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Extra resources for Introductory Solid State Physics (Second Edition)
This is the origin of the incompressible character of liquids and solids. Diagrammatically, we can express the energy of the solid relative to the same mass of dilute vapour in terms of a pair potential that is the above difference in energy per atom described as a function of interatomic spacing; it contains attractive and repulsive terms and has the form shown in Fig. 6. In principle this pair potential is calculable, but in practice the difﬁculties are great, although signiﬁcant progress has been made in recent years.
They are different combinations of the same digits. What would the indices be in the conventional Miller system? 9 In Fig. 13(c) both primitive and unit cells of the fcc lattice are shown. g. (100), (110), (111). If instead we were to use the primitive cell for our coordinate axes, what would the above-mentioned planes then have for Miller indices? 10 There are only ﬁve two-dimensional Bravais lattices. An obvious example is the square net; what are the other four Bravais nets? 11 Consider the conventional bcc unit cell, choose an origin at (000) and form the shortest translational vectors required to deﬁne the lattice.
1) The numbers n are necessarily integral and the vectors a, b and c are fundamental units of the translational symmetry; the latter are arbitrary, but a sensible choice is usually that which gives the shortest vectors or the highest symmetry to the unit cell. 2. The volume associated with a single lattice point is called the primitive cell, and this usually takes one of two forms. Either the lattice point is conﬁned to the centre of the primitive cell, which is then determined by the planes bisecting the lines joining the particular point with its neighbours, or the primitive cell may be described as the unit of the mesh formed by the lines connecting lattice points; in the latter case points lie at the vertices of the cell and this is the primitive cell most often used in crystallography.