Kinetics of the topochemical reaction of the solid solutions of magnesia spinels: Mg(Cr0.5Fe0.5)2O4, Mg(Al0.5Cr0.5)2O4, Mg(Al0.5Fe0.5)2O4 with sulphur oxides

Article abstract of DOI:10.1016/j.tca.2019.178344

Spinel-containing materials belong to an important group of refractories used as high-temperature unit linings. A crucial element of the conditions in which they are used is gaseous corrosion caused by sulphur oxides: SO₂ and SO₃. In previous investigations into reactions of magnesia spinels with sulphur oxides it was found that spinels’ reactivity could be considerably influenced by a phase transition (order – disorder) in the cation sublattice, resulting in a change of their reactivity in relation to SO₂/SO₃. The aim of the study was to investigate the kinetics of topochemical reactions between equimolar solid solutions of magnesia spinels and sulphur oxides before and after the order – disorder phase transformation in the structure begins. Research into the reaction of equimolar solid solutions Mg(Cr_0.5Fe_0.5)₂O₄, Mg(Al_0.5Cr_0.5)₂O₄, Mg(Al_0.5Fe_0.5)₂O₄ with SO₃ was undertaken due to the fact that spinels form solid solutions in basic refractories. To conduct kinetic measurements, a semi-flow reactor was designed and constructed, in which investigations were carried out at the temperatures of 773 and 973 K and time range: 0–7 h. A mixture of air and SO₂ (13%) was used. The obtained results have been compared with the kinetic results from the previous work obtained on two-cation spinels: MgAl₂O₄, MgFe₂O₄, MgCr₂O₄. The influence of the degree of inversion in spinel structure on the kinetics of the process was discussed.

Full text of DOI:10.1016/j.tca.2019.178344

Thermochimica Acta 680 (2019) 178344
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Kinetics of the topochemical reaction of the solid solutions of magnesia
spinels: Mg(Cr Fe ) O , Mg(Al Cr ) O , Mg(Al Fe ) O with
0
.5 0.5 2
4
0.5 0.5 2
4
0.5 0.5 2 4
sulphur oxides
a,⁎
b
a
Anna Gerle , Jerzy Piotrowski , Jacek Podwórny
a
b
Institute of Ceramics and Building Materials, Refractory Materials Division in Gliwice, ul. Toszecka 99, 44-100 Gliwice, Poland
Faculty of Chemistry, Department of Inorganic, Analytical Chemistry and Electrochemistry, Silesian University of Technology, ul. B. Krzywoustego 6, 44-100 Gliwice,
Poland
A R T I C L E I N F O
A B S T R A C T
Keywords:
Corrosion
Spinel-containing materials belong to an important group of refractories used as high-temperature unit linings. A
crucial element of the conditions in which they are used is gaseous corrosion caused by sulphur oxides: SO and
2
Spinels
SO . In previous investigations into reactions of magnesia spinels with sulphur oxides it was found that spinels’
3
Refractories
Sulphur oxides
reactivity could be considerably influenced by a phase transition (order – disorder) in the cation sublattice,
resulting in a change of their reactivity in relation to SO
2
/SO .
3
The aim of the study was to investigate the kinetics of topochemical reactions between equimolar solid
solutions of magnesia spinels and sulphur oxides before and after the order – disorder phase transformation in
the structure begins. Research into the reaction of equimolar solid solutions Mg(Cr0.5Fe0.5
)
2
4
O , Mg
(
Al0.5Cr0.5
)
2
O
4
, Mg(Al0.5Fe0.5
)
2
O
4
with SO was undertaken due to the fact that spinels form solid solutions in
3
basic refractories. To conduct kinetic measurements, a semi-flow reactor was designed and constructed, in which
investigations were carried out at the temperatures of 773 and 973 K and time range: 0–7 h. A mixture of air and
SO (13%) was used.
2
The obtained results have been compared with the kinetic results from the previous work obtained on two-
cation spinels: MgAl , MgFe , MgCr . The influence of the degree of inversion in spinel structure on the
kinetics of the process was discussed.
2
O
4
2
O
4
O
2 4
1
. Introduction
with a completely normal structure adopts the value x = 0, and for
spinel with a completely inverse structure x = 1 [1,5,6]. Investigations
[7–10] into the reactions of magnesia spinels with sulphur oxides re-
vealed that spinel reactivity can be considerably influenced by the
order-disorder transformation in the structure of spinel, causing a
This work concerns the problem of high-temperature sulphate cor-
rosion of basic refractory materials based on magnesium spinels.
Spinels are a group of natural and synthetic double oxides with a cubic
crystal structure isostructural to MgAl
2
O
4
[1]. It is known that in the
change of its reactivity in relation to SO
confirmed in the work [11].
2
/SO . This hypothesis was
3
structure of spinel the order-disorder transformation can occur. This is a
second-order phase transformation accompanied by the discontinuity of
free enthalpy second derivative, corresponding to such values as: spe-
cific heat, thermal expansion coefficient and compressibility factor [2].
Inversion of spinel structure can be induced by temperature and is a
reversible phenomenon [3,4]. Spinel structure can change from normal
to inverse or opposite, which means that divalent cations located in
tetrahedral sites swap their positions with trivalent cations and take
octahedral sites. Spinel structure can be described by the degree of
inversion x, which corresponds to the concentration of trivalent cations
in the tetrahedral coordination. The degree of inversion x for spinel
Spinel-containing materials are an important group of refractories
used as linings in high-temperature units [12–14]. An element playing a
crucial role in the conditions of their application is gaseous corrosion
caused by sulphur oxides: SO
2
and SO . Such corrosion affecting a
3
spinel-containing refractory material is most important in non-ferrous
metallurgy, especially copper industry, where gaseous corrosion, due to
reactions between a refractory material and gaseous phase containing
SO
2
and SO , occurs in the convertor’s gas zone, over the copper matte
3
[15–17]. As spinel forms solid solutions in basic refractories, the aim of
this work was to examine the kinetics of the topochemical reaction of
⁎
Corresponding author.
E-mail address: a.gerle@icimb.pl (A. Gerle).
https://doi.org/10.1016/j.tca.2019.178344
Received 17 April 2019; Received in revised form 9 July 2019; Accepted 22 July 2019
Available online 23 July 2019
0040-6031/ © 2019 Elsevier B.V. All rights reserved.

A. Gerle, et al.
Thermochimica Acta 680 (2019) 178344
equimolar spinel solid solutions Mg(Cr0.5Fe0.5
)
2
O
4
, Mg(Al0.5Cr0.5
)
2
O
4
,
parameter u(T), the lattice parameter a (T) and the cation site occu-
0
Mg(Al0.5Fe0.5
)
2
O
4
with sulphur oxides and compare them with the re-
pancies Occ(T) in each temperature by the Rietveld method. The cation-
anion distances in tetrahedral TO(T) and octahedral MO(T) coordina-
tion in each temperature were calculated by means of Bond_Str program
belonging to the same FullProf_Suite package.
action of two-cation spinels MgAl
2
O
4
, MgFe
2
O
4
, MgCr
2
O with sulphur
4
oxides.
Thus obtained results were used to calculate the degree of inversion
in the structure of investigated spinels by means of two methods using
various results of calculations.
2
. Experimental procedure
2.1. Spinels synthesis
The first method involved determining the occupation number of
+
+
tetra- and octahedral sites in the spinel sublattice by 2 and 3 cations
using the Rietveld method. The degree of inversion (x) was determined
The precursors of Mg(Cr0.5Fe0.5
)
2
O
4
,
Mg(Al0.5Cr0.5
)
2
O
4
,
Mg
(
Al0.5Fe0.5
)
2
O
2
4, MgAl O
4
, MgFe
2
O
4
, MgCr
2
O spinels were obtained by
4
+
by calculating the occupation number of tetrahedral positions by 3
the method of co-precipitation of sulphates from water solutions, using
ammonium carbonate as a precipitating factor. The co-precipitation
reaction can be written as the following stoichiometric equation:
+
+
cations. This method can only be applied when 2 and 3 cations
occupying particular sites in the sublattice differ considerably in their
atomic scattering factors. In this work the condition was fulfilled for
R
2
(SO
4
O
)
3
∙nH
2
O + MgSO
4
∙7H
2
O + 4(NH
4
)
2
CO
3
O
→
MgFe
2
O
4
and MgCr O .
2 4
MgR
2
4
∙nH
2
O + 4(NH
4
)
2
CO
3
+ 4CO + nH
2
2
(1)
In the case of MgAl
2
O
4
, Mg(Cr0.5Fe0.5
)
2
O
4
, Mg(Al0.5Cr0.5)
2
O , Mg
4
2
+
3+
(
Al0.5Fe0.5
)
2
O this condition was not met. Both Mg and Al cations
4
where R means Al, Cr or Fe
have similar values of atomic scattering factor and for this reason the
influence of changes in the occupancy of particular sites in the cation
sublattice on the intensity of diffraction lines is not observed.
Second method of degree of inversion determination was based on
calculation of changes of cation-anion distance. Calculation are based
on assumption that the cation-anion distance changes in particular
positions in the sublattice proportionally to the changes of cations
concentration in this position.
To conduct a co-precipitation reaction, equimolar water solutions
of: chromium and iron sulphates, aluminium and chromium sulphates,
aluminium and iron sulphates, containing 0.25 M of each single sul-
phate, were mixed in 1:1 vol ratio in the case of spinels solid solutions
synthesis. In the case of synthesis of two-cation spinels, a 0.5 M water
solution of appropriate sulphate was prepared. Next, an appropriate
water solution of aluminium, iron and chromium sulphate or mixed
solutions of these sulphates were mixed in the 1:1 vol ratio with 0.5 M
solution of magnesium sulphate. The obtained solutions were added,
while being stirred, to a 2 M solution of ammonium carbonate. The
amount of the precipitating solution was selected in such a way that it
contained 100% excess of ammonium carbonate in relation to the
amount resulting from the stoichiometric reaction (1). All the reagents
used for synthesis were produced by POCH Gliwice (Poland) and were
pure per analysis grade. After finishing the co-precipitation reaction,
the suspension was dried in a sand bath until a solid residue was ob-
tained, which was ground in an agate mill and, next, calcinated at
The details of the method for determining the degree of inversion
have been given in the works [18,19].
2.3. Kinetic measurements
A diagram of a measuring system for kinetic investigations has been
presented in Fig. 1.
The reactor was equipped with a system for weighing samples
without taking them out of the kiln and interrupting the analysed
process. Investigations into spinels corrosion resistance were conducted
at the temperatures of 773 and 973 K. The kinetic measurement pro-
cedure was as follows: a sample of spinels solid solution or two-cation
spinel, dried for 1 h at 383 K, was placed in a previously weighed pla-
tinum boat. The sample excess was collected by moving a flat plate
along the boat walls. This allowed maintaining the flatness of the ex-
amined sample’s surface. The sample in the boat was weighed on an
exterior analytical balance with accuracy to 0.0001 g. The boat with the
sample powder was placed on a platinum sheet, being a part of the
weighing system in the kiln. The kiln with the tested sample was heated
to the pre-set temperature at the rate of 500 K/h. After reaching the pre-
set temperature, the sample was weighed so as to determine its initial
mass (before the reaction). Next, the procedure of pumping a mixture of
air and 13% vol. sulphur dioxide into the reactor was started. The in-
1
473 K for 4 h in order to remove ammonium sulphate produced in the
precipitation reaction. After calcination, the powders were pressed at
20 MPa and fired for 4 h at 1937 K in the case of Mg(Al0.5Cr0.5 O ,
1
)
2
4
MgAl
2
O
4 2
, MgCr O
4
and 1723 K in the case of Mg(Cr0.5Fe0.5
)
2
O , Mg
4
(
Al0.5Fe0.5
)
2
O
4
and MgFe due to the lower melting temperature of
2 4
O
these spinels. The obtained spinels were ground until grain size below
0
.06 mm was obtained.
2.2. Methods of spinels properties testing
Before undertaking kinetic investigations into the reactions of spi-
nels solid solutions and two- cation spinels with sulphur oxides, their
specific surface area was determined by the porosimetric method (using
Gemini 2360 equipment produced by Micromeritics, using nitrogen as
an adsorbed gas) and bulk density by weighing the powder in a vessel of
known volume.
3
tensity of gas flow in the reactor was 69 dm /h. The current composi-
tion of the mixture, dependant on temperature, was established by
determining the concentration of SO at the inlet and outlet of the re-
2
The analysis of phase composition was conducted by the X-ray
diffraction method, using an X'Pert PRO MPD diffractometer produced
by PANalytical, equipped with an X’Celerator detector and a tube with
Cu anode. The temperature at which the order-disorder transition be-
gins in the structure of spinels was determined by the high-temperature
X-ray diffraction method, using an Anton Paar HTK 2000 chamber. This
method allows recording changes of unit cell parameters, atomic co-
ordination and site occupancies of ions as temperature increases.
During the measurement the sample was heated at the rate of 5 K/min
and measurement data was collected using a different step at various
temperature ranges. Up to the temperature of 573 K the step was 100 K;
next, around the inversion temperature, it was 10 K. Before making
each scan, the sample was thermostated for 10 min. The FullProf_Suite
software package was applied to determine the oxygen positional
actor, using Reich’s iodometric method, which involves chemisorption
of SO contained in a particular volume of the analysed gas in a known
volume of a standard iodine solution. Starch was used as an indicator.
Based on the obtained results and the reaction equation 2SO
2
2
+
O
2
= 2SO
3
, the concentration of SO in the reactor was calculated. The
3
spinel sample was weighed after 15 and 30 min following the beginning
of the reaction and, next, every 30 min for up to 7 h. The samples were
weighed in the measuring system scales with accuracy to 0.001 g. Based
on previous investigations [7–11] and a precise thermodynamic ana-
lysis of the examined system [20], it was proved that MgSO is the most
4
thermodynamically stable product of reaction; under experimental
conditions it is stable up to a temperature of 1273 K, whereas Cr (SO
Fe (SO , Al (SO are stable up to 980 K, 920 K and 910 K, respec-
tively. Calculations of spinel conversion were based on following
2
4
3
) ,
2
4
)
3
2
)
4 3
2

A. Gerle, et al.
Thermochimica Acta 680 (2019) 178344
Fig. 1. Diagram of a measuring system for kinetic investigations: 1 – bottle with air, 2 and 7 – reducers, 3 and 9 – manostats, 4 – air dryer, 5 and 10 – rotameters, 6 –
bottle with SO
2
, 8 – SO buffer tank, 11 – gas mixer, 12 and 22 – gas outlet valves, 13 – gas heater, 14 – heater filling, 15 and 20 – controlling thermocouple, 16 –
2
temperature controller, 17 – furnace (reactor), 18 – sample, 19 – balance, 21 - temperature controller, 23 – washer for collecting oleum.
chemical reactions:
2
2
2
Mg(Cr0.5Fe0.5
)
2
O
4
4
4
+ 2SO
3
= 2MgSO
4
+ Cr
2
O
3
+ Fe
2
O
3
(2)
(3)
(4)
(5)
(6)
(7)
Mg(Al0.5Cr0.5
)
)
2
O
O
+ 2SO
+ 2SO
3
3
= 2MgSO
= 2MgSO
4
+ Al
+ Al
2
O
O
3
+ Cr
+ Fe
2 3
O
Mg(Al0.5Fe0.5
2
4
2
3
2 3
O
MgCr
MgFe
2
O
O
4
+ SO
3
= MgSO
= MgSO
4
+ Cr
+ Fe
2 3
O
2
4
+ SO
3
4
O
2 3
MgAl
2
O
4
+ SO
3
= MgSO
4
+ Al
2
O
3
Calculations of spinel conversion are described by Eq. (8):
|
n|
n0
m
Ms
=
=
m0 MSO3
(8)
Fig. 2. X-ray diffraction patterns of Mg(Cr Fe ) O obtained by the method
0.5
0.5 2 4
of co-precipitation of sulphates from water solutions.
where: |Δn| – change of the number of spinel moles, n
0
– initial number
of spinel moles, Δm – sample mass change, g, m
g, MSO3 = 8000 g/mol, M – spinel molar mass, g/mol.
The uncertainty of determining the mass change was established to
be 0.07 g.
0
– initial sample mass,
S
3
. Results and discussion
The X-ray diffraction method analysis of the phase composition of
solid solutions: Mg(Cr0.5Fe0.5
)
2
O
4
O
, Mg(Al0.5Cr0.5
)
2
O
4
, Mg(Al0.5Fe0.5
)
2 4
O
and two-cation spinels: MgCr
2
4
, MgFe
2
O
4
, MgAl
2
O revealed that
4
samples were monophase and did not contain the unreacted starting
materials. In Figs. 2–4 the X-ray diffraction patterns of the solid solu-
tions of magnesia spinels are presented.
Table 1 presents the results of determining the specific surface area
and bulk density of the spinels solid solutions and two-cation spinels.
These powder samples were used for kinetic investigations.
Data presented in Table 1 indicates that spinels powders used for
Fig. 3. X-ray diffraction patterns of Mg(Al0.5Cr0.5
)
2
O obtained by the method
4
of co-precipitation of sulphates from water solutions.
3

A. Gerle, et al.
Thermochimica Acta 680 (2019) 178344
The Mg(Al0.5Fe0.5
MgFe inverse spinel; the structure inversion under the influence of
temperature takes place in each of these spinels, which causes that the
order-disorder transformation in the Mg(Al0.5Fe0.5 solution occurs
in two directions. Al cations move to tetrahedral sites, like in
)
2
O
4
solution contains normal MgAl
2
O spinel and
4
O
2 4
)
O
2 4
3
+
3
+
MgAl
MgFe
lattice, the predominant transition is the one from normal to inverse
structure [10]. At room temperature the Mg(Al0.5Fe0.5 solution has
a mixed structure (x = 0.51), whereas at around 900 K its structure
transforms into an inverse one, reaching the value x1373 = 0.58 at
373 K.
Table 3 presents the current composition of the gaseous phase in the
reactor versus temperature, calculated on the basis of measurements of
2
2
O
4
spinel, and Fe cations – to octahedral sites, as is the case of
3+
4
O spinel. Owing to a larger number of Al cations in the spinel
)
O
2 4
0
1
Fig. 4. X-ray diffraction patterns of Mg(Al0.5Fe0.5
)
2
O
4
obtained by the method
SO concentration in the gas at the inlet and outlet of the reactor. It is
noteworthy that as the temperature increases, the content of SO
gaseous phase drops significantly due to equilibrium SO / SO
2
of co-precipitation of sulphates from water solutions.
3
3
in the
shifts
2
Table 1
towards SO .
2
Specific surface area and bulk density of spinels.
Figs. 5 and 6 present kinetic curves of spinels solid solutions and
two-cation spinels in reactions with sulphur oxides. The course of de-
pendence α = f(t) was determined from Eq. (8).
2
Bulk density (g/cm3)
Spinel
Specific surface area (S
x
m /g)
Mg(Cr0.5Fe0.5
)
2
O
4
4
4
0.668 ± 0.033
0.797 ± 0.040
0.414 ± 0.021
1.168 ± 0,058
0.668 ± 0.033
0.888 ± 0.044
1.94 ± 0.14
1.77 ± 0.13
2.07 ± 0.14
1.41 ± 0.11
1.98 ± 0.18
1.43 ± 0.11
Table 4 presents the phase composition of the product of reaction of
spinels solid solutions and two-cation spinels with sulphur oxides.
Investigations into the products of reaction of spinels solid solutions
as well as two-cation spinels with sulphur oxides revealed that the
Mg(Al0.5Cr0.5
)
2
O
2
Mg(Al0.5Fe0.5
)
O
MgCr
2
2
O
4
4
MgFe
O
MgAl
O
2 4
products of reaction are MgSO
and relevant metal oxides R
3
O . This
4
2
indicates that MgO contained in the structure of magnesia spinels is
responsible for their reaction with SO . An analysis of MgFe spinel
sample phase composition by the X-ray diffraction method, after a re-
action at a temperature of 773 K revealed trace amounts of Fe (SO
sulphate. The obtained results are consistent with a thermodynamic
analysis of the examined system, indicating that MgSO is the most
stable among the sulphate products, whereas the other sulphates
3
2 4
O
kinetic investigations were characterized by similar values of specific
2
surface area (the smallest one 0.414 m /g for Mg(Al0.5Fe0.5
)
2
O and the
4
2
)
4 3
2
largest one 1.168 m /g for MgCr
2
4
O ).
Table 2 presents the results of the degree of inversion determined at
room temperature (x ) and at 1373 K (x1373) as well as its changes (Δx)
and the temperature of the order-disorder transformation beginning
).
Initially, the Mg(Cr0.5Fe0.5
structure (x = 0.50), at a temperature of ca 800 K its structure trans-
forms into a normal one, reaching the value x1373 = 0.45 at 1373 K. In
works [4,19,20] it has been demonstrated that Cr cations do not
change their position in the process of heating. During the order-dis-
4
0
R
2
(SO
4
) remain stable up to the temperature of ca 900 K [20]. The
3
(
T
x
composition of the products of reaction also confirms the correctness of
)
2
O solution is characterized by a mixed
4
the adopted manner of calculating conversion α (Eq. (8)); sulphates
0
other than MgSO
peratures.
4
occurred only in trace amounts and at lower tem-
3
+
As conversion α in a topochemical reaction strongly depends on the
contact area of gaseous and solid substrates, Figs. 7–13 present de-
pendences between the time and α in relation to the specific surface
3
+
order transformation Fe
cations move to octahedral sites, like in
spinel. The change in the degree of inversion of Mg
(Δx = 0.05) is much smaller than in the case of mono-
spinel (Δx = 0.20).
MgFe
O
2 4
area S
x
. Standardization of α/S allowed direct comparison of the ob-
x
(
Cr0.5Fe0.5
)
2 4
O
tained results.
phase MgFe
O
2 4
The kinetic dependences obtained at a temperature of 773 K should
be treated as results obtained before the commencement of the order-
disorder transformation in the structure of the examined spinels,
whereas the data obtained at 973 K are the results of investigations
conducted at the temperature in which the order-disorder transforma-
tion has already begun in all spinels subjected to testing.
Similarly, in the solid solution of Mg(Al0.5Cr0.5
the degree of inversion (Δx) depends on Al
octahedral to tetrahedral sites, as is the case of MgAl
which the degree of inversion changes at 850 K from x
1373 = 0.60. The structure of Mg(Al0.5Cr0.5
temperature is similar to the normal one (x
slightly transformed into the inverse structure at 1373 K x1373 = 0.23.
)
2
O
4
the change in
3
+
cations moving from
2
O
4
0
spinel, in
= 0.45 to
x
)
2
O
4
solution at room
0
= 0.21) and becomes only
As shown in Fig. 7, all the solid solutions of: Mg(Cr0.5Fe0.5
)
2
O
4
, Mg
(
Al0.5Cr0.5
)
2
O
4
and Mg(Al0.5Fe0.5
)
2 4
O
reached a higher conversion (α/
3
+
This indicates that the presence of Cr ions has a stabilizing effect on
S ) at 973 K than at 773 K (before the commencement of the order-
x
the normal structure of Mg(Al0.5Cr0.5
)
2
O solution.
4
disorder transformation). At a temperature of 773 K, after 7 h, similar
values of conversion in relation to specific surface area α/Sx were ob-
tained for Mg(Cr0.5Fe0.5
)
2
O
4
and Mg(Al0.5Fe0.5
)
2
O
4
solutions – 0.32 g/
solu-
obtained after
Table 2
2
2
m
and 0.31 g/m , respectively. In the case of Mg(Al0.5Cr0.5
)
2 4
O
Initial degree of inversion at room temperature x
0
, inversion temperature T ,
x
tion, conversion in relation to specific surface area α/S
x
degree of inversion at 1373 K x1373, and degree of inversion change Δx of spi-
nels.
2
7
h was considerably lower, reaching 0.05 g/m . Similarly, the values of
conversion in relation to specific surface α/S
x
obtained for Mg
Spinel
x
0
T
x
(K)
X
1373
Δx
(
Cr0.5Fe0.5
)
2
O
4
and Mg(Al0.5Fe0.5
)
2
O
4
solutions at a temperature of
2
2
Mg(Cr0.5Fe0.5
)
2
O
4
4
4
0.50
0.21
0.51
0.03
0.90
0.45
790-810
970
0.45
0.23
0.58
0.03
0.70
0.60
0.05
0.02
0.07
–
973 K, after 7 h, reached 0.77 g/m and 0.78 g/m , respectively, and
2
Mg(Al0.5Cr0.5
Mg(Al0.5Fe0.5
)
2
O
2
0.29 g/m for the Mg(Al0.5Cr0.5
)
O solution.
2
4
)
O
870–910
–
In the case of both solid solutions containing iron
-
Mg
(Figs. 10 and 11),
of the solid solution
and MgCr or
MgCr
2
2
O
4
4
(
Cr0.5Fe0.5
)
2
O
4
(Figs. 8 and 9) and Mg(Al0.5Fe0.5
)
2 4
x
O
MgFe
O
700
0.20
0.15
conversion in relation to specific surface area α/S
MgAl
O
2 4
850
at 773 K is between α/S
x
obtained for MgFe
2
O
4
O
2 4
4

A. Gerle, et al.
Thermochimica Acta 680 (2019) 178344
Table 3
Current concentration of SO
3
and conversion of SO
2
in the gaseous phase.
partial pressure
Temperature (K)
Mole fraction and SO
3
2 3
Conversion of SO to SO (A)
(
at total pressure of 1 bar) (XSO3, bar)
7
9
73
73
0.0514 ± 0.0041
0.0374 ± 0.0030
0.382 ± 0.031
0.287 ± 0.023
Fig. 5. Conversion α of Mg(Cr0.5Fe0.5
)
2
O
4
(MCF), Mg(Al0.5Cr0.5
)
2
O
4
(MAC), Mg
Fig. 7. Mg(Cr0.5Fe0.5
)
2
O
4
(MCF), Mg(Al0.5Cr0.5
)
2
O
4
(MAC) and Mg
(
Al0.5Fe0.5
)
O
2 4
(MAF), MgCr
O
2 4
(MC), MgFe (MF), MgAl
2
O
4
2
O
4
(MA) versus
(
Al0.5Fe0.5
)
2
O
4
(MAF), conversion α versus time in relation to spinel specific
time at 773 K.
surface area S
x
at the temperatures of 773 K and 973 K.
Fig. 8. Mg(Cr0.5Fe0.5
α versus time in relation to spinel specific surface area S
73 K.
)
2
O
4
(MCF), MgCr
2
O
4
(MC) and MgFe
2
O
4
(MF) conversion
Fig. 6. Conversion α of Mg(Cr0.5Fe0.5
)
2
O
4
(MCF), Mg(Al0.5Cr0.5
)
2
O
4
(MAC), Mg
x
at a temperature of
(
Al0.5Fe0.5
)
O
2 4
(MAF), MgCr
O
2 4
(MC), MgFe (MF), MgAl
2
O
4
2
O
4
(MA) versus
7
time at 973 K.
Table 4
Phase composition of spinels solid solutions and two-cation spinels after a re-
action with sulphur oxides (+ means presence of the substance in the sample,
−
means absence of the substance in the sample, R means Al, Cr or Fe).
Spinel
Temperature (K)
Phase composition
MgR
2
O
4
MgSO
4
R
2
4
(SO )
3
2 3
R O
Mg(Cr0.5Fe0.5
)
2
O
4
4
4
773
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
−
−
−
−
−
−
−
−
−
+
−
−
+
+
+
+
+
+
−
+
9
73
773
73
773
73
773
73
773
73
773
73
Mg(Al0.5Cr0.5
)
2
O
O
9
Mg(Al0.5Fe0.5
)
2
9
MgCr
2
O
4
4
Fig. 9. Mg(Cr0 Fe ) O (MCF), MgCr O (MC) and MgFe O (MF) conversion
.5
0.5
2
4
2
4
2 4
9
α versus time in relation to spinel specific surface area S at a temperature of
x
MgFe
2
O
+ (traces)
9
73 K.
9
−
−
−
MgAl
O
2 4
9
(Cr0.5Fe0.5
)
O
(Fig. 9) the value of α/S
spinel, but, with time, it reaches values
. At a temperature of 773 K, when
the phenomenon of inversion does not occur in any of the examined
spinels, Mg(Cr0.5Fe0.5 and Mg(Al0.5Fe0.5 solutions behave like
a mixture of particular two-cation spinels. At 973 K - the temperature at
is initially closer to the value of
2
4
x
α/S
x
obtained for MgCr
2 4
O
closer to those obtained for MgFe
O
2 4
MgAl
2
O
4
spinels. At 973 K, conversion in relation to specific surface
of the solid solution is close to the value α/S of MgFe
spinel, which contains Fe. It is worth noting that in the case of Mg
area α/S
x
x
O
2 4
)
2
O
4
)
O
2 4
5

A. Gerle, et al.
Thermochimica Acta 680 (2019) 178344
Fig. 10. Mg(Al0.5Fe0.5
)
2
O
4
(MAF), MgFe
2
O
4
(MF) and MgAl
2
x
O
4
(MA) conver-
Fig. 13. Mg(Al0.5Cr0.5
)
2
O
4
(MAC), MgCr
2
O
4
(MC) and MgAl
2
x
O (MA) conver-
4
sion α versus time in relation to spinel specific surface area S
at a temperature
sion α versus time in relation to spinel specific surface area S
at a temperature
of 773 K.
of 973 K.
1
– 3(1−α)2/3 + 2(1−α) = kt
(9)
were used to calculate the reaction rate constant k. The SCM model
kinetic equation was used because of the best fitting to the experimental
data. After including the partial pressure of a gaseous substrate pSO on
3
the reaction rate constant k (k’ = k/pSO ) the activation energy E was
3
calculated based on the Arrhenius equation:
lnk’ = −E/RT + C
(10)
where: where: k’ – reaction rate constant taking into account the real
concentration of SO in the reactor; E – activation energy, J/mol;
R = 8314 J/(mol K) – gas constant; T– temperature, K; C– constant.
3
In the case of MgAl
2
O spinel, the activation energy of reactions
4
Fig. 11. Mg(Al0.5Fe0.5
)
2
O
4
(MAF), MgFe
2
O
4
(MF) and MgAl
2
x
O
4
(MA) conver-
with sulphur oxides at the temperature before the order-disorder
transformation begins is 92.3 kJ/mol, and after exceeding the tem-
perature of this transition commencement, it increases to the value of
sion α versus time in relation to spinel specific surface area S
of 973 K.
at a temperature
1
54.3 kJ/mol. A reverse situation is observed in the case of MgFe
O
2 4
spinel reaction with sulphur oxides - at the temperature before the
order-disorder transformation the activation energy in the spinel
structure is 133.3 kJ/mol, whereas after its commencement it drops to
the value of 38.5 kJ/mol. Changes in reaction activation energy after
exceeding the temperature of the commencement of the order-disorder
transformation in the structure of spinels are most probably the reason
for an unexpectedly large increase in the value of conversion α/S
x
of the
at a temperature of 973 K.
at a temperature of 773 K (Fig. 12),
solid solutions of spinels containing MgFe
In the case of Mg(Al0.5Cr0.5
the solution reacts similarly to MgCr O spinel. Conversion in relation
O
2 4
)
O
2 4
2
4
to specific surface area α/S
x
obtained after 7 h for both the Mg
2
(
Al0.5Cr0.5
)
2
O
4
solution and monophase MgCr
2
O
4
spinel is 0.06 g/m ,
whereas at 973 K (Fig. 13) the solution of Mg(Al0.5Cr0.5
)
2
4
O reacts like
Fig. 12. Mg(Al0.5Cr0.5
)
2
O
4
(MAC), MgCr
2
O
4
(MC) and MgAl
2
x
O
4
(MA) conver-
MgAl
2
O
4
spinel. After 7 h, the value of conversion in relation to specific
sion α versus time in relation to spinel specific surface area S
at a temperature
2
surface area α/S
x
was 0.29 g/m for both samples. Among the examined
of 773 K.
solutions only in the case of the Mg(Al0.5Cr0.5
)
2
O solid solution the
4
values of α/S
x
at 773 K were not mean values of α/S for respective
x
which the order-disorder transformation has begun in both Mg
two-cation spinels, whereas at a temperature of 973 K the values of α/S
x
(
Cr0.5Fe0.5
)
2
O
4
and Mg(Al0.5Fe0.5
)
2
O
4
solution, the values of α/S
x
are
are the same as those observed for the weakest reacting spinel – in this
higher than indicated by the average value of α/S
x
obtained for re-
case MgAl O . It is also the only spinel in which the phenomenon of the
2
4
spective two-cation spinels.
order-disorder transformation occurring in monophase MgAl O spinel
2
4
was practically blocked by the presence of Cr3+ cations.
Investigations into the kinetics of the reactions of two-cation mag-
nesia spinels: MgAl
2
O
4
, MgFe
2
O
4
, MgCr
2
4
O with sulphur oxides have
demonstrated that the order-disorder transformation in both the
4
. Conclusions
structure of MgAl
2
O
4
and MgFe
O
2 4
influences the value of the activa-
tion energy of these spinels’ reaction with sulphur oxides [10,11].
Conversion α determine at temperature before and after order-disorder
transformation begins, presented at [10] and the integral form of the
kinetic equation of the Shrinking Core Model (SCM) corresponding to
diffusion resistance in the solid product layer for sphere-shaped parti-
cles:
Problems encompassed by the conducted investigations are parti-
cularly important in copper metallurgy as they are connected with the
durability of refractory linings used in this industry. The phenomena of
corrosion caused by sulphur oxides cannot be eliminated, but they can
be limited. Knowledge about the reactivity of particular phases in re-
lation to sulphur oxides will allow reducing their contents in refractory
6

A. Gerle, et al.
Thermochimica Acta 680 (2019) 178344
materials, which are the least resistant to the destructive effect of gases
containing sulphur oxides. The results of this work demonstrate that at
a temperature of 973 K the presence of Fe in solid solutions of magnesia
spinels increases the reactivity of these solutions in relation to sulphur
oxides. This is related to the order-disorder transformation in the
structure of these solid spinel solutions under the influence of tem-
perature. On the other hand, the reactivity of the solid solution of Mg
(Amsterdam) 36 (1933) 153–157.
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[
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2 4
(
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the System MgR -SO -O , Doctor’s Thesis Faculty of Chemistry of the Silesian
Technical University, Gliwice, Poland, 2001 in Polish.
of less reactive MgAl
2
O
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2 4
O
2
O
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2
3
+
spinel structure stabilization by Cr
may play an important role.
From the point of view of refractory materials’ corrosion caused by
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gas-solid state processes in MgO-MgR
2 4 2 2
O (R: Al, Cr, Fe) spinels-SO -O system”,
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composition of refractory materials. Since it can be treated as an ad-
mixture from raw materials, such as chrome ores and periclase-spinel
co-clinkers, special attention should be paid to a maximum reduction of
iron contents in raw materials already at the stage of designing the
composition of a refractory material to be used as a lining in the zone
exposed to the attack of sulphur oxides.
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activity of MgAl
Proceedings of the Unified Int. Technical Conference on Refractories (2007).
10] A. Gerle, J. Piotrowski, J. Podwórny, The influence of order in the cation sublattice
2 4 2 4 2 4
O , MgCr O and MgFe O spinels at elevated temperature,
[
[
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Oxides, Doctor’s Thesis Faculty of Chemistry of the Silesian Technical University,
Gliwice, Poland, 2013, pp. 88–90 in Polisch.
From the practical point of view, MgAl
2
O
4
and MgCr
2
O spinels are
4
the most important in refractory materials. It is worth noting that, due
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to the pro-ecological trend in global economy, which involves elim-
inating the use of chromium compounds, MgAl
2
O spinel becomes
4
2
079–2085.
particularly important, as it provides an alternative to MgCr
2
O
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[13] S.C. Carnigla, G.L. Barna, Handbook of Industrial Refractories Technology
Principles, Types, and Applications, Noyes Publications, Westwood New Jersey,
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that elimination of Cr from the composition of a refractory material is
unfavourable due to the fact that Cr atoms, which stabilize the structure
1
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of MgAl
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O spinel, increase its resistance to the effect of sulphur oxides
4
[
[
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