Journal of the European Ceramic Society 34 (2014) 1611–1621
Critical evaluation and thermodynamic modeling of the Al–Mn–O(Al2O3–MnO–Mn2O3) system
Saikat Chatterjee, In-Ho Jung ∗Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, Quebec H3A 0C5, Canada
Received 23 September 2013; received in revised form 5 December 2013; accepted 10 December 2013Available online 2 January 2014
bstract
n the present study, a complete thermodynamic description of the Mn–Al–O (MnO–Mn2O3–Al2O3) system has been carried out. All the experi-ental phase diagram data from metal saturation to 1 atm oxygen partial pressure, thermodynamic data for spinel and liquid phases and structural
ata for spinel were critically evaluated and optimized in order to obtain Gibbs energies of all phases as functions of temperature and composition.he MnAl2O4–Mn3O4 spinel solution was modeled using the Compound Energy Formalism considering the cation distribution between tetrahedralnd octahedral sites. The slag phase was described using the Modified Quasichemical Model considering both, the Mn2+ and Mn3+ species.
The MnO–Al2O3 system is important for the steelmak-ng process and the production of ferro-manganese. Recently,igh Mn steels, such as the TWIP (TWinning-Induced Plas-icity) steel containing about 15–30 wt.% Mn,1 are gettinguge attention due to the increasing demand of superior-qualityutomotive steel. When Al is used as the deoxidizing agent,nAl2O4 is readily formed as a non-metallic inclusion. How-
ver, one must keep in mind that the main slag system for theroduction of ferro-manganese is the CaO–MnO–SiO2–Al2O3ystem, so when the slag interact with refractories composedf MgO–C and MgO–Al2O3, the MnAl2O4–MgAl2O4 spinelhase is rather formed. In addition, Mn can have numer-us oxidation states and MnO, Mn2O3, and MnO2 can beonsidered as oxide components at oxygen partial pressuresower than 1 atm. Due to its importance, one of the presentuthors already performed the thermodynamic modeling of thenO–Al2O3 system2 by correcting the previous optimization
3
esults of Eriksson et al. However in this new modeling of thenO–Al2O3 system,2 MnAl2O4 spinel was defined as a stoi-
hiometric compound instead of a solid solution and MnO was
he only oxide considered; no Mn2O3 and MnO2 were takennto account. Moreover, new heat capacity data were recently
easured for MnAl2O4. Consequently, the MnO–Al2O3 sys-em must be first re-optimized in order to model properly the
nO–Mn2O3–Al2O3 system.In the thermodynamic “optimization” of a chemical system,
ll available thermodynamic and phase equilibrium data arevaluated simultaneously in order to obtain one set of modelquations for the Gibbs energies of all phases as functions ofemperature and composition. From these equations, all thehermodynamic properties and phase diagrams can be back-alculated. In this way, all the data are rendered self-consistentnd consistent with thermodynamic principles. Thermodynamicroperty data, such as activity data, can aid in the evaluationf the phase diagram, and phase diagram measurements cane used to deduce thermodynamic properties. Discrepanciesn the available data can often be resolved, and interpolationsnd extrapolations can be made in a thermodynamically correctanner.Numerous studies were performed to optimize the
nO–Al2O3 system. The system was first optimized byriksson et al.3 In their optimization, Eriksson et al. employed
he Gibbs energy of MnAl2O4 listed in the compilation of Barin.4
owever, Jung et al. realized that this Gibbs energy is erroneousnd for this reason, they re-optimized the system by correctinghe Gibbs energy of MnAl2O4 from the original experimental
1612 S. Chatterjee, I.-H. Jung / Journal of the Europe
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MnO
Mn2O3 Al2O3mole f raction
A
BC
D
E:
EFGH
+ C-Sp
Corundu m (Cor)
D: Mono + T-Sp
C: C-Sp + Mono +
Tetragon al Spin el (T-S p)
B: Cubi c Spin el (C-S p) + Mon o
A: Mono xid e (Mono )
I
F: Cor + C-Sp
+ Bixbyite (Bix)
G: C-Sp + Bix
H: C-Sp + T-Sp + Bix
I: T-Sp + Bix
Bix Cor
T-Sp C-Sp
Mn3O4
Galax ite(MnAl2O4)
Fa
dawMeadettoeses
ctpotiitta
2
(p
aswcce
2
dsnph1stmMow
(s
dMsdoao
oe
G
ig. 1. Calculated phase diagram of the MnO–Mn2O3–Al2O3 system at 1000 ◦Cnd 1 atm total pressure.
ata. In this way, the activity of MnO in the binary, ternarynd higher order systems of the MnO-CaO-Al2O3–SiO2 systemas well reproduced. Recently, Farina and Neto5 modeled thenO–Al2O3 system with a MnAl2O4 spinel solution consid-
ring the distribution of Mn2+ and Al3+ between tetrahedralnd octahedral sites of spinel, but they were not able to repro-uce the experimental Gibbs energy of MnAl2O4.6–11 Navarrot al.12 considered MnAl2O4 as a stoichiometric compound inheir modeling. Although they did not explicitly mention inheir modeling results like Farina and Neto,5 their Gibbs energyf MnAl2O4 was not consistent with the experimental Gibbsnergy of MnAl2O4. Moreover, no previous study considered thepinel solution MnAl2O4–Mn3O4 and no thermodynamic mod-ling were performed at various oxidation states in the Mn–Al–Oystem.
The purpose of the present study is thus to perform theritical evaluation and optimization of all the experimen-al data related to the phase diagrams and thermodynamicroperties of the Al–Mn–O (Al2O3–MnO–MnO2) system atxygen partial pressures going from metallic saturation upo 1 atm. In particular, the MnAl2O4–Mn3O4 spinel solutions properly modeled according to structural data. This studys part of a large thermodynamic database development ofhe CaO–MgO–Al2O3–SiO2–FeO–Fe2O3–MnO–Mn2O3 sys-em for steelmaking, refractories and general pyrometallurgicalpplications.
. Phases and thermodynamic models
The calculated phase diagram of the Al–Mn–OAl2O3–MnO–Mn2O3) system at 1000 ◦C and 1 atm totalressure is shown in Fig. 1. The solution phases are:
Cubic spinel (encompassing cubic-Mn3O4 and MnAl2O4 with
limited solubility of Al2O3):
(Mn2+, Al3+)T
[Mn2+, Mn3+, Mn4+, Al3+, Va]O2 O4
waG
an Ceramic Society 34 (2014) 1611–1621
Tetragonal spinel (limited solution extended from tetragonal-Mn3O4):
(Mn2+, Mn3+, Al3+)T
[Mn2+, Mn3+, Al3+, Va]O2 O4
Slag (molten oxide phase): MnO–MnO1.5–AlO1.5Monoxide: MnO-rich solution containing small amounts ofAlO1.5 and MnO1.5Bixbyite: Mn2O3-rich solution containing considerableamounts of Al2O3Corundum: Al2O3-rich solution containing small amounts ofMn2O3Metallic phases: liquid, bcc, fcc, sigma and so on.
Note that cations within brackets occupy the same sublatticend T and O represent the tetrahedral and octahedral cationicites in spinel, respectively. The magnetic properties of bixbyiteere not modeled in detail in the present study because the
ritical temperatures are lower than 100 K; however, magneticontributions to heat capacities were considered to calculate thentropy at 298 K.
.1. Spinel: cubic and tetragonal
There are two different cation sites in spinels: tetrahe-ral and octahedral. Cation distribution between these twoublattices is the most important physical and thermody-amic property of spinel. There are two types of spinelhases in the Mn–Al–O system: cubic and tetragonal. Mn3O4as a tetragonal structure and transforms to cubic form at172 ◦C in air.13 Although tetragonal Mn3O4 can dissolvemall amounts of MnAl2O4, cubic Mn3O4 can extend upo MnAl2O4. Using their electrochemical seed-back experi-
ental technique, Dorris and Mason14 found that these twon3O4 spinels have different ionic configuration. In the case
f cubic spinel, the tetrahedral sites are occupied by Mn2+
hile the octahedral ones are taken by Mn2+, Mn3+ and Mn4+:
Mn2+)T
[Mn2+, Mn3+, Mn4+]O2 O4. In the case of tetragonal
pinel, Mn2+ and Mn3+ cations can enter both, the tetrahe-
ral and octahedral sites: (Mn2+, Mn3+)T
[Mn2+, Mn3+]O2 O4.
oreover, when Mn3O4 is mixed with MnAl2O4 to form aolid solution, Al3+ can enter in the tetrahedral and octahe-ral sites. Vacancies are then produced in the octahedral sitesf the cubic and tetragonal spinels by dissolution of �-Mn2O3nd �-Al2O3. This structural information was implemented inur thermodynamic models of cubic and tetragonal spinels.
The two spinel models were developed within the frameworkf the Compound Energy Formalism (CEF).15 The Gibbs energyxpression in the CEF per formula unit is:
=∑
i
∑j
YTi YO
j Gij − TSC + GE (1)
here YTi and YO
i represent the site fractions of constituents ind j on the tetrahedral and octahedral sublattices; Gij is theibbs energy of an “end-member” (i)T[j]O
2 O4 of the solution,
uropean Ceramic Society 34 (2014) 1611–1621 1613
isto
S
G
wcaasiawi
L
L
ea
L
L
gwmpTtpeiitcsLr
2
[vee
Table 1Optimized model parameters of all the solutions present in theMnO–Mn2O3–Al2O3 system (J/mol and J/mol-K).
Notations F, J, K, L and V are used for Al3+, Mn2+, Mn3+, Mn4+ andvacancy, respectively. The model parameters for Al–O spinel solutioncan be found elsewhere.22
Notations F, J, K, L and V are used for Al3+, Mn2+, Mn3+, Mn4+, andvacancy, respectively. The model parameters for Al–O spinel solutioncan be found elsewhere22
n which the first sublattice is occupied only by cation i and theecond only by cation j; GE is the excess Gibbs energy; and SC ishe configurational entropy assuming random mixing of cationsn each sublattice:
C = −R
⎛⎝∑
i
YTi lnYT
i + 2∑
j
YOj lnYO
j
⎞⎠ (2)
The excess Gibbs energy is expanded as:
E =∑
i
∑j
∑k
YTi YT
j YOk Lij:k +
∑i
∑j
∑k
YTk YO
i YOj Lk:ij (3)
here the parameters Lij:k are related to interactions betweenations i and j on tetrahedral sites when all octahedral sitesre occupied by k cations, and similarly the parameters Lk:ijre related to interactions between i and j cations on octahedralites when the tetrahedral sites are all occupied by k cations. Onemportant assumption according to the model is that the inter-ction between the same two cations present on one sublatticeill not change on changing the cation on the other sublattice,
.e.,
k:ij = Ll:ij = . . . (4)
ij:k = Lij:l = . . . (5)
Redlich–Kister power series expansions16 can be used toxpress the dependence of interaction energies on compositions follows:
ij:k =∑m
mLij:k(yTj − yT
i )m
(6)
k:ij =∑m
mLk:ij(yOj − yO
i )m
(7)
The main model parameters are the end-member Gibbs ener-ies, Gij. Certain linear combinations of the Gij parameters,hich have a physical significance, are used as the optimizedodel parameters. Degterov et al.17 had already discussed the
hysical significance of these linear combinations (I and Δ).hey are related to the energies of classical site exchange reac-
ions of cations. In this way, the model parameters have certainhysical meaning and it was found (Degterov et al.,17 Jungt al.,18 Jung et al.,19 Jung et al.,20 and Jung21) to be much eas-er to complete the whole thermodynamic modeling than settingndividually each Gij parameters without any reason. Moreover,he model has a high predictive ability. Details of the linearombinations of Gij parameters for both, cubic and tetragonalpinels, are given in Table 1. Please note that notations F, J, K,
and V were used for Al3+, Mn2+, Mn3+, Mn4+ and vacancy,espectively.
.1.1. Cubic spinel
Cubic spinel has a (Mn2+, Al3+)T
2+ 3+ 4+ 3+ O
Mn , Mn , Mn , Al , Va]2 O4 structure includingacancy (Va) on octahedral sites. Ten end-member Gibbsnergies are required for the model. Among them, four Gibbsnergies were already determined in a previous optimization of
q31MnO,MnO1.5
= −20, 920.00a
No excess parameter was required for the MnO1.5–AlO1.5 solution
1614 S. Chatterjee, I.-H. Jung / Journal of the Europe
Other Gibbs energies of the gas components are obtained from the FACTPSdatabase.27
a The model parameters for the Mn-O system were optimized previously.21
d
tieNcaecp
G
2
F
F
trtpbdeapoddi
2
[(a
pMdpi
etds
(oTws
2
tn
MspcMa
on
(
wG
G
wgmfiotoncaiT
b The Gibbs energies of the corundum species come from the FToxidatabase.27
he Mn–O system (Mn3O4)21 and another two (GFF and GFV)n a study of the Mg–Al–O system.22 The remaining four Gibbsnergies (Eqs. (8)–(11)) were determined in the present study.ote that many end-members are not neutral and have some
harges associated to them while the spinel solution itself has neutral charge. In order to determine the Gibbs energy of thend-members, physically meaningful combinations of Gij wereonsidered. These are the model parameters optimized in theresent study.
JF : Gibbs energy of completely normal MnAl2O4
spinel end-member (8)
JF = FF + FJ : IJF = GFF + GFJ − 2GJF (9)
F + JK = FK + JF : ΔFJ :KF = GFK + GJF − (GFF + GJK) (10)
For example, reaction (9) is basically a site exchange reac-ion between normal and inverse spinel. The Gibbs energy of thiseaction (IJF) is the one which affects the degree of inversion ofhe spinel the most. So, proper variation in this ‘I’ parameter waserformed in order to reproduce the experimental cation distri-ution data and Gibbs energy of formation of the spinel, afteretermination of GJF. Similarly, Δ parameters of two other sitexchange reactions (ΔFJ:KF and ΔFJ:LF) were optimized in such
way that they can correctly reproduce all other experimentalhase diagram data. Excess Gibbs energy parameters were alsoptimized in order to reproduce mainly the solubility of corun-um in the spinel phase at high temperature along with cationistribution data. All the optimized model parameters are listedn Table 1.
.1.2. Tetragonal spinel
Tetragonal spinel has a (Mn2+, Mn3+, Al3+)T
Mn2+, Mn3+, Al3+, Va]O2 O4 structure including vacancy
Va) on octahedral sites. Twelve end-members Gibbs energiesre necessary to model the solid solution; eight of them were
uptt
an Ceramic Society 34 (2014) 1611–1621
reviously determined in the optimization of the Mn–O21 andg–Al–O22 systems. The remaining four Gibbs energies were
etermined in the present study. The model parameters areresented in Table 1. Due to the low solubility of MnAl2O4n Mn3O4, the most important model parameter is the Gibbs
nergy of tetragonal MnAl2O4 spinel ((Mn2+)T
[Al3+, Va]O2 O4)
hat is unstable in normal conditions. This Gibbs energy wasetermined to reproduce the solubility limit of Al in tetragonalpinel.
The GJF (Gibbs energy of normal spinel,
Mn2+)T
[Al3+]O2 O4) and ΔJFK parameters were the only
ptimized parameters; all the other parameters were set to zero.he optimization of the parameters for the tetragonal spinelas performed in a manner similar to the one done for the cubic
pinel.
.2. Molten oxide (slag)
The Modified Quasichemical Model (MQM),23–25 whichakes into account the short-range ordering of second-nearest-eighbor cations in ionic melt, is used to model the slag.
The components of the slag are taken asnO–MnO1.5–AlO1.5. Although Mn can have higher oxidation
tates, only the divalent and trivalent oxidation states, whichredominate at oxygen partial pressures less than 1.0 atm, areonsidered in the present study. Mn2O3 and Al2O3 are taken asnO1.5 and AlO1.5 to indicate that all Mn3+ and Al3+ cations
re distributed independently between oxygen.In the binary MnO–AlO1.5 solution, for example, short range
rdering is taken into account by considering the second-nearest-eighbor pair exchange reaction:
Mn–Mn) + (Al–Al) = 2(Mn–Al) : �gMnAl (12)
here Mn–Al represents a second-nearest-neighbor pair. Theibbs energy of the solution is given by:
= (nMnOgOMnO + nAlO1.5g
OAlO1.5
) − T�Sconfig
+nMnAl(�gMnAl/2) (13)
here ni and gOi are the number of moles and molar Gibbs ener-
ies of the components, respectively, nMn–Al is the number ofoles of (Mn–Al) bonds at equilibrium, �Sconfig is the con-gurational entropy of mixing for the random mixing of bondsver ‘bond sites’ in the Ising approximation which is a func-ion of nMn–Al, and �gMn–Al is the molar Gibbs energy changef reaction (12) which can be expanded as an empirical poly-omial function in the mole fractions of the components. Theoefficients of this polynomial are obtained by optimizing thevailable experimental data. The value of nMn–Al at equilibriums obtained by setting ∂G/∂nMn–Al = 0 at constant composition.he details of the model can be found elsewhere.21
The binary sub-system MnO–MnO1.5 was critically eval-21
ated and optimized previously ; their optimized model
arameters were used in the present study without any modifica-ion. The MnO–AlO1.5 system was optimized by Jung et al.2 andheir liquid parameters were modified according to the change
uropean Ceramic Society 34 (2014) 1611–1621 1615
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2
tAttiiatwfctMmft
G
waT
Mpp
2s
satsde
G
wA
Sample No. 1
Sample No. 2
Sample No. 3
Temperature, K
Hea
t ca
paci
ty (
J/m
ol-
K)
0 200 400 600 800 1000 1200 1400 1600
0
20
40
60
80
100
120
140
160
180
200
Fm
miot
2
pnJn
3
3s
3
ptordcaaeMiwctN
S. Chatterjee, I.-H. Jung / Journal of the E
f the Gibbs energy of the spinel phase. The binary param-ters of the MnO–AlO1.5 and MnO1.5–AlO1.5 slag solutionsTable 1) were optimized as described in the following sections.he Gibbs energy of the ternary liquid AlO1.5–MnO–MnO1.5olution is estimated using the symmetric Kohler-like interpo-ation technique.26 No ternary model parameter was used in theresent study.
.3. MnO (monoxide)
The monoxide solution has a rock–salt structure. In ordero describe this MnO-rich solution with limited solubility ofl2O3 and Mn2O3, a simple random mixing model is used
o keep the consistency with the previous monoxide solu-ion of CaO–MgO–MnO–FeO–NiO–Al2O3–Fe2O3–Mn2O3. Its modeled as a simple random mixture of Mn2+, Mn3+ and Al3+
ons on cation sites. It is assumed that cation vacancies remainssociated with Mn3+ and Al3+ ions and so do not contributeo the configurational entropy. Binary excess Gibbs energiesere modeled by simple polynomial expansions in the mole
raction.26 The properties of the ternary monoxide solution arealculated from the binary parameters of the MnO–AlO1.5 sys-em optimized by Jung et al.2 and the binary parameters of the
nO–MnO1.5 system optimized previously21 by using the sym-etric Kohler-like approximation.26 No parameters were used
or the AlO1.5–MnO1.5 system. The Gibbs energy per mole ofhe solution is expressed as:
m =∑
i
XiGoi + RT
∑i
Xi lnXi
+∑
i
∑j
XiXj
(Xi
Xi + Xj
)m(Xj
Xi + Xj
)n
qmnij + gex
ternary
(14)
here G◦i is the Gibbs energy of components like MnO, MnO1.5
nd AlO1.5, and Xi is the mole fraction of the component.he binary model parameters qmn
ij of the MnO-AlO1.52 and
nO–MnO1.521 systems were optimized previously. No binary
arameter for the MnO1.5–AlO1.5 system and no ternary excessarameter (gex
ternary) were employed.
.4. Mn2O3 (bixbyite) and Al2O3 (corundum) solidolutions
Bixbyite is the Mn2O3-rich solid solution that has a cubictructure above room temperature; it can dissolve a certainmount of Al2O3. Corundum is the Al2O3-rich solid solutionhat has a trigonal structure based on the hcp oxygen-packingcheme; a limited amount of Mn2O3 can be dissolved into corun-um. The Gibbs energy per mole of each binary solution isxpressed as:
m = (XAG◦A + XBG◦
B) + 2RT (XA lnXA + XB lnXB)∑
+ qmn
AB(XA)m(XB)n (15)
here G◦i is the Gibbs energy of components like Mn2O3 and
l2O3, and Xi is mole fraction of the component. The binary
t83c
ig. 2. Heat capacity of MnAl2O4 calculated from the present spinel solutionodel along with the experimental data of Navarro et al.12
odel parameters qmnij of the bixbyite phase were optimized
n the present study while those of the corundum phase wereptimized previously27 and used without any modification. Allhe optimized model parameters are listed in Table 1.
.5. Metallic phases
In this study, the FSstel database28 was employed for all thehases present in the Al-Mn metallic system. The thermody-amic properties of these phases were optimized previously byansson29 using all the available phase diagram and thermody-amic data.
. Critical evaluation and optimization
.1. Thermodynamic properties of the MnAl2O4 spinelolution
.1.1. Heat capacity of MnAl2O4
The calculated heat capacity (Cp) of MnAl2O4 from theresent spinel model is shown in Fig. 2 with the experimen-al data of Navarro et al.12 Note that the calculated curve is notbtained from the theoretical spinel end-member but from theeal MnAl2O4 spinel solution which is subject to some cationistribution effects. Navarro et al.12 recently measured the heatapacity of stoichiometric MnAl2O4 spinel using thermal relax-tion calorimetry between 2 and 300 K. Their experimental datare the average values of 3 independent Cp measurements atach temperature. They also calculated the molar entropy ofnAl2O4 spinel at 298.15 K (S◦
298.15) to be 116 ± 5 J/mol-K byntegrating their low temperature Cp data. A certain anomalyas observed at about 40 K, but no further investigation was
arried out by Navarro et al.12 to find the reason. High tempera-ure (323 < T < 873 K) Cp measurements were also performed byavarro et al.12 with the help of a differential scanning calorime-
er. First of all, the MnAl2O4 samples were heated from 373 to73 K at a rate of 20 K/min. They were then cooled from 873 to23 K at a rate of 20 K/min with isothermal stops at systemati-ally separated temperatures. Each isothermal temperature was
1 uropean Ceramic Society 34 (2014) 1611–1621
mfltwa
aaaficM9toi
chmfo
3
asrMtftw1oMietie1eatoMfimaAAbt
m
Fig. 3. Optimized isothermal Gibbs energy of formation of MnAl2O4 from solidMnO and Al2O3 along with experimental data.6–11 Evaluated and calculatedrc
sfMimWwffAas
twpbtMmwrfi−F2
3
sdt
616 S. Chatterjee, I.-H. Jung / Journal of the E
aintained for two minutes, enough to reach a constant heatux, and a polynomial function of temperature was used to fit
he measured isothermal fluxes. The heat capacity of MnAl2O4as then calculated based on the properties of a standard (Al2O3)
nd the crucible (Al).As mentioned above, the experimental Cp data in Fig. 2
re in fact the Cp of (Mn2+, Al3+)T
[Mn2+, Al3+]O2 O4 spinel
t the stoichiometric MnAl2O4 composition. MnAl2O4 is not perfect normal spinel because its cation distribution deviatesrom ideal stoichiometry. Therefore, experimental heat capac-ty data may contain some cation distribution effects, i.e., theation distribution may change with temperature. In the case ofgAl2O4, the cation distribution is almost frozen below about
73 K22 so that the change in cation distribution does not con-ribute to the heat capacity. In fact, the cation distribution dataf MnAl2O4 spinel has a quite normal distribution (inversions less than 0.05 at 500 K), so the heat capacity appear to be
lose to the (Mn2+)T
[Al3+]O2 O4 end-member. Our calculated
eat capacity curve is in very good agreement with the experi-ental Cp data. Our calculations give a value of 115.32 J/mol-K
or S298.15◦, which is nearly identical to the experimental valuef 116 ± 5 J/mol-K.
.1.2. Gibbs energy of MnAl2O4
The Gibbs energy of formation of MnAl2O4 from MnOnd Al2O3 was determined by many researchers. The firsttudy was performed by Lenev and Novokhatskii6 byeducing MnAl2O4 with hydrogen gas. Using the reaction
nAl2O4 + Mn + O2 + Al2O3 at known O2 partial pressures,hey determined the Gibbs energy of formation of MnAl2O4rom MnO and Al2O3 between 1550 and 1700 ◦C. In con-rast, Kim and McLean7 equilibrated liquid Fe and Al2O3ith additions of FeAl2O4–MnAl2O4 spinel solid solutions at550, 1600 and 1650 ◦C and by using the known activitiesf Mn and O in liquid Fe, the Gibbs energy of formation ofnAl2O4 was derived. Jacob8 and Zhao et al.9 performed sim-
lar experiments where MnAl2O4 and Al2O3 were respectivelyquilibrated with Pt–Mn and Ag–Mn alloys under fixed par-ial pressures of oxygen. By using the known activity of Mnn the alloys and the Mn contents of the alloys, the Gibbsnergy of formation of MnAl2O4 was determined at 1600 and650 ◦C by Jacob8 and between 1300 and 1550 ◦C by Zhaot al.9 and Dimitrov et al.10 equilibrated liquid Fe with Al2O3nd MnAl2O4 and used a solid-state emf method to measurehe partial pressure of oxygen and derive the Gibbs energyf formation of MnAl2O4 at 1550 and 1600 ◦C. Timucin anduan11 equilibrated NiO–MnO/NiAl2O4–MnAl2O4/Ni under
xed partial pressures of oxygen at 1300 and 1400 ◦C and deter-ined the Gibbs energy of formation of MnAl2O4 from MnO
nd Al2O3 using a ternary Gibbs-Duhem integration technique.ll the experimental data listed above are depicted in Fig. 3.lthough the data appear quite scattered, they are mostly located
etween −20 and −30 kJ/mol in the temperature range of 1400o 1600 ◦C.
Timucin and Muan11 are the only researchers to have deter-ined the Gibbs energy of formation of MnAl2O4 under MnO
b
sX
esults obtained by Barin,4 Jung et al.2 and Navarro et al.12) are also shown foromparison.
aturation; all the other experimental studies6–11 were per-ormed under Al2O3 saturation. As the homogeneity range of the
nAl2O4 spinel solution is toward both, Mn3O4 and Al2O3, its possible that the experimental Gibbs energy of formation waseasured for some non-stoichiometric MnAl2O4 compositions.ith the exception of Jacob8 and Zhao et al.,9 all the experimentsere carried out with metal saturation (Mn, Ni or Fe) and there-
ore MnAl2O4 is probably stoichiometric. Interestingly, evenor the experimental data of Jacob8 and Zhao et al.,9 the excessl2O3 seems to be insignificant. Therefore, it appears reason-
ble to consider that all the experimental data were collected fortoichiometric MnAl2O4.
As can be seen in Fig. 3, the optimized Gibbs energy of forma-ion of MnAl2O4 is in good agreement with experimental dataithin experimental error ranges. This is not the case for thereviously optimized Gibbs energy of formation of MnAl2O4y Navarro et al.12 and Barin4 which are much more nega-ive than experimental data. The Gibbs energies of formation of
nAl2O4 at 1600 ◦C is also similar to the Gibbs energies of for-ation of FeAl2O4 and MgAl2O4 from their constituent oxideshich are about −18.5 kJ/mol30 and −40 kJ/mol at 1600 ◦C,22
espectively. The calculated enthalpy of formation of MnAl2O4rom MnO and Al2O3 at 298 K from the present spinel models −12.8 kJ/mol, in comparison to −27.7 kJ/mol and around
23.5 kJ/mol for MgAl2O4 by Jung et al.22 and Zienert andabrichnaya31 respectively, and −37.4 kJ/mol for FeAl2O4
30 at98 K.
.1.3. Cation distribution of MnAl2O4 spinel solutionAt low temperature MnAl2O4 is considered as a normal
pinel,32–39 that is, Mn2+ and Al3+ occupy mostly the tetrahe-ral and octahedral sites, respectively. However with increasingemperature, the degree of inversion (disorderliness) of cationsetween the sites increases, which is shown in Fig. 4.
Greenwald et al.32 annealed at 1400 ◦C for 1–2 h somepinels, quenched them to room temperature, and determined byRD the cation distribution to be 0.29 ± 0.04. Roth33 prepared
S. Chatterjee, I.-H. Jung / Journal of the European Ceramic Society 34 (2014) 1611–1621 1617
Tristan et al. (2005 )
Haleniu s et al. (2011 )
Gree nwald et al. (1954 )
Roth (1964 )
Temper ature, °C
Fra
ctio
n o
f A
l3+ c
ati
on
s on
tet
rah
edra
l si
tes
0 20 0 40 0 60 0 80 0 100 0 120 0 140 0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Fig. 4. Calculated variation of cation distribution in MnAl2O4 as a function oftemperature along with experimental data of Greenwald et al.,32 Roth,33 Tristane
Matiefimtpd5bahakst7oX
oproaf
3
MtMsP
Fig. 5. The activity of MnO (with respect to solid standard state) in theMnO–Al O system at 1600 and 1650 ◦C under reducing atmosphere (p =1a
sdtorar
3
3
riir
dmMptoasFwaaetNi 2
t al.37 and Halenius.39
nAl2O4 samples under controlled partial pressures of oxygen,nnealed them at an unspecified temperature, performed a struc-ural analysis by neutron diffraction, and obtained a degree ofnversion of 0.084 ± 0.044. Tristan et al.37 carried out similarxperiments where samples were also annealed at an unspeci-ed temperature, and by using XRD with Rietveld analysis, theyeasured a degree of inversion of 0.06. This value is lower than
he one obtained earlier by Roth33 probably because their samplereparation temperature was lower. According to Roth,33 cationiffusion is negligible below 600 ◦C; for Tristan et al.,37 it is00 ◦C. Jung et al.22 considered the Tfroz (i.e. the temperatureelow which there is no inversion due to slow kinetics) to bebout 700 ◦C. It is also known22 that if the temperature is tooigh (about 927 ◦C), the cation distribution cannot be quenchednd cations will be redistributed during quenching due to fastinetics. Since no specific temperature was mentioned in thetudies of Roth33 and Tristan et al.,37 the temperature at whichhe structure of their samples was frozen (Tfroz) was chosen as00 ◦C. Recently, Halenius39 determined the cation distributionf a MnAl2O4 sample quenched from 900 ◦C using single crystalRD. They measured a degree of inversion of 0.16 at 900 ◦C.As can be seen in Fig. 4, the variation of cation distribution
f MnAl2O4 with temperature can be well reproduced by theresent spinel model. The IJF parameter was used mainly toeproduce the cation distribution data. The degree of inversionf MnAl2O4 is slightly lower than that of MgAl2O4 and FeAl2O4t the same temperature (for example, 0.20 for MnAl2O4, 0.28or MgAl2O4 and 0.27 for FeAl2O4 at 1200 ◦C).
.1.4. Activity of MnO in the MnO–Al2O3 systemSharma and Richardson40 and Jacob8 equilibrated
nO–Al2O3 mixtures with Pt–Mn foils under fixed par-ial pressures of oxygen at 1600 and 1650 ◦C. The activity of
nO (with respect to solid standard state) in MnO–Al2O3ystem was then calculated from the known activity of Mn int foils and the controlled oxygen partial pressure.
p1w
2 3 O2
0−5 atm). Experimental points are from Sharma and Richardson40 and Jacob8
nd the calculated lines are from the present study.
Our optimized activity of MnO (with respect to solid standardtate) in the MnO–Al2O3 system is compared with experimentalata in Fig. 5. The present results are very similar to those fromhe previous optimization of Jung et al.2 Note that the activityf MnO in the two phase region Al2O3 + MnAl2O4 is directlyelated to the Gibbs energy of MnAl2O4, as pointed out by Jungnd Kang.41 The experimental activities of MnO on the MnO-ich side are well reproduced in the present study.
.2. Phase diagram of the Mn–Al–O system
.2.1. Under reducing atmosphere: MnO–Al2O3
The calculated phase diagram of the Mn–Al–O system ateduced oxygen partial pressures along with experimental datas shown in Fig. 6. The phase diagram under reducing conditionss typically drawn as MnO–Al2O3. However, Mn3O4 can beeadily formed depending on the oxygen partial pressure.
Hay et al.42 employed thermal analysis to determine the phaseiagram in the MnO-rich region (Al2O3 ≤ 50 wt.%). They deter-ined the liquidus of spinel (they claimed it was MnAl2O4) andnO and also the eutectic of the MnO-rich region. They also pro-
osed that spinel melts peritectically at 1560 ◦C. Unfortunately,he atmosphere was not tightly controlled and it seems that thexygen partial pressure was not sufficiently low. Later, Oelsennd Heynert43 reported a phase diagram for the MnO–Al2O3ystem in reduced conditions by extrapolating the liquidus of theeO–MnO–Al2O3 system saturated with liquid Fe. The samplesere contained in Al2O3 crucibles and quenched. They found
eutectic at 1520 ◦C in the MnO-rich region and a peritectict 1720 ◦C in the Al2O3-rich one. Fischer and Bardenheuer44
mployed a similar technique and observed the eutectic inhe MnO-rich region at about 70 wt.% MnO and 1580 ± 5 ◦C.ovokhatskii et al.45 measured the melting point of MnAl2O4
n a gas mixture of Ar and H under controlled oxygen partial
ressure. The congruent melting of MnAl2O4 was observed at850 ◦C and the eutectics in the MnO- and Al2O3-rich sidesere measured at 1520 ± 10 ◦C and 1770 ± 15 ◦C, respectively.
1618 S. Chatterjee, I.-H. Jung / Journal of the European Ceramic Society 34 (2014) 1611–1621
F ondit −5 −6 −8
e rdenhs
Na
e1mMaaloAamouai
a
FmaeMottmtaiteuit
ig. 6. Calculated phase diagrams of the Mn–Al–O system under reducing cxperimental data (Jacob,8 Hay et al.,42 Oelsen and Heynert,43 Fischer and Bapinel, Mono: monoxide, Cor: corundum, Bix: bixbyite.
ovokhatskii et al.45 claimed, from XRD results, that Al2O3nd MnAl2O4 exhibited virtually no mutual solid solubility.
Jacob8 measured the liquidus at 1600 and 1650 ◦C byquilibration and quenching under oxygen partial pressures of0−5–10−6 atm and results were analyzed with the electronicroprobe as shown in Fig. 6. The solubility of Al2O3 in solidnO is about 1% and MnO is not soluble in MnAl2O4. Jacob
lso equilibrated some Mn and MnO in sealed Al2O3 cruciblest 1600 and 1650 ◦C and quenched them. Results were ana-yzed by electron microprobe analysis (EPMA). The solubilityf MnO in Al2O3 is approximately 1% and the solubility ofl2O3 in MnAl2O4 is about 3%. The invariant temperatures
nd the melting points of pure MnO, Al2O3 and MnAl2O4 wereeasured by Jacob8 by examination, either visual or under an
ptical microscope, of pellets quenched from high temperaturender purified Ar. He reported that MnAl2O4 melts congruentlyt 1850 ◦C and hence that the invariant point shown at 1769 ◦C
n Fig. 6 is actually a eutectic.
The calculated phase diagrams of the MnO–Al2O3 systemt oxygen pressures of 10−5–10−6 atm are presented in Fig. 6.
wet
ions at (a) 10 atm, (b) 10 atm, (c) 10 atm and (d) Mn-saturation witheuer44 and Novokhatskii et al.45 L: slag, C-Sp: cubic spinel, T-Sp: tetragonal
ig. 6 also shows predicted phase diagrams at 10−8 atm and atetal saturation. Under the oxygen partial pressures of 10−5
nd 10−6 atm, the spinel solution of MnAl2O4 is calculated toxtend almost to Mn3O4. In reducing conditions, the amount ofn3+ in the liquid phase is negligible. The maximum amount
f Mn2O3 in the slag at 1600 ◦C is about 2.7 wt.%. Therefore,he Gibbs energy of the liquid phase is mainly determined byhe interaction between MnO and Al2O3. That is, in the present
odeling, the MQM parameters for the liquid MnO–Al2O3 solu-ion were determined to reproduce the phase diagram in Fig. 6,fter the Gibbs energy of MnAl2O4 was determined as shownn Fig. 3. All experimental data8,42–44 under reducing condi-ions were compared in Fig. 6(a). It should be noted that all thexperimental data were not obtained at 10−5 atm. Since the liq-idus and solidus of the calculated MnO–Al2O3 phase diagramn Fig. 6 did not change significantly with partial pressure ofhe system under reducing condition, we thought it was worth-
hile to compare all the experimental data in one diagram. The
xperimental liquidus and solidus reported by Jacob8 at con-rolled oxygen partial pressure, which can be considered to be
S. Chatterjee, I.-H. Jung / Journal of the European Ceramic Society 34 (2014) 1611–1621 1619
(a) (b)
BixT-Sp
L + C-Sp
L
L + Cor
C-Sp + Cor
T-Sp + Cor
Cor + Bix
Rang anathan et. al. (1962 )
T-Sp + C-Sp
T-Sp + Bix
C-Sp
C-Sp
L + C-Sp
L
L + Cor
Cor + BixC-S p + Bix
Bix
C-Sp
Cor + C-Sp
T-Sp
T-Sp+
T-S p + Bix
Mn mole fraction Al
Tem
per
atu
re,
0C
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
700
900
1100
1300
1500
1700
1900
2100
2300
2500
Bix
T-Sp + Bix
Bix + Cor
C-Sp + CorC-Sp + Bix
T-Sp and Bix + T-Sp
Bobov et al. (1984)Dekker & Rieck (1975)
C-Sp
T-Sp
C-Sp + T-Sp
Bix and Bix + T-Sp
Bix + T-Sp (C-S p)
B + C-Sp and C-Sp
C-Sp and C-Sp + Cor
C-Sp and C-Sp + Cor
Golikov et al. (1995)
C-SpC-Sp + Cor
Cor + Bix
Bix
L
L + C-Sp
L + Cor
T-S p + BixC-S p + Bix
T-Sp
C-S p + T-Sp
Mn mole fraction Al
Tem
per
atu
re,
0C
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
700
900
1100
1300
1500
1700
1900
2100
2300
2500
F xperie Mon
twTJGigJmwrsa
iepsrstwmaTb
aAtgAlhei
imbsdiMo
3
a
rmmrRprbatt
oindmtt
ig. 7. Calculated phase diagrams of the Mn–Al–O system in air along with et al.48 and Golikov et al.49 L: slag, C-Sp: cubic spinel, T-Sp: tetragonal spinel,
he most reliable data out of all the experimental results, areell reproduced except for the congruent melting of MnAl2O4.he same difficulty was found in the previous optimization byung et al.2 As it was mentioned in the work by Jung et al.,2 theibbs energy of MnAl2O4 spinel must be much more negative
n order to reproduce the phase diagram accurately with the con-ruent melting reported by Jacob. However, as pointed out byung et al.,2 a more negative Gibbs energy of MnAl2O4 induces aore negative interaction of MnO and Al2O3 in the liquid phase,hich causes a poor reproduction of the activity of MnO (with
espect to solid standard state) in the MnO–Al2O3–CaO–SiO2ystem. The optimized MQM parameters for the liquid phasere listed in Table 1.
The newly optimized phase diagram in the MnO-rich regions almost the same as the diagram optimized previously Jungt al.2 where MnAl2O4 was considered as a stoichiometric com-ound. The phase diagram of the MnO–Al2O3 system with Mnaturation is also similar to that of FeO–Al2O3 with Fe satu-ation. In particular, the equilibria of MnAl2O4 and FeAl2O4pinel solutions with their respective liquids are very similar. Inhe previous optimization by Jung et al.,2 the liquidus of Al2O3as intentionally flattened to reproduce the melting of stoichio-etric MnAl2O4 compound in the MnO–Al2O3 system using
positive model parameter of liquid phase in Al2O3 rich side.his induced a metastable miscibility gap in Al2O3 rich sideelow 1400 ◦C. This has been resolved in the present study.
In the present modeling, the spinel solution between Mn3O4nd MnAl2O4 with excess solubility of Al2O3 was considered.s can be seen in Fig. 6, a wide spinel solution at sub-solidus
emperatures is predicted from Mn3O4 (MnO side) at oxy-en partial pressures of 10−5–10−6 atm. The amount of excessl2O3 solubility in MnAl2O4 on the Al2O3-rich side is a bit
arger than the experimental data of Jacob.8 In the modeling,
owever, it is found that this solubility is highly related to thexcess solubility of Al2O3 in the oxidizing conditions depictedn Fig. 7. The solubility of Al2O3 in MnAl2O4 appears nearly
p
nR
mental data by (a) Ranganathan et al.,46 and (b) Dekker and Rieck,47 Bobovo: monoxide, Cor: corundum, Bix: bixbyite.
ndependent of oxygen partial pressure. In the present opti-ization, the solubility of Al2O3 in MnAl2O4 was optimized
ased on the phase diagram of the Mn–Al–O system in air ashown in Fig. 7 which was well determined by two indepen-ent studies.45,46 In order to reproduce the solubility of Al2O3n MnAl2O4, positive excess interaction parameters between
n2+ and Al3+ in the tetrahedral site, 1LFJ:i (i = any cation inctahedral site), were needed.
.2.2. Under oxidizing atmosphere: Mn2O3–Al2O3 systemThe calculated phase diagram of the Mn–Al–O system in air
long with experimental data is shown in Fig. 7.Ranganathan et al.46 were the first to determine the phase
elations in the Mn2O3–Al2O3 system in air using the quenchingethod followed by optical microscopy and XRD phase deter-ination. Samples were prepared over the entire composition
ange and equilibrated between 800 and 1700 ◦C. Dekker andieck47 used a similar technique to determine the sub-solidushase equilibria. Bobov et al.48 prepared samples in the Mn3O4-ich region between 800 and 1000 ◦C to determine the phaseoundary of tetragonal spinel more accurately. Golikov et al.49
lso concentrated their investigation between 900 and 1300 ◦Co find the phase boundaries of tetragonal and cubic spinel usinghe quenching technique and in situ high temperature XRD.
Due to the presence of a Jahn-Teller effect in the structuref cubic spinel with Mn3+, the quenched cubic spinel phases tetragonally distorted and easily misinterpreted as tetrago-al. In the present study, the tetragonally distorted cubic spinelue to a Jahn-Teller effect is treated as a second order transfor-ation of cubic spinel, which is different from the first order
ransformation to tetragonal spinel. The present modeling ofhe spinel solution can successfully reproduce the experimental
hase diagram data shown in Fig. 7.
As discussed above, the phase boundary between tetrago-al and cubic spinels was mainly determined by Dekker andieck,47 Bobov et al.48 and Golikov et al.,49 while other areas
1620 S. Chatterjee, I.-H. Jung / Journal of the European Ceramic Society 34 (2014) 1611–1621
(a) (b)
(c) (d)
CUB_A13
AL8 ML
CUB_A13 + Cor
C-S p + Cor
C-Sp
C-S p + Mono
CUB_A13 + C-Sp
T-S
p
Mono
L +AL8 M
HCP_A3 BCC _A2
Al mole fraction Mn
log
p(O
2),
ba
r
0 0.2 0.4 0.6 0.8 1
-40
-35
-30
-25
-20
-15
-10
-5
0
BCC _A2
L +
HC
P_A
3
L
BCC _A2 + Cor
C-S p + CorC-S p + Mono
C-Sp
Mono
BCC_A2 + C-Sp
HC
P_A
3
Al mole fraction Mn
log
p(O
2),
ba
r
0 0.2 0.4 0.6 0.8 1
-40
-35
-30
-25
-20
-15
-10
-5
0
L + Cor
Cor + C-Sp
C-S p + Mono
C-Sp
L + C-Sp
Mono
L
Al mole fraction Mn
log p
(O2),
ba
r
0 0.2 0.4 0.6 0.8 1
-30
-25
-20
-15
-10
-5
0
L
L + Cor
C-S p + Cor
C-Sp
C-SpSlag
Mono + SlagMono
+ Slag
Al mole fraction Mn
log
p(O
2),
ba
r
0 0.2 0.4 0.6 0.8 1
-30
-25
-20
-15
-10
-5
0
F (a) 1e nal sp
woottioais
obtwMa
3
po
sca
4
Mcmi(tttpt
ig. 8. Calculated (predicted) Mn–Al–O phase diagrams at temperatures of:
ere established for the most part by Ranganathan et al.46 More-ver, as mentioned in the previous section, the excess solubilityf Al2O3 in MnAl2O4 in reducing conditions (Fig. 6) is relatedo the homogeneity range limit of the cubic spinel phase towardhe Al2O3-rich side at about 1700 ◦C (up to Al/(Mn + Al) = 0.75)n Fig. 7. That is, in order to reproduce the homogeneity rangef cubic spinel toward the Al2O3-rich side in air, a noticeablemount of excess solubility of Al2O3 in MnAl2O4 is expectedn reducing conditions. The homogeneity range of tetragonalpinel was mainly determined by the end-member Gibbs energy
f tetragonal (Mn2+)T
[Al3+]O2 O4. The homogeneity range of
ixbyite was also reproduced by an excess interaction parame-er. The MQM parameters for the Mn2O3–Al2O3 binary systemas determined to reproduce the liquidus and solidus of then–Al–O system in air. All the optimized model parameters
re summarized in Table 1.
.2.3. Mn–Al–O2 phase diagramUsing our optimized model parameters, experimentally unex-
lored phase diagrams can be predicted. For example, thexygen partial pressure-composition diagrams of the Mn–Al–O
rdp
000 ◦C, (b) 1200 ◦C, (c) 1400 ◦C and (d) 1600 ◦C. Molar metal ratio versusinel, Mono: monoxide, Cor: corundum, AL8M: Al8Mn5.
ystem at various temperatures between 1000 and 1600 ◦C arealculated in Fig. 8 with the help of the newly optimized databasend the FSstel28 database.
. Summary
All the thermodynamic and phase diagram data in then–Al–O system from reducing to oxidizing conditions were
ollected and critically evaluated for the thermodynamic opti-ization of the system. The present optimization properly takes
nto account the cubic and tetragonal spinel solution phasesMn3O4–MnAl2O4 with excess Al2O3) for the first time, unlikehe previous optimizations. All the cation distribution data andhermodynamic data of the spinel and phase diagram related tohe spinel solution are well reproduced. The optimized modelarameters can reproduce all the reliable experimental data ofhe Mn–Al–O system at any oxygen partial pressures from
oom temperature to upper liquidus temperatures. The optimizedatabase was also used to predict experimentally unexploredhase diagrams of the Mn–Al–O system.
urope
A
tRHJ
R
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2223
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
S. Chatterjee, I.-H. Jung / Journal of the E
cknowledgements
The current work is part of a large steelmaking consor-ium project supported by the Natural Sciences and Engineeringesearch Council of Canada in collaboration with Tata Steel,yundai Steel, Posco, Nucor Steel, Rio Tinto, Sumitomo Metals,
FE Steel, Nippon Steel, RHI and Voestalpine.
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