The materials encountered in metallurgy are usually crystalline. Melts and vapour and, very recently, glassy materials (supercooled, frozen melts) are considered only as limiting cases. We start by assuming that we know the crystal structure of every substance. It can be determined by the well-known X-ray methods and described crystallographically in terms of atomic positions, symmetry, unit cell, etc. (A structural description can be given for non-crystalline substances also, but the atoms do not adhere to it as strictly as in a crystal.) As stated in the introduction, bulk metal does not normally consist of a single crystal but of many crystal ‘grains’, in other words it possesses a microstructure. The grains differ from one another in orientation and sometimes also in crystal structure or composition. In the former case the system is described as homogeneous, in the latter heterogeneous. The constituents of the latter, which are in themselves homogeneous, are called phases. The crystal structure, composition and volume fraction of each vary in such a way that the free enthalpy of the system in equilibrium is a minimum. Phases as defined here transform into one another by first-order transformations (defined thermodynamically by discontinuities in the first derivative of the enthalpy with respect to temperature) such as melting (see chapter 5).