Abstract

We describe, using the example of the one non--trivial rank--4 orthorhombic Bravais class, a procedure to determine the low-rank space groups that can arise from a given high-rank space group through a continuous phase transition. Consider a continuous structural phase transition whose only effect in Fourier space is a slight distortion of the lattice of wave vectors that lowers its rank, possibly with a reduction of its point group. Suppose we know the space group describing the crystal in its high-rank phase. What are the possible space groups describing the crystal in its low-rank phase? We illustrate here how this question is answered in the language of Fourier space crystallography. When the rank is lowered, two issues arise that are not relevant to rankpreserving transitions. (1) Lowering the rank introduces new linear relations among formerly independent wave vectors. This imposes new constraints on the linear phase functions that describe the point group symmetry of the mate...

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