The cluster component method in theory of solutions
A.Men, I.Sinitsky*
Department of Physics
Technion-Israel Institute of Technology
Haifa 32000, Israel
*Gordon Pedagogical college, Haifa
1 Structure and energy estimation of ground states for spinel phases of alumina
Cation redistribution in alumina with the spinel structure is studied using a crystallographic analysis of the structure. The specific features of the distribution are due mainly to stoichiometric structural defects in the spinel lattice. It is shown that only the formation of defect clusters allows for partial filling of the so-called illegal sites in the cation sublattice. Madelung constants are derived for spinel structures with partially filled "illegal" positions with the account of effective charge of lattice sites as function of cation redistribution. By fitting the lattice constant for -alumina, the total energy and lattice parameters of all the structures are calculated. As a result, three several structural classes of cubic symmetry alumina are distinguished by differences in their total energies .The role of several factors has been investigated for six cubic polytypes of spinel aluminas derived as low energy modifications. Tetragonal distortions of the initial lattice are taken into account to evaluate structural stability. The search for stabilizing spatial shifts has been provided in the framework of the model of a single molecule of alumina in the unit cell of a spinel structure with completely filled a vacant tetrahedral positions. Both tetragonal distortions and molecular sites shifts lead to strong degeneration and could change the relative structural stability.
2 Ground states and thermodynamic polytypes of aluminas and hydrated aluminas.
Alumina has a large number of metastable cristalline phases in addition to the thermodynamically stable rhombohedral -Al2O3 phase.
The metastable alumina polymophs include ,,- )cubic spinel(, -)tetragonal or orthorombic(, -)monoclinic(, -)orthorombic(, -)hexagonal(.
We consider the simple case of transition from cubic -spinel phase (V0=a03, a0-lattice parameter of unit cell) to orthorhombic phase [V1=)1x2x1.5(a03[. The analysis of transition -spinel from cubic to orthorhombic have two aspects. The first of them is connected with study the change of structure this transition and second-with apprasial energy of transition.
Existent in the literature cubic model of -spinel )-Al2O3( suppose that 16d and 32e positions completely filled by ions Al and O accordingly and only 2/3 Al3+ occupied 8a tetrapositions in space group m3m
We consider more detail the transition in -spinel from cubic to orthorhombic using maximal subgroups of the three-dimensional crystallographic point groups m3m(cubic)-23(cubic)-222(orthorhombic). Cubic class 23 maintains 5 spase groups P23, F23, I23 ,P213, I213 from with only 3 (P23, F23, .P213( may be used for description the structure -spinel (Al16/3aAl16d O32e(.
The physical sense of this transition (m3m-23) in -phase is connected with the modification of probability occupation by ions Al8a spinel positions (Pala(. So in -phase 8a positions occupy by 16/3 ions of Al,what correspondingPAla=2/3 and PVa=1/3 )V-vacancy), PAld=1,POe=1 From physical point of vision this agreement of statistical distribution 144 ions Al3+ on 216 tetrapositions in cubic spinel with lattice parameter3 aO
The orthorhombic group P21212 D23 contaiting spinel positions 8a,16d,32e,with unit cell V1=)1x2x1.5( a03, may be use for description theorthorhombic spinel structure of composition Al16aAl48d O96e.
The transition 23-222 (P21212( coupling with occupying by 144 ions Al3+ all tetrapositions with the probability eqully to 1.The disappearance smearing presence the reason of phase transition cubic-orthorhombic.
Naturally to propose that transition 23-222 (cubic- orthorhombic) is connected with disappearance of spread ions Al occupy corresponding positions in group P21212 with possibility equally 1.This situation may be description with model of effective ions Al occupying the all of permission tetrapositions with the probability equally to1 but with the charge smaller than +3 )qAltet=+1,+2; qAloct=+3 (
We propose the model of effective ions, with allow not only described the structure transition -, but also evalute the change of Madelung constant by this transition .
3 Structure of interfaces & reactions in alumina phases
Thermodynamic calculations on relative grain boundary energy for alumina-based ceramics have been realized. Two situations, pure tilt and pure twist boundaries, have been analyzed for a lattice model using statistical thermodynamics. The common feature of techniques developed is an attempt to apply structural thermodynamics to a relatively simple model of an 'effective' representation of boundary structure with effective atoms/ions on lattice sites and configurational, geometrical restrictions.
To classify special tilt boundary configurations, the relative boundary energies of a rigid, non-shifted boundary region with different atomic arrangements have been estimated using step-type interatomic potentials. To evaluate the influence of dopants on the energy spectrum, we have used a Bragg-Williams approximation for entropy and Coulomb potentials.
The geometry of twist boundary for specific values of S (inverse coincidence site density) has been investigated in order to construct possible atomic configurations to fit the adjacent bulk structure. This description has been made in terms of the 'displacement shift complete' lattice (DSC) which allows an estimate of the width of the zone required to provide atomic reconstruction. The arrangement of ions in these layers, including new ionic configurations on the DSC lattice and self-consisting packing of clusters, has been considered.
Using a simple structural description, the influence of both the misorientation angle and the ionic distribution (including the order parameters) on the relative boundary energy has been evaluated for the case of unrelaxed, symmetrical tilt boundaries in MgO-doped -Al2O3. The unrelaxed, symmetrical tilt boundary geometry is shown to be determined by the charge distribution, and for a homogeneous representation (zero-charged atoms with identical interaction parameters) the minimum energy state for symmetrical (001) tilt boundaries corresponds to S = 5 (q=36.90(. The boundary energies for a given S change slowly with changes in the ratio of the interaction energies for the initial (bulk crystal) and the new (boundary) interionic spacings.
Because of the difficulty of performing direct calculations of the interaction parameters, parametric and Coulomb approximation calculations have been made. For typical interaction energies, the symmetric (S) boundary with S = 5 appears to have the minimum internal energy. However, for some specific combinations of the interaction constants, the antisymmetric (AS) boundary may be energetically favorable for some relatively large S values.
In the Coulomb approximation, the minimum energy tilt boundary configuration is defined by the ionic distribution, and corresponds to S = 13, AS-type for vacancy-rich tetrahedral sites, but to S = 5, S-type for the case of vacancy-rich octahedral positions. Small dopant concentrations are predicted to change the stable boundary structure in some cases. The predicted low energy configurations may be interpreted as the more probable local states of a real grain boundary, although any population of real boundaries is expected to include a distribution of these "special" grain boundaries which have relatively low boundary energies.
A simple twist boundary with <100> rotation (S=5) has also been simulated. Using the structural thermodynamics approach, the distribution of effective atoms on "upper" and "lower" bulk positions in the (100) layers has been derived in a point approximation of the entropy. The distribution derived indicates that the twist boundary shows a sharp transition from the bulk to the boundary region. A specificspatial ionic configuration is proposed to fill the intermediate boundary layers.
Professional ecperience. Research.
4. 1. Statistical Theory of Solids
Statistical theory of atoms ,molecules and crystals (Thomas-Fermi method(.
Quasichemical theory of multi-component,multi-sublattce solid solutions and calculation of physicochemical properties
Theory of associated liquid solutions.
4. 2. Crystal Chemistry and Thermodynamics of Real Solid Solutions
The thermodynamics and kinetics of oxidation and reduction processes. Equilibrium of solid phases in contact with gas mixtures.
Structure, composition and properties of solid solutions. Elaboration of the cluster component method. Metallic alloys,compounds with the NaCl structure )carbides, nitrides oxides, hydrides and their solutions), stoichiometric and non-stoichiometric oxides (including the stability of defect compounds and modulated structures), spinels, garnets, orthofer rites ,aluminium oxides phases ,superionic compounds and high temperature superconductors.
Properties of irradiated magnetic materials.
4. 3. Microtheory.
The theory of vibrational spectra in solid solutions (alloys, oxides)
The theoretical-group method of classification and calculation of the energy spectra for impurity ions and complexes in crystal.
Microscopic calculations of the energy band structure by the MOLCAO method.
Calculation of the preference energy of ions in different lattices.
Theory of isostructural phase transitions described by several order parameters and phase equilibria in associated systems.
4. 4. Consulting.
Application of thermodynamics, phase equilibria and properties of oxides )ferrites, garnets, superionics and high Tc supercoductors) in the electrical, electronic and metallurgical industries.
5.The list of monographs A.Men .
1. S.V. Vonsovsky, S.V. Grum-Grzimaylo, V.I.Tcherepanov, A.N Men,
D.T.Sviridov,Yu.T. Smirnov, A.E. Nikiforov
The theory of the crystal field and the optical spectra of the impurity ions with the unfilled 3d-shell, Nauka, M.,1969,p.179
2. G.I. Tchufarov, A.N. Men, V.F. Balakirev, M.G. Zuravleva,A.A. Tshepetkin
The thermodynamics of the oxidation processes of the metal oxides, Metallrgy, M.,1970, p. 399.
3. A.N. Men, Yu.P. Vorobiev, G.I. Tchufarov
Crystal chemistry and thermodynamics of defects interacted, Itogi nauki i techniki, Chimia tverdogo tela, v.1,M., VINITI,1973, v.1, p. 87.
4. A.N. Men, Yu.P. Vorobiev, G.I. Tchufarov
Physico-chemical properties of non-stoichiometric oxides, Chimia, L., 1973,p. 223.
5.A.N. Men, M.P. Bogdanovitch Yu.P. Vorobiev, R.Yu. Dobrovinsky, V.M. Ka-
mishov, V.B. Fetisov,
Composition-presence of defects-property of solid phases. Clustercomponent method, Nauka, M.,1977,p. 246.
6.Yu. P. Vorobiev, A.N. Men, V.B. Fetisov
Calculation and prediction of oxide properties, Nauka, M.,1983, p.287.
7.B.N. Gotshitsky, A.N. Men, I.A. Sinitsky, Yu.G. Chukalkin
Structure and magnetic properties of oxide magnetics, irradiated by rapid neutrons, Nauka, M., 1986, p.174.
8.A.A. Likasov, C. Carel, A.N. Men, M.T. Varshavsky, G.G. Michailov
Physico-chemical properties of wustites and its solutions,RISO, Sverdlovsk, 1987, p. 227.
9.M.T. Varshavsky, V.P. Pastchenko, A.N. Men, N.V. Suntsov, A.G. Miloslav-
sky,
Presence of defects of the structure and physico-chemical properties of ferrospinels, Nauka, M., 1988, p. 244.
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