Introduction

It is a universally acknowledged truth that any useful artifact is made of materials. A material is a substance, or combination of substances, which has achieved utility. To convert a mere substance into a material requires the imposition of appropriate structure, which is one of the subtlest of scientific concepts; indeed, the control of structure is a central skill of the materials scientist, and that skill makes new artifacts feasible.

Any structure involves two constituents: building blocks and laws of assembly. Crystal structure will serve as the key example, with wide ramifications. Any solid element, pure chemical compound, or solid solution ideally consists of a crystal, or an assembly of crystals that are internally identical. (The qualification “ideally” is necessary because some liquids are kinetically unable to crystallize and turn instead into glasses, which are simply congealed liquids.) Every crystal has a structure, which is defined when (1) the size and shape of the repeating unit, or unit cell, and (2) the position and species of each atom located in the unit cell have all been specified. At one level, the unit cells are the building blocks; at another level, the individual atoms are. The laws of assembly are implicit in the laws of interatomic force: once we know how the strength of attraction or repulsion between two atoms depends on their separation and what angles between covalent bonds issuing from the same atom are stable then, in principle, we can predict the entire arrangement of the atoms in the unit cell. Once the crystal structure has been established, many physical properties, such as the cleavage plane, melting temperature, and thermal expansion coefficient, are thereby rendered determinate. In the fullest sense, structure determines behavior.