By Gonzalez Szwacki N., Szwacka T.
This publication is a whole and transparent creation to the sector of crystallography. It comprises an intensive dialogue of the 14 Bravais lattices and the reciprocal to them, easy recommendations of element team symmetry, the crystal constitution of components and binary compounds, and masses extra. the aim of this textbook was once to demonstrate instead of describe "using many phrases" the constitution of fabrics. The chapters are observed by way of routines designed in any such solution to inspire scholars to discover the crystal buildings he/she is studying approximately. the whole notation during this publication is in line with the overseas Tables for Crystallography.
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Extra info for Basic elements of crystallography
43b and 43c there are shown other examples of the shortest translation vectors in the bcc lattice. At least one of such vectors has to appear in each set of basis vectors that define a primitive unit cell of this lattice (see Fig. 43), since both, the lattice point located in the center of the cubic cell and the point from its vertices, are then represented by the lattice point from vertices of the primitive unit cell. 10. Face Centered Cubic Lattice First, let us consider the lattice points within the cubic unit cell of the fcc lattice.
Three-Dimensional Crystal Lattice 21 Figure 24 Each diagonal of a cube represents one of its threefold rotation axis. It is easy to show that the body diagonals of the cube represent its threefold axes. We can see in Fig. 24 that the displayed body diagonal connects two opposite cube vertices. The remaining 6 vertices form two groups, with 3 vertices each, that represent the vertices of two equilateral triangles. Each of the triangles is lying in a plane orthogonal to the diagonal and its geometric center overlaps with the point where the diagonal intersects the plane of the triangle.
55. We can see in this figure that the trigonal lattice points that are inside the hexagonal prism define two equilateral triangles in planes orthogonal to the sixfold hexagonal prism symmetry axis. The axis is crossing these planes at the geometric centers of the triangles. Just such distribution of the trigonal lattice points, which are inside the hexagonal prism, reduces the sixfold axis of a hexagonal lattice to the threefold axis of a trigonal lattice. The basis vectors a h , b h , c h in Fig.