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• Part of the book series (GTP) Abstract Our main concern in this book is to describe the electronic properties of crystalline solids. The existence of translation symmetries associated with such ordered crystal structures leads to specific features in the electronic structure and to a specific representation of the energy states in wave vector space. 2.1, we explain how a crystal structure can be described formally by defining a crystal lattice of non-material points together with a repeated material motif, known as the basis. This periodic structure of matter causes diffraction of electromagnetic waves, or equivalently, of quantum particles. We shall see in Sect.

2. 2 that these diffraction phenomena lead to the notion of reciprocal lattice in wave vector space, and this will be important later for characterising the electronic states of these solids. 2.3, we outline the experimental methods used to determine the crystal structures of solids using diffraction methods.