Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.2, p. 10   | 1 | 2 |

Section 1.2.1. Introduction

P. Coppensa*

aDepartment of Chemistry, Natural Sciences & Mathematics Complex, State University of New York at Buffalo, Buffalo, New York 14260–3000, USA
Correspondence e-mail:

1.2.1. Introduction

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The structure factor is the central concept in structure analysis by diffraction methods. Its modulus is called the structure amplitude. The structure amplitude is a function of the indices of the set of scattering planes h, k and l, and is defined as the amplitude of scattering by the contents of the crystallographic unit cell, expressed in units of scattering. For X-ray scattering, that unit is the scattering by a single electron (2.82 × 10−15 m), while for neutron scattering by atomic nuclei, the unit of scattering length of 10−14 m is commonly used. The complex form of the structure factor means that the phase of the scattered wave is not simply related to that of the incident wave. However, the observable, which is the scattered intensity, must be real. It is proportional to the square of the scattering amplitude (see, e.g., Lipson & Cochran, 1966[link]).

The structure factor is directly related to the distribution of scattering matter in the unit cell which, in the X-ray case, is the electron distribution, time-averaged over the vibrational modes of the solid.

In this chapter we will discuss structure-factor expressions for X-ray and neutron scattering, and, in particular, the modelling that is required to obtain an analytical description in terms of the features of the electron distribution and the vibrational displacement parameters of individual atoms. We concentrate on the most basic developments; for further details the reader is referred to the cited literature.


Lipson, H. & Cochran, W. (1966). The Determination of Crystal Structures. London: Bell.

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