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.
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 MNDO-simulation 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,
el.un. / qО,
el.un. / sSi, nm / sO,
nm / DО,
nm / akit, n/m / , deg / bkit, n/m / n / mSi,
10-26 kg / mО,
10-26 kg
2,92 / -1,46 / 0,022 / 0,128 / 0,162 / 200 / 109,5 / 150 / 10 / 4,66 / 2,66
IM:
qSi,
el.un. / qО,
el.un. / qMg,
el.un. / sSi, nm / sO,
nm / sMg,
nm / mSi,
10-26 kg / mО,
10-26 kg / mMg,
10-26 kg / n
2,92 / -1,46 / 1,46 / 0,022 / 0,128 / 0, 082 / 4,657 / 2,655 / 4,05 / 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 Born-Carman 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 numbers, average lengths of bonds, 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
on 30-50K above a melting point of the given composition on the phase diagram of a system [6].
In fig. 2 series of partial RDF are indicated. The first peaks of RDF for Si-O 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 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, , , , , 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), - sum of cations- network-formers in a complex T(), - sum of atoms of oxygen in a complex T(), - sum of nonbridging atoms of oxygen in a complex T(), - sum of bridging atoms of oxygen in a complex Т(). Formula recording of the 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.