SIMULATION OF CRYSTAL STRUCTURE OF COMPLEX OXIDES BY THE USE OF INTERATOMIC BOND CHARACTERISTICS
Galina A. Geguzina,
Rostov State
University, Institute of Physics, 194 Stachki Ave.,
Rostov-on-Don, 344090, Russia;
e-mail: curil@math.rsu.ru
Keywords: complex oxydes, cristalline structure, chemical composition, ferroelectric properties, oxygen-octahedral structures, interatomic bond lengths, strains, unit cell parameters, determination a'priori, existence areas, boundaries, perovskite-like structures.
Objects of investigation: the complex oxides with structures of following types: perovskite (binary, ABO3, ternary, A'a1A''a2 BO3 or AB'b1B''b2O3 oxides) [1, 2]; pyrochlore (binary, A2B2O7, and ternary, A'A'' B2O7 or A2B'B''O7, oxides) [3], Bi-containing layered perovskite-like (An-1Bi2BnO3n+3, where n=2; 2.5; 3.5; 4 and 5) [4]. All these structures are similar that B atoms in them are mainly in oxygen octahedra in voids between which the A atoms are located. Many representatives of these families have ferroelectric properties. That's why these families are interesting for directed search for new substances to be used in practice.
The problem of specified structure simulation at specific oxide's chemical composition becomes one of urgent problems of crystal chemistry at this point of view. The given paper is dedicated to solution of this problem. For this purpose it is necessary to determine a'priopi several parameters of crystalline structure. The following characteristics may be chosen: interatomic bond lengths and their strains in complex oxides, the unit cell sizes etc. a'priori. Designed procedures of such theoretical crystal structure details definitions for several oxygen-octahedral structures are shown here. They allow to compute cell parameters for reasons of chemical composition on the basis of geometry and sometimes of energy principles. These structure parameters may be applied for construction of structure existence areas (EA), various correlations between electrophysical properties, crystalline structure and chemical composition, for check of obtained composition fitness to specified one etc. It allows to investigate strains in specified structure. It was stated that values of unstrained bond lengths and interatomic bond tensions directly affect the possibility of appearance and values of ferroelectric properties in oxides with specified structure.
The computational formula of perovskite cell parameters <ac> of perovskite and perovskite-like complex oxides [4-6] on the basis of elastic energy minimum principle for crystalline cell is following:
<ac> = ( 21/2Si ai ni L0A i0 + 2Sj bj nj L0B j0 ) / (Si ai ni + Sj bj nj ),
where ai and bj are respective atom numbers; ni and nj are their valences, and unstrained interatomic bond lengths L0A i0 and L0B j0 are tabulated in [5, 6]. Computed unit cell parameter cc for Bi-contained layered perovskite-like structure are defined by formula: c = 1.08(2m + 2)<ac> [4], where m is perovskite-like layers number in them. The computational formula of pyrochlore cell parameters of A2B2O7, oxides and its derivatives was obtained for the geometric reasons [7]: <ac> = k(L0AO + DAO + L0BO- DBO), where k is a coefficient computed with the use of the strained interatomic bond lengths and DAO and DBOare tabulated interatomic bond strains with the L0AO and L0BO[7]. The computed cell parameters <ac> of all mentioned above complex oxides are defined. The relative difference between <ac> and experimental <ae>is not above 1%.
It is necessary to detect principal possibility of existence of oxygen-octahedral structures in a specific structure type at directional search for new complex oxides with these structures including new ferroelectrics. The EA are stated for mentioned above structures. It is possible to anticipate forming specified structure by usage of boundaries of EA. It is proposed here to use EA of above mentioned structures, specified by extreme interatomic bond strains. This strain is a relative difference between lengths of strained interatomic bond in oxide with given structure and unstrained (free) same interatomic bond.
EA are stated by the use of following interatomic bond characteristics: unstrained (free) bond lengths Ai - O(L0A i O) or Bj - O(L0B j O), strained bond lengths Ai - O(LA i O) or Bj - O(LA j O) (in complex oxides) and the resulted relative bond strains (RBS) Ai - O,(dAiO) or Bj - O,(dBjO): dAiO = (LAi O - L0Ai O)/L0Ai O; dBjO = (LBj O - L0Bj O)/L0B j O. Values of the L0Ai O and L0Bj O are specified in existing systems [5-7], LA i O and LBj O values are found from computed [1-4] or experimental data on unit cell parameters of complex oxides: LAi O = <a>/ 21/2; LBj O = <a> /2. EA are plotted on the diagrams (L0A , dAO) or (L0B , dBO ) by the use of experimental data on crystalline structures of known complex oxides of corresponding compositions.
One may anticipate forming specific structure when computing values of expected dAiO or dBjO or in hypothetic specified oxides and comparing them with extreme values, which can be computed from composed equations of EA of specified structure. If dAiO and dBjO do not exceed EA then oxide must be formed in specified structure. Otherwise its forming in specified structure is impossible, at least at normal pressure. The matter is that at high pressures the approach of A and O atoms is possible but at pressure release the structure is damaged. For instance, MgTiO3 may be perovskite at high pressure, but without pressure it is ilmenite. Systems of all obtained EA boundary equations are given [1-4].