Perovskites hexagonal

There exists quite a number of hexagonal oxidic perovskites 183, 332), but there seem to be only three types in the case of ternary fluorides. Their occurrence again clearly depends on the tolerance factor wich thus proves to be useful in classifying the hexagonal perovskites also. After having described their structures in detail they will be further discussed under a common point of view. 

The compormd CsMnFs was prepared for the first time by Simanow et al. 287), and as the first ternary fluoride assigned to the hexagonal BaTiOa- 

As in all the perovskites — they might be defined that way — the A-and F-ions in the CsMnFs-structure form common close-packed layers AFs, in which the A-ion (Cs) displays a C. N. of 12 (Cs—F =3.12... 3.22 A in CsMnFs). The sequence ABC of three layers, characteristic of cubic perovskites, has been changed, however, to a hexagonal sequence of six layers ABC—ACB. This explains the relation found between the lattice constants ( hex = V2 eub Chex = 2 ]/3 acuu) from which follows Chex/ hex = ]/2 /3 = 2.45 or a value nearby. 

As a consequence of this repulsion the MnFe-octahedra of these groups MnaFg are distorted, the Mn—F-distances are 3 x 2 16 A and 3 X 2 12 A resp. The latter values correspond to the Mn—F-distances in the nearly undistorted MnFe-octahedra of the structure, which share comers only and like in the cubic perovskites bring about the three-dimensional netting of the lattice. 

The structure of the hexagonal oxide perovskite BaRuOa, recently described by Donohue et al. 84), is also adapted by the ternary fluoride CsCoFs 11). The positional parameters (not listed above) are almost the same in both compounds. 

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Summarizing the features of the hexagonal fluoroperovskites it should be noted, that the structures of the BaTiOs- and BaRuOs-types are but different mixed forms of both, the purely cubic perovskites, e.g. CsCdFs with 3 layers in sequence ABC, and the purely hexagonal perovskites , e.g. CsNiFs with 2 layers in sequence AB. The dimensions of the c-axes are given by the number of layers and are therefore larger in the case of the mixed structures than for the basic types (e.g. CsMnFa 6 layers, CsCoFs 9 layers). 

There are a number of solid phases of the types MScCl and ScCl where the formal oxidation state of scandium is less than three. They are usually made by direct combination at elevated temperatures of MCI, ScCl3 and metallic scandium. Their structures often show evidence of Sc—Sc bonds. Thus CsScCl3 is made by action of Sc on Cs3Sc2Cly at 700 °C. The shiny blue product has the hexagonal perovskite CsNiCl3 structure. This is similar to the Cs3Sc2Cl9 structure but with all Sc positions filled. Non-stoichiometric phases exist between the two end structures.128 When scandium is heated with ScCl3 at 940-960 °C in a sealed Ta... 

Low-temperature structural phases of Jahn-Teller hexagonal perovskites 656... 

In this chapter an effective Hamiltonian for a static cooperative Jahn-Teller effect is proposed. This Hamiltonian acts in the space of local active distortions only and possesses extrema points of the potential energy equivalent to those of the full microscopic Hamiltonian, defined in the space of all phonon and uniform strain coordinates. First we present the derivation of this effective Hamiltonian for a general case and then apply the theory to the investigation of the structure of Jahn-Teller hexagonal perovskites. 

Due to ferro-ordering of distortions in the ab planes and the lack of uniform strains [16-18], the problem of equilibrium structural phases of hexagonal perovskites is reduced to a single chain [25]. Passing to polar coordinates for... 

We can conclude that orbital-dependent exchange interaction in hexagonal perovskites does not contribute essentially to the ordering of orbitals and Jahn-Teller distortions on sites but only results in a slight renormalization of the force constant Kt and, therefore, of A2 and, 42 parameters of the basic model in equation (37). 

We can see that only two types of ordering can become equilibrium configurations. Moreover, these are precisely the two low-temperature structural phases found in hexagonal perovskites (Fig. 1). The parameters A, and A2 are expected to have different signs, which is in agreement with their definition in equation (37). According to the theory, the helical ordering (Fig. la) is achieved at A2j A I < 1/2. 

A part of the work related to hexagonal perovskites was done in collaboration with Michail Korotkov. 

Nickel(iv).—The production of single crystals of BaNi03 by reaction of Ba2Ni2Os and oxygen at 600 °C and 2000 bar has been reported. The product is diamagnetic with a hexagonal perovskite structure.621 Solvolysis of K2NiF6 in anhydrous HF has... 

Fig. 4—Schematic illustration of linkage or BO oclahedra in hexagonal perovskites with B-site vacancy ordering (a) Ba,Ta40I5 (b) Ba.,Re20 (c) Ba.,Te2Og (d) Ba.,W20,2 (e) Ba8Re2W,0J4 and If) Ba Nb6WO-7.

Table 1—Hexagonal Perovskite Oxides Exhibiting B-Site V acancy-ordering...

Defects in perovskite oxides can be due to cation vacancies (A or B site), amon vacancies or anion excess. Cation-deficient oxides such as A,WOj give rise to oxide bronze structures, W03 itself representing the limiting case of the A-sile deficient oxide A-site vacancies are seldom ordered in these metallic systems. B-site vacancies are favoured in hexagonal perovskites and ordering of these vacancies gives rise to superstructures in some of the oxides. 

Figure 3a Sheared Sr03-substructure of the hexagonal perovskite structure as model for the hypothetical compound Na3N. N3 -ions are surrounded by Nations forming cubic close packed distorted anti-cube-octahedra. Nations are depicted as black spheres (not drawn to scale). Average Na-Na- and Na-N-distance about 2.6 A (space group PmmnZ, no. 59).

There is little doubt that many materials that at present are described as containing ordered arrays of point or extended defects will be successfully described as notionally defect-free modulated structures. For example, the intergrowth Aurivillius phases, described as containing extended planar defects, have recently been described compactly as modulated structures. " The same formalism has been applied to hexagonal perovskite structures and superconducting copper oxides. Others will certainly follow. 

Figure 19 View of cubic (3L) and hexagonal perovskites along the close-packed AF3 layers. 6L RhZnF3, 9L CSC0F3, 2L CsNip3...

Fig. 12 Hexagonal perovskite crystal structure of the parent compound CsNiCfi. Black circles represent transition metal atoms, Ni in this case. White circles are ligands. Shaded circles are atoms of Cs . Face-sharing octahedrons [NiCle] are packed in linear chains (From [57])...

The three-state extended pseudo spin model is equivalent to the Potts model well-known in solid state physics. Its application to JT structural phase transitions was developed by Hock et al. [63]. Also, as a useful tool, it was mentioned by Kugel and Khomskii [9]. It was applied to hexagonal perovskites by Crama and Maaskant [64]. It has multiple applications to layered manganites (e.g., see [65]). 

Fig. 22 Derivative OK edge XAS spectra (a) empty band edge d empty Mn " " states for hexagonal perovskite, h-HoMn03 and (b) virtual bound d resonance states of Mn for hexagonal...

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