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Indexing a powder diffraction pattern
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, ch. 3.4, pp. 270-281 [ doi:10.1107/97809553602060000949 ]
Chapter 3.4. Indexing a powder diffraction pattern This chapter provides a general overview of the process of identifying cell parameters from a powder diffraction pattern. The main theoretical, computational and applicative ...

Graphical tools in EXPO
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.9.7, p. 410 [ doi:10.1107/97809553602060000957 ]
Graphical tools in EXPO 4.2.9.7. Graphical tools in EXPO A user-friendly graphical interface supports all the principal procedures of ...
     [more results from section 4.2.9 in volume H]

Resolution bias modification (RBM)
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.8.3, pp. 405-406 [ doi:10.1107/97809553602060000957 ]
... measured experimental domain of the reciprocal space is finite. As a consequence, series-truncation errors can distort the map: negative values ... Altomare, Cuocci, Giacovazzo, Kamel et al., 2008 ; Altomare, Cuocci, Giacovazzo, Moliterni & Rizzi, 2008 ), reciprocal space (Altomare, Cuocci et al., 2009 ) and ... The procedure is based on two main steps: (1) Determining a resolution bias correction function and applying it to the ...
     [more results from section 4.2.8 in volume H]

Maximum-entropy methods
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.7, pp. 403-404 [ doi:10.1107/97809553602060000957 ]
... et al., 1991 ) and macromolecular data [see Gilmore (1996 ) for a general review]. ME methods (MEM) were found to be ... data or intensities affected by errors (Gilmore, 1996 ). If a discrete probability distribution is considered, given by a set of M probabilities P = {p1, p2,, pM}, the ...

Charge flipping
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.6, pp. 401-403 [ doi:10.1107/97809553602060000957 ]
... . In its many variants it has been applied to a wide range of crystallographic problems: structure solution from single-crystal ... aperiodic structures; quasicrystals; and protein heavy-atom substructures. It is a dual-space iterative method switching back and forth between real ... sign of the density of all pixels with densities below a given (small) threshold positive value [delta]. The value ...

The use of the Patterson function for estimating integrated intensities
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.5.1, p. 401 [ doi:10.1107/97809553602060000957 ]
... adopts the squaring method, and has the following steps: (1) A P(u) map is calculated. The intensities of the strongly ... overlapping reflections are derived by equipartitioning the cluster intensity. (2) A modified Patterson map PM(u) is derived by setting to ... respect to the true amounts. In an attempt to obtain a distribution of intensity containing both small and large values, ...
     [more results from section 4.2.5 in volume H]

Systematic decomposition
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.4.3, p. 400 [ doi:10.1107/97809553602060000957 ]
... sorted according to their values and only those larger than a threshold are actively used in the phasing process. Procedures have ... The clusters containing the reflections that are expected to play a minor role in DM applications, i.e.. those for which no ... This approach uses the Le Bail decomposition and carries out a systematic partition of the overall intensity of each of ...
     [more results from section 4.2.4 in volume H]

How direct methods work
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.3.4, pp. 397-399 [ doi:10.1107/97809553602060000957 ]
... There are two basic methods of assigning phases to reflections: (a) Random values between 0 and 360 are assigned to reflections. ... it is possible to solve crystal structures by starting with a large set of phases (more than 40-50) even if ... to seed the phasing process, it is necessary to choose a larger number, which then constitutes the `starting set'. ...
     [more results from section 4.2.3 in volume H]

Intensity extraction for RS methods
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.2, p. 395 [ doi:10.1107/97809553602060000957 ]
... following approaches: the iterative Le Bail method usually combined with a profile-fitting procedure, or the least-squares-based Pawley method ... function (Altomare, Foadi et al., 1998 ), and the location of a partial structure fragment (Altomare, Giacovazzo et al., 1998 ). The ... but still effective) one is to equipartition the intensity of a cluster of overlapping reflections among the single reflections belonging ...

Introduction
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.1, p. 395 [ doi:10.1107/97809553602060000957 ]
... of more powerful computers made it feasible, and there is a need to know the crystal structure of materials of chemical ... the end of the last century, direct-space methods became a viable alternative to reciprocal-space methods. The main differences between ... the one-dimensional experimental pattern. This unavoidable situation results in a loss of experimental information and has serious consequences: Bragg ...

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