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Published online by Cambridge University Press: 05 June 2013
Again! again! again!
THOMAS CAMPBELLTranslational symmetry
A theory of the physical properties of solids would be practically impossible if the most stable structure for most solids were not a regular crystal lattice. The N-body problem is reduced to manageable proportions by the existence of translational symmetry. This means that there exist basic vectors, a1; a2, a3such that the atomic structure remains invariant under transtation through any vector which is the sum of integral multiples of these vectors.
In practice, this is only an ideal. A laboratory specimen is necessarily finite in size, so that we must not carry our structure through the boundary. But the only regions where this matters are the layers of atoms near the surface, and in a block of Ar atoms these constitute only about N⅔ atoms—say 1 atom in 108 in a macroscopic specimen. Most crystalline solids are also structurally imperfect, with defects, impurities and dislocations to disturb the regularity of arrangement of the atoms. Such imperfections give rise to many interesting physical phenomena, but we shall ignore them, except incidentally, in the present discussion. We are mainly concerned here with the perfect ideal solid, and with the properties it shows; the phenomena which are associated with the solid as the matrix, vehicle, or background for little bits of dirt, or tiny cracks and structural flaws, belong to a different realm of discourse.
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