International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 5.2, p. 491

## Section 5.2.1.2. Errors and aberrations: general discussion

W. Parrish,a A. J. C. Wilsonb and J. I. Langfordc

aIBM Almaden Research Center, San Jose, CA, USA,bSt John's College, Cambridge CB2 1TP, England, and cSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England

#### 5.2.1.2. Errors and aberrations: general discussion

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The relation between the lattice spacing d, the angle of incidence (Bragg angle) θ, and the wavelength λ is Bragg's law: The lattice spacing d is related to the lattice parameters a, b, c, α, β, γ and the indices of reflection h, k, l. In the simple case of cubic crystals, the relation is where a is the single lattice parameter. The general relation is where a, b, c are the edges of the unit cell, and are the functions of the angles of the unit cell given in Table 5.2.1.1.

 Table 5.2.1.1| top | pdf | Functions of the cell angles in equation (5.2.1.3) for the possible unit cells
FunctionCell
Cubic
tetragonal
orthorhombic
HexagonalMonoclinic (c unique)RhombohedralTriclinic
A 1 1 1
B 1 1 1
C 1
D 0 0 0
E 0 0 0
F 0
G 1

Differentiation of (5.2.1.1) shows that the errors in the measurement of d are related to the errors in the measurement of λ and θ by the equation Wavelength and related problems are discussed in Section 5.2.2 and geometrical and other aberration problems in Section 5.2.3.