Thermodynamic optimization of the PbO–FeO–Fe2O3–SiO2 system

Calphad 67 (2019) 101670

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Thermodynamic optimization of the PbO–FeO–Fe2O3–SiO2 system M. Shevchenko , E. Jak

T

∗

Pyrometallurgy Innovation Centre (PYROSEARCH), The University of Queensland, Brisbane, QLD, 4072, Australia

ARTICLE INFO

ABSTRACT

Keywords: Slags Lead Iron Silica Phase diagrams Thermodynamic assessment

Liquidus phase equilibrium data of the present authors for the PbO–FeO–Fe2O3 system at various oxygen potentials, PbO–“Fe2O3”–SiO2 system in air, and PbO–“FeO”–SiO2 in equilibrium with metallic Pb, combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the PbO–FeO–Fe2O3–SiO2 system. The modified quasichemical model is used for the liquid slag phase. For the liquid phase, the PbO–FeO, PbO–Fe2O3, PbO–FeO–Fe2O3, PbO–FeO–SiO2 and PbO–Fe2O3–SiO2 parameters are optimized in the present study. From these model parameters, the optimized ternary phase diagram is back calculated. Present set of parameters describe previous and new experimental data well, and can be used for predictions of the PbO–FeO–Fe2O3–SiO2 phase equilibria over wide ranges of oxygen partial pressured, compositions and temperatures, as well as multicomponent systems.

1. Introduction

2. Literature review

The present thermodynamic optimization was performed using FactSage thermodynamic software package [1] as part of the development of the self-consistent thermodynamic database for the seven-component gas–slag–solid–metal PbO–ZnO–FeO–Fe2O3–Cu2O–CaO–SiO2 system for zinc/lead/copper smelting and recycling industries by integrated experimental and thermodynamic modelling studies. Experiments are performed to support thermodynamic database development. Thermodynamic predictions are used to identify gaps and discrepancies and to plan further experiments. A thermodynamic ‘‘optimization’’ of a system using the CALPHAD approach involves critical simultaneous evaluation of all available phase equilibria and thermodynamic data to obtain one set of model equations for the Gibbs energies of all phases as functions of temperature and composition [2–4]. The thermodynamic properties and the phase diagrams can then be back-calculated from the model equations to ensure that all data have been reproduced within the experimental error limits. Thermodynamic property data, such as activity data, can aid in assessing the phase diagram, and phase diagram measurements can be used to derive the thermodynamic properties. If discrepancy in the available data is found during the development of the model, new experimental measurements are undertaken to provide the data essential for further refinement of the model equations.

The PbO–SiO2 system has been reassessed by Shevchenko et al. [5], and the FeO–Fe2O3–SiO2 system by Hidayat et al. [6]. The PbO–FeO–Fe2O3 system has been recently experimentally studied by the present authors [7] in air, in equilibrium with metallic Pb, and at intermediate oxygen potentials along the spinel Fe3O4 – magnetoplumbite Pb1+xFe12-xO19-x boundary. Literature review of the earlier studies on the PbO–“Fe2O3” system in air [8–28] has also been conducted [7]. Liquidus of the PbO–FeO–Fe2O3–SiO2 system has been recently studied by the present authors in air [29] and in equilibrium with metal [30]. Kudo et al. [31] measured the PbO concentrations in PbO–“FeO”–SiO2–CaO slags in equilibrium with metallic liquid Pb and solid Fe. The recent data [30] reported twice higher solubility of PbO in slags at similar conditions, indicating that the samples in the study by Kudo et al. [31] might not reach equilibrium. Selected study of the PbO–“FeO”–SiO2 and PbO–“FeO”–CaO–SiO2 systems in equilibrium with Pb and Fe metals [30,32] confirm that the data by Kudo et al. [31] underestimate the PbO concentrations in slag in equilibrium with liquid Pb and solid Fe, when the latter are above ~0.5 wt%. Hollitt et al. [33] investigated the PbO–“FeO”–SiO2 slags in equilibrium with tridymite and liquid Pb or Pb–Ag alloy, reporting the p(O2)

∗

Corresponding author. E-mail address: [email protected] (M. Shevchenko).

https://doi.org/10.1016/j.calphad.2019.101670 Received 9 August 2019; Received in revised form 3 September 2019; Accepted 4 September 2019 0364-5916/ © 2019 Elsevier Ltd. All rights reserved.

Calphad 67 (2019) 101670

M. Shevchenko and E. Jak

in equilibrium with such samples that can be recalculated into activities of PbO in slags. Previous thermodynamic assessments of this system [34–37] have significant discrepancies with the recent data listed above [7,30,38,39]. A complete thermodynamic assessment of the PbO–FeO–Fe2O3–SiO2 system is undertaken in the present study to incorporate the new data.

silicates (PbSiO3, Pb2SiO4, Pb11Si3O17, Pb5SiO7), hematite Fe2O3, fayalite Fe2SiO4 (olivine endmember), melanotekite Pb2Fe2Si2O9, iron barysilite Pb8FeSi6O21, “P5FS” = Pb10Fe2Si2O17, and massicot PbO are treated as stoichiometric compounds. Magnetoplumbite PbFe12O19–Pb2Fe11O18, plumboferrite Pb2Fe10O17–Pb2Fe12O20, 1:1 lead ferrite Pb2Fe2O5–Pb3Fe2O6, and “P6FS” = Pb12Fe2Si2O19–Pb2Fe2O5 are described as solutions with Bragg-Williams model. Models for wustite (FeO–Fe2O3, Bragg-Williams) and spinel (Fe3O4+x, compound energy) are taken from Hidayat et al. [6] unchanged. The heat capacities and entropies of formation from pure oxides for binary and ternary oxide compounds are evaluated using an increment method [3,44], i.e. linear combinations of certain constants close to the properties of pure oxides, adjusted from existing experimental multicomponent data for groups of complex stoichiometric oxides. Parameters for liquid metal (Pb–Fe–O solution) and solid metal

3. Thermodynamic optimization In the present work, the Modified Quasichemical model (MQM) is used to model the liquid phase. The liquid oxide phase is described as an ionic liquid where Pb2+, Fe2+, Fe3+, and Si4+ cations mix on one sublattice, while oxygen anions occupy the other sublattice. The model has been described in detail by Pelton and co-workers [40–43]. Silica polymorphs (cristobalite, tridymite, quartz SiO2), lead

Table 1 Thermodynamic parameters of liquid and solid phases in the PbO–FeO–Fe2O3–SiO2 system. Compound a

Quartz (h) , SiO2 Tridymite (h), SiO2 Cristobalite (h), SiO2 Hematite, Fe2O3 Massicot, PbO Alamosite, PbSiO3 Pb2SiO4 Pb11Si3O17 Pb5SiO7 Fayalite (olivine), Fe2SiO4 Melanotekite, Pb2Fe2Si2O9 Fe-Barysilite, Pb8FeSi6O21 P5FS, Pb10Fe2Si2O17

Temperature range, K 298–1996 298–1991 298–1996 298–2500 298–1159 298–1200 298–1200 298–1200 298–1200 298–2000 298–1500 298–1400 298–1200

ΔHo298, J/mol

So298, J/(mol·K)

−908627 −907045 −906377 −824287 −218062 −1143420 −1362677 −5178045 −1996782 −1478483 −3101820 −7579121 −4740474

Cp(T), J/(mol·K)

Reference −2

44.207 45.524 46.029 87.729 68.699 115.818 189.312 917.836 418.045 150.294 347.864 933.397 973.380

−3

−0.5

80.012–3546684T +491568369T -240.276T 75.373–5958095T−2 +958246122T−3 −2 −3 83.514–2455360T +280072194T -374.693T−0.5 137.009–2907640T−2 47.639 + 0.01225T −45546016T−3 -65.753T−0.5 −35.227–0.13966T + 9.6807T0.5 −24.98–0.17976T + 12.475T0.5 22.199–0.64383T + 46.7T0.5 48.714–0.21725T + 16.78T0.5 248.927–139104009T−3 -1923.852T−0.5 66.555–0.27932T -2907640T−2 +19.3614T0.5 −43.667–0.86838T + 60.2296T0.5 -69552004T−3 -961.926T−0.5 477.034–0.35952T -2907640T−2 +24.95T0.5

Solution

Model

Parameters, J/mol or J/(mol·K)

P6FS, Pb12Fe2Si2O19–Pb2Fe2O5*

Ideal

1:1 lead ferrite, Pb2Fe2O5–Pb3Fe2O6

Ideal

Plumboferrite, Pb2Fe10O17–Pb2Fe12O20

Ideal

Magnetoplumbite, PbFe12O19–Pb2Fe11O18

Bragg-Williams

ΔHo298(Pb12Fe2Si2O19) = −5197102 So298(Pb12Fe2Si2O19) = 1075.067 Cp(Pb12Fe2Si2O19) = 607.036–0.35952T -2907640T−2 +24.95T0.5 ΔHo298(Pb2Fe2O5*) = −1229620 So298(Pb2Fe2O5*) = 248.930 Cp(Pb2Fe2O5*) = 242.136 + 0.02451T −5576782T−2 +434535856T−3 -131.507T−0.5 * means metastable endmember, different from stable Pb2Fe2O5 below ΔHo298(Pb2Fe2O5) = −1248448 So298(Pb2Fe2O5) = 248.930 Cp(Pb2Fe2O5) = 242.136 + 0.02451T −5576782T−2 +434535856T−3 -131.507T−0.5 ΔHo298(Pb3Fe2O6) = −1426344 So298(Pb3Fe2O6) = 317.629 Cp(Pb3Fe2O6) = 289.775 + 0.0367648T −5576782T−2 +388989840T−3 -197.26T−0.5 ΔHo298(Pb2Fe10O17) = −4475445 So298(Pb2Fe10O17) = 634.569 Cp(Pb2Fe10O17) = 829.57 + 0.02451T −27883910T−2 +2537047403T−3 -131.507T−0.5 ΔHo298(Pb2Fe12O20) = −5280342 So298(Pb2Fe12O20) = 763.725 Cp(Pb2Fe12O20) = 966.579 + 0.02451T −30791550T−2 +2537047403T−3 -131.507T−0.5 ΔHo298(PbFe12O19) = −4513101 So298(PbFe12O19) = 657.790 Cp(PbFe12O19) = 918.94 + 0.012254936T −30791550T−2 +2582593419T−3 -65.753T−0.5 ΔHo298(Pb2Fe11O18) = −4793454 So298(Pb2Fe11O18) = 721.006 Cp(Pb2Fe11O18) = 801.696 + 0.0551179T −27748068T−2 +2011419516T−3 +1369.393T−0.5

Monoxide (wustite), FeO1+x Spinel, Fe3O4+x Liquid, FCC, and BCC metal, Fe–Pb–O

Bragg-Williams Compound energy Bragg-Williams

11 qPbFe

12 O19, Pb2 Fe11 O18

[46] [46] [46] [45] [3] [5] [5] [5] [5] [6] This study This study This study

= −4000

[6], no Pb solubility [6], no Pb solubility FSStel and FSCopp FactSage databases [1] Fe–O system updated by Ref. [45]

(continued on next page)

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Table 1 (continued) Solution

Model

Parameters, J/mol or J/(mol·K)

Liquid Oxide/ Slag-Liq, PbO–FeO–Fe2O3–SiO2

Modified quasichemical (MQM)

Z Pb2 +

2+

2+

Pb2 +

Pb

2+

= Z Fe2 + Fe

Fe2 +

2+

= Z Fe2 + Fe

Pb2 +

= Z Pb2 +

2+

Fe2 +

Pb

= Z Fe2 +

Si 4 +

Fe

2+

= Z Fe2 + Fe

Fe3 +

2+

= Z Pb2 + Pb

Fe3 +

=,

1.3774 2+

= 2.1662 ,

Z Pb2 +

Pb Si 4 + 4+ Z Si4 + 4 + = Si Si 3+ Z Fe3 + 3 + Fe Fe

=

4+

4+

Z Si4 +

= Z Si4 +

Pb2 + 3+ Fe Z 3+ 2+ Fe Pb Si

=

o o o o gSiO , gFeO , gFe [6]; gPbO [3], 2 O3 2

go

Pb2 +, Fe2 +

go

Pb2 +, Fe

4+

= Z Si4 +

Fe 2 + 3+ Fe Z 3+ 2+ Fe Fe Si

Si

=

Fe3 +

= 2.7549 ,

3+ Z Fe3 + 4 +=2.0662 Fe Si

= 21422.08 (Bragg-Williams)

3 + = −9857.504 (Quasichemical)

= −6359.68 Pb , Fe3 + g o 2 + 4 + = −18463.992 + 0.389112*T (GUTS) Pb , Si q102 + 4 + = −16945.2; q102 + 4 + = −16945.2 [5] Pb , Si Pb , Si

g 012 +

= 12911.824; q012 + 4 + = −24840.408 Pb , Si 4 + Pb , Si 02 q 2 + 4 + = 52300; q072 + 4 + = −26087.24 [5] Pb , Si Pb , Si q092 + 4 + = 29187.584 [5] Pb , Si

q202 +

g o 2 + 3 + = 0 (Quasichemical) [6] Fe , Fe 20 q 2 + 3 + = −2092 [6] Fe , Fe q012 + 3 + = −20957.656 [6] Fe , Fe g o 2 + 4 + = −29116.456 + 14.294163208*T Fe , Si q202 + 4 + = 12480.872 [6] Fe , Si q062 + Fe

, Si 4 +

= 66607.10432 , Si 4 +

q013 + Fe Fe

, Si 4 +

Fe

, Si

[5]

(Quasichemical) [6]

= 366501.664–134.728984*T [6]

= 27213.9912 Fe3 +, Si 4 +

(Quasichemical) [6]

go

q073 +

[5]

[6]

= 439890.86496–133.888*T; [6]

FeO–Fe2O3–SiO2, PbO–FeO–SiO2, PbO–Fe2O3–SiO2: Toop grouping with SiO2 as a special component [41,47]. PbO–FeO–Fe2O3: Kohler grouping [41,47]. g 3012 + 4 + 3 + = 91742.568 [6] , Fe

g1012 +

= −71270.256 [6]

g 0012 +

= −36777.36

g 0612 +

= −39748

Fe , Si 4 +, Fe3 + g 0122 + 4 + 3 + = 54392 [6] Fe , Si , Fe g 0212 + 4 + 3 + = 69454.4 [6] Fe , Si , Fe g 2013 + 4 + 2 + = −62760 [6] Fe , Si , Fe

Pb , Si 4 +, Fe2 + g 0312 + 4 + 2 + = 22007.84 Pb , Si , Fe g 0012 + 4 + 2 + = 28325.68 Fe , Si , Pb g 0322 + 4 + 2 + = −72048.48 Fe , Si , Pb

Fe

, Si 4 +, Pb2 +

g 0012 +

= −21087.36

g1012 +

= 39873.52

Pb

, Si 4 +, Fe3 +

Pb , Fe3 +, Si 4 + g 0612 + 4 + 3 + = −38994.88 Pb , Si , Fe g1022 + 4 + 3 + = 15146.08 Pb , Si , Fe g 0322 + 4 + 3 + = 51044.8 Pb , Si , Fe a

(h) are high-temperature modifications of quartz, tridymite, and cristobalite.

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Table 2 Root mean square (RMS) uncertainties in liquidus temperatures ΔT (K) by primary phase fields in the PbO–FeO–Fe2O3–SiO2 system. Phase field

In air

In equilibrium with Pb metal

Number of points

RMS, present work

RMS, [31]

Number of points

RMS, present work

RMS, [31]

Quartz, tridymite, cristobalite SiO2 Hematite Fe2O3 Spinel Fe3O4 Magnetoplumbite Pb1+xFe12-xO19-x

30

32.5

144.0

39

17.3

35.0

56 4 57

25.8 11.2 23.9

36 2

20.5 23.8

Melanotekite Pb2Fe2Si2O9 Plumboferrite Pb2Fe10O17

31 14

10.2 20.1

5

45.1

86.9 60.8a PbFe10O16 10.4

1:1 lead ferrite Pb2Fe2O5 P5FS, Pb10Fe2Si2O17 P6FS, Pb12Fe2Si2O19

13 3 4

13.9 12.8 3.0

6 5

8.5 9.2

Alamosite, PbSiO3 Lead orthosilicate, Pb2SiO4 P11S3, Pb11Si3O17

3 5 2

12.6 6.5 2.6

6.5 13.8a Pb10Fe2Si2O17

6 4

1.6 2.7

Massicot PbO Wustite FeO1+x Fayalite (olivine) Fe2SiO4 Iron barysilite Pb8FeSi6O21 Fe metal (weighted error) Total

5

8.8

33.3 39.9 40.3a PbFe10O16 51.5 80.8a PbFe4O7 31.1 4.2 10.9a Pb10Fe2Si2O17 8.6 18.8 15.0a Pb4SiO6 7.3

227

22.7

66.5

8 1 12 13 2 139

9.6 5.5 7.9 15.4 63.8 19.3

16.0 5.3a Pb4SiO6 7.3 9.8 25.4 n.a. 709.8 103.4

a

Calculated as present in public FactSage database [31]: “PbFe10O16”, “PbFe4O7”, “Pb10Fe2Si2O17”, “Pb4SiO6”.

(BCC and FCC) phases are taken unchanged from previous assessments [1,45]. The ranges of mutual solubility of Fe and Pb in liquid and solid states are very narrow. For the liquid slag phase, the PbO–FeO, PbO–Fe2O3, PbO–FeO–Fe2O3, PbO–FeO–SiO2 and PbO–Fe2O3–SiO2 parameters are optimized in the present study; the rest of parameters are taken from previous assessments.

thermodynamic model agrees with the recent experimental data [30,32] and describes twice higher concentration of PbO in slag at these conditions. Despite an improvement in the database, the two immiscible liquids range is predicted much wider than the experimental. The oxygen partial pressures measured with EMF technique [33] for the equilibrium with Pb–Fe–Si–O slag, Pb–Ag metal and tridymite at 1200 °C are compared to the present model calculation in Fig. 4. The predictions agree with the experimental data within the experimental accuracy. Present set of parameters describe previous and new experimental data well, and can be used for predictions of the PbO–FeO–Fe2O3–SiO2 phase equilibria over wide ranges of p(O2), compositions and temperatures, as well as multicomponent systems.

4. Results and discussion Optimized thermodynamic properties of the liquid slag and solid solutions and stoichiometric compounds are listed in Table 1. The root mean square (RMS) deviation of calculated liquidus from experimental data is chosen as a quantitative measure of the model performance during optimization of parameters: RMS error Tliq = (Σ(ΔT2)/N)0.5, where N is the number of points for a given phase field and conditions (air, reducing, etc.); ΔT = Tliq(calc) – Tliq(exp) for each liquidus data point. Its distribution by all primary phase fields that have liquidus points measured in the ternary system is shown in Table 2. As seen, for three out of four most important primary phase fields (quartz + tridymite + cristobalite, spinel, hematite), there is a 2–4 times reduction of uncertainty in liquidus temperature, and a total 3–5 times reduction of uncertainty, compared to the previous study [31]. The experimental results are compared to the optimized thermodynamic model calculations for the pseudoternary liquidus PbO–“FeO”–SiO2 in equilibrium with metallic Pb and PbO–“Fe2O3”–SiO2 in air are presented in Figs. 1 and 2. The low-PbO part, corresponding to equilibrium with both Fe and Pb metals, is presented in Fig. 3. The new

5. Conclusions A critical evaluation of phase equilibria and thermodynamic data for the PbO–FeO–Fe2O3–SiO2 system has been carried out using previous as well as most recent experimental data, the latter produced by the authors as part of the integrated research program. The modified quasichemical model is used to describe the Gibbs energy of the slag phase. The new model parameters reproduce the available data within experimental error limits. Compared to the previous assessment by Kudo, Jak et al. [31], better agreement with the experimental data was obtained, since the liquidus surface of the PbO–“Fe2O3”–SiO2 and PbO–“FeO”–SiO2 systems was not available at that time. All of these changes are significant for the industrial applications of the database. The optimized database can be used as a basis for the simulation of various high temperature metallurgical processes, for the evaluation of

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Fig. 1. Liquidus projection of the PbO–“FeO”–SiO2 system in equilibrium with metallic Pb, calculated using the current optimized thermodynamic model, compared with recent experimental results [30].

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Fig. 2. Liquidus projection of the PbO–“Fe2O3”–SiO2 system in air, calculated using the current optimized thermodynamic model, compared with recent experimental results [7,29,38].

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Fig. 3. Solubility of PbO in “FeO”–SiO2 slags at liquidus (wustite, fayalite, tridymite and cristobalite) in equilibrium with both Fe and Pb metals. Present model and experiment [30,32] are compared to the previous study [31].

Fig. 4. Comparison of experimentally measured [33] p(O2) in equilibrium with Pb–Fe–Si–O slag, Pb–Ag metal and tridymite at 1200 °C, and the values calculated with the present model.

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possible improvement of the existing operations, or for the development of new processes.

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Acknowledgements The authors would like to thank Nyrstar (Australia), Outotec Pty Ltd (Australia), Aurubis AG (Germany), Umicore NV (Belgium), and Kazzinc Ltd, Glencore (Kazakhstan), and Australian Research Council Linkage project LP150100783 for their financial support for this research. The authors are grateful to Prof. Peter C. Hayes (UQ) for valuable comments and suggestions. Data availability The raw/processed data (thermodynamic parameters) required to reproduce these findings are provided in supplementary file. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.calphad.2019.101670. References [1] C.W. Bale, E. Belisle, P. Chartrand, S.A. Decterov, G. Eriksson, K. Hack, I.-H. Jung, Y.-B. Kang, J. Melancon, A.D. Pelton, C. Robelin, S. Petersen, FactSage thermochemical software and databases - recent developments, Calphad 33 (2009) 295–311. [2] G. Eriksson, A.D. Pelton, Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CaO-Al2O3, Al2O3-SiO2, and CaO-Al2O3-SiO2 systems, Metall. Trans. 24 (1993) 807–816. [3] E. Jak, S.A. Decterov, P. Wu, P.C. Hayes, A.D. Pelton, Thermodynamic optimisation of the systems PbO-SiO2, PbO-ZnO, ZnO-SiO2 and PbO-ZnO-SiO2, Metall. Mater. Trans. B 28B (1997) 1011–1018. [4] E. Jak, S.A. Decterov, P.C. Hayes, A.D. Pelton, Thermodynamic optimisation of the systems CaO-Pb-O and PbO-CaO-SiO2, Can. Metall. Q. 37 (1998) 41–47. [5] M. Shevchenko, E. Jak, Thermodynamic optimization of the binary systems PbOSiO2, ZnO-SiO2, PbO-ZnO, and ternary PbO-ZnO-SiO2, Calphad 64 (2019) 318–326, https://doi.org/10.1016/j.calphad.2019.01.011. [6] T. Hidayat, D. Shishin, S.A. Decterov, E. Jak, Experimental study and thermodynamic Re-evaluation of the FeO-Fe2O3-SiO2 system, J. Phase Equilibria Diffusion 38 (2017) 477–492, https://doi.org/10.1007/s11669-017-0535-x. [7] M. Shevchenko, E. Jak, Experimental phase equilibria studies of the Pb-Fe-O system in air, in equilibrium with metallic lead and at intermediate oxygen potentials, Metall. Mater. Trans. B 48 (2017) 2970–2983, https://doi.org/10.1111/jace.15208. [8] E.J. Kohlmeyer, Uber bleioxyd und eisenoxydulferrite (Lead-Oxide and Iron-Oxide Ferrites), Metallhuttenwesen und Erzbergbau einschl, Aufbereitungstechnik 10 (1913) 447–462. [9] L.I. Paramonov, Lead ferrites, Tsvetn. Met. (Moscow, Russ. Fed.) (1934) 79–88. [10] A. Cocco, Ricerche sul sistema binario PbO-Fe2O3, (research on the binary system PbO-Fe2O3), Annali di Chimica-Roma 45 (1955) 737–753. [11] W. Berger, F. Pawlek, Kristallographische und magnetische untersuchungen im system bleioxyd (PbO) - eisenoxyd (Fe2O3), (Crystallographic and magnetic investigations in the system PbO-Fe2O3), Arch. Eisenhuttenwes. 28 (1957) 101–108. [12] E.V. Margulis, N.I. Kopylov, Investigation of the system PbO-Fe2O3, Russ. J. Inorg. Chem. 5 (1960) 1196–1199. [13] A.J. Mountvala, S.F. Ravitz, Phase relations and structures in the system PbO-Fe2O3, J. Am. Ceram. Soc. 45 (1962) 285–288. [14] D.M. Chizhikov, T.E. Konyshkova, the system lead oxide-iron oxide, Tr. Inst. Met. im. A. A. Baikova, Akad. Nauk SSSR (1963) 72–78. [15] J. Cassedanne, The equilibrium diagram α-Fe2O3-PbO, An. Acad. Bras. Cienc. 36 (1964) 417–422. [16] V.E. Rudnichenko, B.L. Dobrotsvetov, D.M. Kheiker, Composition of ferrites in the PbO-Fe2O3 system, Sb. Nauchn. Tr. Gos. Nauchn.-Issled. Inst. Tsvetn. Metal. 23 (1965) 389–399. [17] H.D. Jonker, Investigation of the phase diagram of the system PbO-B2O3-Fe2O3Y2O3 for the growth of single crystals of Y3Fe5O12, J. Cryst. Growth 28 (1975) 231–239. [18] J. Mexmain, S.L. Hivert, Preparation and characterization of lead ferrites, Ann. Chim. 3 (1978) 91–97. [19] S.A. Shaaban, M.F. Abadir, A.N. Mahdy, The system Pb-Fe-O in air, Br. Ceram. Trans. J. 83 (1984) 102–105. [20] M. Nevriva, K. Fischer, Contribution to the binary phase diagram of the system PbO-

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