Crystal symmetries atomic arrangement

Crystals A crystal may be defined as a solid composed of atoms arranged in an orderly, repetitive array. The interatomic distances in a ciyst of any definite material are constant and are characteristic of that material. Because the pattern or arrangement of the atoms is repeated in all directions, there are definite restrictions on the lands or symmetry that crystals can possess. 

X-ray Diffraction Structural characterization of single crystal samples can reveal both the atomic arrangement and the composition of a sample. The unit cell size and symmetry alone can quickly establish whether a crystal is a known material or a new phase. A detailed discussion of X-ray diffraction studies of the known superconductors is the topic of another chapter in this book. 

GdNi crystallizes in the orthorhombic CrB type of structure (space group Cmcm). The Gd atoms are located on the 4c sites with point symmetry mm (0, yGd % 0.14, ). The Ni atoms also occupy the 4c sites with yNi 0.43 (see e.g. Buschow (1980)). It is interesting to note that among the RNi compounds there exists a second type of orthorhombic structure. Only the compounds with R from La to Gd crystallize in the CrB type. The compounds with R from Dy to Tm and Y show the less symmetric FeB type with space group Pnma (see e.g. Burzo et al. (1990)). As reported by Blanco et al. (1992) TbNi crystallizes in a monoclinic intermediate structure. Figure 26 shows the orthorhombic unit cell and the atomic arrangement of the CrB type of structure. (The shown orthorhombic cell is not the... 

Two pieces of information about the fundamental atomic pattern may be deduced from the actual shape of a crystal, provided this crystal shows a sufficient variety of faces and is large enough to permit measurements of the angles between the faces. One is a knowledge of the shape and relative dimensions of the unit of pattern. The other is a partial knowledge of the symmetries of the atomic arrangement. 

And this is not all. Each type of unit cell may arise from a number of different types of atomic arrangement, and some of the symmetry characteristics of these different types of atomic arrangements are revealed by shape-symmetries. In classifying crystals we can first of all divide them into several systems according to unit cell types, and then each system can be divided into several classes according to those symmetry characteristics which are revealed by shape. The consideration of crystal symmetry may thus take us farther than the mere derivation of unit cell type. 

There is one other element of symmetry possessed by sodium chloride crystals. For each face, edge, or corner of the cube or octahedron there is an exactly similar face, edge, or comer diametrically opposite the centre of the cube or octahedron (Fig. 19) is therefore called a centre of symmetry. The centre of symmetry possessed by these shapes corresponds with the centre of symmetry in the atomic arrangement the centre of any sodium or chlorine ion is a centre of symmetry, since along any direction from the selected ion the arrangement encountered is exactly repeated in the diametrically opposite direction. 

Sodium nitrite, NaN02, forms orthorhombic crystals of the shape of Fig. 179. This shape has holohedral symmetry mmm the internal symmetry might, however, be lower than this (see p. 269), and therefore atomic arrangements in all three classes of the orthorhombic system (mmm, 222, and mm2) may be considered. 

The suggestion that in metal crystals the atoms are arranged in closest packing was made by Barlow before the development of the x-ray technique, in order to account for the observations that many metals crystallize with cubic or hexagonal symmetry and that in the latter case many of the observed values of the axial ratio lie near the ideal value 2y/2/ v 3 = 1.633 for hexagonal closest packing. 

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