THERMODYNAMIC CHARACTERISTICS OF REACTIONS
IN METAL–SLAG–GAS SYSTEMS
M. P. Shalimov1, M. I. Zinigrad2 and V.L. Lisin3
1
Ural State Technical University–Ural Polytechnic Institute, Russia
2
College of Judea and Samaria, Israel
3
Institute of metallurgy, Ural’s Division of Russian Academy of Science, Russia
ABSTRACT. The investigation and mathematical modeling of real metallurgical processes requires
knowledge of the parameters and characteristics that determine the thermodynamic state of the
system.
This paper examines the application of theoretical and experimental methods for estimating
the thermodynamic characteristics in metal–slag–gas systems for a series of components.
Method for calculating the equilibrium concentration distribution
of elements in multicomponent systems
Methods for calculating the values of equilibrium concentrations are most often based on the
use of the equilibrium constants of the reactions that are possible in the system under investigation
as starting data [1, 2]. At the same time, the use of equilibrium constants expressed in terms of
concentrations, rather than in terms of the activities of the components, can lead to errors in the
calculations.
Let us consider the following method as one of the possible methods for calculating the
equilibrium concentrations of the elements in a multicomponent carbon-containing molten metal
and a multicomponent slag [3] using the reactions
[C] + 2 [О] = {CO2}
(1)
[C] + [О] = {CO}
(2)
n[Ei] + m[O] = (EinOm),
(3)
where Ei denotes Fe, Ni, Al, Si, B, etc.
Oxidation reactions are chosen because they have been studied in fairly great detail and the
equilibrium constants of most reactions have been expressed in terms of the activities of the
components [4]
Pco
[C] f [O] f
Pco
 log
[C ] f [O] f
1
log K eq
 log
2
2
c
log K eq2
c
log K eq3  log
n
[Ei]
(4)
2
o
(5)
o
a EinOm
m
n
f E i[O]
f
(6)
m
o
Here fi is the Wagner interaction parameter.
We express the temperature dependence of the equilibrium constants of reactions (1)–(3) as
1 - 130
log Keq = A/T + B
Pco
(7)
We perform several transformations with Eqs. (4) and (5), taking into account that PCO = 1 –
. We assume that the equilibrium concentrations of all the elements in the melt apart from
2
carbon are insignificant, and, therefore, their influence on fC can be neglected. Then f = fCc and PCO
can be found for assigned values of the temperature and the carbon concentration in the metal.
Knowing PCO, we can easily obtain
1  Pco
1
2
(8)
log[ O]  log f  log
 log K eq  log K eq  D.
P
o
co
For the reaction of the main component of the alloy (for example, iron) with oxygen, we
write
a
log K eq  log
Fe
 log a FeO  log[ Fe]  log[ O]  log
FeO
[Fe][O]
f
f
o
 log a FeO  log[ Fe]  D . (9)
o
To calculate the equilibrium concentrations of the elements, we assign the temperature, the
slag composition respect to all the components apart from FeO, and the concentration of carbon in
the metal.
Let us examine the sequence of calculations in the example of a system consisting of an
iron–carbon alloy and an oxide slag.
We first find the concentration of iron in the alloy:
[Fe] = 100 – [C].
(10)
We determine the values of PCO and D, and from Eq. (9) we obtain the activity of ferrous oxide.
Taking into account that FeO = 0 [5], we can write
N FeO 
a FeO .
(11)
2
Since all the remaining concentrations of the components in the original slag are assigned,
the mole fraction (wt. %) can be expressed as follows:
(wt. %)FeO
N
FeO
M


FeO
(wt. %)E in O m
ME O
in
m

(wt. %)FeO
M
,
(12)
FeO
whence the mass concentrations are easily found.
Taking into account the FeO content, we find new values of the concentrations of the
remaining components in the slag. Knowing the composition of the slag, we can use the equations
of the theory of regular solutions to calculate the activities of the components in the slag [6]. When
there are complex-forming ions in the slag, we recalculate the activities using the relations that were
presented in [6].
Using equations similar to (9), we find the values of the concentrations of all the
components in the metal [Ei] apart from iron and carbon. We then calculate the Wagner interaction
parameters for each of the i components from the relation
f
Ei

C
Ei i
Ei
Ei
f f
(13)
1 - 131
From relation (8) we find the concentration of oxygen in the metal, assuming that
f
O

O
C
O
O
f f
П
fE
i
(14)
O
This completes the first calculation cycle.
The second calculation cycle starts with determination of the Wagner interaction parameter
for carbon with allowance for the influence of oxygen and all the components in the metal.
These calculations are performed according to the procedure described. Here the
concentration of iron in the metal is determined from the equation
[Fe] = 100 – [C] – [О] -  [Ei].
(15)
The calculation is repeated until the values of all the concentrations of the elements in the
metal coincide (with an assigned error) in two successive iterations.
The accuracy of the results obtained by this calculation method is determined by the
completeness of the data on the Wagner interaction parameters for different temperatures and melts
with different carbon concentrations, including a carbon concentration close to saturation, as well as
by the heats of mixing of the oxides.
Using the data in [7], we estimate the values of Qij for systems in which these values have
not been determined experimentally.
Let us examine the application of the method described to the calculation of equilibrium
concentrations of components in the case of concrete systems.
Distribution of boron, aluminum, and phosphorus
between the metallic and slag phases
An oxide phase similar in composition to the phases used in non-furnace steel working and
the AN-28 and AN-30 reference fluxes. The basic oxide melt had the following composition (wt.
%): 51Al2O3, 43CaO, 6MgO. Up to 15 wt. % B2O3 or up to 10 wt. % P2O5 were added to it. An Fe–
C melt with a carbon content equal to 0.5–3 wt. % was also employed as the starting melt.
The method described was used to calculate the equilibrium concentrations of the
components in the metal and the slag [3].
Published values of the Wagner interaction parameters [1, 4], heats of mixing [6, 7],
equilibrium constants [4, 8], and distribution constants (Li) [9, 10] were used in the calculation.
The calculation results demonstrate the non-monotonic character of the dependence of the
boron and aluminum concentrations in the metal on its carbon content. This is because carbon in a
concentration greater than 2 wt. % in the metal is a stronger reducing agent than boron and
aluminum at corresponding concentrations. Since the oxygen concentration passes through a
minimum at [C]  2 wt. %, the concentrations of boron and aluminum accordingly pass through a
maximum. According to the data in [4], the carbon concentration which ensures the minimal
oxygen content in iron at 1873 K equals 2.25 wt. %. This value is fairly close to the value that we
obtained.
Let us analyze the dependence of the metal-slag distribution coefficients of boron and
aluminum, which equal
LB 
( B 2 O3)
[ B]
L Al 
( Al 2 O3)
[ Al ]
on various parameters.
1 - 132
(16)
They depend on temperature and on the carbon concentration in the metal. In addition, in
analogy to [8], we assume that they are linearly dependent on the concentration of the oxide in the
slag:
LB = a + b (B2O3),
LAl = a1 + b1 (Al2O3)
(17)
Treatment of the data obtained yielded equations for calculating LB and LAl and the limits for their
use:
  47830
 1

 42310

(18)
 20.23   exp 
 20,96 ( B2 O3)
.
L B  exp 

 T

  T
 C 

 72800

 73200
 1
 30,8 ( Al 2 O3)  exp 
 27,6 
.
 T

 T
 C 1,5
L Al  exp 

(19)
These equations allow us to calculate the values of LB and LAl in the 1723–1973 K temperature
range for concentrations of B2O3 in the slag up to 25 wt. % and concentrations of Al2O3 in the slag
up to 55 wt. %.
It is noteworthy that similar results with respect to the values of the equilibrium
concentrations of aluminum and their dependence on the carbon content in the metal for slag and
metallic systems not containing boron were obtained in [11].
At low concentrations of (B2O3) in the slag, Eq. (18) undergoes a slight transformation. At
(B2O3) ≤ 3 wt. %, LB is scarcely dependent on the concentration of boron oxide in the slag and can be
calculated using the following expression

 47830
 1
 20,23 
.
 T
 [C ]
L B  exp 

(20)
To test the calculated data obtained, we undertook the experimental determination of the equilibrium
distribution coefficients of boron. The compositions of the metal and the slag in the experiments were similar
to those used in the calculations. The metals were prepared by fusing powders of carbonyl iron,
spectroscopically pure graphite, and amorphous boron; the slag was prepared from CaO, Al2O3, MgO, and
B2O3. The carbon concentration in the metal was 1.0, 1.5or 2.0 wt. %, and the boron concentration ranged
from 0 to 0.3 wt. %.
Three series of experiments were performed to ensure approach to the equilibrium position from
both sides. In the first series, the boron content in the metal significantly exceeded the equilibrium
concentration, and there was no B2O3 in the original slag. Conversely, in the second series, the metal did not
contain boron, and the concentration of B2O3 in the slag was 5, 10, or 15 wt. %. In the third series, boron was
present in both the metal and the slag.
Equal Weighed portions of the preliminarily ground metal and slag of equal weight were taken and
mixed. The contact surface between the phases was thus maximized for the purpose of shortening the time
needed for the system to achieve an equilibrium state and of eliminating the influence of the mass of the
metallic and slag phases on the distribution coefficient of boron. The mixture was placed in the isothermal
zone of a carbon resistance furnace and held at a constant temperature for 60 min. The temperature was
monitored by a platinum–rhodium thermocouple. To eliminate any possibility of the components of the
metal interacting with the gaseous phase, the heating zone was isolated from the carbon heating element by a
corundum covering and purged with argon. The purging was discontinued after the phases melted, because
an air atmosphere does not have an appreciable influence on the composition of the reacting melts [11].
The experimental data allow us to conclude that equilibrium with respect to boron does not always
manage to be established under the conditions of our experiments. However, the character of the variation of
1 - 133
its concentrations in the metal and the slag is such that convergence of the experimental points on the
calculated curve can be expected.
Therefore, the method described can be used to calculate the equilibrium concentrations in a system
consisting of an iron–carbon metal and an oxide slag.
Expressions for calculating the ratios between the equilibrium concentrations for the following
reactions were also derived on the basis of the data obtained:
2/3(BO1,5) + [C] =2/3[B] + {CO}
(21)
2/3(BO1,5) + [Fe] =2/3[B] + (FeO)
(22)
2/3(AlO1,5) + [C] =2/3[Al] + {CO}
(23)
2/3(AlO1,5) + [Fe] =2/3[Al] + (FeO)
(24)
13413
 5,676,
T
4012
lg K 22
 2,013,
P 
T
lg K 21
P 
(25)
(26)
lg K 23
P 
21005
 8,077,
T
(27)
lg K 24
P 
12340
 0,793.
T
(28)
Expressions (25)–(28) were used in our work both for carrying out the kinetic analysis of
multicomponent systems containing boron and aluminum and for developing mathematical models of
technological processes.
We similarly presented calculations for the distribution of phosphorus between a metal and a slag. In
this case, instead of reaction (3), for phosphorus we considered the following equation
(29)
whose equilibrium constant is described by the expression [4, 5]
log K
29
eq
a p o Fe
 log
[ P] f a
2
2/5

5
2/5
P
22910
 15,414.
T
(30)
FeO
The results of the calculations are presented in Table 1.
Table 1. Equilibrium concentrations of components in the metal and slag
T,K
(P2O5), wt. %
5
1873
10
1923
10
[С], wt. %
1.0
0.5
1.0
1.5
1.0
[Р], wt. %
0.27
0.15
0.49
0.75
0.92
The data obtained allow us to draw some conclusions.
1 - 134
LP=(P2O5)/[P]
18.5
66.7
20.4
13.3
10.9
The distribution coefficient depends weakly on the concentration of (P2O5) in the slag, in agreement
with the data in [12]. At the same time, LP depends to a considerable extent on the concentration of carbon
in the metal. A decrease in the carbon concentration results in an increase in LP to values close to the values
obtained in [12] for a carbon-free metal and to nearly complete constancy of the distribution constant of
phosphorus.
To test the calculated data, we performed experiments to determine the distribution coefficient of
phosphorus between the metal and slag. In particular, it was found for T = 1973 K and a carbon content in
the metal equal to 0.3 wt. % that LP = 28.6 when equilibrium is approached form the slag side. When
equilibrium is approached from the metal side, LP = 4.3. At the same time, LPcalc for these conditions equals
25.5.
Treatment of the results yielded the following expressions for the distribution constant of phosphorus
between the metal and slag:
for (P2O5) > 0.5 wt. %

 1
 42250

 49930

 19,79   exp 
 27,57 ( P 2 O5)
,
1,5
 T

 T

 [C ]
L P  exp 

(31)
for (P2O5) ≤ 0.5 wt. %

 1
 42250

 49930

 19,79   exp 
 27,57 ( P 2 O5)
,
1,5
 T

 T

 [C ]
L P  exp 

(31)
Expression for calculating the ratio between the equilibrium concentrations for reactions involving
phosphorus were also obtained:
2/5 (PO2,5) + [C] = 2/5 [P] + {CO},
(33)
8120
 3,81,
T
(34)
lg K 34
P 
2/5 (PO2,5) + [Fe] = 2/5 [P] + (FeO),
lg K 34
P 
(35)
15740
 11,29.
T
(36)
Equilibrium Distribution of Tungsten between Liquid Metallic and Slag Phases
When a tungsten-containing metal comes into contact with an oxide melt, the main process
determining the distribution of tungsten between the interacting phases can be represented by the
reaction
1/ 3
(W O3 ) [ Fe]
1/3[W] + (FeO) = 1/3(WO3) + [Fe],
(37)
,
КW 
1/ 3
[W ] ( FeO)
where KW is the ratio between the equilibrium concentrations.
The direction of the reaction for phases with assigned compositions can easily be
determined from the value of KW. Moreover, this constant is needed for calculations of the chemical
composition of the metal and slag during their interaction with tungsten. However, there are no
experimental values of this ratio for phases with compositions close to the compositions observed in
the oxidative smelting of tungsten-containing scrap.
1 - 135
It is virtually impossible to use theoretical methods to find the equilibrium concentrations of
the components since the literature data on the thermodynamic parameters of reaction (37) are very
sparse and contradictory. According to the data in [13, 14], the difference between the values of KW
found by theoretical and experimental methods is as high as 150%. Therefore, we shall use only
experimental methods to determine the equilibrium concentrations for this system.
It should be noted that the presently available data on the distribution of tungsten between a
metal and a slag [13–18] refer to oxide systems containing at least 30 wt. % ferrous oxide. At the
same time, there are no data on the distribution of tungsten between a metal and a slag for FeO
concentrations smaller than 20 wt. %, which are typical of steel-smelting slags.
The equilibrium distribution of tungsten between a carbon-containing metal and slag was
studied experimentally at 1773–1873 K in [19] according to the method described.
The starting materials used were a slag based on the low-melting eutectic composition
(wt. %) 51Al2O3 + 43CaO + 6MgO with additions of 0.5–20.0 wt. % FeO and 5–20 wt. % WO3 and
a metal based on iron containing 0.5–3 wt. % carbon and up to 6 wt. % tungsten.
For the purpose of determining the time during which the metal must be held with the slag
for the system to achieve an equilibrium state, we performed experiments that permitted estimation
of the dependence of the reactant concentrations on the interaction time of the molten phases.
Experiments were performed at 1823 K with initial concentrations of ferric oxide in the slag
and of carbon and tungsten in the metal equal to 10, 1.1, and 6 wt. %, respectively. These
experiments showed that the composition of the metal and slag scarcely varies with time after 10–
15 min of holding. This time is probably sufficient for the system to achieve a state close to
equilibrium. Experiments employing phases with other compositions were carried out with a
holding time of 30 min.
It follows from the results obtained that an increase in the concentration of FeO in the final
slag leads to significant lowering of the values of LW = [W]/(WO3). When (FeO) > 7.0 wt. %,
variation of the temperature and increases in the concentration of ferrous oxide in the slag have
scarcely any influence on LW. Fairly similar results were obtained in [14, 16, 17]. At the same time,
the values of LW for FeO concentrations in the slag less than 3 wt. % were obtained for the first
time. Under these conditions, LW exhibits strong temperature dependence, and the values of the
distribution coefficient are significantly higher than the previously known values.
It is noteworthy that the concentrations of the components vary in the experiments because
of the interactions with carbon and FeO. The experimental data suggest that reaction (37) reaches a
state close to equilibrium at the end of each experiment. In fact, it follows from the experimental
data that KW remains essentially constant at an assigned temperature in the range of phase
compositions obtained after each experiment. The experimental data were used to estimate the
dependence of the mean values of KW on the temperature at which the phases interacted. It can be
linearized in log KW versus 1/T coordinates and described by the expression
1/ 3
lg К W  lg
(W O3 )
1/ 3
[W ]
[ Fe]
( FeO)

14860
 7,05 .
T
(38)
It follows from (38) that raising the temperature results in displacement of the equilibrium
of reaction (37) to the left, in agreement with the conclusion drawn in [14, 16, 17] that this process
is exothermic.
The literature offers practically no data on the influence of carbon on the distribution of
tungsten. It is only known [14] that raising the carbon concentration results in an increase in KW.
1 - 136
The experimental data in [14] yield the following dependence of LW on the carbon content in the
metal:
LW = A [C]b,
(39)
where b = 0.7–0.85.
The experimental dependence of LW on [C] derived from the data obtained in our
experiments is described by Eq. (39), in which b = 0.5–0.6.
In our opinion, the dependence of LW on the initial concentration of carbon in the metal is
interesting. This dependence, which can be used for approximate calculations, has the form
A1 ,
LW 
[C ]0
(40)
where [C]0 is the initial concentration of carbon in the metal, wt. %.
The value of A1 can be estimated from the following data:

If the initial value of (FeO) in the slag is greater than 7.0 wt. %, A1 = 8.88 at 1673–
1973 K.
If the initial value of (FeO) in the slag is less than 4 wt. %, A1 can be calculated from
the expression

ln A1  
10310
 8,88.
T
(41)
Theoretical and Experimental Determination of the Equilibrium
Distribution Coefficients of Sulfur
The equilibrium distribution of sulfur between immiscible oxide and metallic phases is often
described by the ratio of equilibrium concentrations
LS = (S)/[S].
(42)
When the composition of the interacting phases remains constant, the coefficient LS is
proportional to the equilibrium constant of the desulfurization processes.
For a system consisting of an iron–carbon melt and an oxide slag, the desulfurization
reaction is written [20] in the form
[FeS] + (CaO) + [C] = (CaS) + [Fe] + {CO},
)
or in the ionic form
(43
[S] + (О)2- +{C} = (S)2- + {CO}
(44)
The expression for the equilibrium constant of process (43) can be written in the form
KP 
a( s )2  P CO
a[ S ] a[C ] a(o)2 
.
(45)
We assume that the equilibrium partial pressure of carbon monoxide (PCO) equals unity. This
assumption is valid if CO bubbles form on the metal–oxide boundary when the external pressure
equals 1 atm. In addition, we assume that the activity coefficients of sulfur and oxygen in the slag
1 - 137
are equal to 1, and we express the activities of sulfur and carbon in the metal using the Wagner
interaction parameters. Equation (45) is then simplified.
Let us express the equilibrium distribution coefficient of sulfur LS on the basis of Eq. (45).
We assume that N(S2-) = N(S). This assumption is fully permissible at a low (less than 3
wt. %) sulfur content in the slag. Then the expression for LS can be written as
LS = (S)/[S} = AKP[C]fCfS N(O2-)
(46)
where A is a constant that allows for the replacement of N(S2-) by (S), Keq is the equilibrium constant
of reaction (43), [C] is the concentration of carbon in the metal (wt. %), fC is the activity coefficient
of carbon in the metal, jC is the activity coefficient of sulfur in the metal, and N(O2-) is the ion
fraction of “free” oxygen in the slag.
The value of Keq was determined from the equation [20]
lg K 43
P 
3800
 3,71.
T
(47)
The activity coefficients of carbon and sulfur were calculated using a method that employs the
Wagner interaction parameters [1, 4].
The feature distinguishing the calculation in this case from all the preceding variants of the
calculation of LS based on the expression (46) is that the ion fraction of “free” oxygen N(O2-) in the
oxide melt was determined using the polymer theory of molten slags. Taking into account that the
MgO content in the slag under investigation is insignificant and that the properties of calcium oxide
and magnesium oxide are similar, we used the method that we developed for the Al2O3–CaO
system to determine the ion fraction of “free” oxygen appearing in Eq. (46). In our opinion, this
approach should lead to refinement of the calculated values of LS and better agreement with the
experimental data.
The results of the calculations of LS based on Eq. (46) for various temperatures and
concentrations of carbon in the metal are presented in Table 2. As follows from the table, the value
of the desulfurization factor increases with increasing temperature and increasing concentrations of
carbon in the metallic phase.
Table 2. Dependence of the calculated equilibrium distribution coefficients of sulfur on the
temperature and carbon concentration in the metal
[C], wt. %
T, K 0.2
0.3
0.4
0.5
0.6
0.9
1.0
1.1
1.3
1.6
1.9
2,0
Equilibrium distribution coefficient of sulfur, LS
1773 18
22
33
46
52
85
99
110 132 175 225 250
1823 20
27
38
52
65
110 112 124 160 215 280 301
1873 22
33
45
60
75
115 128 157 188 265 350 375
The main shortcoming of most of the experimental studies designed to determine LS was the
approach toward equilibrium from only one side. We attempted to take into account this
circumstance [3, 21].
The most interesting values are the values of LS for the metal containing less than 1.5 wt. %
carbon. This carbon content is close to the conditions of the non-furnace treatment of steel by
synthetic slags. Therefore, a metal containing 0.5–1.9 wt. % carbon was used in the experiments.
The procedure for preparing the melts and performing the experiments was previously described.
For the purpose of ensuring the approach to the state of equilibrium from both sides, three series of
experiments were performed:
1 - 138



The sulfur concentration in the starting metal was greater than the equilibrium
concentration obtained in a calculation.
The sulfur content corresponded to the equilibrium value.
There was no sulfur in the starting metal.
In each series of experiments, the concentration of sulfur in the oxide melt was varied: 0.5,
1.0, 2.0, and 3.0 wt. %.
The metal was analyzed to determine the carbon and sulfur content, and the slag was
analyzed to determine the sulfur content. The carbon concentration [C] remained practically
constant during the experiments. It follows from the experimental data that equilibrium between the
metal and oxide metal with respect to sulfur is achieved after 30 min when the phase boundary is
sufficiently developed.
Figure 2 presents the experimental results on the distribution of sulfur between the molten
metal and the oxide melt. The points mark the initial and final concentrations of sulfur, and the
arrows indicate the direction of their variation.
A comparison of the calculated and experimental data (Fig. 2) allows us to conclude that the
assumptions made in the calculation do not distort the values of LS obtained.
The influence of the carbon concentration on the value of LS is illustrated in Fig. 3. As
follows form the figure, LS increases as [C] increases. The experimental values of LS were close to
the calculated values (Fig. 3).
Therefore, Eq. (46) can be recommended for determining the numerical value of the
equilibrium distribution coefficient of sulfur between Fe–C–S melts and an oxide melt with the
composition (wt. %) 51Al2O3 + 43CaO + 6MgO, as well as oxide melts with a similar content of
“free” oxygen.
The treatment of the experimental data yielded the following equation for calculating the
distribution coefficient of sulfur.
lg K P  
3700
 4,10  1,25 lg[ C ].
T
(48)
Investigation of the Equilibrium Concentrations of the Components
in a Nickel-Alloy/Oxyflouride- Slag System
The smelting and welding of nickel and nickel alloys is carried out with special oxide–
fluoride mixtures (fluxes), which, in their molten form, protect the metal from the action of the gas
phase and prevent oxidation of the alloying components. CaO, MgO, Al2O3, and CaF2 are most
often employed as flux components. At the same time, such elements as Cr, Ti, and Co, which can
undergo oxidization and pass into the slag, are specially added to nickel alloys. Taking into account
that the welding materials used for welding nickel and its alloys contain transition-metal carbides,
which are readily oxidized to the corresponding oxides, the slag in contact with the liquid metal can
contain oxides of chromium, titanium, etc.
For this reason, we carried out experiments to determine the equilibrium concentrations of
Ni, Ti, and Cr distributed between a metal and an oxyfluoride melt.
The starting phases chosen had the following compositions:


Slag (wt. %): 50Al2O3 + 30CaO + 15 CaF2 + 5MgO.
Metal (wt. %): Ni (base) + 0.1C.
Two types of experiments were performed. In one series we investigated the equilibrium
distribution of the metals after up to 15 wt. % TiO2 was introduced into the slag. In the other series
we investigated the equilibrium distribution after up to 15 wt. % TiO2 was introduced into the
metal.
1 - 139
The equilibrium concentrations of the components in the metal and the slag were first
calculated according to the method described. The temperature dependence of the equilibrium
constants [4, 8] and the values of the Wagner interaction parameters [4, 8], heats of mixing [6, 22],
and correction factors for making the transition from regular solutions to real solutions [9, 10] were
borrowed from the literature.
It was also assumed that
aNiO = NNiO.
(49)
The results of the calculations are presented in Table 3.
Table 3. Equilibrium concentrations of the components in a nickel-alloy/oxyfluoride-slag system
[C], wt.%
Т,К
(NiO)eq, wt.% (TiO2)eq, wt.%
[Ti]eq, wt.%
LTi= (TiO2)/[Ti]
-4
1773
13.0
2.0
4878
4.110
-3
11.7
15.0
3750
4.010
-3
8.7
2.0
1053
1.910
1873
7.6
10.0
0.011
909
7.0
15.0
0.021
714
-3
5.6
2.0
263
7.610
1973
5.5
10.0
0.037
270
4.8
15.0
0.073
205
0.1
Т,К
(NiO)eq, wt.% (Cr2O3)eq, wt.%
[Cr]eq, wt.%
LCr = (Cr2O3)/[Cr]
13.3
5.0
0.65
7.7
1773
12.6
10.0
1.00
10.0
11.5
20.0
1.50
13.3
10.8
30.0
1.85
16.2
7.1
1.4
1.0
1.4
1873
6.9
5.8
2.0
2.9
6.7
12.8
3.0
4.3
639
25.0
4.0
6,3
In addition to the calculations, we performed experiments to study the equilibrium
distribution of the components between a metal and a slag with the composition indicated above.
The procedure for preparing the samples and carrying out the experiments was previously
described. We only note that in this case the metal was prepared by melting powdered nickel with
the alloying components. The alloying components used were titanium and metallic chromium. The
crucibles with the melts were held isothermally for about 60 min.
The results of the chemical analysis of the metal and slag after each experiment showed that
equilibrium could not be achieved when it is approached from the metal side or from the slag side.
In our opinion, there are several reasons for this.
First, the equilibrium concentrations of titanium in the metal are not very high even when
the content of its oxide in the slag is high. Therefore, it is difficult to approach an equilibrium state
from the metal side, especially within a short time.
Second, the slag with the composition investigated has a negligible oxidation potential.
Therefore, the reaction rates on the nickel-alloy/oxyflouride-slag boundary are small, The reactions
virtually cease when a considerable portion of the CaF2 is removed from the slag by vaporization.
For this reason, the correctness of the theoretical data obtained can be confirmed only
indirectly, by comparison with known literature data.
1 - 140
In particular, it is known [23, 24] that the final slag obtained after the welding of nickel and
nickel alloys using molten and ceramic fluxes contains 6–8 wt. % NiO, in agreement with our data
(Table 3).
The calculations of the activity of TiO2 in multicomponent slag systems in [25, 26] exhibit a
significant negative deviation from ideality. In particular, when the titanium dioxide concentration
fell in the range from 34.0 to 44.0 wt. %, its activity at 1873 K varied form 0.041 to 0.106,
depending on the composition of the slag. Our calculations exhibit a similar dependence. As the
TiO2 concentration in the slag varies from 2.0 to 15.0 wt. %, the activity at 1873 K increases form
0.002 to 0.02.
In addition, the similar calculations presented in the preceding sections display fairly good
agreement with experiment.
Approximate ratios of the equilibrium concentrations were obtained on the basis of these
data for the following reactions:
1/2[Ti] + (NiO) = 1/2(TiO2) + [Ni],
(50)
1/2[Cr] + (NiO) = 1/2(Cr2O3) + [Ni].
(51)
Their temperature dependence is given by the equations
lg K 50
P 
4440
 0,22,
T
(52)
lg K 51
P 
1000
 0,68.
T
(53)
Relations (52) and (53) were used for the mathematical modeling of metallurgical processes
in multicomponent systems.
1 - 141
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1 - 143
Influence of the temperature on the equilibrium
concentration ratio for reaction (37)
log LW
1.4
1.3
1.2
1.1
1.0
0.9
0.8
5.3
5.5
5.7
Fig. 1
1 - 144
104/Т
Equilibrium distribution of sulfur
between oxide and iron–carbon melts
[S], wt. %
0.08
a)
0.06
0.04
0.02
0
1.0
2.0
3.0
0.04
4.0
b)
0.02
0
1.0
2.0
3.0
Fig. 2
а – [C] = 0.5 wt. %; b – [C] = 1.9 wt. %
Lines – calculation; points – experiment;
- initial concentrations;
- final concentrations.
1 - 145
(S), wt. %
Influence of the carbon content in the metal
on the equilibrium distribution of sulfur between
a molten metal and an oxide melt
LS= (S)/[S]
400
2
300
1
200
100
0
0.5
1.0
1.5
Fig. 3
Lines – calculation:
1 – Т = 1773 К; 2 – Т = 1873 К;
Points – experiment:
- data from [27] for Т = 1773 К;
- our data for Т = 1873 К
1 - 146
2.0
[C], wt. %