Alloy Phase Diagram Database™

Composition of the Pearson Symbol

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The Pearson symbol was introduced to classify crystal structures. It is composed of three distinct parts, the first of which is a lower-case letter representing the crystal system.

anorthic = triclinic
hexagonal, trigonal

This is followed by an upper-case letter designating the Bravais lattice, and the sum of multiplicities of all atom sites in the structure. There exist 14 distinct Bravais lattices: aP, mP, mS (formerly mA, mB, mC), oP, oS (formerly oA, oB, oC), oF, oI, tP, tI, hP, hR, cP, cF, cI. The letter S, grouping A, B, and C-face centered lattices, is recommended by a subcommission of the International Union of Crystallography, since this notation is independent of the actual space group setting (P = primitive, A = A-face centered, B = B-face centered, C = C-face centered, F = all-face centered, I = body centered, R = rhombohedrally centered). For a structure without vacancies the latter corresponds to the number of atoms in the unit cell. The similar term Pearson code is used when the number is defined as the number of atoms in the unit cell. The number may in this case be a non-integer, whereas the number in the Pearson symbol is always an integer. The sum of multiplicities given for a trigonal structure with R-lattice refers to the triple hexagonal cell, and is thus always a multiple of 3.

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ASM Alloy Phase Diagrams Center, P. Villars, editor-in-chief; H. Okamoto and K. Cenzual, section editors;, ASM International, Materials Park, OH, USA, 2006-2016