Throughout the previous chapter we emphasised the idea of the symmetry of crystalline materials. Another way of referring to the translational symmetry of crystals is to say that a perfect crystal has long range order in the arrangement of atoms. A solid with no long range order is said to be amorphous. Ordinary glass is a good example. The randomness of the atomic arrangement and the consequent lack of symmetry means that, on average, every direction in an amorphous structure is equivalent to every other. If we were to measure some physical property which depends on direction, it would not vary with orientation in glass, i.e. an amorphous solid is isotropic. Crystalline materials, on the other hand, are generally anisotropic, which means that the magnitude of many physical properties will depend on direction in the crystal.

Some physical properties are clearly nondirectional, i.e. they are scalar properties. For example the density of a mineral, or its heat capacity can be measured without reference to direction. Other properties such as surface energy and hence chemical reactivity do depend on the crystallographic orientation of the surface plane, but are not in themselves direction-dependent quantities. However, the thermal conductivity of a mineral is defined as the ratio of the heat flow to the temperature gradient, both of which need to be specified by direction as well as magnitude (i.e. they are vector quantities).