Thermodynamic Assessment of the Cu-Fe-O System

JPEDAV DOI: 10.1007/s11669-011-9951-5 1547-7037 ASM International

Basic and Applied Research: Section I

Thermodynamic Assessment of the Cu-Fe-O System Alexnadra V. Khvan, Olga B. Fabrichnaya, Galina Savinykh, Robert Adam, and Hans J. Seifert

(Submitted July 7, 2011; in revised form August 17, 2011) The system Cu-F-O was assessed with CALPHAD technique using computerized optimization procedure (PARROT). Two solid phases CuFe2O4 and Fe3O4 forming solid solution at high temperatures were modeled with compound energy formalism. Presence of Cu1+ on tetrahedral sites in the samples with compositions close to CuFe5O8 reported in the literature was taken into account. The second ternary compound, CuFeO2, was modeled as a stoichiometric phase. For the liquid phase, an ionic two-sublattice model was used. In total 17 adjustable parameters were optimized (9 for the spinel phase, 2 for the delafossite and 6 for the liquid phase) to describe the experimental data. The consistent dataset, which gives a description of the properties from 923 to 1273 K, was obtained.

Keywords

phase diagrams, thermodynamic modeling

1. Introduction Thermodynamic modeling of the Cu-Fe-O system is important for electrode materials for conversion type Li-ion batteries as well as in slag formation in copper metallurgy.[1,2] The Cu-Fe-O system has been investigated several times experimentally in the past including phase equilibria and some thermodynamic properties. A thermodynamic modeling is not available so far and therefore the aim of the present study was to obtain a thermodynamic dataset for the Cu-Fe-O system. Previously assessed Cu-Fe and Cu-O binary systems reported by Ansara and Jansson[3] and Hallstedt and Gauckler[4] respectively were accepted. Sundman[5] reported thermodynamic evaluation and optimization of the Fe-O system. The models for wustite and magnetite phases were fully described in this paper. In later work of the models Kjellqvist et al.[6] for the bcc and fcc phases were changed and parameters were re-optimized. Experimental investigation of phase relations in the CuFe-O system[7] indicated that the Fe3O4 magnetite forms a solid solution with the CuFe2O4 spinel phase at high temperatures, which decomposes with eutectoid formation of the Fe2O3 and delafossite CuFeO2 phases at lower temperatures. Both end-members CuFe2O4 and Fe3O4 are inverse spinels. Several papers on crystallographic investigations of the spinel solid solution reported presence of monovalent copper in the solid solution.[8-11] The maximum content Alexnadra V. Khvan, Olga B. Fabrichnaya, Galina Savinykh, and Robert Adam, Technical University of Freiberg, Freiberg, Germany; Hans J. Seifert, Institute for Applied Materials-Applied Materials Physics, Karlsruhe Institute of Technology, Karlsruhe, Germany. Contact e-mail: [email protected].

was reported to correspond to CuFe5O8 composition in accordance with papers.[9,11,12] This causes changes in the inversion degree of the spinel phase which corresponds to the concentrations of Fe3+ tetrahedral sites.[12,13] To suit these data the Cu1+ ion was allowed to occupy the tetrahedral sublattice in the present work. The thermodynamic description of the liquid phase is available only for binary systems so the liquid phase for the ternary system was taken as extrapolation from binaries.

2. Experimental Techniques Experiments were undertaken to confirm experimental literature data. Powders of Fe3O4 (99.997% purity), Fe2O3 (99.99% purity) and CuO2 (99.99% purity) were used for sample preparation. The tablets made of powders were pelletized and then annealed at different temperatures under helium protection atmosphere. The weight loss was controlled during the experiment to control possible oxygen loss. The temperatures of the transformations were determined using DTA analysis (SetSys evolution 1750 SETARAM) as on set point. The analysis was carried up to 1073 K under protection atmosphere of helium the heating rate was 10 K/min cooling rate 30 K/min. The weight loss observed during experiments did not exceed 0.1%, what is within measurements error. To determine phase composition of samples the XRD analysis was carried utilizing diffractometer URD6 SeifertFPM using Co Ka x-ray (k = 0.1789 nm) in a conventional Bragg-Brentano geometry. The 2h = 20-150, the time period for each point 30 s and step width 0.05 were used. The relative amounts of the individual phases were calculated using software MAUD[14] (Rietveld-like routine for analysis of XRD data).

3. Thermodynamic Models The CALculation of PHAse Diagrams (CALPHAD) method was employed in the present work. The calculations

Journal of Phase Equilibria and Diffusion

Section I: Basic and Applied Research are based on Gibbs Free energies as functions of temperature and compositions for each phase in the system. The basic methodology of thermodynamic database design, construction and optimization has been described in detail many times (e.g. Ref 15-18). The temperature dependence of the Gibbs energy for a stoichiometric compound is described by: X bi Hi/ ð298:15 KÞ ¼ a þ bT þ cT ln T þ dT 2 þ fT 1 Ga i

ðEq 1Þ where a-f are adjustable parameters. The compound energy formalism (CEF)[17-19] was applied for the description of the phases using two or more sublattices (e.g. spinel and halite phases). X X X ysJ ln ysJ þ E Gm Df Gend PysJ þ RT ns Gm ¼ ðEq 2Þ where J-specie ns stoichiometry in each sublattice s, y terms P are site fractions and the Gend PysJ represents a weighted average over all end-members. The excess Gibbs energy related on the different sublattices is defined as: X X E ytB LA;B:D:G... þ PysJ ytB LA;B:D:E:G... þ Gm ¼ PysJ ðEq 3Þ 3.1 Delafossite

CuFeO2 has a trigonal structure ( 32=m space group R3m). The composition of the delafossite phase is very close to the stoichiometric CuFeO2 compound. In the present assessment the delafossite phase was treated as a stoichiometric phase. 3.2 Spinel The application of CEF for the description of spinel phases has been discussed several times (e.g. Ref 5, 20-22) and a similar description was used in the present work. Due to the literature data that magnetite and CuFe2O4 form a continuous solid solution at temperatures about 12531268 K, these two phases were described as one spinel phase. The model for Fe3O4 phase was accepted from Sundman.[5] The deviations of magnetite from ideal stoichiometry at high oxygen potentials and temperatures as well as towards excess iron in equilibrium with halite were also described[5] but were not taken into account in the present work due to practical purpose. As a result the model was simplified to (Fe3+,Fe2+)1(Fe2+,Fe3+)2(O2)4. The following parameters appear from this model: GFe3þ Fe3þ , GFe3þ Fe2þ , GFe2þ Fe3þ , GFe2þ Fe2þ and were accepted from Sundman.[5] The complete description of the CuFe2O4 spinel phase is rather complicated so it is logical to begin with the description of stoichiometric spinel. The CuFe2O4 is an inverse spinel with the tetrahedral sites filled with Fe3+ and with Cu2+ and Fe3+ on the octahedral sites. For description of inversion degree between 0 (normal spinel

Cu2þ Fe2 3þ O4 2 ) and 1 (inverse spinel) Cu2+ ions were allowed to the tetrahedral sites. The thermodynamic model of the stoichiometric CuFe2O4 can be presented as (Fe3+,Cu2+)(Cu2+,Fe3+)2(O2)4. The model is described with following parameters:

GCu2þ Fe3þ

GFe3þ Cu2þ 2 GCu2þ Fe3þ þ GFe3þ Fe3þ ¼ DG1

GCu2þ Cu2þ GFe3þ Cu2þ GCu2þ Fe3þ þ GFe3þ Fe3þ ¼ DG2

The parameter GCu2þ Fe3þ , corresponds to normal spinel CuFe2O4, the parameters GCu2þ Cu2þ follows from reciprocal reaction and GFe3þ Cu2þ describes the degree of inversion. However, at temperatures above 1268 K CuFe2O4 forms a solid solution with magnetite. This could be described by adding Fe2+ into both octahedral and tetrahedral sites. This allows formation of the spinel solid solution from Fe3O4 to CuFe2O4 and describes changes of the degree of inversion occurring at high temperature. Consequently, spinel solid solution from Fe3O4 to CuFe2O4 is described by formula: 3þ Fe ; Cu2þ ; Fe2þ 1 Cu2þ ; Fe2þ ; Fe3þ 2 O2 4 The compound energy model when applied to the spinels solid solution was discussed by Decterov et al.[20] including detailed description of the set of model parameters and a sequence of their optimization. The similar set of parameters was used in the present work.

GCu2þ Cu2þ þ GFe3þ Fe2þ GFe3þ Cu2þ GCu2þ Fe2þ ¼ DG3

GFe2þ Fe2þ þ GFe3þ Cu2þ GFe2þ Cu2þ GFe3þ Fe2þ ¼ DG4

The parameters DG3 and DG4 come from reciprocal reactions and were chosen to be zero as it is commonly accepted in CALPHAD.[5,20,22] The change in the valency of copper ions from +2 to +1 in the spinel phase has been reported several times (e.g. Ref 12, 13). The highest concentration of Cu1+ ions corresponds to the CuFe5O8 composition. To take into account presence of Cu1+ in the spinel solid solution the model was presented by formula: 1þ Cu ; Cu2þ ; Fe3þ ; Fe2þ 1 Cu2þ ; Fe3þ ; Fe2þ 2 O2 4 All end-members and neutral planes for spinel solid solution are shown in Fig. 1. The addition of the Cu1+ ions into tetrahedral sublattice corresponds to the reaction Fe3+ + Cu1+ M Fe2+ + Cu2+ To describe the concentration of the Cu1+ ions and its influence on the degree of inversion of the spinel phase three additional parameters DG5, DG6, DG7 were introduced. These parameters could be related to the other parameters by reciprocal relations:

GCu1þ Cu2þ GCu2þ Cu2þ GFe2þ Cu2þ þ GFe3þ Cu2þ ¼ DG5

GCu1þ Fe3þ GCu2þ Fe3þ GFe2þ Fe3þ þ GFe3þ Fe3þ ¼ DG6

GCu1þ Fe2þ GCu2þ Fe2þ GFe2þ Fe2þ þ GFe3þ Fe2þ ¼ DG7


Basic and Applied Research: Section I 3.5 Halite (Wustite) The (FeO) phase has the NaCl-type structure (Stukturbericht B1). The generic name of the phase is halite. The iron in the wustite phase has two valency states Fe2+ and Fe3+, respectively, as a result the phase has solid solubility within the concentration range of oxygen 51.26-54.57 at.%.[25] In order to describe deviation from stoichiometry and maintain electroneutrality, vacancies were introduced to the cation sublattice as it has been reported,[5] where the phase is represented as (Fe2+,Fe3+,Va)1(O2)1. 3.6 Liquid

Fig. 1 Pseudocomponents and possible (neutral) composition range of the spinel (Cu1+,Cu2+,Fe3+,Fe2+)1(Cu2+,Fe3+,Fe2+)2(O2)4

The Gibbs energy of spinel phase is presented as: Gm ¼ yTCu1þ yO GCu1þ Cu2þ þ yTCu2þ yO GCu2þ Cu2þ Cu2þ Cu2þ þ yTFe2þ yO GFe2þ Cu2þ þ yTFe3þ yO GFe3þ Cu2þ Cu2þ Cu2þ þ yTCu1þ yO GCu1þ Fe2þ þ yTCu2þ yO GCu2þ Fe2þ Fe2þ Fe2þ þ yTFe2þ yO GFe2þ Fe2þ þ yTFe3þ yO GFe3þ Fe2þ Fe2þ Fe2þ þ yTCu1þ yO GCu1þ Fe3þ þ yTCu2þ yO GCu2þ Fe3þ Fe3þ Fe3þ þ yTFe2þ yO GFe2þ Fe3þ þ yTFe3þ yO GFe3þ Fe3þ Fe3þ Fe3þ

þ RT ½yTCu1þ ln yTCu1þ þ yTCu2þ ln yTCu2þ þ yTFe2þ ln yTFe2þ þ yTFe3þ ln yTFe3þ þ 2ðyO ln yO þ yO ln yO Fe2þ Fe2þ Cu2þ Cu2þ þ yO ln yO Þ Fe3þ Fe3þ

ðEq 4Þ

No mixing parameters had to be introduced. 3.3 Low Temperature Tetragonal Spinel The composition of the low temperature tetragonal spinel phase CuFe2O4 ((tI56) space group I41/amd) is very close to the stoichiometric CuFe2O4 compound. In the present assessment this phase was treated as a stoichiometric phase. 3.4 Corundum (Hematite) The hematite (a-Fe2O3) is very close to stoichiometric Fe2O3 phase and it was treated as stoichiometric phase in previous assessments.[5,23,24] It was later described with an additional interstitial sublattice with Fe3+, respectively, and vacancies to have ability to use the description for the modeling diffusivity of ionic species by Kjellqvist et al.[6] However, in the present work the previous description[5] was used to simplify the model. In accordance with assessment[5] the lambda anomaly in the corundum heat capacity at 943 K was described using a magnetic model.

In the present work the liquid phase is described by the two-sublattice model for ionic liquids[26] as an extrapolation from the binary systems. However, calculations indicated unwanted presence of liquid phase below 1273 K in equilibrium with the spinel phase. Therefore, additional parameters were to be introduced. Liquid phase in both Cu-O and Fe-O systems is characterized by miscibility gaps between metallic liquid (copper liquid and iron liquid correspondingly) and oxide liquid. The liquid phase in the Cu-O system has been discussed several times starting with a paper of Schmid[27] in 1983, where the associated solution model for the liquid phase was applied using Cu, O and Cu2O species. The more recent assessment was done by Hallstedt and Gauckler[4] using a partially ionic two sublattice model for liquid phase. Schramm et al.[28] introduced Cu3+ ions in the liquid phase which corresponds to Cu2O3 species to suit experimental data at high oxygen pressures. Simultaneously, the system was reassessed by Clavaguera-Mora et al.[29] and the partially associated regular solution model. One excess parameter was used with aim of getting a more simplified description for easier extrapolation to high-order systems. In the present work the description of Hallstedt and Gauckler[4] for the Cu-O system was accepted to be compatible with other binary systems. The Cu3+ ions were not included to simplify the model for the extrapolation to ternary system and due to the fact that high pressures are not applied in present work. The two sublattice model was applied to liquid in the Fe-O system by Sundman.[5] Later the Fe3+ was replaced by a neutral species FeO1.5.[30] The same model was later used by Kjellqvist et al.[6] As a result of extrapolation from binary systems, the following model considering Fe2+, Fe3+, Cu1+, Cu2+, O2, Va and FeO1.5 was obtained: (Fe2+,Cu1+,Cu2+)P(O2, VaQ,FeO1.5)Q, where the stoichiometric factors P and Q vary with the composition to keep electro-neutrality also charged vacancies are introduced for this purpose. This corresponds to the formula: P¼

X

yi ðvi Þ þ yVa Q

i

Q¼

X

yi vj

j


ðEq 5Þ

Section I: Basic and Applied Research

where vi is the valency of ion i. All charged constituents i and j are summed on the second and first sublattices correspondingly. The Gibbs energy for the liquid phase is expressed by: Dmix G ¼ yFe2þ yO2 GFe2þ :O2 þ yCu1þ yO2 GCu1þ :O2 þ yCu2þ yO2 GCu2þ :O2 þ QðyFe2þ yVa GFe2þ :Va2 þ yCu1þ yVa GCu1þ :Va1 þ yCu2þ yVa GCu2þ :Va2 þ yFeO1:5 GFeO1:5 þ RTP½yFe2þ lnðyFe2þ Þ þ yCu1þ lnðyCu1þ Þ þ yCu2þ lnðyCu2þ Þ þ RTQ½yO2 lnðyO2 Þ þ yVa lnðyVa Þ þ yFeO1:5 lnðyFeO1:5 Þ þ Dmix Gex

ðEq 6Þ

Six adjustable parameters 0 LCu1þ ;Fe2þ :O2 , 1 LCu1þ ;Fe2þ :O2 , 0 1 LCu1þ ;Fe2þ :O2 , LCu1þ :O2 ;FeO1:5 , LCu1þ :O2 ;FeO1:5 , 0 LCu1þ :Va;FeO3=2 were introduced to avoid unwanted presence of liquid phase below 1000 C in equilibrium with spinel phase. As the result the excess Gibbs energy expression is given by: 2

E

system. One of the earliest assessments was provided by Kubaschewski et al.[32] The solubility of the Cu in c-iron is rather low in accordance with a published dataset.[32] Simultaneously another assessment was provided by Hasebe and Nishizawa,[33] which allowed solubility of Cu in c-iron. Later, in 1980, the system was reassessed twice by Hasebe and Nishizawa[34] and Lindqvist and Uhrenius[35] The assessment of Hasebe and Nishizawa paid attention to the retrograde solidus curve and effect of magnetic transition on the copper solubility. Lindqvist and Uhrenius studied Cu-Fe system between 1423 and 1723 K experimentally and on the basis of experimental results recalculated the system using a sub-regular thermodynamic description similar to the description presented by Kubaschewski et al.[32] The next assessment was reported by Chen and Jin[36] in 1995. A new reassessment was made by Ansara and Jansson[3] covering all existing by that time experimental data. Recent reassessments of the Cu-Fe system were made by Turchanin et al.[37] in 2003. The possibility of a metastable monotectic reaction L2 M L1 + d in the region of metastable crystallization of the e-phase was described by Turchanin et al.[37] as

Gm ¼ yCu1þ yFe2þ yO2 LCu1þ ;Fe2þ :O2 þ yCu1þ yCu2þ yO2 LCu1þ ;Cu2þ :O2 þ yCu2þ yFe2þ yO2 LCu2þ ;Fe2þ :O2 þ Qy2Va ðyCu1þ yFe2þ LCu1þ ;Fe2þ :Va þ yCu1þ yCu2þ LCu1þ ;Cu2þ :Va þ yCu2þ yFe2þ LCu2þ ;Fe2þ :Va þ yVa yCu1þ yO2 LCu1þ ;O2 :Va þ yCu2þ yO2 LCu2þ ;O2 :Va þ yFe2þ yO2 LFe2þ ;O2 :Va þ yCu1þ yO2 yFeO1:5 LCu1þ :O2 ;FeO1:5 þ yCu2þ yO2 yFeO1:5 LCu2þ :O2 ;FeO1:5 þ yFe2þ yO2 yFeO1:5 LFe2þ :O2 ;FeO1:5 þ QyVa ðyCu1þ yFeO1:5 LCu1þ :FeO1:5 ;Va þ yCu2þ yFeO1:5 LCu2þ :FeO1:5 ;Va þ yFe2þ yFeO1:5 LFe2þ :FeO1:5 ;Va þ Qy3Va yCu1þ yCu2þ yFe2þ LCu1þ ;Cu2þ ;Fe2þ :Va þ yVa yCu1þ yFe2þ yO2 LCu1þ ;Fe2þ :O2 ;Va þ yCu1þ yCu2þ yO2 LCu1þ ;Cu2þ :O2 ;Va þ yCu2þ yFe2þ yO2 LCu2þ ;Fe2þ :O2 ;Va

4. Binary Systems 4.1 Cu-O The Cu-O binary system is given in Masslaski[25] as a result of critical evaluation from Elliot and Schmid.[27,31] The system was assessed several times. The assessment of Hallstedt and Gauckler[4] was accepted for binary system. 4.2 Fe-O The Fe-O system was reassessed several times.[5,30] The most recent reassessment was made by Kjellqvist.[6] The oxygen solubilities in bcc and fcc phases were modeled with the interstitial model. The description of hematite was modified by introducing an interstitial sublattice to enable deviation from stoichiometry. This assessment was accepted in present work with assumption of stoichiometric hematite. 4.3 Cu-Fe The critical evaluation of the Cu-Fe system is given in Massalski.[25] No intermediate phases are reported in this

ðEq 7Þ

well as solid solubility limits of bcc- and fcc-solutions in application to the melt quenching. However, the parameters of mixing for the liquid phase are essentially different from those reported by Ansara and Jansson[3] and the temperature dependence is physically unlikely. The values calculated in the work of Ansara and Jansson[3] and data of Turchanin et al.[37] for enthalpy of mixing at 1873 K are similar to each other and both are within uncertainty of available experimental data. In the present work the description of Ansara and Jansson[3] was chosen for the present description as long as used models are in a good agreement with the other two systems.

5. Experimental Phase Diagram Data The available experimental data concerns mainly phase diagram data, such as phase equilibrium and potential diagrams at different temperatures. There are lots of papers on crystallographic analysis of the spinel phase. However, there is lack of information on the liquidus surface. Existing


Basic and Applied Research: Section I experimental thermodynamic data for ternary compounds is rather conflicting and required additional critical evaluation.

The low temperature phase equilibria were described by Yund and Kullerud.[39] Yund have shown that tie-line changes at 948 K from CuFeO2-Fe3O4 to Cu-Fe2O3. Preliminary calculations did not confirm the change of the tie-line, for this reason additional experiments were carried to observe low temperature transformations.

5.1 Cu-Fe-O Phase Diagram Data One of the recent critical evaluations is provided by Perrot et al.[38] The evaluation covers literature analysis of the papers published till 2007. The system has been investigated several times experimentally in the past. The first complete experimental description of the system was proposed by Yund and Kullerud.[39] The description of isothermal section at 1073 K (total pressure 1 atm) was represented,[39] corresponding well with later works. In the same year Schmahl and Mueller[40] published their investigation of the system at 1273 and 1473 K. Schmahl and Mueller analysed changes in the phase equilibria in dependence of partial pressure in the region CuO-Cu2O-Fe2O3-Fe3O4. Presence of the solid solution between Fe3O4 and CuFe2O4 phases was observed at partial pressures between 0.013 and 0.171 atm. The presence of the solid solution between Fe3O4 and CuFe2O4 and its eutectoid decomposition into Fe2O3 and CuFeO2 at 1268 K was also reported[7] in 1969. It was later confirmed Schaefer et al.,[41] where experiments were done over a range of partial pressures 103 to 0.5 atm. It was found that temperature of the eutectoid reaction varied from 1250 to 1173 K at partial pressures 103 and 102.77 atm. Jacob et al.[42] observed the temperature of eutectoid decomposition as 1253 K with an experimental partial pressure of 104 atm. From these it must be noticed that data of Jacob et al.[42] and Schaefer et al.[41] are not in quantitative agreement. The lattice parameters of the Fe3O4-CuFe2O4 solid solutions initially increase with increase of Cu concentration until the composition CuFe5O8, then the lattice parameters decrease until the composition reaches CuFe2O4.[9,10] This was explained by the presence of monovalent copper in the solid solution, which was confirmed by crystallographic investigations of the spinel solid solution.[8,11,13] The maximum content was reported to correspond to CuFe5O8 composition in accordance with reported data.[9,11,12] This causes changes in the inversion degree of the spinel phase.[12,13] The lower temperature modification of CuFe2O4 phase has a tetragonal structure caused by Jahn-Teller-distortion along c-axes. Table 1

5.2 Thermodynamic Data on the Ternary Compounds The thermodynamic data was mentioned by Yund and Kullerud.[39] The Gibbs energy of formation of delafossite from oxides was modeled as a linear function of temperature. Experimental thermodynamic data on ternary compounds were analyzed by several research groups.[42-44] The data of Jacob et al.[42] were obtained using oxygen potential measurements with solid oxide galvanic cells (Table 1). While the data provided by Navrotsky and Kleppa[43] for the heat of formation of the spinel phase CuFe2O4 at 970 K was provided using solution drop calorimetry (see Table 1). The data from Jacob et al.[42] and Navrotsky and Kleppa[43] essentially vary with what could be explained by difficulties of determination of the pure spinel phase CuFe2O4. For the optimization the calorimetric data of Navrotsky was used. The data of King et al.[44] included in the compilation of Barin[45] provides full information for the Cp measurements[44] both for delafossite and for the CuFe2O4 phase, these data were also used for optimization.

6. Experimental Results The lower temperature transformation from higher temperature equilibria between Fe3O4 and CuFeO2 phases into lower temperature Cu + Fe2O3 equilibria at 948 ± 25 K was examined. The tablets of samples with starting composition consisting of Cu2O-Fe2O3-Fe3O4 phases were annealed at 1073 K and then rapidly cooled. The analysis of the annealed sample showed the formation of the delafossite phase in accordance with the reaction Cu2O + Fe2O3 fi 2CuFeO2. The excess of the Cu2O phase was only 2.6 wt.% and Fe2O3-CuFeO2-Fe3O4 phases were in equilibria. Two temperature arrests at 948 and 829 K in DTA were observed. To analyze the phase equilibria at temperatures below the observed temperature arrest, the sample was isothermally

The thermodynamic data on ternary compounds Calculation

Phase

Temperature, K

DH of formation from oxides (per formula unit)

First optimization results obtained for normal spinel CuFe2O4 970 21131 CuFeO2 970 24374.5 Results of final optimization for inverse spinel CuFe2O4 970 21169.4 1273 24893 CuFeO2 970 39692 1273 41256

Experimental data

DS of formation from oxides (per formula unit)

DH of formation from oxides (per formula unit)

DS of formation from oxides (per formula unit)

21129.2[43] 17150[42] 24374.5[44] 25938[44]/10080[44]

21.986[44]

18.787 11.7975 50.97 54.17 32.3495 5.3265


13.2735[44] 14.7495[44]/4.38[42]

Section I: Basic and Applied Research annealed at 908 K for 60 h and quenched. XRD analysis showed that the amount of delafossite and Fe3O4 phases decreased from 37.12 to 17.16 wt.% while the amount of Fe2O3 phase increased from 30.61 to 55.26 wt.% and metallic Cu phase appeared. This confirms the existence of the lower temperature transformation reported by Yund and Kullerud.[39] The lower temperature arrest could correspond to the transformation in Fe3O4 phase. This is indirectly confirmed by the considerable decrease of the peak area on DTA curves with decreasing of the amounts of this phase.

7. Optimization At the first step the calculation with the stoichiometric ternary compounds were carried out using data of Navrotsky

and Kleppa[43] for enthalpy of formation for spinel (CuFe2O4) phase. The standard entropy and Cp for spinel and delafossite were taken after King et al.[44] The isothermal section at 1273 K (total press 1 atm) was calculated (Fig. 2a). It could be seen from a plot of a calculated variant we have a tie line between wustite and delafossite, but no solid solution between two spinel phases as it is shown at the experimental phase diagram (Fig. 2b). For this reason we developed a model for the spinel phase described above in the model section. The experimental data for the formation of the miscibility gap at 1253 K reported by Jacob et al.[42] was also used at the next step of optimization. The new calculation of isothermal sections and phase equilibria in the system Cu-Fe-O as a function of oxygen partial pressure (total pressure 1 atm) at 1273 K showed good agreement with experimental data. The calculated thermodynamic parameters for ternary phases

Fig. 2 Isothermal section at 1273 K (total pressure 1 atm): (a) calculated using stoichiometric ternary compounds, (b) experimental equilibria observed by Yund and Kullerud,[39] and (c) calculated with developed spinel model


Basic and Applied Research: Section I were in a good agreement experimental data (Table 1). However, the calculation of the inversion degree for the spinel phase showed that after optimization normal spinel for CuFe2O4 phase was obtained but not the inverse one. For this reason the system was re-optimized one more time taking into account the inversion degree. The optimization process in this case was complicated and parameters were conflicting with each other. As one of the intermediate results of optimization we obtained the non-existing equilibrium between spinel phase and Cu2O phase at temper-

atures below 1273 K. To avoid this it was needed to let free parameters for the delafossite, but the data for enthalpy of formation of cuprospinel was saved as a parameter for optimization. As a result of optimization the thermodynamic parameters for the Cu-Fe-O system were obtained (Table 3). The calculations of the isothermal sections were retained to compare with experimental data[7,39,42,46] (Fig. 2-4) as well as potential diagrams (Fig. 5, 6). Thermodynamic parameters were calculated and compared with experimental data (Table 1). There is serious mismatch with data for delafos-

Fig. 3 Isothermal section at 1200 K (total pressure 1 atm): (a) calculated and (b) experimental equilibria reported in Ref 38

Fig. 4 Isothermal section at 1073 K (total pressure 1 atm): (a) calculated and (b) experimental equilibria observed by Yund and Kullerud[39]



Fig. 5 Phase equilibira in the system Cu-Fe-O as a function of oxygen partial pressure (total press 1 atm) at 1273 K: (a) calculated for normal spinel, (b) calculation for inverse spinel, and (c) experimental equilibria observed by Jacob et al.[42]

Fig. 6

Potential diagram at 1273 K: (a) calculated and (b) experimental observed by Inaba et al.[46]


Basic and Applied Research: Section I

Fig. 7 Isothermal sections: (a) at 1443 K, (b) at 1473 K, and (c) (total pressure 1 atm) experimental data observed by Acuna et al.[48] at 1473 K (total pressure 1 atm). The section was included into system report of Perrot et al.[38]

site. However, the experimental data for this phase from the literature is rather uncertain. The calculated distribution of the atoms in the sublattices of the spinel solid solution is presented in Table 2. The second step of optimization touched the low temperature transformations. It is known from the literature data that CuFe2O4 turns from cubic spinel to tetragonal at the temperature 948 K. The lower temperature modification of the CuFe2O4 phase was described as a stoichiometric phase.

Attempts to reproduce tie-line changes at 948 K from CuFeO2-Fe3O4 to Cu-Fe2O3 described by Yund and Kullerud[39] by reoptimization of the system were made. For optimization we could vary parameters for the delafossite phase only. Calculations have shown that to describe the change of the tie-line from CuFeO2-Fe3O4 the parameter for the delafossite phase has to be for 21790 J more positive than those achieved with determined assessment. Such change of the parameters was leading to the appearance of



Fig. 8 Sections of Cu-Fe-O system at constant partial pressures: (a) pO2 = 0.21 atm, (b) pO2 = 1 atm, and (c) pO2 = 0.01 atm

non-existing equilibria at higher temperatures. It was found to be impossible to fix one set of parameters describing the experimental data for high temperatures as well as at the temperatures below 948 K. Finally at the last stage the ionic liquid phase was optimized. It was mentioned above that the ionic liquid phase was described as extensions from binary systems. Six adjustable parameters 0 LCu1þ ;Fe2þ :O2 , 1 LCu1þ ;Fe2þ :O2 , 2 LCu1þ ;Fe2þ :O2 , 0 LCu1þ :O2 ;FeO1:5 , 1 LCu1þ :O2 ;FeO1:5 , 0 LCu1þ :Va;FeO1:5 were optimized. The optimization was carried with the aim of using the following experimental data: absence of liquid phase at 1273 K in equilibrium with spinel phase, the data on melting temperature of delafossite phase (1453 K) reported by Zhao and Takei[47] as well as suppressing the appearance of a maximum on solidus and liquidus surfaces over the spinel phase. The calculations of equilibria at 1443 K and 1473 K at total pressure 1 atm are presented in Fig. 7a, b. The isothermal section at 1473 K corresponds with the experimental data reported by Acuna et.al.[48] and provided in the system report of Perrot et al.[38] (Fig. 7c) for this

temperature. It must be noticed that isothermal section presented by Acuna et.al.[48] is not completed in the field of high oxygen concentrations, so the calculated isothermal sections predicting possible phase equilibrium in this concentration ranges impossible. Three sections presenting dependences of temperature from composition (Cu/(Cu + Fe)) at different constant partial pressures of oxygen are shown on Fig. 8(a)-(c). In accordance with calculations the delafossite phase is stable at temperature range of 1200-1350 K and is limited by phase fields Cu2O + Spinel and CuO + Spinel at constant partial pressure of oxygen equal to 0.21 atm (Fig. 8a). The temperature of reaction of decomposition of delafossite into CuO + Spinel was obtained from calculations as 1200 K, while literature data is 1277 K[41] and 1288 K.[40] However, when constant partial pressure of oxygen is equal to 1 atm (Fig. 8b) the delafossite phase is unstable in whole temperature range, what corresponds to calculations carried by Jacob et al.[42] At 102 atm partial pressure of oxygen delafossite is stable at temperatures below melting temper-


Basic and Applied Research: Section I ature (Fig. 8c). What is in accordance with equilibria observed by Schaefer et al.[41] The reported eutectoid decomposition of spinel solid solution could be observed at low partial pressures what corresponds with the data Table 2

reported by Jacob et al.[42] However the calculated temperature of eutectoid reaction Spinel = Fe2O3 + CuFeO2 appeared to be lower than reported in literature.[41,42] The calculations at 1173 K showed that eutectoid reaction can

Distribution of ions in spinel solid solution First sublattice 1+

Composition

Temperature, K

Cu

CuFe2O4 CuFe5O8 CuFe2O4

1273 1273 1073

1.52E06 0.04569 4.18E08

Table 3

2+

Cu

0.015 0.0163 0.014

Second sublattice 2+

Fe

8.10E06 0.15292 1.49E07

3+

Fe

0.9849 0.7850 0.9860

2+

Cu

0.492 0.0939 0.4930

Fe2+

Fe3+

4.18E05 0.27569 1.27E05

0.5075 0.6303 0.50698

The thermodynamic parameters for the Cu-Fe-O system

Liquid: (Fe2+,Cu1+,Cu2+)P(O22,Va2Q,FeO1.5)Q

SER GFe2þ :O2 2H SER ¼ 4GFEOLIQ Fe 2H O GFe2þ :Va 2H SER ¼ GFELIQ Fe SER GFeO1:5 1:5H SER ¼ 2:5GFEOLIQ 89819 þ 39:962T Fe 1:5H O SER SER GCu1þ :O2 2H Cu HO ¼ þ3GCU2OLIQ SER GCu2þ :O2 2H SER ¼ 4GCU2OLIQ þ 16236 20T Cu 2H O SER GCu1þ :Va HCu ¼ GCULIQ SER GCu2þ :Va HCu ¼ GCULIQ2 0 LCu1þ ;Cu2þ :O2 ¼ 106048 þ 70T 0 LCu1þ ;Fe2þ :O2 ¼ 75000 1 LCu1þ ;Fe2þ :O2 ¼ 29500 2 LCu1þ ;Fe2þ :O2 ¼ 10000 0 LCu1þ :O2 ;Va ¼ þ13287 þ 11:82T 1 LCu1þ :O2 ;Va ¼ 17125 þ 11:52T 2 LCu1þ :O2 ;Va ¼ 21762 10:15T 0 LCu1þ :O2 ;FeO1:5 ¼ 27500 1 LCu1þ :O2 ;FeO1:5 ¼ 90000 0 LFe2þ :O2 ;FeO1:5 ¼ 26362 1 LFe2þ :O2 ;FeO1:5 ¼ 13353 0 LFe2þ :O2 ;Va ¼ 176681 16:368T 1 LFe2þ :O2 ;Va ¼ 65655 þ 30:869T 0 LCu1þ ;Fe2þ :Va ¼ 36088 2:32968T 1 LCu1þ ;Fe2þ :Va ¼ 324:53 0:0327T 2 LCu1þ ;Fe2þ :Va ¼ 10355:4 3:60297T 0 LCu1þ :Va;FeO1:5 ¼ 29000 0 LFe2þ :O2 ;FeO1:5 ¼ 110000 GHSERCU (298.15 < T < 1357.77) = 7770.458 + 130.485235T 24.112392T ln(T) 0.00265684T2 + 1.29223E07T3 + 52478T1 GHSERCU (1357.77 < T < 3200) = 13542.026 + 183.803828T 31.38T ln(T) + 3.64167E + 29T9 GCULIQ (298.15 < T < 1357.77) = +12964.735 9.511904T 5.8489E21T7+ GHSERCU GCULIQ (1357.77 < T < 3200) = 46.545 + 173.881484T 31.38T ln(T) GCULIQ2 (298.15 < T < 6000) = 3GCULIQ 2GCU2OLIQ + 16236 20T GHSERFE (298.15 < T < 1811) = 1225.7 + 124.134T 23.5143T ln(T) 0.00439752T2 5.8927E08T3 + 77359T1 GHSERFE (1811 < T < 6000) = 25383.581 + 299.31255T 46T ln(T) + 2.29603E+31T9 GFELIQ (298.15 < T < 1811) = 12040.17 6.55843T 3.67516E21T7 + GHSERFE GFELIQ (1811 < T < 6000) = +14544.751 8.01055T + GHSERFE 2.29603E+31T9 GCU2OLIQ (298.15 < T < 6000) = 38315 + 102.66T 22.57T ln(T) GFEOLIQ (298.15 < T < 6000) = 137252 + 224.641T 37.1815T ln(T) GO2GAS (298.15 < T < 1000) = 6961.74451 51.0057202T 22.2710136T ln T 0.0101977469T2 + 1.32369208E06T3 76729.7484/T GO2GAS (1000 < T < 3300) = 13137.5203 + 25.3200332T 33.627603T ln T 0.00119159274T2 + 1.35611111E08T3 + 525809.556/T GO2GAS (3300 < T < 6000) = 27973.4908 + 62.5195726T 37.9072074T ln T 8.50483772E04T2 + 2.14409777E08T3 + 8766 421.4/T


Section I: Basic and Applied Research Table 3

Continued 1+

Spinel: (Cu ,Cu2+,Fe3+,Fe2+)1(Cu2+,Fe3+,Fe2+)2(O22)4

SER GCu1þ :Cu2þ :O2 3HCu 4HOSER ¼ þ3GCUFE2O4 14GFE3O4 þ 3BFE3O4 þ 16184:5519 35:0591518T þ 25018:7304 þ 28:4795291T 20000 SER GCu2þ :Cu2þ :O2 3HCu 4HOSER ¼ 3GCUFE2O4 14GFE3O4 þ 2BFE3O4 þ 16184:5519 35:0591518T þ 25018:7304 þ 28:4795291T SER SER GFe2þ :Cu2þ :O2 2HCu HFe 4HOSER ¼ þ2GCUFE2O4 7GFE3O4 þ 2BFE3O4 þ 16184:5519 35:0591518T SER SER GFe3þ :Cu2þ :O2 2HCu HFe 4HOSER ¼ 2GCUFE2O4 7GFE3O4 þ BFE3O4 þ 16184:5519 35:0591518T SER SER GCu1þ :Fe2þ :O2 HCu 2HFe 4HOSER ¼ þGCUFE2O4 þ 2BFE3O4 þ 25018:7304 þ 28:4795291T 20000 SER SER GCu2þ :Fe2þ :O2 HCu 2HFe 4HOSER ¼ þGCUFE2O4 þ BFE3O4 þ 25018:7304 þ 28:4795291T SER GFe2þ :Fe2þ :O2 3HFe 4HOSER ¼ 7GFE3O4 þ BFE3O4 SER GFe3þ :Fe2þ :O2 3HFe 4HOSER ¼ þ7GFE3O4 SER SER GCu1þ :Fe3þ :O2 HCu 2HFe 4HOSER ¼ GCUFE2O4 þ BFE3O4 33000 SER SER GCu2þ :Fe3þ :O2 HCu 2HFe 4HOSER ¼ GCUFE2O4 SER GFe2þ :Fe3þ :O2 3HFe 4HOSER ¼ 7GFE3O4 SER GFe3þ :Fe3þ :O2 3HFe 4HOSER ¼ þ7GFE3O4 BFE3O4 Magnetic properties: For compounds containing only Fe cations TC = 848 and b = 44.54 All other compounds TC = 0 and b = 0 GFE3O4 (298.15 < T < 3000) = 161731 + 144.873T24.9879T ln(T) 0.0011952256T2 + 206520T1 BFE3O4 (298.15 < T < 3000) = 46826 27.266T GCUFE2O4 (298.15 < T < 675) = 139.6201T 139.6201T ln(T) 0.0588898T2 + 1171520T1 967968 146.758T 54721.2 + 843.794T + 20000 GCUFE2O4 (675 < T < 795) = 227.191T 227.191T ln(T) 897390 295.737T 153353.925 + 1480.08409T + 20000 GCUFE2O4 (795 < T < 953) = 166.021T 166.021T ln(T).0205015T2 870127 332.912T 144944.156 + 1141.34242T + 20000 GCUFE2O4 (953 < T < 1358) = 166.021T 166.021T ln(T).0205015T2 870127 332.912T 144944.156 + 1141.34242T GCUFE2O4 (1358 < T < 3000)= +225.936T 225.936T ln(T) 738753 454.502T 306821.088 + 1629.84996T

Low temperature tetragonal spinel CuFe2O4 SER SER GCu2þ :Fe3þ :O2 HCu 2HFe 4HOSER ¼ GCUFE2O42 GCUFE2O42 (298.15 < T < 675) = 139.6201T 139.6201T ln(T) 0.0588898T2 + 1171520T1 967968 146.758T 54721.2 + 843.794T GCUFE2O42 (675 < T < 795) = 227.191T 227.191T ln(T) 897390 295.737T 153353.925 + 1480.08409T GCUFE2O42 (795 < T < 1358) = 166.021T 166.021T ln(T).0205015T2 870127 332.912T 144944.156 + 1141.34242T GCUFE2O42 (1358 < T < 3000) = +225.936T 225.936T ln(T) 738753 454.502T 306821.088 + 1629.84996T

Delafossite CuFeO2 SER SER GCu1þ :Fe3þ :O2 HCu HFe 2HOSER ¼ GCUFEO2 15318 0:5T GCUFEO2 (298.15 < T < 1091) = 97.98928T 97.98928T ln(T) 0.0037656T2 + 899560T1 512958 88.868T 35584.5 + 570.668T GCUFEO2 (1091 < T < 1470) = 91.50408T 91.50408T ln(T).0075312T2 435128 212.938T 108795.196 + 656.49039T GCUFEO2 (1470 < T < 3000) = +126.7083T 126.7083T ln(T) 328788 289.706T 186261.201 + 924.08587T

appear at oxygen partial pressure equal to 29105 atm. As it follows from calculation results the parameters of eutectoid reaction needs to be experimentally reinvestigated due to the fact that known experimental data is conflicting. A data set for the Cu-Fe-O system has been created (Table 3), which reproduces well available experimental data in the temperature range between 948 and 1473 K. The calculated isothermal section at 1473 K and vertical section CuO-Fe2O3 gives predictions of phase equilibria in the parts of the phase diagram that have not been studied experimentally. However, some improvements are still needed especially with regard to equilibria below 948 K.

Acknowledgments This paper represents work, which was done in the frame of the sub-project Thermodynamic description of stabiliza-

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