PROPERTIES OF A SYSTEM FeO-SiO2-CAO-MgO
BY RESULTS OF COMPUTER EXPERIMENT
Voronov V.I., Voronova L.I., Rizhov N.I., Gusev A.I.
Kurgan state university, Kurgan, voronova@zaural.ru
The summary
The outcomes of computer experiment for a multicomponent slag system FeO-SiO2-CaOMgO are considered. The simulation was carried out by program complex “Slag Melt”, realizing
calculations in a complex model, including cluster quantum-chemical, molecular-dynamic and
statistical-geometrical simulation with use of the approaches of the polymeric theory of scorias.
Four makeups of scorias are investigated at different temperatures. The structural characteristics
of the short-range order (function of radial distribution of atoms, distribution of coordination
numbers, distribution functions of angles between bonds, average lengths of bonds, coordination
numbers, angles between bonds) are defined, the features of nanostructure (are found polyanions
of a different degree of complexity, their distribution functions on characteristic parameters are
constructed, the time of life of polyanions is calculated) a thermodynamic properties (heat
capacity, compressibility, expansions ratio) is calculated, the kinetic transfer coefficients
(diffusion constants and viscosity) are found, the characteristics of polimerisation of a system are
defined at temperatures close to melting temperatures. The comparison of model outcomes with
the experimental data displays the satisfactory consent.
Introduction
In work some outcomes of computer experiment on exploration structural - responsive
properties of melts of a system FeO-SiO2-CaO-MgO are given. These melts are characteristic
for smelting processes of steels in oxygen converters, in steel-teeming ladles, Martin ovens. In
particular, the values of heat capacities of such scorias are necessary in thermal accounts of
processes between metal and scoria, for exposition of interaction of scoria with fire-resistant
lining. The important property of a melt is its dynamic viscosity and its association on
temperature. The outcomes of simulation of structure of the presented scorias will allow not only
to know about their structure, but also to solve a number of tasks connected to interaction of
scorias to refractories.
The computer experiment was carried out with the help of a program complex “Slag_Melt”
[6], realizing a complex computer model, which contains a number of component, provides
different stages of complex MNDO-MD-SG simulation. The structure of a complex model is
presented in Tab. 1.
76
At complete realization of model
Table 1.The structure of a complex MNDOin the complex MNDO-MD-SG
MD-SG model
experiment it is possible to receive a
Cluster quantum-chemical model: is realized with
series of practically important outcomes:
the help of semiempirical quantum-chemical
parameters of potential functions;
method MNDO
thermodynamical parameters; transport
(modified neglect of diatomic differentional
properties; structure of melts with
overlap)
different levels of approximations,

characteristic of polymerisation a
Ionic or ionic - covalent model of oxide: a
system, visualization of a history of life
parametrization of peak-a-boo potentials by methods of a model system.
of many-dimensional optimization, on a base of an
MNDO-simulation. At the first
basic MNDO–datas array
stage the parametrization of potential

functions in ionic (IM) or in ionic Particles model: is realized in molecularcovalent (ICM) model was made and
dynamic experiment
then it used in molecular-dynamic

experiment. The type of potential
Two-level model of structure (short-range
function was determined by attributes of
order, nanostructure): is realized in the statisticala particle and conditions formulated in
geometrical (SG) experiment
ICM. [3]

For
calculating of
potential
Model of structure by the “Covalent bonds network
parameters was made quantum-chemical
covering method” (CBNC)
MNDO simulation in a cluster

approximation for silicium-oxygen
Model of process of polymerisation by the
complex anions of a different degree of
method of distribution functions of polyanionic
complexity: SikOlМеm(An), where Me –
complexes
Fe, Ca, Mg; A – pseudo-atom closing

torn bonds in a cluster, the inferior
Calculation of polimeric theory of scorias
indexes
are
determined
using
parameters by the results of statistical-geometrical
stoichiometrical reasons and vary from 1
modelling
up to 20. The parameters of potential
functions determining interparticle interaction in a system FeO-SiO2-CaO-MgO in ionic and
ionic – covalent model are given in table 2. Here m, q and  - characteristics of an ion: m weight q – effective charge,  - radius of a hard orb, dО, 0 – equilibrium distance Si-O and angle
O-Si-O, kit, kit – force constant of two and three-partial interactions, n – exponent in aside–part
of potential.
Table 2
Attributes of model particles and parameters of potential functions
Systems Si-O- Fe-Ca-Mg
Model
Ion
ICM
IM
-//-//-//-
Si
O
Fe
Ca
Mg
m, 10-26,
kg
4,66
2,66
9,33
6,57
4,05
q,
el. un.
2,92
-1,46
1,46
1,46
1,46
, nm
0.022
0.128
0.06
0.102
0.065
dО,
nm
0,162
-
77
kit,
N/m
200
-
0,grad
109,5
-
kit,
H/m
150
-
N
10
-
MD-simulation. In tab. 3 the data-ins of simulation are given. The density () of a modeled
system is calculated from molar volumes of the appropriate solid phases, with increase on 10%.
There are presented: a melting temperature (Тmelt), temperature of simulation (T1mod, Т2mod),
molar volume (). Т1mod of compositions were selected with overflow on 30-40 K above Тmelt of
the given composition, and Т2mod approximately on 100 K.
Table 3.
Data-ins of simulation
Slag
1
2
3
4
Тmelt, К
composition
FeO
20
20
20
25
CaO
50
50
50
40
SiO2
30
25
20
20
Т1mod, Т2mod, , kg/m3 , 10-4
m3/mole
К
К
MgO
5
10
15
1903
1873
1813
1773
1939
1911
1842
1809
1933
1878
3210
3200
3200
3200
0.188
0.185
0.182
0.182
At MD-simulation the classical approach, approximating of the differential equations on
a method Beemen was used; periodic boundary conditions of Born-Carman, volume of cube
depend on a density of a melt, number of particles in the cube ~ 1500, temporal step 0.5*10-15s.
A primal destacking of particles on a crystal lattice SiO2, heating-up of a system up to 5000К, for
security of a free diffusion of particles and running off up to a melting temperature on 5000
steps. The phase of thermostabilisation, at Тmod made 300 steps, phase of a thermodynamic
equilibrium - 20 macrosteps and 250 microsteps. Thus length of a segment of a trajectory in
configuration space for any temperature point made 5000 steps. The homogenization for
thermodynamical characteristics was carried out on 10 macrosteps, consisting from 500
microsteps. The number of the initial moments of homogenization ACF made 1000 (for ACF of
speed) and 2000 (for others ACF) steps.
For all compositions the error of saving of a full energy did not exceed 0,05 %, the error of
saving of a kinetic energy made 1-3 %, that is quite accepted for MD-simulation.
SG-simulation. Is realized on a base of statistical-geometrical information processing
about coordinates of modeled particles on each configuration. Allows to investigate structure
with different levels of detailing (short-range order, nanostructure), to find structural groupings
of a different degree of complexity, to describe process of polymerisation / depolymerisation of a
melt on a base of the distribution functions of polyanionic complexes, to determine correlations
composition-structure-characteristic with engaging of the polymeric theory.
The modern theory of metallurgical melts represents metallurgical scoria as ionic covalent system with processes of polymerization. The degree of polymerization
influences all characteristics of a melt. We have applied to exploration of structure
singularities of polymerizing melts a method of localization of polyanionic complexes.
The model system is consisting from cations – network formers, cations - modifying
agents and atoms of oxygen of a different type. In a model system was found elementary
structural groupings (ESG), their join in more complex structural groups of the different
form and complexities.
In outcome on each configuration the coordination numbers and their distributions,
function of an angular distribution of atoms, fraction of nonbridging, bridging and free
atoms of oxygen, an absolute number of different polyanions and selfcontained
structures, charge of them are determined. Then the distribution functions of polyanionic
78
complexes on a series of characteristic parameters (рaram), identifying complexes (Т) are
constructed: name - type of a complex, is determined by number of varied particles in it,
N - " length of a complex ", its total number of particles, N cat , N O , N O , NO - amount of
cations – network formers, atoms of oxygen, nonbridging and bridging atoms of oxygen
in a complex. In a model calculated: degree of polymerization, constant of
polymerisation, fractions of different polyanions, ionic fraction of free oxygen, activity of
participating oxides.

0
Outcomes of structural exploration.
The structural characteristics of the short-range order.
For all types of particles depending on makeup the partial functions of radial distribution
are received. In a fig. 1 the partial functions of radial distribution for Me-O, where Ме = Si, Fe,
Ca, Mg and O-O are given. All partial RDF have the legibly expressed first peaks. The
maxheight of peaks in a system is observed for bond Si-O (~18) their average half-width does
not exceed 0,02 nm. The second peaks in investigated melts practically are not expressed. That
speaks about lack of the second coordination sphere on Si-O. The first peaks RDF for remaining
Ме-O also are explicitly expressed, but is much lower (~5,6-4,5) and it is wider, than for Si-O,
the second peaks practically are absent. Relative height of these peaks practically does not
depend on makeup of a melt. The first peak RDF for О-О wide also is daubed, does not exceed
values 2,8.
Besides were received RDF for Si-Si, Si-Me, Ме-Ме. For all couples of cations relative
height of the first peaks does not exceed 2,5 units, and half-width about 0,5А. That speaks about
weak correlation in a disposition between cations. The Me ions chaotically moving inside a melt,
being mainly in an oxygen environment.
Depending on composition the character of RDF essentially does not vary. The marked
singularities of RDF allow speak about presence of the short-range order in melts.
79
Figure.1. Radial distribution functions (RDF) for 1: Si-O, 2: Fe-O, 3: Ca-O, 4: Mg-O, 5: O-O.
In figures 2-3 the average distances L between particles (bond length) and coordination
numbers Z are given depending on composition. Average distance for Si-O is equal 0.164 nm,
for Ме-O place in a range of values 0.2-0.25 nm, near to values in pure oxides. The coordination
number Si-O in all a range of compositions is stored constant and equally to four, that speaks
about presence of elementary tetrahedral complexes. The remaining coordination numbers also
practically do not vary.
Figure 2. Bond lengths.
Figure 3. Coordination numbers.
The average angles Si-O-Si and O-Si-O between bonds on a base of angle distribution
functions were calculated. These values also practically do not depend on composition and are
equal approximately: the angle Si-O-Si is equal 109, angle O-Si-O in breaking points 135-140,
that correlates with persistence of coordination numbers.
The more detailed information about nanostructure of a melt is determined through a
method «covalent bonds network covering» [5].
0
0
0,1 0,2 0,3 0,4
0,2
0,4
0,6
Si (10 and more)
Si (10 and more)
Si (4-9)
Si (4-9)
lifetime
Si (3)
Si (2)
lifetime
Si (3)
portion
portion
Si (2)
Si (1)
Si (1)
0
0
50 100 150 200
a)
20
40
60
b
80
0
0,2 0,4 0,6 0,8
0
Si (10 and more)
0,2
0,4
0,6
Si (10 and more)
Si (4-9)
Si (4-9)
lifetime
Si (3)
Si (2)
lifetime
Si (3)
portion
portion
Si (2)
Si (1)
Si (1)
0
20
40
60
0
20
40
60
c)
0,0
80
d)
0,2
0,4
0,6
0
Si (10 and more)
0,2
0,4
0,6
Si (10 and more)
Si (4-9)
Si (4-9)
lifetime
Si (3)
Si (2)
lifetime
Si (3)
portion
portion
Si (2)
Si (1)
Si (1)
0
20
40
0
60
20
40
60
80
e)
f)
Figure 4. Fractions of complexes with the different contents of atoms Si and their times of life:
a) slag 1, b) slag 2, c) slag 3 Т=933 К, d) slag 4 Т=1848 К, e)slag 3 Т=842 К, f) slag 4 Т=1809 К
On Fig.4 the outcomes of calculating of a fraction of polyanions of a different degree of
complexities received by a method CBNC are given. The entry Si(n) means, that the complex
contains n of atoms Si. The received outcomes testify about weak polymerization of melts. For
all compositions predominate silica-oxygen complexes of low dimension containing 1-3 atoms
of network formers. The fraction of ortho groups SiO44- makes from 25 % up to 35%. Are
present di-ortho groups Si2O7, which fraction makes up to 25 % from total number of
complexes. It is possible to assume, that it is an index of presence in a system pyrosilicates.
Besides the composition contain polyanions Si(3) (rings) and larger groupings Si(4-9) and Si(1023). The time of life of complexes is insignificant. For any temperature there is a stationary
process of transferring of one complexes in others, interchanging of atoms of oxygen, shattering
and reduction of polyanions.
0,7
free
nonbridgin
bridgin
0,6
0,5
0,4
0,3
0,2
0,1
0
1
2
3(1)
3(2)
4(1)
4(2)
Figure 5. Fractions of oxygen of a different type
81
On Fig.5 the data on distribution of free (О2-), nonbridging (O-) and bridging (О0) oxygen
are given depending on composition of a melt. The presence of all types of atoms of oxygen is
marked. For all compositions the nonbridging oxygen concentration is more than 60%. The
concentration of free oxygen (О2-) is from 20 % up to 40 %. The concentration of bridging
oxygen is low from 10 % up to 15 % that characterizes degree of polymerization of a system. A
dimensional grid is not observed in one composition.
At simulation of melts some thermodynamical characteristics were received which are
given on Fig.6. The unit measures, appropriate everyone parameter are enumerated below:
intrinsic pressure P_in(kbar); molar heat capacity at constant pressure Cp(Joule/(mol*К); factors:
thermal expansions Alp(bar/K), an adiabatic compressibility Bs(10-12m2/N), thermal pressure (7)
Alv(10-6m2/N).
80
P_in
Cp
Bs
Alp
Alv
60
40
20
0
1
2
3(1)
3(2)
4(1)
4(2)
Figure 6. Thermodynamical characteristics
For all compositions of a modelled system the heat capacity at constant volume Сv always
is less, than the heat capacity at constant pressure Сp and always is positive. All received
thermodynamical characteristics unsignificantly differ from makeup to makeup, that speaks
about proximity of their thermodynamic properties.
D, 10^-9, m^2/c; Vis,10^-5 Pa*c
D(Si)
D(O)
D(Fe)
D(Ca)
3(1)
3(2)
D(Mg)
Vis
2,5
2
1,5
1
0,5
0
1
2
4(1)
4(2)
Figure 7. Diffusion constants of ions and shift viscosity
82
For an estimation of transport properties of melts of a system the diffusion constants Dal
through mean square displacement of atoms were calculated. The diagram of received
dependence of a diffusion constant from composition of a slag is on fig.7. D(Si) remains
practically constant in all a range of compositions and has the smallest value as contrasted to by
other ions. The diffusion constants Fe, Mg, Ca are 1,5-2 times more than D(Si). The correlation
between D(Si) and D(O) is observed, that is connected to existence in all compositions of steady
complexes SiO4.
In the same figure the values of factor of shift viscosity are given which have values of the
order (0.5-2)*10-9Pa*s.
ACKNOWLEDGMENTS
The work is executed by support RFBR, grant № 01-07-96506
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