Some interesting aspects of the temperature dependence of the Planck’s functionφ and heat capacities of metals exhibiting the h.c.p. ⇄ b.c.c. transformation have been brought to light by the use of reduced temperature (T*) and Planck’s function (-φ T*). It has been shown that tangents drawn to the -φ T* vsT* plots of these metals at any chosen value ofT* intersect at a point whose coordinates are defined by the slope and intercept ofφ vs entropy plots at any homologous temperature and the selectedT* value. A generalized expression obtained for the temperature dependence ofφ has been used to demonstrate that the heat capacity of these metals may be visualized to have structural and material components.

The Wigner-Seitz cell of a lattice inn-dimensional space displays the complete point group of such a lattice. The vertices of the cell when projected onto pseudo space can serve as the outer shape of acceptance domain or motif. This general procedure leads to acceptance domain or motif identical to those discussed in literature for primitive orthogonal hyperlattices.

Example of 4d non-orthogonal hyperlattices corresponding to 12-fold symmetry will be considered. It will be shown that the first Wigner-Seitz cell degenerates into more than one shape in 2d pseudo space and can serve as a natural partition of the motif. Following a parallel procedure, the consequence of projection of first 4d Brillouin zone will also be discussed.