INVESTIGATIONS OF STRUCTURE OF A
SYSTEM SIO2-MGO BY THE METHOD OF
“COVALENT BONDS NETWORK COVERING”
Voronov V.I., Voronova L.I.
The results of complex computer experiment for a magnesium-silicate system
SiO2-MgO with usage of the ionic - covalent model (ICM) are discussed. The
complex MNDO (modified neglect by diatomic differential overlapping) -MD
(molecular-dynamic) simulating was applied. With usage of the classical approach
and method of “Covalent bonds network covering” the nanostructure of melts for five
compositions of the given system is explored. The radial distribution functions of
atoms (RDF), coordination numbers, average lengths of bonds, angles distribution
functions (ADF) , average angles between bonds, distribution functions of complex
anions on a number of characteristic parameters, lifetime of complexes,
polymerization degree of a system at temperatures, close to melting points are
determined. The matching of model results with experimental data shows the
satisfactory consent.
INTRODUCTION
The creation of new metal stuffs with the preset properties is one of priority
branches in modern physical chemistry. Properties of a melt, its fluid phases: metal
and slag, the interaction between them, in many respects determine physical-chemical
properties of a received stuff. Therefore researching of properties of oxide melts (the
base of the most of metallurgical slags) is actual. During last decades for these
purposes the computer experiment, and in particular, molecular-dynamic simulation is
widely used. Some mathematical methods of researching the structure, founded on
processing of a number (list) of coordinates of particles of a system for the given
configuration are known. First of all, it is the classical method of determination of the
average structural parameters of the short-range order on the base of RDF, and
statistical-geometrical methods allowing to detail an extended structure. There are
also methods allowing on the base of studying a structural equilibrium of a melt to
receive the information on thermodynamic properties of a system and complex
anions, existing in a melt.
System SiO2-MgO is one of the binary silicate systems playing an important
role in metallurgy. It is used in composition of welding fluxes and slags for an
electroslag remelting process and as the most of metallurgical slags is inclined to a
polymerization. Elementary structural units in an investigated system are the anions
SiO44-, of which the continuous network is formed. At an increase of the temperature
or adding magnesia, the network starts to destroy and the complex anion groups of a
different degree of complexity are obtained. Thus, any modifications in the
nanostructure of a melt lead to a modification of the degree of polymerization of a
system and radical modification of its physical-chemical properties.
474
SIMULATION OF A SYSTEM BY A PROGRAM COMPLEX «MD_MELT»
The complex simulation of a system was realized by means of a program
complex «MD_Melt» [1], developed in Kurgan State University (Russia). In the
complex the approach based on complex usage of a semiempirical quantum-chemical
method of MNDO (modified neglect by diatomic differential overlapping) [2], the
method of molecular dynamics (MD) and statistical-geometrical (SG) methods of
calculation of the structure has been realized [3,4].
The ionic - covalent model
Most often at MD simulation the ionic model (IM) of a melt is used, the
interaction between the particles in which is described by a spherically - symmetric
Coulomb potential.
At MD-simulation we apply the ionic - covalent model (ICM) of a melt, which
is more adequate for systems characterized by availability of stable elementary
structural groups, existing in a melt at the expense of bonds with a high portion of
covalence and having a long lifetime. Thus the type of a potential function, describing
this or that particle, is defined by attributes of a particle and condition of a
belonging/nonbelonging of a particle to an elementary structural group. The detailed
description of the model and the formulas for superimposed potentials are given in
[5].
For computation of potential parameters we realized preliminary MNDOsimulation of silicate-oxygenic complex anions of a different degree of complexity:
Si2O8Mg(A6), Si3O11Mg(A8), Si3O12Mg2(A6), Si5O17Mg(A12), Si5O18Mg2(A12). The
obtained values of effective charges on atoms, equilibrium lengths of bonds and
valence angles were data-ins for the program of multidimensional optimization
program. This program is using a harmonic approaching for a potential and a principle
of superposition of forces. Thus the search of varied parameters (force constants of
two and three-partial interactions), was realized by minimization of criterion function,
which was built as the sum of squares of deflections of forces, computed in a linear
approaching with usage of a lapse rate of a superimposed potential and force
constants, obtained in MNDO-simulation. In table 1 the parameters of potential
functions describing interparticle interaction in a system SiO2-MgO both in an ionic,
and in an ionic - covalent approaching are indicated.
Table 1. Parameters of potential functions of a system SiO2-MgO
ICM:
qSi,
qО,
Si,
el.un. el.un. nm
2,92
-1,46
O,
nm
DО,
nm
kit,
n/m
qO ,
deg
0,022 0,128 0,162 200
IM:
qSi,
el.un.
qО,
el.un.
qMg,
el.un.
Si,
nm
2,92
-1,46
1,46
0,022 0,128
O,
nm
kit,
n/m
109,5 150
Mg,
nm
mSi,
10-26
kg
0, 082 4,657
475
n
10
mО,
10-26
kg
2,655
mSi,
10-26
kg
4,66
mMg,
10-26
kg
4,05
mО,
10-26
kg
2,66
n
10
MD-simulation
For a molecular-dynamic simulation the classical approach was used: the
approximating of the differential equations by finite-difference was realized on a
method of Beeman; on a model cube the periodic boundary conditions of BornCarman were imposed, a real volume of a cube depended on density of a melt, a
number of particles in cube - 475.
Primarily particles were placed on a crystal lattice MgO, and then the necessary
amount of atoms of silicon was introduced into a system and the number of atoms of
oxygen was corrected. The system was artificially warmed up to the temperature of a
gaseous state (5000К) for “forgetting” a primary state. However, the experiments as
have shown, at such temperature there is no free diffusion of particles and the
introduced motives of a crystal lattice are not destroyed completely.
The first phase of MD simulation is connected with the temperature decreasing
from a gaseous state up to Tmod, for this on 50 temperature points the velocity of
particles was multiplied by quotient 0.9998 and during 100 steps of simulating the
system was stabilized on each temperature point.
At achieving of necessary starting temperature (Tmod) the system passed through
a phase of thermostabilisation. This phase consists of the following: the program tests
fluctuations of temperature on hundred steps of simulation. If the fluctuations have
exceeded 23К, the system is stabilized the next hundred steps; if they are in the limits
23К, the system is considered thermally stable and passes to a phase of a
thermodynamic equilibrium.
The phase of a thermodynamic equilibrium consists from 10 macrosteps, each
of them consists of 100 microsteps, that allows to realize statistical processing of the
obtained data. Particularly on this phase recording of coordinates of particles in the
file is realized, as a result the file can keep pictures of all microsteps. Thus the
averaged on phases thermodynamic, kinetic, structural properties are taken and the
checking of the degree of polymerization of a system is realized.
Calculation of structural parameters of the short-range order by results of
MD-simulation
At the third stage a
calculation of structural parameters
of the short-range order was done.
For this purpose the classical
approach,
connected
with
construction and processing of
partial radial distribution functions
of atoms (RDF) was used. The
analytical formula of a problem is
indicated in [5]. Angle distribution
functions (ADF), coordination
Figure 1. Densities  and temperatures of
numbers, average lengths of bonds,
simulation Tmod for different compositions
average angles between bonds were
also calculated.
The simulation was processed for some compositions of SiO2 with a molecular
ratio NSiO2: = 0.08; 0.29; 0.53; 0.7; 0.9. In fig.1 the densities and temperature of
simulation Tmod of different compositions are indicated. Tmod were elected with excess
476
a)
b)
Figure 3. Dependence of а) average
bond length L и b) coordination
numbers Z from composition of a melt
Figure 4. Angles between bonds Si-O-Si
and O-Si-O
on 30-50K above a melting point of the
given composition on the phase diagram
Figure 2. Radial distribution functions
of a system [6].
for NSiO2 = a)0.08; b)0.29; c)0.53;
In fig. 2 series of partial RDF are
d)0.7; e)0.9
indicated. The first peaks of RDF for SiO are rather high and are well allowed, second peaks are also distinct. RDF Mg-O and
O-O have lower and wide first peaks and «spread» second. In dependence on the
composition the character of RDF does not vary essentially. The characteristic
features of RDF allow to speak about availability of the short-range order in a melt.
On RDF the lengths of bonds (L) and coordination numbers (Z) were designed,
for which the dependencies on the composition are indicated in fig. 3.
An average distance for Si-O and for Mg-O changes about values 0.164nm and
0.225nm accordingly, being values of the average length of bonds for net oxides. The
sharp rise of the curve corresponding to distance Mg-Mg is connected with a low
477
portion of Mg in a system and is defined by the volume of a simulated system. The
coordination number Si-O in the whole range of compositions is constant and equals
to four, that speaks about availability of tetrahedral complexes even at the small
contents of SiO2. The coordination number Si-Si for compositions 0.4-0.5NSiO2 passes
from 2 up to 8 and remains in this range, being lifted up to 10 in net SiO2.
The ADF of bonds Si-O-Si and O-Si-O were defined, on which the average
angles between bonds were designed. The results are presented in figure 4.
The modification of angles between bonds in dependence on composition of a
simulated system correlates with a modification of coordination numbers. The
constance of a coordination number Si-O results in a constance of an angle O-Si-O
both for acidic compositions, with the greater contents of SiO2, and for the alkaline
compositions, with the low contents of oxide-networking. An average value of an
angle of 109.5 degrees, practically does not depend on, whether a melt represents a
network or the sum total of individual elementary tetrahedrons SiO44-, characteristic
for the alkaline compositions.
The augmentation of the average value of an angle Si-O-Si from 120 up to 144
degrees is revealed at ascending NSiO2. The augmentation of the value of this angle at
the great contents of SiO2 correlates with the test data and characteristic for a
continuous network.
Program realization of a method of “Covalent bonds network covering” (CBNC)
We investigate polymerization of a melt and define a degree of its
polymerization through a method of “Covalent bonds network covering” on particles
in a model cube [5]. Thus more detailed information about the nanostructure of a
melt, on which series of structure-sensitive properties depend, is being revealed.
The essence of the method consists of the following: in a melt on the given
configuration there are complexes of a various degree of complexity varying in
dependence on an amount of the oxide-modifier which they have. The complexes are
shaped by a principle of the bridging of the first coordination spheres of elementary
structural groups, i.e. such elementary structural groups are combined in a complex,
which atoms lie apart, at the shorter or equal to 1.5r0 (r0- the equilibrium length of
bond cation network-former-oxygen). For this purpose the lists of atoms, belonging to
concrete elementary groups are made up, in groups there appear anions lying at the
distance shorter or equal to average length of bond “cation network-former -anion”.
The lists of the nearest neighbours are created and for atoms of oxygen. As the result
of “network covering” the sum of nonbridging, bridging and free atoms of oxygen for
a running configuration, coordination numbers averaged for types of particles are
defined.
For all simulated compositions we have received the distribution functions of
complexes (CDF), i.e. complex anions, on various characteristic parameters рarm of
complexes T: рarm = Tyрe, N,  cat ,  O ,  O , O0 , where Tyрe - the type of a
complex, is defined by number of varied particles which are included in a complex
T(Tyрe), N - a total number of particles in a complex T(N),  cat - sum of cationsnetwork-formers in a complex T(  cat ),  O - sum of atoms of oxygen in a complex
T(  O ),  O  - sum of nonbridging atoms of oxygen in a complex T( O  ),  O0 - sum
of bridging atoms of oxygen in a complex Т(  O0 ). Formula recording of the
478
distribution functions of complex anions, account of their lifetime and the contents of
oxygen of various types in them are indicated in [5].
The stated approach is realized by the way of a software product - software
package of mathematical processing MD_РOLIMER, which is the constituent of an
informational-exploratory complex "MD_Melt". In this package the mathematical and
statistical data processing about a configurational system condition received at
computer simulation by a MD-complex is realized.
The structure of a program complex MD_Рolimer includes four subprograms:
 DISTING-abjection of complexes, receiving of coordination numbers and lengths
of bonds;
 RINGER - abjection of selfcontained structural groups and plane rings;
 STATIST- statistical processing of results of work of the first two programs;
 MAKEADF - construction of ADF.
All programs as input data use the file with a list of coordinates for the given
time range of simulation. In an operating time the package MD_Рolimer shapes
natural files with the intermediate information, which afterwards is used by packages
of a pictorial data representation.
On each configuration in the corresponding files the information on complexes
accumulates:
 Numbers of complexes and complete information on their structure, including
numbers of particles, included in a complex;
 Types of complexes (the amount of particles of each type in a complex) is
indicated, lifetime of a complex, configuration of appearing;
 Amount and numbers of complexes for each configuration.
The information on complexes of a current configuration is accumulated in
memory. The complexes of previous and current configurations are compared for
revealing the broken complexes (information about which accrues in the conforming
file) and for determination of complexes conterminous on numbers of particles (the
information on them is not duplicated, and "lifetime" of a complex is taken into
account). In this file the information on number of free and bridging atoms of oxygen
in a phase, and also coordination numbers are recorded. The information on
elementary structural groups of each configuration accrues in the separate file for the
subsequent visualization.
At the end of a phase of a thermodynamic equilibrium the statistical processing
of obtained results - is carried out the distribution functions of complexes and
"lifetime" of complexes in dependence on different characteristic parameters, portions
of oxygen of various types are counted, the selfcontained structural classifications and
plane rings are determined. Also charges of complexes are defined.
The information on the distribution functions is removed in the conforming files
in tabular form. Usage of special record formats of the obtained data allows through
the local interface with a package of pictorial programs MD_Рlot to receive it in a
pictorial kind.
Results of calculation of the structure by the CBNC-Method
As the analysis of histograms indicated in fig. 5 shows in an explored system at
augmentation of a molecular ratio of a silicon oxide, there is process of
polymerization expressed in that the elementary structural complexes SiO44- combine
in polyanions of a rising degree of complexity. And, in a phase of a thermodynamic
equilibrium for any temperature point there is a constant process of transition of some
479
Figure 5. Histogram of distribution FT(parm) and lifetime  of complex anions.
On abscissa axis: a) type of complex type, b) number of particles of different types
in the complex N, c) number of silica in the complex cat, d) number of oxygen
atoms in the complex O, e) number of nonbridging oxygen in the complex O-,
f) number of bridging oxygen in the complex O0, g) lifetime of complexes .
complexes to the other, exchange of atoms of oxygen, destruction and regeneration of
polyanions.
480
Figure 6. The portions of oxygen of different
types
a)
b)
In the range of the alkaline
compositions
silica–oxygen
complexes of low dimensionality
containing 1-2 atoms of cationnetwork-former dominate. In the
range of acidic compositions,
beginning with NSiO2=0,5 the
concentration of composite silicaoxygen groups is intensively
enlarged, their amount comes
nearer to 1 at NSiO2=0,61. In the
intermediate range (0,1-0,6) NSiO2
there are groups containing from
c)
d)
Figure 7. Structure of melts of system SiO2-MgO for compositions:
NSiO2=а)0.08, b)0.29, c)0.53, d)0.9
2 up to 30 of atoms of silicon. The portion of these groups varies from 0,05 up to 0,5
fT(Type). From NSiO2=0,61, the process of polymerization of a system runs intensively,
there appears one complex having more than 50 atoms of silicon, and the high portion
of complexes SiO44- is great only owing to constant regenerating of macrocomplexes
Si(55-57)O(143-147). At augmentation of a molecular ratio NSiO2, the process of
polymerization is finished, the continuous network will be formed, that is confirmed
by the data indicated in fig.5 and fig.6.As follows from fig.5, the greatest possible
lifetime of a complex is equal to max=2.5*10-12с. At the molecular ratio of oxidemodifier more than 0.5 of the most long-lived are the complexes SiO4 and Si2O7.
However, their lifetime is less then 0.1max and it speaks that the cation-modifier (Mg)
has major mobility. Evidently, the complexes are blasted in very short time, and then
are again regenerated, but even if an aged and new complexes have completely
coinciding numbers of particles included in them in calculation they are identified as
new complex anions. In composition NSiO2=0.7 already there is a complex Si75O178,
which lifetime is more than half of the maximum one. The remaining complexes in
this composition have a very low concentration and, evidently, are scraps of a major
complex owing to the same causes, as at small compositions. At acidic compositions
the continuous network will be formed, which lifetime is maximum, i.e. the system
represents a uniform complex.
481
In fig.6 the data on distribution of free (О2-), nonbridging (O1-) and bridging
(О0) oxygen in dependence on the composition of a melt are indicated. The
concentration of free oxygen (О2-) is equal to one at NMgO=1 and is reduced to zero at
NSiO2=0,5. The amount of nonbridging oxygen is characterized by the convex curve,
which maximum ( Dn O =0,7) corresponds to composition NSiO2=0,35. From
composition NSiO2=0,1 there appears bridging oxygen, which concentration will
increase to one with augmentation of a molecular ratio of a silicon oxide and which
characterizes the polymerization degree of a system.
In fig.7 the structure of explored melts is indicated. At the small contents of
NSiO2 in a melt there are solitary complexes SiO44-, which combine in larger at
augmentation of number of cations-network-formers and for compositions with the
contents of NSiO2>0.7 the spatial network is noted, in which hollows there are atoms
of magnesium.
ACKNOWLEDGMENTS
The work is executed by support RFBR, grant №97-03-32531
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