October
物理化学学报(Wuli Huaxue Xuebao)
Acta Phys. -Chim. Sin. 2015, 31 (10), 1853–1863
[Article]
doi: 10.3866/PKU.WHXB201508121
1853
www.whxb.pku.edu.cn
MgO-P2O5和CaO-P2O5体系的热力学优化
丁国慧1
谢
伟1
JUNG In-Ho2
乔芝郁1
杜广巍1
曹战民1,*
(1北京科技大学钢铁冶金新技术国家重点实验室, 冶金与生态工程学院, 北京 100083;
麦吉尔大学矿业与材料工程系, 蒙特利尔 QC H3A 0C5, 加拿大)
2
摘要: 基于严格评估的相图和热力学实验数据, 采用相图计算方法对MgO-P2O5和CaO-P2O5体系进行热力学
优化. 液相采用修正的似化学模型进行描述, 考虑了对近似处理液相中存在的短程有序. 为了描述M3(PO4)2
(M = Mg, Ca)组分处的最大短程有序, 将 3¡
4 当作液相中P2O5的基本组成单元. 体系中所有的中间相都看作
线性化合物并考虑了晶型转变. 获得一套合理、可靠、自洽的模型参数用来描述体系中各相的热力学性质, 在
实验误差范围内很好地重现了相图、焓、熵和活度实验数据, 为炼钢脱磷过程中熔渣体系热力学数据库的建
立打下了坚实的基础.
关键词: MgO-P2O5;
CaO-P2O5;
修正的似化学模型;
热力学;
相图
中图分类号: O642
Thermodynamic Assessment of the MgO-P2O5 and CaO-P2O5 Systems
DING Guo-Hui1
XIE Wei1
JUNG In-Ho2
QIAO Zhi-Yu1
1
DU Guang-Wei
CAO Zhan-Min1,*
(1State Key Laboratory of Advanced Metallurgy, School of Metallurgical and Ecological Engineering, University of Science &
Technology Beijing, Beijing 100083, P. R. China; 2Department of Mining and Materials Engineering, McGill University,
Montreal QC H3A 0C5, Canada)
Abstract: The MgO-P2O5 and CaO-P2O5 systems have been thermodynamically assessed based on the
available phase diagram and thermodynamic data using the Calculation of Phase Diagram (CALPHAD)
method. The liquid phase is described by the modified quasichemical model with the pair approximation,
3¡
which takes short-range ordering in liquid solution into account. The
4 is considered as the basic
building unit of P2O5 in the liquid solution since the maximum short-range ordering occurs at the M3(PO4)2
(M = Mg, Ca) composition. All intermetallic phases are treated as stoichiometric compounds and the phase
transformations are considered. A set of self-consistent model parameters is obtained to describe the
thermodynamic property of every phase in these two binary systems, by which the published phase
diagram, enthalpy, entropy, and activity data are reproduced well within experimental error limits. The
present study can be used as a basis for the development of a thermodynamic database of molten slag
system for the steelmaking dephosphorus process.
Key Words: MgO-P2O5;
CaO-P2O5;
Modified quasichemical model;
Thermodynamics;
Phase diagram
1 Introduction
Since phosphorus is one of the harmful elements in general
steel, decrease of phosphorus content in hot metal is an important issue for steel plants. During the basic oxygen furnace
Received: April 30, 2015; Revised: August 12, 2015; Published on Web: August 12, 2015.
*
Corresponding author. Email: [email protected]; Tel: +86-10-62332530.
The project was supported by the National Key Basic Research Program of China (973) (2014CB643401).
国家重点基础研究发展规划项目(973) (2014CB643401)资助
© Editorial office of Acta Physico-Chimica Sinica
1854
Acta Phys. -Chim. Sin. 2015
(BOF) process, phosphorus is removed from hot metal by reactions with basic oxides in the slag, so that the molten slag typically consists of the MgO-CaO-FeO-Fe2O3-SiO2-Al2O3-P2O5 system.1 In order to control the dephosphorization capacity of molten slag and understand phosphorus distribution ratio between
the slag and hot metal, the phase diagrams and thermodynamic
properties of the multi-component slag system are very significant. However, no systematic thermodynamic modeling of the
slag system containing P2O5 has been conducted to date. To
achieve this, each binary system must be modeled before they
are used to simulate the higher order systems. In other words,
the MgO-P2O5, CaO-P2O5, and other binary systems should be
modeled firstly. It is a basis for the development of thermodynamic database of the multi-component slag system. Besides
steelmaking, the MgO-P2O5 and CaO-P2O5 systems are also important in the biomaterials field due to the extensive use of calcium phosphate-based biomaterials. These materials commonly
belong to the higher order systems, such as MOx-CaO-P2O5,
where MOx is ZnO, MgO or SiO2.2,3 It is well known that good
phase diagram and thermodynamic descriptions of the MgOP2O5 and CaO-P2O5 systems are essential for materials design.
For the MgO-P2O5 system there is no thermodynamic assessment (optimization or modeling) can be found to date. This system presents four intermediate compounds and the liquid phase
exhibits maximum short-range ordering (SRO) at the M3(PO4)2
composition. The emphasis is on the selection of a suitable thermodynamic model and liquid species for the liquid phase.
For the CaO-P2O5 system it has been thermodynamically assessed by Serena et al.4 and Hudon and Jung5 using different
models to describe the liquid phase. Serena et al.4 modeled the
liquid phase by the ionic two-sublattice model, i.e., (Ca2+)P(O2–,
2¡
3¡
P O¡
3 , P O 2=7 , P O 4 , PO5/2)Q. Although the ideal distribution of
phosphate species in liquid solution could be reproduced by this
model, considering all possible phosphate species results in the
use of excessive model parameters (15) for the liquid phase.
When expanding to the higher order systems, this model will
become very complex and the compatibility will reduce. In addition, according to the assessment of Serena et al.4 the calculated temperatures of invariant reactions involving liquid phase
are considerably higher than the experimental data. For example, the calculated temperature of L = Ca 3 (PO 4 ) 2 +
Ca4(PO4)2O (L: liquid phase) is 2011 K which is 158 K higher
than the experimental value of 1853 K.6 Evidently, more liquid
parameters used by Serena et al.4 cannot reproduce the phase
diagram well. Furthermore, the Ca4P6O197 and Ca10(PO4)6O8,9
compounds, numerous phase equilibrium and thermodynamic
data, such as the activity of CaO(s) in liquid phase10 and reaction Gibbs free energies of Ca 2 P 2 O 7 , Ca 3 (PO 4 ) 2 , and
Ca4(PO4)2O11,12 were not considered by Serena et al.4 Ignoring
amounts of experimental data would possibly make the model
parameters obtained by Serena et al.4 unreliable.
Recently, Hudon and Jung5 reassessed the CaO-P2O5 system
using the modified quasichemical model (MQM)13,14 to describe
the liquid phase. The phase diagram was reproduced well ex-
Vol.31
cept for the liquidus of Ca4(PO4)2O, which was slightly higher
than the experimental data. For the sake of simplicity in the
thermodynamic modeling, only P 2O 4¡
7 species was considered
by Hudon and Jung5 as the basic building unit of P2O5 to describe the SRO of liquid solution. In fact, however, the P O 3¡
4
species is dominant at the maximum SRO occurring at the
Ca3(PO4)2 composition. Therefore, it is necessary to remodel
the liquid phase with P O 3¡
4 species.
The aim of the present work is to perform thermodynamic assessment of the MgO-P2O5 and CaO-P2O5 systems based on all
available phase diagrams and thermodynamic data using the
Calculation of Phase Diagram (CALPHAD) method. The liquid phase is described by the MQM in the pair approximation,
which takes SRO in liquid solution into account and has been
widely applied to describe the thermodynamic properties of
many liquid oxide solutions.5,15 All calculations of phase diagrams and thermodynamic properties will be done by the
FactSage software.16
2 Literature review
2.1 MgO-P2O5 system
The MgO-P 2 O 5 system contains four intermediate compounds: Mg3(PO4)2 (M3P), Mg2P2O7 (M2P), Mg(PO3)2 (MP),
and MgP4O11 (MP2). Among these compounds, only Mg2P2O7
undergoes polymorphic transition. A summary of their crystallographic description is presented in Table 1.17–30
2.1.1 Phase transformations of intermediate compounds
2.1.1.1 Mg3(PO4)2
Berak 31 and Bobrownicki and Slawski 32 respectively observed a polymorphic transition of Mg3(PO4)2 at 1328 and 1323
K by thermal analysis, but the high temperature form cannot be
stabilized by quenching in water. Other studies19,33,34 did not observe the thermal effect resulting from the polymorphic transition. Due to no details like lattice parameter and stability field
were given by Berak 31 and Bobrownicki and Slawski, 32 the
phase transition of Mg3(PO4)2 was not taken into account in the
present work. By thermal analysis, Berak,31 Bobrownicki and
Slawski, 32 Oetting and McDonald, 34 Bookey, 35 Stevens and
Turkdogan,36 and Ando37 observed that Mg3(PO4)2 congruently
melted at 1630, 1628, (1626 ± 5), (1703 ± 5), 1621, and 1623
K, respectively. Baykal et al.19 and Czupinska33 also reported
melting points of 1457 and 1630 K by differential thermal analysis (DTA), respectively. These data are in good agreement
with each other except for the values reported by Baykal et al.19
and Bookey.35 The reason is not clear because the experimental
information given by them is limited.
2.1.1.2 Mg2P2O7
The low-temperature transformation of Mg2P2O7 was first observed at (341 ± 2) K by Roy et al.38 by DTA, and the X-ray
powder diffraction (XRD) patterns for the α and β forms were
reported. Oetting and McDonald34 also observed this transition
in both the low temperature adiabatic calorimeter and the drop
No.10
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DING Guo-Hui et al.: Thermodynamic Assessment of the MgO-P2O5 and CaO-P2O5 Systems
Table 1
Phase
Mg3(PO4)2
Crystal structures of the intermediate compounds in the MgO-P2O5 system
Crystal structure
Space group
Phase prototype
Method
Reference
monoclinic
P21/b
mP26
XRD
17
monoclinic
P21/n
mP26
XRD
18
monoclinic
P21/n
mP26
XRD
19
monoclinic
P21/n
mP26
XRD
20
monoclinic
P21/n
mP26
XRD
21
XRD
22
triclinic
P1
aP52
α-Mg2P2O7
monoclinic
C2/m
mS22
XRD
23
β-Mg2P2O7
monoclinic
P21/c
mP44
XRD
24
monoclinic
P21/c
mP44
XRD
25
monoclinic
C2/c
mS72
XRD
26
monoclinic
C2/c
mS72
XRD
27
monoclinic
P21/c
mP64
XRD
28
monoclinic
P21/c
mP64
XRD
29
orthorhombic
Pmc21
oP138
XRD
30
Mg(PO3)2
MgP4O11
XRD: X-ray diffraction; α, β: the polymorph from high temperature to low temperature
calorimeter results. The obtained transition temperature of
(342 ± 1) K is in good agreement with the result reported by
Roy et al.38 Calvo et al.23,25 found that the phase transition was
reversible and included coexistence of both phases from 335 to
338 K and 332 to 336 K by XRD and electron spin resonance
(ESR), respectively. Czupinska33 studied the YPO4-Mg2P2O7
system by DTA and reported two polymorphic transitions of
Mg 2 P 2 O 7 . The low temperature transition at 341 K caused
strong thermal effect on the DTA curves over the whole testing
process, while the thermal effect from the high temperature
transition at 1373 K could only be observed in the composition
range from 40% to 100% (w, mass fraction) Mg2P2O7. In the
present work, only the generally reported low-temperature
transformation of Mg2P2O7 is considered. Berak31 and Oetting
and McDonald34 respectively observed that the Mg2P2O7 congruently melted at 1655 and 1668 K by thermal analysis, and
Czupinska33 reported a melting point of 1658 K by DTA.
2.1.1.3 Mg(PO3)2
No polymorphic transition was reported for the Mg(PO3)2
compound. Thilo and Grunze,39 Berak,31 Andrieu and Diament,40
Rakotomahanina-Rolaisoa et al.,41 and Czupinska42 respectively
determined the congruently melting points of 1433, 1438, 1436,
1425, and 1438 K by DTA, and Sarver and Hummel43 also observed a melting point of (1438 ± 5) K by quenching experiments. These data are consistent with each other and the most
values are around about 1438 K.
2.1.1.4 MgP4O11
No polymorphic transition was reported for the MgP4O11
compound. Only Meyer et al.29 determined the congruently
melting point of 1183 K by DTA. The sample was heated up to
373 K above the melting point in open corundum crucible and
then was cooled in the air.
2.1.2 Liquidus and invariant reactions
The liquidus was only determined by Berak31 using thermal,
microscopic, and X-ray analysis in the composition range from
30% to 78% (w) P2O5. Three eutectic reactions of L = MgO +
Mg3(PO4)2, L = Mg3(PO4)2 + α-Mg2P2O7, and L = α-Mg2P2O7 +
Mg(PO3)2 were reported to occur at 1598, 1555, and 1423 K,
respectively. Using the cooling curve by means of a bare Pt/PtRh thermocouple immersed in the MgO-P2O5 melt, Bookey35
determined that the Mg3(PO4)2-MgO eutectic temperature was
(1603 ± 5) K, which is consistent with the result obtained by
Berak.31
2.1.3 Thermodynamic data
2.1.3.1 MgO and P2O5
Recently, Jung and Hudon44 critically evaluated and optimized the thermodynamic properties and phase diagrams related
to solid and liquid P2O5 and obtained the best set of Gibbs free
energies for all phases. In the present work, thermodynamic
data of the MgO and P2O5 are taken from the FactSage FToxide database16 and Jung and Hudon,44 respectively.
2.1.3.2 Mg3(PO4)2
Berthelot45 determined the standard enthalpy of formation at
ª
298 K (¢fH 298
K ) for Mg 3 (PO 4 ) 2 from elements by solution
calorimetry, and the obtained value was –3811.636 kJ mol–1.
Lopatin and Semenov46 studied the thermodynamic property of
Mg 3 (PO 4 ) 2 by the mass spectroscopy, and the extrapolated
ª
–1
¢fH 298
K from elements was (–3895 ± 70) kJ mol . Stevens
ª
and Turkdogan36 determined the ¢fH 348 K of Mg3(PO4)2 from
oxides by solution calorimetry. This value could be used to esª
timate the ¢fH 298
K because the error involved in such an estimation is negligible compared with the magnitude of the uncertainty. In order to compare this result with the previous
ª
data,45,46 it is convenient to convert it to ¢fH 298
K from elements and the corresponding value is (–3812.725 ± 29.300)
kJ mol–1. Abdelkader et al.20 determined the solution heat of
Mg3(PO4)2 in a 9% (w) nitric acid solution by isoperibol calorimeter. Combining this result with those found by dissolving
other products involved in thermochemical cycles, Abdelkader
ª
et al.20 obtained that the ¢fH 298
K of Mg 3 (PO 4 ) 2 was –3706
¢
¢
¢
1856
Vol.31
Acta Phys. -Chim. Sin. 2015
¢
kJ mol–1. This value is less negative compared with the other
data,36,45,46 and it may be attributed to the traces of nitrates and
water observed by infrared spectroscopy which would lower the
observed heat of formation. Oetting and McDonald34 measured
the heat content of Mg3(PO4)2 by a copper block drop calorimeter in the temperature range from 298 to 1700 K, and calcuª
lated the standard entropy at 298 K (S 298
K ) of Mg3(PO4)2 by
low temperature heat capacity measurements. Bookey35 determined the reaction Gibbs free energy of Mg3(PO4)2(s) + 5H2(g) =
3MgO(s) + P 2 (g) + 5H 2 O(g) in the temperature range of
1273–1523 K by gas equilibrium method, and the value is
(786.94 – 0.26T) kJ mol–1.
¢
2.1.3.3 Mg2P2O7
Oetting and McDonald 34 determined the heat content of
Mg2P2O7 by a copper block drop calorimeter in the temperature
ª
range from 298 to 1700 K and calculated the S 298
K of Mg2P2O7
by heat capacity measurements. Lopatin et al.47 studied the thermodynamic properties of Mg3(PO4)2 and Mg2P2O7 by the vapor
mass spectroscopy. The reaction Gibbs free energy of
3Mg2P2O7(s) = 2Mg3(PO4)2(s) + 2PO2(g) + 0.5O2(g) was determined to be (1135 ± 12) kJ mol–1.
¢
2.1.3.4 Mg(PO3)2
Lopatin et al. 47 studied the thermodynamic properties of
Mg2P2O7 and Mg(PO3)2 by the vapor mass spectroscopy. The
reaction Gibbs free energy of 4Mg(PO3)2(s) = 2Mg2P2O7(s) +
P4O10(g) was determined to be (462 ± 12) kJ mol–1.
¢
2.1.3.5 Liquid phase
The only available thermodynamic data of liquid phase is
P2O5(l) activity at 1673 K from Iwase et al.48 by means of solid
oxide galvanic cell, in which P-containing liquid copper was
brought into equilibrium with P2O5-containing slag. The equilibrium oxygen partial pressures of 2P (in Cu) + 2.5O 2 (g) =
P2O5(in slag) were measured by solid state galvanic cell: Mo/Mo +
MoO2/ZrO2(MgO)/(Cu-P)alloy + (MgO-P2O5)slag/Mo. Hence, the
P2O5 activity could be calculated from above reaction based on
some other thermodynamic data44,49 involved in the thermochemical cycles. Since the activity is not directly measured but
calculated from data with different sources, the error is unavoidable and a lower weight is given in the present assessment.
2.2 CaO-P2O5 system
The CaO-P 2 O 5 system includes eight intermediate compounds: CaP 4 O 11 (CP 2 ), Ca 2 P 6 O 17 (C 2 P 3 ), Ca(PO 3 ) 2 (CP),
Ca4P6O19 (C4P3), Ca2P2O7 (C2P), Ca3(PO4)2 (C3P), Ca10(PO4)6O
(C 10 P 3 ), and Ca 4 (PO 4 ) 2 O (C 4 P). Among these compounds,
Ca4(PO4)2O, Ca3(PO4)2, Ca2P2O7, Ca(PO3)2, and CaP4O11 undergo polymorphic transformations. All crystal structures, phase
equilibrium, and thermodynamic data of this system have been
well reviewed by Hudon and Jung,5 so it is rather redundant to
describe the details of experimental studies in the CaO-P2O5
system. However, all available experimental data will be compared with the present optimization results in Section 4.2.
3 Thermodynamic model
3.1 Stoichiometric compounds
All solid phases are described as stoichiometric compounds
and the standard Gibbs free energy of these phases is expressed
as follows:
T
T
ª
Gª
T = ¢fH 298 K +
298
ª
C pdT ¡ T[ S 298
K +
(C p=T)dT ] (1)
298
ª
where ¢fH 298
K is the standard enthalpy of formation for a given compound referring to stable element reference (SER) at 298
ª
K, S 298
K is the standard entropy at 298 K, and Cp is the heat
capacity.
3.2 Liquid phase
The MQM, which takes into account the SRO of secondnearest-neighbor (SNN) cations in liquid solution, is used to describe the liquid oxide melt. Since oxygen is always combined
to cations in oxide melts, the breakage of the P2O5 network by
MgO or CaO can be simulated by consideration of SRO of
SNN cations.5 In the MgO-P2O5 and CaO-P2O5 liquid solutions,
4¡
3¡
P O¡
3 , P 2O 7 , and P O 4 are the basic building units of P2O5
and contents of these species vary with different oxide compos4¡
3¡
itions. Strictly speaking, P O ¡
3 , P 2O 7 , and P O 4 can all exist
in the liquid phase. However, in order to reduce the model parameters and describe the maximum SRO at Mg3(PO4)2 (M = Mg,
Ca) composition, only P O 3¡
4 species is used in the present work
for thermodynamic modeling, which is different from the previous assessments.4,5
In order to adopt P O 3¡
4 as a building unit of P 2 O 5 in the
MQM, PO3+, which can be surrounded by three broken oxygen
to form P O 3¡
4 , is used as a cation species for the P 2 O 5 component. Therefore, for a binary MO-P2O5 liquid solution, the
following SNN pair exchange reaction between M2+ and PO3+ is
considered.
M ¡ M + P O ¡ P O = 2M ¡ P O
¢gM P O
(2)
where M-M and PO-PO represent SNN pairs, and ¢gM P O is
the Gibbs free energy change of the quasichemical reaction (2).
Then, the molar Gibbs free energy of the MO-P2O5 liquid solution in the MQM can be expressed as below.
¡
¡
G m = n MO G MO + n P 2O 5G P 2O 5 ¡ T¢S con¯g +
(n M P O ¢gM P O =2)
¡
(3)
¡
where n MO and n P 2O 5 are the numbers of moles of MO and
P2O5, respectively, and nM-PO is the number of moles of M-PO
pairs. GMO and G P 2O 5 are the molar Gibbs free energies of pure
liquid MO and P2O5, respectively. ¢S con¯g is the configurational entropy of mixing given by random distribution of the M-M,
PO-PO, and M-PO pairs. The ¢gM¡P O is the model parameter
to reproduce the Gibbs free energy of the liquid phase, which is
expanded as a polynomial in terms of the pair fraction as follows.
X
X
0j
¢gM P O = ¢gMo P O +
gMi0P O (X M M)i +
gM P O (X P O P O )j
(4)
¡
¡
¡
¡
j ¸1
i¸1
¡
¡
where XM-M and XPO-PO are the pair fractions of M-M and PO-PO
o
0j
pairs, respectively. ¢gM P O , gMi0 P O , and gM P O are adjustable tem¡
¡
¡
No.10
1857
DING Guo-Hui et al.: Thermodynamic Assessment of the MgO-P2O5 and CaO-P2O5 Systems
perature dependent model parameters. In the MQM, the coordination numbers (Z) of the cations are also adjustable parameters that allow modifying the internal structure of the solution and do not represent real physical values. In the assessment, Z is usually determined to set a composition of maximum SRO. According to the previous work for many oxide systems reported by Pelton and Blander,50 the Z of divalent cation
was always set to be 1.3774. Therefore, in order to reproduce
the maximum SRO occurring at Mg3(PO4)2 composition, the Z
values of M2+ and PO3+ are set to be 1.3774 and 2.0661, respectively, i.e., Z P O 3+ =Z M2+ = 3=2 . Since the maximum SRO occurs at the Mg3(PO4)2 composition, M-PO pair is dominant and
o
the ¢gM P O parameter gives a major influence in this region. MM and PO-PO pairs are dominant in the MO-rich region and
0j
P2O5-rich region, respectively. Therefore, gMi0 P O and gM P O para-
optimized to reproduce the liquidus on each side. The details of
the MQM can be found elsewhere.13,14
4 Results and discussion
The optimization is carried out step by step to get full agreement with the available phase diagram and thermodynamic
data. Since the thermodynamic data of liquid phase is scarce,
the thermodynamic properties of intermediate compounds are
firstly determined followed by the initial optimization of the liquid phase to reproduce the phase diagram. Finally, the thermodynamic parameters of all phases are simultaneously optimized to reproduce all available experimental data within error
ª
limits as much as possible. Table 2 presents the ¢fH 298
K and
ª
S 298 K of compounds in the MgO-P2O5 and CaO-P2O5 systems.
ª
ª
For the CaO-P 2 O 5 system the ¢fH 298
K and S 298 K of
Ca3(PO4)2, Ca4P6O19, Ca10(PO4)6O, and CaP4O11 are slightly
modified to fit the phase equilibrium better, the corresponding
values of other intermediate compounds are taken from Hudon
¡
¡
¡
meters mainly have influence on the Gibbs free energy of the liquid phase in the MO-rich region and P2O5-rich region, respectively. The model parameters can be more or less independently
Table 2
System
MgO-P2O5
CaO-P2O5
Enthalpies and entropies of compounds in the MgO-P2O5 and CaO-P2O5 systems compared with the experimental data5, 16, 44
Phase
¢
ª
–1 a
¢fH 298
K /(kJ mol )
¢
ª
–1 b
¢fH 298
K /(kJ mol )
¢
¢
ª
–1
K–1)a
S 298
K /(J mol
¢
Reference
MgO(l)
–545.35
MgO(s)
–601.50
26.95
16
P2O5(l)
–1498.04
124.39
44
H-P2O5(s)
–1504.97
114.39
44
O-P2O5(s)
–1539.40
91.60
44
O'-P2O5(s)
–1539.01
92.75
MgMg3(PO4)2
–3808.00
–498.53
189.00
–6.24
this work
α-Mg2P2O7
–3155.88
–447.91
153.00
–15.29
this work
β-Mg2P2O7
–3155.20
–447.23
155.00
–13.29
this work
Mg(PO3)2
–2346.31
–239.84
138.80
–2.54
this work
MgP4O11
–3882.47
–271.03
260.00
4.27
this work
CaO(l)
CaO(s)
–555.59
27.00
¢
ª
–1
K–1)b
S 298
K /(J mol
44
65.69
–635.09
16
16
37.75
16
α-Ca4(PO4)2O
–4751.50
–706.17
270.00
4.61
β-Ca4(PO4)2O
–4766.50
–721.17
253.49
–11.90
5
α-Ca3(PO4)2
–4068.58
–658.34
215.00
–12.64
this work
β-Ca3(PO4)2
–4057.76
–647.52
241.57
13.93
this work
γ-Ca3(PO4)2
–4097.90
–687.66
236.60
8.96
this work
α-Ca2P2O7
–3314.81
–539.66
194.06
4.17
5
β-Ca2P2O7
–3321.51
–546.36
189.33
–0.56
5
γ-Ca2P2O7
–3321.78
–546.63
189.02
–0.87
5
Ca4P6O19
–8275.09
–1219.83
483.60
–10.57
this work
α-Ca(PO3)2
–2472.88
–332.82
148.55
–3.59
5
β-Ca(PO3)2
–2474.88
–334.82
146.94
–5.20
5
γ-Ca(PO3)2
–2476.88
–336.82
144.36
–7.78
5
Ca2P6O17
–6526.62
–741.54
385.00
–33.67
5
α-CaP4O11
–4045.65
–400.62
243.40
–23.13
this work
–4048.15
–403.13
239.33
–27.20
this work
–12946.38
–2080.58
744.61
23.94
this work
β-CaP4O11
Ca10(PO4)6O
a
5
stable elements as reference; bsolid oxides as reference, i.e., MgO(s), CaO(s), P2O5(hexagonal). O,O'-P2O5: orthorhombic, low temperature and high temperature
modifications of P2O5, respectively, H-P2O5: hexagonal, thermodynamically unstable but most well studied P2O5
1858
and Jung5 without any modification. Table 3 gives the Cp of
compounds in the MgO-P2O5 and CaO-P2O5 systems. For CaOP2O5 system the Cp values of all intermediate compounds are
taken from Hudon and Jung.5 Table 4 shows the optimized
model parameters of liquid phase using the MQM.
Mg-PO pair fraction in the liquid phase is almost 100% at this
composition. Due to the scarce liquidus data on P2O5-side, only
01
one parameter gMg¡P O is required to mainly reproduce the liquidus of Mg 2 P 2 O 7 and Mg(PO 3 ) 2 compounds. In addition,
10
gMg
P O is needed to reproduce the invariant reaction of L = MgO +
Mg3(PO4)2. The calculated liquidus in the composition range
from Mg(PO3)2 to P2O5 is tentative and the predicted temperatures of L = Mg(PO3)2 + MgP4O11 and L = MgP4O11 + O'-P2O5
are 1045 and 601 K, respectively. Further experiments are
needed to verify these results.
The thermodynamic data of compounds mainly focus on the
Mg3(PO4)2 and Mg2P2O7. Fig.2 shows the calculated heat contents of Mg3(PO4)2 and Mg2P2O7 in the temperature range from
298 to 1700 K compared with the experimental data.34 The calculated heats of fusion of Mg3(PO4)2 and Mg2P2O7 are 139.47
¡
4.1 MgO-P2O5 system
The calculated phase diagram of the MgO-P2O5 system compared with the experimental data29,31,33–35,41 is shown in Fig.1. The
calculated invariant reactions and phase transitions are listed in
Table 5. Reasonable agreement is obtained between the calculated and experimental results. In order to reproduce the liquidus well, three model parameters of liquid phase are needed
in the present work. Since the maximum SRO occurs at
o
Mg3(PO4)2 composition, a large negative value of ¢gMg¡P O is
needed to mainly fit the liquidus of Mg3(PO4)2. The calculated
Table 3
System
MgO-P2O5
Vol.31
Acta Phys. -Chim. Sin. 2015
Heat capacities of compounds in the MgO-P2O5 and CaO-P2O5 systems compared with the experimental data5, 16, 44
MgO(l)
¢
¢
Cp/(J mol–1 K–1)
Phase
–3
–2
–0.5
72.795562 – 3.142 × 10 T + 522751.6T – 296.2T
–3
+ 5844612T
66.944
MgO(s)
61.10965 – 621154T–2 – 296.199T–0.5 + 5844612T–3
16
298–3098
–21.643407 + 0.3362284T – 1.12629 × 10–4T2 – 3516373.2T–2 + 22900.402T–1
–4
2
–2
–1
–21.643407 + 0.3362284T – 1.12629 × 10 T – 3516373.2T + 22900.402T
225
Mg3(PO4)2
298–3098
16
3098–3500
225
H/O/O'-P2O5(s)
Reference
3098–3500
66.944
P2O5(l)
T/K
298–853
44
853–6000
44
298–1000
44
> 1000
216.73 + 0.512554T – 4.30116T–2 – 5.5021 × 10–4T2 – 1956.47T–0.5 + 2.1358 × 10–7T3 –
44
298–1700
this work
298–1700
this work
0.0339544T–3
α/β-Mg2P2O7
385.1 + 0.03658T – 7.49048T–2 – 6.51343 × 10–6T2 – 3672.24T–0.5 + 2.96458 × 10–8T3 –
0.0566895T–3
CaO-P2O5
Mg(PO3)2
Cp(MgO) + Cp(P2O5)
298–6000
this work
MgP4O11
Cp(MgO) + 2Cp(P2O5)
298–6000
this work
CaO(l, s)
58.7912 – 1147146T–2 – 133.9T–0.5 + 1.02979 × 10–8T–3
298–2845
16
62.76
2845–3500
α/β-Ca4(PO4)2O
317.5164047 + 0.089909858T – 6287652.317T–2
298–2000
5
α-Ca3(PO4)2
340.272
298–2003
5
β-Ca3(PO4)2
318.572
298–1748
5
γ-Ca3(PO4)2
201.83616 + 0.16602112T – 2092000T–2
298–1373
5
330.536
α-Ca2P2O7
1373–2000
221.87752 + 0.06175584T – 4669344T–2
298–1413
318.6116
β-Ca2P2O7
221.87752 + 0.06175584T – 4669344T–2
298–1413
309
γ-Ca2P2O7
Ca4P6O19
5
1413–1627
5
1413–1627
221.87752 + 0.06175584T – 4669344T–2
298–898
5
271.537416
898–1627
606.434930568 + 0.138072T – 14778617.98248T–2 – 133.903999616T–0.5 +
298–1500
5
1029787.864T–3
α/β/γ-Ca(PO3)2
182.54792 + 0.046024T – 4543824T–2
298–2000
5
Ca2P6O17
343.4524331 + 0.428276402T – 12604021.135T–2 – 0.000112629T–2 + 22900.40185T–1
298–1200
5
α/β-CaP4O11
160.9045131 + 0.382252402T – 8060197.135T–2 – 0.000112629T–2 + 22900.40185T–1
298–1200
5
298–1373
5
Ca10(PO4)6O
–2
720.1887 + 0.42195208T – 10471652.2T
1294
1373–3000
No.10
1859
DING Guo-Hui et al.: Thermodynamic Assessment of the MgO-P2O5 and CaO-P2O5 Systems
Table 4
¢
and 184.59 kJ mol–1, respectively, which are slightly higher
than the experimental data.34 In the present assessment, the heat
capacities of Mg3(PO4)2 and Mg2P2O7 are optimized based on
the data shown in Fig.2. ForMg(PO 3 ) 2 and MgP 4 O 11 compounds, since lack of the experimental data of heat capacities, it
is assumed that the following additive equations are applied:
C p (MgP 2 O 6 ) = C p (MgO) + C p (P 2 O 5 ) and C p (MgP 4 O 11 ) =
Cp(MgO) + 2Cp(P2O5).
ª
ª
Figs.3 and 4 present the calculated ¢fH 298
K and S 298 K of
compounds (here given for 1 mol of components MgO(s) plus
P 2 O 5 (hexagonal)) in MgO-P 2 O 5 system compared with the
Model parameters of the MgO-P2O5 and CaO-P2O5 liquid
phases using the MQM
System
MgO-P2O5
Coordination number (Z)
¢
Model parameter/(J mol–1)
Z Mg2+ = 1:3774
o
¢gMg
= ¡285556+16T
PO
Z P O 3+ = 2:0661
10
gMg
= ¡50654
PO
¡
¡
01
gMg
= ¡200036
PO
¡
CaO-P2O5
Z Ca 2+ = 1:3774
o
¢gCa
Z P O 3+ = 2:0661
10
gCa
= ¡28000
PO
¡P O
= ¡435350+45T
¡
01
gCa
= ¡116000
PO
¡
02
gCa
= ¡236000 + 73T
PO
¡
04
gCa
= 100000
PO
¡
Table 5
Calculated invariant reactions and phase transitions of the MgO-P2O5 system compared with the experimental data16, 24, 25, 29, 31–44
Reaction
L = MgO
L = MgO + Mg3(PO4)2
Type
congruent fusion
eutectic
T/K
Liquid composition/%*
3098
0
16
3098
0
this work
1598
23
31
1596
23
this work
1630
25
31
1621
25
36
1658
25
32
1626 ± 5
25
34
1630
25
33
1623
25
37
1630
25
this work
1555
27.6
31
1563
27.7
this work
1655
33.3
31
1668
33.3
34
1658
33.3
33
1658
33.3
this work
1603 ± 5
L = Mg3(PO4)2
L = Mg3(PO4)2 + α-Mg2P2O7
L = α-Mg2P2O7
β-Mg2P2O7 = α-Mg2P2O7
L = α-Mg2P2O7 + Mg(PO3)2
L = Mg(PO3)2
congruent fusion
eutectic
congruent fusion
transition
eutectic
congruent fusion
Reference
35
341 ± 2
38
342 ± 1
34
335–338
25
332–336
24
337
this work
1423
46.8
31
1410
46.9
this work
1438
50
31
1433
50
39
1436
50
40
1425
50
41
1438
50
42
1438
50
this work
1438 ± 5
43
L = Mg(PO3)2 + MgP4O11
eutectic
1045
61.5
this work
L = MgP4O11
congruent fusion
1183
66.7
29
1183
66.7
this work
L = MgP4O11 + O'-P2O5
eutectic
601
77.5
this work
L = O'-P2O5
congruent fusion
853
100
44
853
100
this work
*calculated by P2O5 atom fraction
1860
Vol.31
Acta Phys. -Chim. Sin. 2015
Fig.1
Calculated phase diagram of the MgO-P2O5 system compared
Fig.4
with the experimental data29,31,33–35,41
Calculated entropies of formation in the MgO-P2O5 system
compared with the experimental data34
reference state: MgO(s), P2O5(hexagonal)
Fig.2
Calculated heat contents of Mg3(PO4)2 and Mg2P2O7
compounds in the temperature range from 298 to 1700 K compared
Fig.5
with the experimental data34
Calculated activity of P2O5(l) in liquid phase at 1673 K
compared with the experimental data48 and modified values
effusion method cannot obtain reliable enthalpies of comª
ª
pounds. In the present assessment, the ¢fH 298
K and S 298 K of
Mg 3 (PO 4 ) 2 and Mg 2 P 2 O 7 are primarily estimated based the
data34,36 shown in Figs.3 and 4. Then, these values are modified
ª
to fit the experimental phase diagram data better. The ¢fH 298
K
ª
and S 298 K of other compounds are optimized according to the
invariant reactions and phase transformations shown in Table 5.
Using the optimized parameters of Mg3(PO4)2, the reaction
Gibbs free energy of Mg 3 (PO 4 ) 2 (s) + 5H 2 (g) = 3MgO(s) +
P2(g) + 5H2O(g) can be calculated, which is 37 kJ mol–1 higher
than the data reported by Bookey.35 In the present work, for
Mg3(PO4)2 compound, more weight is given to the enthalpy,36
entropy, and heat capacity.34 Therefore, heat capacity, enthalpy,
and entropy of Mg3(PO4)2 are reproduced well as can be seen in
Figs.2–4, but the data reported by Bookey35 cannot be reproduced well simul-taneously.
Iwase et al.48 measured the equilibrium oxygen partial pressures of 2P(in Cu) + 2.5O2(g) = P2O5(in slag) by solid state galvanic
cell. To obtain the P2O5(l) activity in liquid phase, Iwase et al.48
used the Gibbs free energy of formation for P2O5(l) at 1673 K
reported by Turkdogan and Pearson49 for the following reaction:
P2(g) + 2.5O2(g) = P2O5(l). In the present work, however, the
Gibbs free energy of formation for P2O5(l) evaluated by Jung
and Hudon44 is used. To reduce the difference between both val-
¢
Fig.3
Calculated enthalpies of formation in the MgO-P2O5 system
compared with the experimental data36,45–47
reference state: MgO(s), P2O5(hexagonal)
experimental data, 34,36,45–47 respectively. Strictly speaking,
hexagonal P2O5 is metastable at 298 K, but it is the most commonly used polymorph as a reference state for solid P2O5. The
ª
ª
–1
minimum values of ¢fH 298
K and S 298 K are –141.23 kJ mol
–1
–1
and –14.74 J mol K at the Mg2P2O7 composition, respectively. The calculated results are in agreement with the experimental data except for the enthalpies measured by the Knudsen
effusion method,46,47 which is far from the trend. In the CaOª
P2O5 system, the measured ¢fH 298
K of Ca3(PO4)2 by the same
method also has the same question.5 It is not clear why Knudsen
¢
¢
¢
No.10
1861
DING Guo-Hui et al.: Thermodynamic Assessment of the MgO-P2O5 and CaO-P2O5 Systems
ues,44,49 the activity data reported by Iwase et al.48 should be
modified and the corresponding result is lg aP 2O 5(modi¯ed) . Fig.5
shows the calculated P2O5(l) activity in liquid phase at 1673 K
compared with the experimental data48 and the modified values.
The P2O5 activity shows a rapid increase at 25% (atom fraction)
P2O5, indicating the maximum SRO occurs at this composition.
4.2 CaO-P2O5 system
Table 6
Calculated invariant reactions in the CaO-P2O5 system compared with the experimental data4–7, 29, 51–55
Reaction
L + CaO = α-Ca4(PO4)2O
L = α-Ca3(PO4)2 + α-Ca4(PO4)2O
L = α-Ca2P2O7 + β-Ca3(PO4)2
L + β-Ca2P2O7 = Ca4P6O19
L = Ca4P6O19 + β-Ca(PO3)2
L + β-Ca(PO3)2 = Ca2P6O17
The calculated phase diagram of the CaO-P2O5 system compared with the experimental data6,9,29,51–57 is presented in Fig.6.
The calculated invariant reactions involving liquid phase are
listed in Table 6. Reasonable agreement is obtained between the
calculated and experimental results. Since the thermodynamic
data of intermediate compounds are almost taken from Hudon
and Jung 5 without modification, the calculated polymorphic
Type
T/K
Liquid composition/%*
peritectic
1993
21
6
1983 ± 20
21
53
1913
21
51
2016
22
4
2021
20
5
1974
21
this work
1853 ± 10
23
6
1853
23
53
2011
22
4
1887
23
5
1854
23
this work
1560
30
6
1563 ± 10
30
53
1559
30
54
1557 ± 5
30
55
1563
31
4
1569
29
5
1571
30
this work
1258 ± 1
47
52
1273
43
7
1242
48
4
1242
46.5
5
1270
46
this work
1243
45.6
51
1243 ± 1
47.6
52
1242
47.7
4
1242
47
5
1245
47.7
this work
1047 ± 2
61
52
eutectic
eutectic
peritectic
eutectic
peritectic
1053
L = α-CaP4O11 + Ca2P6O17
L = O'-P2O5 + α-CaP4O11
eutectic
eutectic
Reference
29
1074
62
4
1040
62.7
5
1036
62
this work
1019 ± 5
63
52
1066
64
4
1034
63
5
1032
63
this work
763
82
52
803
94
4
738
85
5
736
84
this work
*calculated by P2O5 atom fraction
1862
Vol.31
Acta Phys. -Chim. Sin. 2015
transition temperatures of compounds are consistent with
Hudon and Jung and not be presented in Table 6. In order to reproduce the liquidus well, five model parameters of liquid
phase are needed in the present work. Since the maximum SRO
occurs at the Ca3(PO4)2 composition, a large negative value of
o
¢gCa
P O is needed to mainly fit the very steep liquidus of
Ca3(PO4)2. The calculated Ca-PO pair fraction in the liquid
phase is almost 100% at this composition. Three model pa01
02
04
rameters, gCa
, gCa
, and gCa
, are optimized to mainly rePO
PO
PO
¡
¡
¡
¡
produce the liquidus of Ca2P2O7, Ca(PO3)2, and CaP4O11 com10
pounds, respectively. One parameter gCa
is needed to reproPO
¡
duce the liquidus on the CaO-rich side. Compared with the previous assessments,4,5 the phase diagram can be reproduced better using the P O 3¡
4 as the basic building unit of P2O5 in liquid
solution with the present model parameters. In the work of
Hudon and Jung,5 the liquidus of Ca4(PO4)2O and the peritectic
reaction of L + CaO = α-Ca4(PO4)2O cannot be reproduced well
simultaneously. The calculated peritectic point is at 20% (atom
fraction) P2O5, which is almost equal to the composition of
Ca4(PO4)2O. If the liquidus of Ca4(PO4)2O is optimized to be
close to the experimental data, the reaction type of L + CaO =
α-Ca4(PO4)2O will become eutectic. In the present assessment,
however, this problem is successfully resolved as can be seen in
Fig.6. The liquidus of Ca4(PO4)2O and the peritectic reaction of
L + CaO = α-Ca4(PO4)2O are both reproduced well. In the work
of Serena et al.,4 amounts of model parameters were used to describe the liquid phase, but the calculated temperatures of invariant reactions involving the liquid phase are much higher
than the experimental data as discussed in Section 1. In the
present assessment, however, this problem is also resolved as
shown in Table 6. The calculated invariant reactions are in good
agreement with the experimental data. The Ca 4 P 6 O 19 and
Ca10(PO4)6O compounds which were not considered by Serena
et al.4 are also presented in Fig.6 since they were confirmed to
exist by Hudon and Jung5 by evaluating much experimental information. It should be noted that the present melting point of
CaO is consistent with that of Hudon and Jung,5 but it is much
lower than the value calculated by Serena et al. 4 Hudon and
Fig.7
Calculated activity of CaO(s) at 1923 K in the CaO-P2O5 system
compared with the experimental data10
Jung5 suggested that the lower melting point was more reasonable by the analysis of experimental data and extrapolation of
CaO liquidus in many binary CaO-containing systems.
Since the thermodynamic data of intermediate compounds
are almost taken from Hudon and Jung,5 the calculated Gibbs
free energies of formation from Ca(l), P 2 (g), and O 2 (g) for
Ca(PO3)2, Ca2P2O7, Ca3(PO4)2, and Ca4(PO4)2O compounds are
almost identical with the results calculated by Hudon and Jung.5
Fig.7 shows the calculated CaO(s) activity in liquid phase at
1923 K compared with the experimental data using electromotive force (EMF) method.10 The CaO activity shows a rapid decrease at 25% (atom fraction) P2O5, indicating the maximum
SRO occurs at this composition.
5 Conclusions
The thermodynamic assessments of the MgO-P2O5 and CaOP2O5 systems have been performed based on the available phase
diagram and thermodynamic data. The liquid phase is described by the MQM and the P O 3¡
4 is considered as the basic
building unit of P2O5 in the liquid solution since the maximum
SRO occurs at the M3(PO4)2 (M = Mg, Ca) composition. A set
of self-consistent model parameters is obtained and the experimental data are reproduced well within experimental error limits. Compared with the previous assessments of the CaO-P2O5
system, the liquidus of Ca4(PO4)2O and invariant reactions involving the liquid phase can be reproduced better in the present
work. The calculated activity curves show sharp changes at
25% (atom fraction) P2O5, indicating the maximum SRO occurs at this composition. This study can be used as a basis for
the development of a thermodynamic database of molten slag
system for the steelmaking dephosphorus process.
References
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Calculated phase diagram of the CaO-P2O5 system compared
with the experimental data6,9,29,51–57
2916.2006.01207.x
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