The challenge of designing solid state compounds with predicted compositions and structures could be partly met using concepts that employ phase homologies. Homologous series of compounds not only can place seemingly diverse phases into a single context; they can also forecast with high probability specific new phases. A homologous series is expressed in terms of a mathematical formula that is capable of producing each member. Within a homologous series, the type of fundamental building units and the principles that define how they combine remain preserved, and only the size of these blocks varies incrementally. In this Account, we present this approach by discussing a number of new homologies and generalize it for a wide variety of systems.
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