91338 - 15.278·T L2(CoO,Co) = 27113 - 10.0 ·T Solid solutions Ca1−x Cox O (RS): L0(CaO,CoO) = 31018 - 1.263·T L1(CaO,CoO) = 10755 - 10.117·T [Ca2+ ,Co2+ ]10 [Co3+ ,Ca2+ ]5
[Co3+/4+ ]8 [O,Va]4 O27 :
∆HC2 = 45000 ∆HC4 + ∆HC3 = 52000 2∆HC4 + ∆HO = -30000
reproduce the eutectic melting in air (Table 3). In order to extend the model to lower oxygen activities, two additional temperature dependent R-K parameters are considered for Co(l)-CoO(l) subsystem whose values (Table 3) were adopted from the assessment of the Co-O system by Chen et al [16] who applied two-sublattice model for ionic liquids. If higher oxygen content xO > 0.5 relevant only at extremely high oxygen activities (aO2 > 102 ) is neglected, the model can be simplified, by disregarding the occurrence of Co3+ species, to a phenomenological binary solution Co(l)-CoO(l) used in this study. All essential features of the Co-O phase diagram for xO < 0.5 including the miscibility gap between the oxide and
Table 4 Calculated (FactSage) and measured (DSC) temperatures of phase transitions in the subsolidus region. T1 : Ca3 Co3.9+x O9+δ + Co3 O4 Ca1−x Cox O, T2 : Ca3 Co3.9+x O9+δ + Co3 Co2 O6 + Ca1−x Cox O, T3 : Ca3 Co2 O6 Ca1−x Cox O (#1 + #2) pO2
6
FactSage
DSC T1
T2
T3
T1
T2
T3
0.21
1169±5
1.00
1228±3
1222±13
1313±7
1168
1211
1312
1275±4
1386±10
1222
1269
1384
As preceded in Section 3, the misfit cobaltite should be actually considered as a non-stoichiometric phase with respect to both the variable Ca/Co ratio and the oxygen content. We confirmed the limited miscibility around the ideal stoichiometry by XRD analysis of samples annealed at 900◦ C and quenched to room temperature. The samples with coefficient x =-0.13, -0.03, +0.02 and +0.07 in the net formula Ca3 Co3.93+x O9+δ were found single phase while those outside this stoichiometry range (x =-0.23 and +0.17) contained the corresponding impurity phases, namely Ca3 Co2 O6 and Co3 O4 from the Carich and Co-rich part of the phase diagram, respectively. Let us note that nearly identical results have been reported by Zhou et al.[17]. The homogeneity range of the misfit phase can be thus delimited as x ∈ ⟨−0.13; 0.07⟩, or 3.93 + x ∈ ⟨3.8; 4.0⟩. The original idea of this part of the study was to modify the misfit ratio by varying the cation stoichiometry. However this turned out to be nearly constant over the entire studied range. In fact it slightly decreased from the value q = 1.6185 for x =-0.13 towards q = 1.6175 for x =+0.07. Such a variation is close to fitting error of the Rietveld refinement and, moreover, it exhibits an opposite slope to account for the observed departure from ideal stoichiometry. Accordingly, the formation of substitutional defects on two different cation sublattices within the RS block as proposed in Section 3 seems to be a reasonable model for the solid solubility in the misfit phase. The two isoactivity sections of the Ca-Co-O phase diagram calculated for air and oxygen atmosphere are shown in Fig. 3, both exhibiting the narrow homogeneity range of the misfit cobaltite being in a fair accordance with our experiments. Unfortunately, the limitation of the CEF model imposing the necessity of using only the low temperature form of the “ideal”phase Ca3 Co3.9 O9.3 from which all end-members are derived, as well as the approximation of the real misfit ratio by two adjacent members of the Fibonacci series brings about a higher stability of the misfit phase compared to Ca3 Co2 O6 which starts to form at higher temperature (1060 K in air and 1100 K in oxygen). In this respect, considering the misfit phase as stoichiometric gives more realistic results. On the other hand, CEF model implements the experimentally observed non-stoichiometry while preserving all other essential features of the phase diagram such as temperatures of phase transitions in the sub-solidus region. The CEF model for the misfit cobaltite also de-
(a)
L
Ca1-xCoxO
1800
T(K)
1600
Co1-xCaxO
1000 0
0.2
0.4
Co3O4
1200
Ca3Co3.9+xO9+δ
Ca3Co2O6
1400
0.6
xCo
0.8
1
(b) L Ca1-xCoxO
1800
T(K)
1600
Ca1-xCoxO
1000 0
0.2
0.4
xCo
Co3O4
1200
Ca3Co3.9+xO9+d
Ca3Co2O6
1400
0.6
0.8
1
Fig. 3. Calculated phase diagram of Ca-Co-O system for fixed oxygen activity (a) pO2 = 0.21 (air atmosphere), (b) pO2 = 1.0 (oxygen atmosphere). The solid circles represent the on-set temperatures of DSC effects determined in this study
scribes the oxygen non-stoichiometry by allowing the vacancy formation on four from the total number of 31 anion sites. The total oxygen content 9+δ calculated for the ratio Ca/Co = 3/3.9 (ideal with respect to the used CEF mode) is plotted as a function of temperature and partial pressure of oxygen. As mentioned, the variable oxygen content has been in detail studied by thermogravimetry performed under atmosphere with controlled oxygen activity and the corresponding pO2 − T − δ plots have been reported by Shimoyama et al.[9] for the composition Ca/Co = 3/3.93. The analysis of their data revealed three different regions of oxygen nonstoichiometry behavior and the values of relative partial molar enthalpy and entropy of oxygen varying considerably 7
1800 9.30
1
Ca1-xCaxO + Liquid
-1
10
1600
9.25 -2
10
9.20
9 +
O2
1400
-3
= 10
Ca1-xCaxO (#1+#2)
T(K)
p
9.15
+ Ca3Ca2O6
1200
-4
10
Ca1-xCaxO
9.10
1000
-5
10
Ca3Ca3.9±xO9.3- δ
9.05
800 -5
9.00 700
800
900
1000
1100
endo
T
T (K)
1200
1150 TGA
DTA
1100 0.60
-2
-1
0
behavior might be at the origin of the small peak observed on the DTA signal accompanied by a slight mass drop detected on the TGA curve prior to the final decomposition effect (see Fig. 5). Clearly, if one starts from the ideal cation composition, the single phase region is crossed ∼50 K below the final decomposition and the second phase, Ca3 Co2 O6 , starts to form under the simultaneous release of oxygen. Finally, the evolution of the individual phase stability fields with variable oxygen activity is depicted on the pO2 − T phase diagram (Fig. 6) calculated for a constant cation composition corresponding to the ideal stoichiometry Ca/Co = 3/3.9 (ideal with respect to the assumed commensurate approximation). The narrow stability field between the pure misfit phase and the product of its complete decomposition (Ca3 Co2 O6 + Ca1−x Cox O) corresponds to a partial decomposition of the misfit phase into Ca3 Co2 O6 . Considering the dependence of this partial decomposition temperature on cation stoichiometry the recommended safety limit for the application of misfit cobaltite in thermoelectric batteries is the maximum operation temperature 850◦ C in air atmosphere.
1250
0.55
log(pO )
Fig. 6. Phase stability diagram pO2 − T of Ca-Co-O system calculated for the cation composition Ca/Co = 3/3.9.
Fig. 4. Calculated oxygen stoichiometry 9 + δ in Ca3 Co3.9 O9+δ as a function of temperature and oxygen partial pressure.
0.50
-3
2
T (K)
m/m %
-4
1200
0.65
0.70
X
Co
Fig. 5. Comparison of the part of Ca-Co-O phase diagram (pO2 = 0.21) involving the misfit phase and the decomposition of the misfit phase (Ca3 Co3.93 O9+δ - dashed line) measured by TGA and DTA.
with δ. The comparison with our calculated curves reveals a steeper variation (descent) of the experimentally determined oxygen content with increasing temperature with a maximum difference of 0.5% at the upper phase stability limit (∼1260 K in O2 ). As seen from the phase diagrams in Fig. 3 and from the blow-up shown in Fig. 5, the homogeneity range of the misfit phase becomes narrower with increasing temperature ending up in a single point at the decomposition temperature and simultaneously slightly diverges towards Co-rich composition. This
6. Conclusions The phase equilibria in Ca-Co-O system were studied with the primary concern to examine the thermodynamic behavior of the misfit cobaltite Ca3 Co3.93+x O9+δ . The incommensurate character of its structure implies a non-integer stoichiometric coefficient even if the phase is perfectly ordered. In this particular case the real composition could be approximated by two integers (members of Fi8
bonacci sequence) and this composition was taken as a basis for the compound energy model. However, if the misfit ratio was not invariant under the change of system predictors (T, pO2 , composition), the system would apparently behave like a solution revealing a definite homogeneity ranger, but without any mixing entropy term. Such a behavior has been indeed observed for example in bismuth based high temperature superconductors where an oxygen excess is established as a result of a cooperative displacement of oxygen and bismuth atoms leaving a space for one extra oxygen atom per modulation period which is generally incommensurate in regard to the parent lattice. A similar structural pattern of bismuth-oxygen double layers derived from rock-salt structure also occurs in bismuth based misfit cobaltites. Let us note that the current programs for thermodynamic modeling provide the possibility to enter real stoichiometry for stoichiometric phases (in FactSage as a special option for advanced users), but the variable stoichiometry due to varying modulation vector has not yet been implemented. A similar situation exists in reciprocal ionic liquid model, however, in this case the variable number of sites on cation and anion sublattice is unambiguously determined by charge balance, while in the case of variable modulation vector or misfit ratio one would have to minimize the Gibbs energy with respect to this parameter.
[9] [10] [11] [12] [13] [14] [15] [16] [17]
Acknowledgement This work was supported by Czech Science Foundation, grant N◦ GA203-09-1036, and Volkswagen AG. References [1] V. Petˇr´ıˇ cek, M. Duˇsek, L. Palatinus, Jana2006. the crystallographic computing system (2006). [2] L. S., H. Leligny, D. Grebille, J. Solid. State Chem. 160 (2001) 322. [3] C. Bale, P. Chartrand, S. Degterov, G. Eriksson, Hack, R. Ben Mahfoud, J. Melan¸con, A. Pelton, S. Petersen, Calphad 26 (2) (2002) 189. [4] I.-H. Jung, S. Decterov, A. Pelton, H.-M. Kim, Y.-B. Kang, Acta Materialia 52 (2004) 507. [5] V. Hardy, M. Lees, A. Maignan, S. H´ ebert, D. Flahaut, C. Martin, M. Paul, J.Phys.:Condens.Matter 15 (2003) 5737. [6] J. Sugiyama, J. Brewer, E. Ansaldo, H. Itahara, D. K., Y. Seno, C. Xia, T. Tani, Phys.Rev.B 68 (2003) 134423. [7] H. Muguerra, D. Grebille, Acta Cryst. B 64 (2008) 676. [8] J. Hejtm´ anek, K. Kn´ıˇ zek, M. Maryˇsko, Z. Jir´ ak, D. Sedmidubsk´ y, O. Jankovsk´ y,
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