International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 63   | 1 | 2 |

## Section 1.3.4.2.1.2. Structure factors in terms of form factors

G. Bricognea

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#### 1.3.4.2.1.2. Structure factors in terms of form factors

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In many cases, is a sum of translates of atomic electron-density distributions. Assume there are n distinct chemical types of atoms, with identical isotropic atoms of type j described by an electron distribution about their centre of mass. According to quantum mechanics each is a smooth rapidly decreasing function of x, i.e. , hence and (ignoring the effect of thermal agitation)which may be written (Section 1.3.2.5.8)By Fourier transformation:Defining the form factor of atom j as a function of h to bewe haveIf and are the real- and reciprocal-space coordinates in Å and Å−1, and if is the spherically symmetric electron-density function for atom type j, then

More complex expansions are used for electron-density studies (see Chapter 1.2 in this volume). Anisotropic Gaussian atoms may be dealt with through the formulae given in Section 1.3.2.4.4.2.