Pearson’s symbol

The second position in the symbol is occupied by a standard notation of Bravais lattice. Thus, the first two elements in the Pearson s symbol are letters and they classify all available alloy structures according to 14 Bravais lattices, as shown in Table 6.1. 

The third (and last) position in Pearson s symbols is occupied by the total number of atoms located in one unit cell of the compound. 

For example, considering the crystal structure of copper, which has cubic face-centered lattice Figure 6.2) and a total of 4 atoms in the unit cell, its Pearson s symbol is cF4. On the other hand, if the material has Pearson s symbol oI32, this means that its crystal structure is orthorhombic, and one body-centered unit cell contains a total of 32 atoms. 

Pearson s classification is insensitive to both chemical compositions and stoichiometries of metallic alloys. It is quite useful because all known intermetallic crystal structures are grouped according to their structural symbols, which are quite simple. Thus, once the symmetry and the content of the unit cell of a new alloy phase have been established, it only makes sense to search for potentially isostructural compounds among those that have identical Pearson s symbols. 

Table 6.1. Pearson s symbols used to designate 14 types of Bravais lattices.

Crystal system Bravais lattice First two parts of Pearson s symbol... 

Tens of thousands of intermetallic phases have been systematized and classified using Pearson s symbols. They are listed in a source commonly known as Pearson s Handbook, which is periodically updated and published by ASM Intemational. The Handbook also provides detailed information about the coordinates of atoms in unit cells of all known structure types of metals, alloys and related phases, which makes it a valuable tool in the structure solution of metallic materials. 

Strictly speaking, in this case it is not necessary to solve the crystal structure fi om first principles, because after finding that the Pearson s symbol of the material is AP6, it is easy to identify the correct structure type of this alloy by consulting Pearson s Handbook. Furthermore, in such a small and high symmetry unit eell the possibilities to place different atoms... 

The first letter denotes the crystal system triclinic (a), monoclinic (m), orthorhombic (o), tetragonal (t), hexagonal (h) and cubic (c). Trigonal (rhombohedral) system is denoted by combination hR. The second letter of Pearson s symbol denotes lattice type primitive (P), edge-(base-) centered (C), body-centered (I) or face-centered (F). The following number denotes number of atoms in the crystal unit cell. 

The systematic description of crystal structures is presented primarily in the well known Structurbericht. The classification of crystals by the Structurbericht does not reflect their crystal class, the Bravais lattice, but is based on the crystallochemical type. This makes it inconvenient to use the Structurbericht categories for comparison of some individual crystals. Thus, there have been several attempts to provide a more convenient classification of crystals. Table 5 presents a compilation of different classifications which allows the reader to correlate the Structurbericht type with the international and Schoenflies point and space groups and with Pearson s symbols, based on the Bravais lattice and chemical composition of the class prototype. The information included in Table 5 has been chosen as an introduction to a more detailed crystallophysical and crystallochemical description of solids. 

Strukturbericht and Pearson s symbol (atoms per formula unit)... 

Formula Sc content (at.%) Structure type Pearson s symbol Element (E) which forms the compound... 

Structure type Pearson s symbol Space group Number of compounds Including binary ternary ... 

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