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The scope of solid-state transitions, from melting temperatures down to 4.2 K, is described for six systems: KxVF3, RbxVF3, CsxVF3, KxCrF3, RbxCrF3, and CsxCrF3 (for x = 0.0 to 1.0). Connections are drawn between the compounds’ compositions and structures with the various transitions and ordering events. Upon solidification from the melt and gradual cooling to room temperature, a sequential descent of symmetry appears to occur, from high-symmetry perovskite phases, through possible reconstructive transitions, to phases designated α, β, and δ, within which ionic ordering finally sets in, forming many new lower-symmetry structures. Many stable new structures are seen at room temperature. Finally, at cryogenic temperatures, magnetic ordering sets in. Other anomalies for these systems are also described. The analysis underscores the overall correspondence of structure, composition, and magnetic properties in these compounds. This lowering of symmetry mirrors what has been chronicled for oxygen-bearing perovskites that have yielded so many high-temperature ceramic superconductors.

The compounds KZnTiF6, KZnVF6, KVScF6, KCrScF6, and KMnScF6 are fluoride analogs of Tetragonal Tungsten Bronze. M2+–M3+ ionic ordering in these fluorides provided systems which contained linear trinuclear complexes of their respective paramagnetic ions. Magnetic coupling within these linear trimers occurred below 100 K in each of the five systems. Derived magnetic susceptibility equations were fitted to observed magnetic susceptibilities for each of the possible spin systems: KZnTiF6 (S=1/2), J/k=−114 K; KZnVF6 (S=1), J/k=−39 K; KVScF6 (S=3/2), J/k=−16 K; KCrScF6 (S=2), J/k=−4 K; and KMnScF6 (S=5/2), J/k=−7.5 K.

A{sub x}VF{sub 3} (A=K, Rb, Cs; x=0-1.0) and A{sub x}CrF{sub 3} compounds were sealed inside high-temperature DTA molybdenum sample cups using electron beam welding techniques. Melting temperatures of the A{sub x}VF{sub 3} compounds ranged from 1050 to 1400 deg. C; those of A{sub x}CrF{sub 3} from 850 to 1200 deg. C. Reconstructive transitions were observed for A{sub x}VF{sub 3} compounds between 650 and 950 deg. C, and for A{sub x}CrF{sub 3} compounds between 550 and 825 deg. C. A displacive transition was observed to occur in VF{sub 3} at 490 deg. C. Order-disorder transitions were determined by X-ray diffraction techniques. In the A{sub x}VF{sub 3} compounds, electronic ordering and ordering of partially filled A{sup +} sites were observed to occur between 100 and 300 deg. C. Ordering phenomena in the A{sub x}CrF{sub 3} compounds (in addition to electronic ordering and ordering of partially filled A{sup +} sites) included Jahn-Teller cooperative ordering. These compounded transitions occurred between 300 and 500 deg. C.

Closed geometrical shapes may be obtained from a hexagonal tiling by substituting 12 pentagons for hexagons and fusing the appropriate edges. Such geometrical shapes describe the fullerenes, demonstrating that this mathematical rule has utility in structural chemistry. Closure from a hexagonal tiling may also be obtained by substituting six squares; or four triangles; or combinations of pentagons (one point each), squares (two points each), and triangles (three points each) so that the total is 12 points. Similar recipes exist for obtaining closed shapes from tetragonal or trigonal tilings. Structures thus obtained may evolve into additional structures having the same symmetry in a manner similar to the evolution of the Archimedean solids from the Platonic solids. Important examples include the deltahedra, a group of eight convex polyhedra consisting of all triangles and belonging to high-symmetry point groups. These polyhedra evolve into additional high symmetry shapes, many of which have already found u...

One aspect of solid state chemistry which has flourished in recent years is the ability of chemists to synthesize new and exciting materials. Unfortunately, the synthesis of most advanced materials has been directed toward applications; as a result, solid state chemistry has become a collection of unrelated topics. Furthermore, chemistry departments have been slow in accepting the solid state as a part of chemistry. Part of the problem is that chemists are obsessed with molecules. Even the models of crystal structures which have been used for almost 75 years are an outgrowth of molecular models (i.e. ball-and-stick models). Our laboratory, has devoted many years to the systematic preparation and characterization of fundamental inorganic systems and we have concluded that the structural behavior of non-molecular solids may be explained better through symmetry models. Our models employ two aspects of symmetry: (1) fundamental structures are represented by tilings and/or packings and (2) dynamic behaviors involving structural changes are governed by laws of symmetry. Results which support these conclusions are presented in this paper.