Pearson symbols

Space Group and Pearson Symbol Pnma, oP20 Composition narrow range of homogeneity (approximately 39 0 at/°C)... 

Lattice Parameter 0.4636 nm Space Group Fm3m Pearson Symbol cF8... 

Lattice Parameter 0.4328 nm Space Group FmSm Pearson Symbol cF8 Composition TiCo,47to TiCg 99 Molecular Weight 59.91 g/mol Color silver gray X-ray Density 4.91 g/cm ... 

Space Group and Pearson Symbol P6m2, hP2 Composition Narrow range of homogeneity, a-WCg gg WCj qo Molecular Weight 195.86 g/mol Color gray... 

Lattice Parameter a = 0.452 nm Space Group Fm3m Pearson Symbol cF8 Composition HfNo 7510 HFNj 12 Molecular Weight 192.497 Color greenish yellow X-ray Density 13.8 g/cm Melting Point 3387°C Debye Temperature 421 K... 

Structure Lattice Parameters hep a=0.4395 nm, c = 0.4338 nm Space Group Pbg/mme Pearson Symbol hP8 Composition NbNo 92 to NbNj ge Molecular Weight i06.91 Color dark gray X-ray Density 7.3 g/cm ... 

More systematic (but not always unambiguous) is the designation by Pearson symbols their use is recommended by IUPAC (International Union of Pure and Applied Chemistry). A Pearson symbol consists of a lower case letter for the crystal system (cf. the abbreviations in Table 3.1, p. 24), an upper case letter for the kind of centering of the lattice (cf. Fig. 2.6, p. 8) and the number of atoms in the unit cell. Example sulfur-< F128 is orthorhombic, face centered and has 128 atoms per unit cell (a-sulfur). 

Phase/ ideal formula/ temperature range (°C) Pearson symbol/ prototype Lattice parameters (pm) (composition at.% Cu) Maximum composition range (at.% Cu)... 

The two special (a) and (b) Wyckoff positions have no free coordinate parameter. The two occupancy parameters are 100%. The Pearson symbol is cP2. 

No free parameters in the atomic positions of Mg and Ge. In this case the two occupancy parameters have been found to be 100%. The Pearson symbol is cF12 (CaF2 is considered the prototype of this structure). 

The occupancy parameter of N is 75% that is three atoms are statistically distributed in the four positions. The real stoichiometry corresponds to Mo2N0.75 and in the unit cell there are 11 atoms instead of the ideal value of 12. The Mo position has the free parameterz for which, in this particular case the value 0.258 has been determined. The Pearson symbol is tI12 (11). 

Figure 3.4. The crystal systems and the Bravais lattices illustrated by a unit cell of each. All the points which, within a unit cell, are equivalent to each other and to the cell origin are shown. Notice that, in the primitive lattices the unit cell edges are coincident with the smallest equivalence distances. For the rhombohedral lattice, described in terms of hexagonal axis, the symbol hR is used instead of a symbol such as rP. In the construction of the so-called Pearson symbol ( 3.6.3), oS and mS will be used instead of oC and mC.

Structure types and unit cell Pearson symbol... 

In this book, the Pearson symbol will be used throughout and the convention has been adopted indicating in every case the number (ideal or effective) of atoms contained in the chosen unit cell. In the case, therefore, of rhombohedral substances for which the data of the (triple primitive) hexagonal cell are generally reported, the number of atoms is given which is in the hexagonal cell and not the number of atoms in the equivalent rhombohedral cell (Ferro and Girgis 1990). So, for instance,... 

If the structure is not known exactly, the prototype indication cannot be added to the Pearson symbol. In some cases, moreover, only incomplete Pearson symbols (such as o 60, cF , etc.) can be used. 

In Fig. 3.27 (c), on the other hand, it is suggested that, for the same structure, an alternative description may be obtained and, according to Pearson, symbolized. 

Pearson symbol and prototype Space group symbol and number Lattice parameters (pm) Wyckoff positions (WP) Representative coordinates x,y, z of the 1st WP Occupancy Coordination polyhedron code Average polyhedron radius (pm) AET... 

Phase conventional name and symbol, Pearson symbol Example and composition range (Okamoto 2000) c/a axial ratio ( ) Villars etal. (1995) Me/ at s,p electrons njnits,p,d electrons... 

Rank order Structural type Pearson symbol Ninnber Rank order Structural type Pearson symbol Number... 

Phase Composition at.% Cu Pearson symbol prototype Strukturbericht designation... 

Crystal structure strukturbericht designation alphabetically arranged by pearson symbol designation... 

Pearson symbol Prototype Strukturbericht designation Pearson symbol Prototype Strukturhericht designation... 

Table 1.1 gives the structures of the elements at zero temperature and pressure. Each structure type is characterized by its common name (when assigned), its Pearson symbol (relating to the Bravais lattice and number of atoms in the cell), and its Jensen symbol (specifying the local coordination polyhedron about each non-equiyalent site). We will discuss the Pearson and Jensen symbols later in the following two sections. We should note,... 

Hydrogen, nitrogen, oxygen,end the halogens bind as dimers that are then weaxly held together on the lattices which are indicated by the Pearson symbol. 

Element Common name Pearson symbol fersen symbol... 

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