Superhard Phases of Simple Substances and Binary Compounds of the B-C-N-O System: from Diamond to the Latest Results (a Review)

The basic known and hypothetic one- and two-element phases of the B-C-N-O system (both superhard phases having diamond and boron structures and precursors to synthesize them) are described. The attention has been given to the structure, basic mechanical properties, and methods to identify and characterize the materials. For some phases that have been recently described in the literature the synthesis conditions at high pressures and temperatures are indicated.Comment: Review on superhard B-C-N-O phase

An application of a polytope (4D-polyhedron) concept for the description of polymorphic transitions: Iron martensite and solid oxygen

A polymorphic transformation between BCC and FCC phases can be described in the framework of the root lattice E$_8$ in a 8D-space as the hypothetical praphase with symmetry group playing a role of the supergroup for both participants of the transformation. The special subset of vectors of the E$_8$ and coinciding topologically with the unit cell of the A15 structure (Cr$_3$Si-type) in the 3D Euclidian space was found, this subset can be regarded as an intermediate configuration during transformation between FCC and BCC structures. The proposed description of the polymorphic transformation is supported by experimentally observed habite planes of martensite in iron based alloys and by the existence ofthe A15-phase in the solid oxygen