This thesis addresses one of the fundamental questions in materials crystal chemistry, namely why do atoms arrange themselves in the way they do? The ability to broadly design and predict new phases [i.e. crystal structures] can be partly met using concepts that employ phase homologies. Homologous series of compounds are those that seem chemically diverse but can be expressed in terms of a mathematical formula that is capable of producing each chemical member in that crystal structure. A well-established strategy to help discover new compounds - or at least to try to develop chemical design strategies for discovery - is to search, organize and classify homologous compounds from known data. These classification schemes are developed with the hope that they can provide sufficient insight to help us forecast with some certainty, specific new phases or compounds. Yet, while the classification schemes (over a dozen have been reported in the last 50 years) have proved to be instructive, mostly in hindsight, but they have had limited impact, if at all, on the a priori design of materials chemistry.

The aim of this research project is to develop a totally new approach to the study of chemical complexity in materials science using the tools of information theory and data science, which link diverse and high dimensional data derived from physical modeling and experiments. A very large scale binary AB2 crystallographic database is used as a data platform to develop a new data mining / informatics protocol based on high dimensional recursive partitioning schemes coupled to information theoretic measures to:

* Identify which type of structure prototype is preferred over another for a given chemistry of compound

* discover new classification schemes of structure/chemistry/property relationships that classical homologies do not detect and finally we

* Extract and organize the underlying design rules for the formation of a given structure by quantitatively assessing the influence of multidimensional electronic structure attributes.

Finally some applications of this new approach are demonstrated; including new ways for linking first principles calculations to crystal structure prediction and group theory to crystal structure transitions.