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 Results for DC.creator="A." AND DC.creator="Altomare" in section 4.2.3 of 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'. ...

Triplet invariants
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.3.3, p. 397 [ doi:10.1107/97809553602060000957 ]
... invariants 4.2.3.3. Triplet invariants Triplet invariants (or simply `triplets') play a central role in DM. A probabilistic formula for estimating triplets was first given by Cochran ... for equal atoms and for non-equal atoms, , L is a normalization term depending only on and . The trend ...

Structure invariants
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.3.2, p. 397 [ doi:10.1107/97809553602060000957 ]
... Structure invariants We now need the concept of structure invariants. A structure factor (whether normalized or not) referred to a new unit-cell origin x0 takes the form , i.e., the ... phase changes according to , while the modulus remains unchanged ( ). A basic question now arises: since the origin can be ...

Normalized structure factors
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.3.1, pp. 396-397 [ doi:10.1107/97809553602060000957 ]
... diffraction intensities provided by X-ray diffraction experiments are on a relative scale and the normalization process corrects for this as ... at rest and for . From equation (4.2.4) we obtain A plot of the left side of (4.2.5) versus s2 should yield a straight line, for which the intercept with the vertical ...

Direct methods
Altomare, A., Cuocci, C., Moliterni, A. and Rizzi, R.  International Tables for Crystallography (2019). Vol. H, Section 4.2.3, pp. 395-399 [ doi:10.1107/97809553602060000957 ]
... inequalities involving unitary structure factors Uh (see Section 4.2.7 for a definition of Uh). Later Sayre (1952 ) derived Sayre's ... diffraction intensities provided by X-ray diffraction experiments are on a relative scale and the normalization process corrects for this as ... at rest and for . From equation (4.2.4) we obtain A plot of the left side of (4.2.5) versus s2 ...

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