Coordinate system rhombohedral

S is the ionic spin and D, ID, and a are crystal field parameters describing the strength of the axial, the rhombohedral, and the cubic crystal field terms, respectively. The coordinate system of the cubic crystal field (ij, rj, g) may differ from that used to describe the axial and the rhombohedral crystal field interactions (x,y,z). 

Although the coordinate systems in these two divisions are of different symmetry, hexagonal axes may be used in the description of rhombohedral crystals and vice versa.)... 

Fig. 2.15. Primitive rhombohedral cell (space group / 32) in hexagonal coordinate system. The hexagonal cell has lattice points at 0,0,0 2/3,1/3,1/3 l/3,2/3,2/3. The threefold axes are indicated by triangles. The twofold axes, whose directions are indicated by broad arrows, occur in pairs separated by Cjj/2 the numbers give the fractional Zh coordinates...

As in the earlier three-dimensional example, where it was convenient to use hexagonal axes involving linear combinations of the rhombohedral basis vectors, it may also be useful here to use an alternative coordinate system to bring out certain symmetry properties. For molecules with a Tj frame, one choice is to take ... 

The term trigonal refers to a crystal system (defined by the presence of a unique 3 or 3 axis) the term rhombohedral refers to a choice of coordinate system a, b, c as well as a Bravais lattice (Section 2.6.1). 

Arrangement of iron and oxygen atoms in the a-Fe203 structure where the circles represent Fe " " ion positions and the dashed lines indicate planes within which oxygen atoms lie. The rhombohedral unit cell is drawn with dashed lines and the arrows mark the orientation of Fe magnetic moments with respect to a coordination crystal system below the Morin transition temperature. (Adapted from Ref. 27 with permission of World Scientific Publishing Company.)... 

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