CUBIC BOND-ORIENTATIONAL ORDER IN THE LIQUID-CRYSTALLINE BLUE PHASES

A thorough numerical analysis of a recently proposed cubic bond orient ational model for Blue Phase III (Longa, L., and Trebin, H.-R., 1993, Phys. Rev. Lett., 71, 2757) is presented. In addition to the standard quadrupolar tensor field Q(alpha beta)(r), describing the cubic space groups of BPI and BPII, a spatially constant fourth-rank hexadecupolar tensor B-alpha beta gamma delta(4) of cubic point group symmetry is u sed to describe a cubic bond orientational order. While in BPI and BPI I both order parameters are present, in BPIII only the hexadecupolar t ensor is non-zero. Hence, BPIII is viewed as a phase of long-range cub ic order. Within this model distinct phase diagrams are computed up to four stars of k-vectors, the elements of a star being related by the point group symmetry operations. In particular, it is possible to acco unt for some of the details found experimentally, such as the dominanc e of BPI over BPII for high chiralities. If, however, the artificial b ody centred cubic structure O-5 is being made metastable, then BPI als o vanishes from the phase diagram.