Reaction sequence and formation kinetics of perovskite by calcium ferrite–titania reaction

Article abstract of DOI:10.1016/j.jallcom.2019.02.325

Controlling the generation of perovskite (CaO·TiO₂, CT) during sintering with vanadium–titanium magnetite (VTM) is the key to improve the strength and yield of VTM sinters. This study determined whether adding pre–formed calcium ferrite (CaO·Fe₂O₃, CF) effectively prevents the formation of CT during sintering with VTM. The formation behavior of CT in the CF–T system was investigated using X–ray diffraction (XRD), scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). Phase composition analysis by XRD indicates that CT is formed significant quantities in the CF–T system when the temperature is higher than the melting temperature of CF. DSC analysis shows that the CF–T samples undergo two reaction stages in continuous heating. Namely, CF first melts and forms its liquid phase, then TiO₂ substitutes Fe₂O₃ in liquid CF to produce CT. SEM images confirm that CT could be generated at regions with a high concentration of CF. Non–isothermal DSC measurements on the formation kinetics of CT indicate that its activation energy reaches 252.00 kJ/mol and that the model function is f(α)=(1–α)², revealing a second–order reaction based on Malek analysis. The kinetics equation of CT formation can be expressed by ln([Formula presented])=2ln(1?α)?[Formula presented]+16.71+10.33α. Quantitative calculation on enthalpy change by DSC curves shows that raising heating rates enhance the consolidation ability of CF–T samples as the melting of CF increases and the formation of CT decreases.

Full text of DOI:10.1016/j.jallcom.2019.02.325

Accepted Manuscript
Reaction sequence and formation kinetics of perovskite by calcium ferrite–titania
reaction
Chengyi Ding, Xuewei Lv, Yun Chen, Gang Li, Wenchao He, Xueming Lv
PII:
S0925-8388(19)30797-2
DOI:
https://doi.org/10.1016/j.jallcom.2019.02.325
JALCOM 49757
Reference:
To appear in: Journal of Alloys and Compounds
Received Date: 11 September 2018
Revised Date: 21 January 2019
Accepted Date: 28 February 2019
Please cite this article as: C. Ding, X. Lv, Y. Chen, G. Li, W. He, X. Lv, Reaction sequence and formation
kinetics of perovskite by calcium ferrite–titania reaction, Journal of Alloys and Compounds (2019), doi:
https://doi.org/10.1016/j.jallcom.2019.02.325.
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ACCEPTED MANUSCRIPT
Reaction sequence and formation kinetics of perovskite by calcium ferrite–
titania reaction
Authors:
Chengyi Ding
Ph.D Student of School of Materials Science and Engineering, Chongqing University, China
E–mail: chengyi_ding@163.com
Xuewei Lv Corresponding Author
Professor of School of Materials Science and Engineering/ Chongqing Key Laboratory of Vanadium–Titanium
Metallurgy and New Materials/ The State Key Laboratory of Mechanical Transmissions, Chongqing University, China
E–mail: lvxuewei@163.com
Yun Chen
Sino–platinum Metals Co., Ltd, Yunnan, China
E–mail: cquchenyun@163.com
Gang Li
Ph.D Student of School of Materials Science and Engineering, Chongqing University, China
E–mail: cquligang2793@163.com
Wenchao He
Ph.D Student of School of Materials Science and Engineering, Chongqing University, China
E–mail: hewenchao1217@163.com
Xueming Lv
Ph.D Student of School of Materials Science and Engineering, Chongqing University, China
E–mail: lvxueming1114@163.com

ACCEPTED MANUSCRIPT
Abstract
Controlling the generation of perovskite (CaO·TiO2, CT) during sintering with vanadium–
titanium magnetite (VTM) is the key to improve the strength and yield of VTM sinters. This
study determined whether adding pre–formed calcium ferrite (CaO·Fe2O3, CF) effectively
prevents the formation of CT during sintering with VTM. The formation behavior of CT in the
CF–T system was investigated using X–ray diffraction (XRD), scanning electron microscopy
(SEM), and differential scanning calorimetry (DSC). Phase composition analysis by XRD
indicates that CT is formed significant quantities in the CF–T system when the temperature is
higher than the melting temperature of CF. DSC analysis shows that the CF–T samples undergo
two reaction stages in continuous heating. Namely, CF first melts and forms its liquid phase, then
TiO2 substitutes Fe2O3 in liquid CF to produce CT. SEM images confirm that CT could be
generated at regions with a high concentration of CF. Non–isothermal DSC measurements on the
formation kinetics of CT indicate that its activation energy reaches 252.00 kJ/mol and that the
model function is f(
kinetics equation
α
)=(1–
α
)2, revealing a second–order reaction based on Malek analysis. The
of CT formation can be expressed by
d
α
216805+70382α




ln
= 2ln 1−
α
−
+16.71+10.33α
. Quantitative calculation on
(
)


dt
RT
enthalpy change by DSC curves shows that raising heating rates enhance the consolidation ability
of CF–T samples as the melting of CF increases and the formation of CT decreases.
Keywords: perovskite, vanadium–titanium magnetite, calcium ferrite, sintering, thermal analysis
1. Introduction
Perovskite (CaO·TiO2, CT), which is easily generated during sintering with vanadium–
titanium magnetite (VTM), can considerably worsen the strength and even reducibility of
sinters[1–5]. Cheng[6] reported that the crushing strength of VTM pellets obviously decreases
with increasing TiO2 content. He[7] found that the strength and yield of VTM sinters decrease
when TiO2 content reaches 6%–10% due to the CT formation. Reducing the generation of CT
during sintering with VTM can improve its utilization in the subsequent blast furnace process[8].
Calcium ferrite (CaO·Fe2O3, CF) is a superior bonding phase with a low liquidus temperature for
a high–strength and –reducibility structure in fluxed sinters[9, 10]. CF can be generated by the
combination of CaO and Fe2O3, and the oxidation of Fe3O4 in raw materials of VTM sintering is
one of the sources of Fe2O3. The formation of CT is a more competitive reaction than that of
CF[11]. However, the effect of adding pre–formed CF as a raw material during sintering on the
sinter quality of VTM remains unclear. Moreover, an economical way to produce CF on an
industrial scale is needed. Oxidized scale[12, 13], mainly comprising FeO and Fe3O4, is largely
idle from steel–forging and hot–rolling products. CF can be produced by roasting treatment of
oxidized scale with lime in air (Fig. 1). This process not only solves the problem of recycling of
oxidized scale but also realizes the industrial production of CF with a reasonable cost. The
purpose of this work is to explore methods to prevent the formation of CT from thermodynamics
and kinetics. Specifically, the phase composition of the CF–T system was analyzed at various
temperatures in a continuous heating process to estimate the critical temperature of CT formation.
As CF instead of CaO is added to the raw materials of sintering with VTM, TiO2 combines with
the CaO in CF to generate CT only when the temperature is high enough. Besides, it is considered
to weaken the CT generation by kinetics analysis including the effect of heating rates on the
consolidation ability of VTM sinters. Meanwhile, kinetics parameters such as the activation

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energy, the pre–exponential coefficient, and the model function of CT formation, which were
rarely explored, are completely calculated by non–isothermal analysis in this study. As an
important phase component, CT was investigated on its effect on VTM sinters or titanium–
bearing slag (Table 1) in previous work. However, this study mainly investigated the formation
mechanism of CT in CF–T system, focusing on the way to strengthen VTM sinters by controlling
the generation of CT with pre–formed CF into raw materials of sintering.
Fig. 1. Oxidized scale and lime as raw materials to produce CF when pre–adding it during
sintering with VTM
Table 1. Effect of CT on VTM sinters or titanium–bearing slag properties by previous studies
Researchers
Samples
Methods
Purposes
Mineral
Major conclusions
structure
analysis and its
influence on
metallurgical
properties of
VTM sinters
Influence on
consolidation
of bonding
phase
CT weakens strength and
reduction of sinters
Bai et. al[14]
VTM sinters
SEM
CT decreases consolidation of
bonding phase and weakens
strength and reduction of sinters
Liu et. al[15]
VTM sinters
SEM, EDS
XRD, SEM
The supersaturation
concentration and coarsening
influence the growth rate of CT;
Oxidized
titanium–
Precipitating
and crystal
Wang et. al[16]
bearing slag
growth kinetics The precipitation kinetics of CT
was obtained
SEM, XRD,
Grain
distribution
test
Oxidized
titanium–
bearing slag
TiO2
Oxidation promotes enrichment
enrichment and
Wang et. al[17]
This work
of TiO2 and growth of CT
CT growth
CF (Bonding
phase in
Formation
sequence and
kinetics
XRD, DSC
Seen in Conclusions section
sinters)

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2. Samples preparation
CF samples were prepared from CaCO3 (
≥
99.99 %, < 100 ꢀm) and α–Fe2O3 (≥ 99.99 %, <
100
ꢀ
m) in a 1:1 molar ratio[18]. The raw materials were uniformly mixed for 30 min in a
mechanical mixer and then pressed into cylindrical samples ( 10*10 mm) with 10 MPa pressure.
Φ
The cylindrical samples were heated in a resistance furnace with MoSi2 at 1073 K for 1 h to
decompose CaCO3 into CaO and were further heated up to 1473 K and held for 10 h for the
sufficient generation of CF. The CF samples were ground into powdery particles below 74
ꢀm
and then mixed and cylinder–shaped with 10 wt.% TiO2 ( 99.99 %, < 100 m). The CF samples
≥
ꢀ
were verified with above 95 % of pure CF by semi–quantitative analysis (Fig. 2). The shaped
CF–T samples were also heated in the resistance furnace to 1173, 1273, 1373, 1473, and 1513 K
and held for 15 min to obtain several reaction products at different temperatures. Samples of
CaO–Fe2O3–TiO2 (C–F–T) were prepared from CaCO3, Fe2O3 and TiO2 with the same process as
the CF–T samples. All of the samples were roasted by solid–state reactions in Al2O3 crucible and
cooled inside the furnace to room temperature. Samples in the entire preparation process were
under air atmosphere. Addition of TiO2 causes the melting point of CF–T system to increase.
Besides, the actual reaction temperature is higher than its theoretical value because of a certain
heating rate in the samples preparation. Therefore, the CF–T (and C–F–T) samples are only
deformed, rather than forming complete liquid phase spreading over the bottom of Al2O3 crucible
even at 1513 K. That is, CF–T (and C–F–T) samples were still produced with solid–state
reactions in which Al2O3 will rarely participate. The chemical compositions of the raw materials
for CF–T and C–F–T are shown in Table 2. Subsequently, the phase transformations of CF–T and
C–F–T were compared to clarify the combination ability of TiO2 and Fe2O3 to CaO.
Table 2. Chemical compositions of raw materials for CF–T and C–F–T (wt. %)
CF
90
TiO2
10
CF+T
CaO
23
Fe2O3
67
TiO2
10
C+F+T

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Fig. 2. XRD patterns of CF samples and standard CF
3. Results
3.1 Thermodynamics calculation on the combination ability of CaO to Fe2O3, TiO2, Al2O3,
and SiO2
The combination ability of CaO to Fe2O3, TiO2, Al2O3, and SiO2 can be judged by their
Gibbs free energy[19]. Factsage 6.0®, as a classic thermodynamic calculation software, can be
well qualified for related theoretical analysis in this study. The Gibbs free energy of each product
generated by one mole of CaO with Fe2O3, TiO2, Al2O3, and SiO2 was calculated in Fig. 3. The
setting parameters were standard atmospheric pressure and oxygen partial pressure of 0.21 kPa.
The results indicate that the Gibbs free energy of CT is more negative than those of CF and CA
(CaAl2O4) at the same temperature; thus, CaO is more likely to combine with TiO2 to produce
stable CT. CaO and SiO2 also react to produce relatively stable C2S (Ca2SiO4) and CS (CaSiO3).
The phase diagram of the C–F–T ternary system at 1427 K is shown in Fig. 4. Based on XRD
analysis, when the temperature range is between 1427 K and 1513 K, the phase composition (CF,
CT, TiO2, and Fe2O3) of C–F–T system remains unchanged, but the phase composition proportion
is different. Therefore, setting the temperature at 1427 K is representative for C–F–T phase
diagram. Results show that the equilibrium phases in the CaO–Fe2O3–TiO2 system mainly include
CF, CT, and Fe2O3 under the compositional conditions (red point) in this study. The results of the
thermodynamics calculation are consistent with those of the phase composition analysis by XRD.
Fig. 3. Gibbs free energy of each product generated by one mole of CaO with Fe2O3, TiO2, Al2O3,
and SiO2

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Fig. 4. Phase diagram of CaO–Fe2O3–TiO2 ternary system at 1427 K
3.2 X–ray diffraction measurement
X–ray diffraction (XRD) was performed using Rigaku D/max2500/PC to identify the phase
compositions. Semi–quantitative analysis was conducted through GSAS® to calculate the
composition proportion of different phases (Fig. 5). The relative error between semi–quantitative
analysis and real value is between 5%–10%. The accuracy of semi–quantitative analysis is related
to the setting of instrument parameters, particle size composition, and crystal structure of tested
sample. In the CF–T samples, CF gradually decreases with raising temperature from 1173 K to
1513 K. TiO2 content slightly changes within the temperature range of 1173 K to 1373 K,
obviously decreases when the temperature is further raised to 1473 K, and finally almost
disappears when the temperature reaches 1513 K. CT was initially detected at 1373 K and
produced in large quantities at 1473 K. The latter stage of rapid CT appearance is accompanied
with a large decrease in CF while Fe2O3 is generated in a large amount. These results indicate that
the following reaction mainly occurs at the temperature range of 1373 K to 1513 K.
CaO Fe O s +TiO s =CaO TiO s +Fe O s
3 ( )
2 ( )
2 ( )
3 ( )
.
(1)
2
2
Therefore, CT is formed by the combination of TiO2 with the CaO that originated from CF in the
CF–T system. Namely, CT is not generated significant quantities at a low temperature (< 1473 K),
which can be close to the melting point of CF. In the C–F–T system, Fe2O3 and TiO2 contents
decrease and CF and CT contents increase as the temperature is increased. Moreover, CF content
increases more distinctly than CT content because Fe2O3 has a greater quantity than TiO2 in the
raw materials. Meanwhile, CT is clearly generated when the temperature reaches 1473 K, that is,

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the combined ability of TiO2 and CaO increases significantly at 1473 K. This conclusion is
consistent with that in the CF–T system.
Fig. 5. Phase content in CF–T and C–F–T samples at different heating stages by semi–
quantitative analysis (a: CF–T, b: C–F–T)
3.3 Morphology observation
The micrographs of CF–T samples prepared at 1513 K were obtained by scanning electron
microscopy (SEM, model TESCAN VEGA 3 LMH) expressed in Fig. 6. Three kinds of phases
with different colors can be found in the observed region, in which three typical spots (A, B, and
C) were analyzed for their atomic mass distribution. Results show that spot A with bright gray is
Fe2O3, spot B with dark gray is CF, and spot C with herringbone structure is CT. Fig. 6 also
exhibits that Fe2O3 and CF are staggered across the region and CT is mainly distributed in areas
with high CF concentrations. This finding also verifies that CT formation is the process of TiO2
substituting Fe2O3 in CF.
Fig. 6. SEM image and spot scanning of CF–T samples at 1513 K

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3.4 DSC analysis
CT formation is the main cause of poor strength of VTM sinters as the skeletal and dendritic
structure of CT increases the crack expansion in sinters[2, 20]. Understanding the generation
kinetics, including activation energy and model function, of CT is important to prevent CT
formation because the reaction rate can be controlled when the formation trend of CT cannot be
inhibited. Uniformly mixed samples of CF and TiO2 with a 1:1 molar ratio were selected in the
thermal analysis. Thermal analysis, mainly consisting of thermogravimetry analysis and
differential scanning calorimetry (DSC) analysis, is an important method to study the mass and
energy change in physical and chemical processes[21, 22]. In this study, non–isothermal DSC
experiments were conducted by a Netzsch thermal analyzer (Model STA 449C). Measurements
were performed in a Pt–crucible with samples (10 mg) that were heated to 1573 K at the rates of
20, 25, and 30 K/min. Figs. 7 (a) and (b) describe the heat flow in the continuous heating of the
CF–T and pure CF samples at different rates in the DSC measurements. Two and one main heat
peaks appear in the CF+T and CF samples, respectively. It is obvious that the endothermic peak
in CF is consistent with the first peak of CF+T according to the range of peak temperature. In a
previous study on Fe2O3–CaO phase diagram[23, 24], the liquidus temperature of CF is 1489 K,
which corresponds to the temperature of peak 1 in CF+T system. This finding suggests that peak
1 is the solid–to–liquid process of CF.
CaO Fe O s =CaO Fe O l
3 ( ) 3 ( )
.
(2)
2
2
1489 K is the melting point of CF, in other words, the temperature at which it completely
melts (liquidus temperature). In fact, CF starts melting before 1453 K in air atmosphere (samples
with shrinking and softening), as the results, endothermic peak of CF melting occurs before 1489
K reflected from DSC curve in Fig. 7(b). In fact, peak 1 also includes two overlapping
endothermic peaks in CF+T system. The description of these two peaks and their heat change are
analyzed in the following discussion part. XRD analysis reveals that 1373 K is the initial
temperature of CT generation from CF and TiO2. The temperature lags behind under fast heating
rates, which leads to a higher reaction temperature of CT formation in DSC experiments than that
in XRD analysis. The CF–T samples (CF/TiO2=1:1) heated from room temperature to 1573 K at
the rate of 25 K/min were analyzed by XRD measurement and the results indicate that samples
mainly comprise CT and Fe2O3, while the contents of CF and TiO2 are not obvious (Fig. 8). It
directly proves that CT is generated by TiO2 substitution for Fe2O3 in CF. Thus, peak 2 in CF+T
is the exothermic peak of CT formation. Subsequently, the kinetics analysis of CT formation is
based on peak 2. As peaks 1 and 2 overlap, the two peaks should be separated by Gauss rule[25,
26]. By fitting calculation, Gauss rule can well describe the actual DSC curve of CF melting with
a relatively high confidence coefficient (R2> 0.94). The separated peak 2 at three heating rates is
presented in Fig. 7 (c), and its corresponding process can be described as
CaO Fe O l +TiO s =CaO TiO s +Fe O s
3 ( ) 2 ( ) 2 ( ) 3 ( )
.
(3)
2
2

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Fig. 7. DSC curves of CF–T and CF samples in continuous heating at different rates, and peak 2
(c) was separated by Gauss rule (a: CF–T, b: CF, c: CT)

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Fig. 8. XRD patterns of CF–T samples (CF/TiO2=1:1) heated from room temperature to 1573 K
at the rate of 25 K/min and standard CT, CF, Fe2O3, and TiO2
In the DSC curve, the reaction degree can be described as
STT
0
α
=
,
(4)
STT
1
0
where
α
is the reaction degree that corresponds to temperature T. STT is the area surrounded by the
0
DSC curve and the baseline from the onset temperature T0 to a fixed temperature T. STT is the
1
0
total area from the onset temperature to the final temperature T1. The reaction degree of CT
formation corresponding to peak 2 was calculated (Fig. 9).
Fig. 9. Reaction degree against temperature for CT formation (peak 2).
The kinetics equation[27, 28] that describes the relation of reaction degree to temperature
can be expressed as
d
α
A
−E
α


=
exp
dT
,
(5)




f
α
β
RT
( )
where
β
is the heating rate, K/min. f(α) is the model function for the reaction process, and A and
Eα correspond to the pre–exponential coefficient (min–1) and activation energy (J/mol) derived
from the Arrhenius equation, respectively. R is gas constant, 8.314 J/(mol·K). Eα, f( ), and A are
the main parameters[29, 30] that should be calculated to reveal a specific kinetics process.
α

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When the reaction degree is increased from 0 to
α
and the temperature is raised from 0 (as
the reaction rates are low in the initial stage, the starting reaction temperature can be regarded as
0) to T, Eq. (5) can be integrated to the following:
α
T
d
α
A
−E
α


=
exp
dT
,
(6)




∫
∫
0
0
f
α
β
RT
( )
The following assumptions are given as
α
dα
G
α =
,
(7)
(8)
( )
∫
0
f
α
( )
−u
u
−e
u2
p u =
du
,
( )
、
∫
∞
where G(α) is one integral forms of f(α), p(u) is called temperature integral that is the key to the
approximate solution of kinetics equation, u=Eα/RT. Eq. (6) can be transformed into
AE
α
G
α
( )
=
p u
( )
,
(9)
β
R
Doyle[31] raised a type of approximate solution to p(u)[32],
p u = 0.00484e−1.0516u
,
(10)
( )
Inputting Eq. (10) into Eq. (9) yields the following equation:



α 
0.00484AE
E
α
ln
β
=ln
−1.0516
,
(11)


G
α
( )
R
RT



α 
0.00484AE
ln
is constant when
α remains unchanged, and the activation energy can be


G
α
( )
R
calculated as
d ln
β
(
)
R
Eα = −
(12)
1
1.0516
 
d
 
T
 
With several non–isothermal DSC experiments at different heating rates, fitting lines can be
drawn from data (1/Ti, lnβi) (i=1,2,3…) at a fixed reaction degree, and the activation energy can
be calculated from the slope of these fitting lines. The method determined by several data points
with the same reaction degree to obtain the activation energy is called the iso–conversional
method[33]. Fig. 10 and Table 3 show the results of activation energy at nine reaction degrees
(0.1–0.9). The average value of activation energy of CT formation is 252.00 kJ/mol with a high
confidence coefficient (R2= 0.9981).

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Fig. 10. ln
β
against 1/T at various reaction degrees (0.1–0.9) based on the iso–conversional
method
Table 3. Activation energy of CT generation at various reaction degrees (0.1–0.9)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
α
Avg.
Eα(kJ/mol) 223.67 233.25 238.91 245.12 250.64 255.33 264.39 271.05 285.60 252.00
R2
0.9973 0.9981 0.9977 0.9978 0.9977 0.9978 0.9985 0.9988 0.9994 0.9981
It is difficult to directly solve the model function f(
α
), but its integral forms G(
α
) would be
relatively easy to obtain.
ART 2
−E
α
0
A
−E




α
,
(13)
G
α
( )
=
exp
dT =
exp








∫
T
β
RT
−
β
Eα
RT
Related to Eq. (5), G(
RT 2
α
) can be converted to the following:
dα
1
,
α
(14)
(15)
G
α
=
( )
when
G 0.5 =
−
β
E dt f
( )
α
α
=0.5,
2
RT0.5
d
α
1



0.5
.
(
)

−
β
Eα dt
f 0.5
(
)

Malek[34] defined a non–dimension parameter y(α) that can be described as
d
α
f
α
G
α



2

( ) ( )
T
dt
α
.
(16)
y
α
( )
=
=
d
f 0.5 G 0.5
(
T0.5


0.5
) (
)




dt

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In thermal analysis kinetics, 41 model functions were identified to reveal different physical and
chemical processes. Malek analysis, as one of the indirective methods to target model function,
was extensively used. The curves plotted of data [αi, y(αi)] (i=1, 2, 3…) from the known 41
functions are called standard curves. In detail, y(αi) can be obtained by the following data: αi, Ti,
(d
experimental data points from [αi, y(αi)] (i=1, 2, 3…) in the DSC curves can also be calculated.
Comparison of the experimental and calculated d /dt is shown in Fig. 11 and discussed in detail
α/dt)i (i=1, 2, 3…) and α0.5, T0.5, (dα/dt)0.5 based on Eq. (16). Following similar principles,
α
later in the paper. The reaction process is identified when its experimental data match a curve of
the 41 model functions. Fig. 11 shows the experimental data points of the CT generation reaction
and standard curves based on Malek analysis. The results indicate that experimental data lie in the
curve of No. 37 model function, which can be expressed as follows:
2
f
α
= 1−
α
.
(17)
( ) (
)
No. 37 model function reveals that CT generation is a second–order reaction, and its reaction rate
increases and then decreases during the whole process.
Fig. 11. Experimental data points and standard curves based on Malek analysis
Inputting the activation energy Eα and model function f(α) into Eq. (5), pre–exponential factor A
can be easily obtained by Eq. (18). The values of A at various reaction degrees are shown in
Table 4. Results show that A slightly changes despite the different heating rates, and the average
value of lnA is 21.88.
d
α
Eα


ln A = ln
+
−ln f
α
( )
.
(18)




dt
RT
Table 4. lnA values at various reaction degrees (0.1–0.9)
0.2 0.3 0.4 0.5 0.6 0.7
α
0.1
0.8
0.9

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20 K/min
25 K/min
30 K/min
Avg.
17.51
17.66
17.84
17.67
18.94
19.08
19.27
19.10
19.84
19.98
20.18
20.00
20.72
20.86
21.06
20.88
21.54
21.68
21.87
21.70
22.30
22.44
22.63
22.46
23.46
23.61
23.80
23.62
24.56
24.70
24.89
24.72
26.58
26.73
26.92
26.75
The results of activation energy and pre–exponential factor reveal that Eα and A positively
correlate with reaction degree . Figs. 12 (a) and (b) show the fitted lines of data (αi, Eαi) and (αi
Aαi), from which the linear relation expression between Eα (or A) and can be obtained,
α
,
α
Eα =216805+70382
α
,
(19)
(20)
ln A=16.71+10.33
α
.
Based on Eqs. (17), (19), and (20), the kinetics equation of CT formation shown in Eq. (18) can
be expressed as
d
α
216805+70382α


ln
= 2ln 1−
α
−
+16.71+10.33
α
.
(21)
(
)




dt
RT
Fig. 12. Liner fitting of activation energy and pre–exponential factor with reaction degree (a:
activation energy, b: pre–exponential factor)
To verify the error range of Eq. (21) with an actual situation, the calculated and
experimental values for reaction rate dα/dt of CT formation under the three heating rates were
compared in Fig. 13. Further calculation shows that the average errors of the experimental and
calculated values under the three heating rates (20, 25, and 30 K/min) are 6.8%, 5.7%, and 2.7%.
Therefore, Eq. (21) can accurately describe the kinetics of CT formation. As the activation
energy, pre–exponential factor, and model function required in theoretical calculation are all the
results of fitting and approximate solution. It is believed that the calculated kinetics equation that
successfully describes the variation trend of reaction rate d
accuracy is commendable.
α/dt and still maintains a descriptive

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Fig. 13. Comparison of calculated and experimental values for reaction rate dα/dt (a: 20 K/min, b:
25 K/min, c: 30 K/min)
4. Discussion
4.1 Melting of CF and formation of CT at different heating rates
The enthalpy change of a process (a heat peak appears) can be calculated from the area
surrounded by DSC curve and baseline,
S
∆Hm =
,
(22)
β
where ∆Hm is the enthalpy change per milligram of mass corresponding to a peak in the DSC
curve, J/mg. S is the peak area surrounded by the DSC curve and baseline, mW/mg. Enthalpy
change obtained by Eq. (22) is the corrected value and close to its actual value. The correction
process of enthalpy change was carried out by measurements on melting of several metals in the
used DSC device. Given the mass of the sample, the molar quantity of a reactant or a product by
inquiring the standard reaction enthalpy of a certain process from Factsage 6.0® can be obtained
as follows:
∆Hm
m
n =
,
(23)
∆H0
where n is the molar quantity (mol) of a reactant or a product. m is the sample mass (mg), and
∆
H0 is the standard reaction enthalpy (32.69 and −77.94 kJ
mol−1 for CF melting (Eq. (2)) and
·
CT formation (Eq. (3)), respectively, which were obtained by Reaction module in Factsage 6.0®).
Thus, the molar quantity of CF melting and CT formation can be calculated by Eq. (23) and the
results are shown in Fig. 14. The results indicate that the melting of CF increases and the
formation of CT decreases with increasing heating rates. Since CF melting is an endothermic
process, the longer this process lasts in the high temperature zone, the more complete the reaction
will be. With the increasing of heating rate, the temperature can rapidly move from low to high
temperature zone. Namely, a higher heating rate delays the real reaction temperature and then
causes melting process to occur in a higher temperature range. Therefore, improving the heating
rate can enhance CF melting process. Given that CF is a superior bonding phase in sinters, its
melting can greatly improve the consolidation with surrounding particles, and CT is not expected
to appear in large amounts in sinters. Therefore, increasing heating rates promotes the
consolidation ability of VTM sinters doped with CF.

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Fig. 14. Melting of CF and formation of CT at different heating rates
4.2 Stage analysis on melting process of calcium ferrite concerning its enthalpy change
The DSC curves of CF–T samples reveal that the first reaction process (CF melting) also
includes two stages as the DSC curve appears two overlapping heating peaks. These two peaks
can be separated by Gauss rule (Fig. 15), and their corresponding enthalpy change can be
calculated by their peak areas. In a previous study[35], 2CaO·Fe2O3 (C2F) can be crystallized in
the crystallization process of CF, it is reasonable that the intermediate C2F appears in the melting
of CF. In addition, Factsage 6.0® was used to calculate that the equilibrium reaction temperature
of Eq. (24) is about 1400 K, which is consistent with the initial reaction temperature
corresponding to stage 1 of CF melting. The two stages are described as follows:
2 CaO Fe O s = 2CaO Fe O s +Fe O s
Stage 1:
(
3)( ) (
)
3 ( )
3 ( )
,
(24)
2
2
2
2CaO Fe O s +Fe O s =2 CaO Fe O l
Stage 2:
(
)
3 ( )
3 ( )
(
3 )( )
.
(25)
2
2
2
There is no thermodynamic data of liquid CF in the Factsage 6.0® database, so the reaction
temperature of Eq. (25) cannot be theoretically calculated. However, considering the existence of
C2F in stage analysis on melting process of CF is still reasonable.

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Fig. 15. Peak fitting of total peak corresponding to CF melting process at various heating rates
The enthalpy change of the two fitted peaks corresponding to stages 1 and 2 of CF melting
process can be calculated by Eq. (22), and the results are listed in Table 5. Results indicates that
the enthalpy change of the two separated stages from CF melting appears higher with increasing
heating rates. Theoretically, enthalpy change of a certain chemical reaction should be constant
despite different heating rates. However, the reactions in this study occurring with non–
isothermal condition always stay in a non–equilibrium state, so that the heat of a chemical
reaction can fluctuate to varying degrees.
Table 5. The enthalpy change (J/mg) of two fitted peaks corresponding to stages 1 and 2 of CF
melting
20 K/min
25 K/min
30 K/min
Stage 1
0.1680
Stage 2
0.1131
Stage 1
0.1724
Stage 2
0.2783
Stage 1
0.2087
Stage 2
0.3691
5. Conclusions
This study adopted XRD measurement and DSC analysis to explore CT generation in the
CF–T system. The following conclusions are obtained:
1) Two reaction stages proceed in CF–T samples with continuous heating process. First, CF
melts and then TiO2 substitutes Fe2O3 in liquid CF to produce CT. CT is not generated
significant quantities when the temperature is below 1473 K in the CF–T system. Thus, low–
temperature sintering can be performed during sintering of VTM doped with CF.
2) According to the iso–conversional method, the activation energy of CT generation from the
CF–T system is 252.00 kJ/mol, and the model function f(
reaction for CT generation based on Malek analysis. The kinetics equation of CT formation is
α)=(1–α
)2 indicates a second–order
d
α
216805+70382α


expressed asln
= 2ln 1−
α
−
+16.71+10.33α .
(
)




dt
RT

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3) Quantitative calculation on enthalpy change by DSC curves shows that raising heating rates
enhance the consolidation ability of CF–T samples as the melting of CF increases and the
formation of CT decreases.
Acknowledgments
This study was performed with the financial support of National Natural Science Foundation
of China (51522403), the Chongqing Youth Science and Technology Talent Training Project
(cstc2014kjrc–qnrc90001) and China Scholarship Council. In addition, I would like to thank my
collaborator Yun Chen for his support to my work. The DSC experiments and data processing
were completed together with him.

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Highlights
•
•
•
•
Oxidized scale is used as raw material to produce industrial-scale calcium ferrite
Perovskite forms by TiO2 substitution for Fe2O3 in liquid calcium ferrite
Activation energy and model function are confirmed by thermal analysis kinetics
Increasing heating rate can inhibit the perovskite formation