By Nevill Gonzalez Szwacki, Teresa Szwacka
This textbook is an entire and transparent advent to the sector of crystallography. It comprises an in depth dialogue at the 14 Bravais lattices and their reciprocals, the elemental strategies of element- and space-group symmetry, the crystal constitution of parts and binary compounds, and masses more.
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Additional resources for Basic Elements of Crystallography
55 on the cell base. Whereas, Fig. 56b shows the projections on the prism base of 6 trigonal lattice points that are inside the hexagonal prism from Fig. 55. In this figure O represents the origin of the triple hexagonal unit cell, defined by basis vectors a h , b h , c h . The coordinate of each point in the c h axis is shown next to the lattice point 52 Basic Elements of Crystallography Figure 56 (a) Projections of the centering points of the triple hexagonal cell R from Fig. 55 on the base of the cell.
48b), that is of this point is ( 0,1 2,1 2 ) , where the coordinates are expressed in units Three-Dimensional Crystal Lattice 43 Figure 48 (a) All-face centered cubic unit cell of the fcc lattice. (b) Positions of the four lattice points within the cubic cell. The coordinates are expressed in units of a, which is the length of the cube edge. of a, which is the length of the basis vectors. In the similar way, we can place the points in the B- and C-faces (see Fig. 48b). Finally, the positions of the four lattice points belonging to the cubic cell of the fcc lattice are: (0,0,0) , (0,1 2,1 2) , (1 2,0,1 2) , and (1 2,1 2,0) .
Figure 42 shows the NNs, NNNs, and TNNs of a lattice point in the sc lattice. In this figure, the NNs of a lattice point placed in the center of a large cube (built of 8 smaller cubes) are placed at the vertices of a regular octahedron. Since the octahedron has 6 vertices, the coordination number for the sc lattice is 6. The NNNs are in the middle of the 12 edges of the large cube, so there are 12 NNNs of a lattice point in the sc lattice. The TNNs of the lattice point in consideration are at the vertices of the large Figure 42 The NNs, NNNs, and TNNs of a lattice point in a sc lattice.
Basic Elements of Crystallography by Nevill Gonzalez Szwacki, Teresa Szwacka