Phase transitions within crystals that are aperiodic by construction

Abstract

Aperiodic crystals possess long-range order without translational symmetry. They constitute a state of matter that has forced a profound paradigm shift in solid-state physics. A common feature of aperiodic crystals is that they recover periodicity in higher dimensional spaces, the so-called crystallographic superspaces. Much work has been dedicated to the structural order within these superspaces and also to their specific dynamics. This paper focuses on the phase transitions within crystallographic superspaces. Aperiodic crystals are divided into three families: incommensurately modulated crystals, composite crystals, and quasicrystals. Incommensurately modulated crystals have been studied heavily and appear now to be relatively well understood, since they possess a periodic high-symmetry phase. The other two members of the family are aperiodic by construction. In this paper, we present a comprehensive and systematic study of a prototype composite host-guest family of $n$-alkane/urea inclusion compounds $[\mathit{n}\ensuremath{-}{\text{C}}_{n}{\text{H}}_{2n+2}/\text{CO}{({\text{NH}}_{2})}_{2}]$. For these materials, which exhibit a rich sequence of phases, the phase transitions are described in terms of group/subgroup symmetry breaking within crystallographic superspaces. Such phase transitions may decrease, increase, or maintain the dimension of the crystallographic superspace. These results highlight the multiplicity of specific structural solutions that aperiodicity offers.