The use of structural information in the phase probability of a triple product

The use of structural information in phase determination

“…In his derivation of the probability distribution of a triple product for space group P1 given different types of structural information, Heinerman (1977) treated the position vector of the group of correctly placed atoms as a primitive random variable, thereby treating this group in the same way as the group of correctly oriented but randomly positioned atoms. In the approach adopted by Giacovazzo (1983), the position vectors of the randomly positioned atoms were regarded as the primitive random variables and the position vector of the group of correctly positioned atoms was not.…”

“…Case (d) was reconsidered by Giacovazzo (1983) and new mathematical formulae were obtained by a proper use of a priori information. Heinerman's (1977) approach can exploit different types of a priori information, but the allowed size of the group of atoms with known position is limited whereas Giacovazzo's (1983) approach does not exploit different types of a priori information but has no limit on the size of the group of atoms with known position.…”

“…A mathematical derivation of this formula was given by Heinerman (1977). Case (d) was reconsidered by Giacovazzo (1983) and new mathematical formulae were obtained by a proper use of a priori information.…”

“…In the first part of the paper we will combine the approach of Heinerman (1977) with that of Giacovazzo (1983) and calculate the probability distribution of a triplet-invariant phase given a priori information. In the second part the sign ambiguity in the SIR case will be resolved by exploiting a priori information using the results of the first part of the paper.…”

“…In the second part the sign ambiguity in the SIR case will be resolved by exploiting a priori information using the results of the first part of the paper. Heinerman (1977) [HI will be used throughout this paper. The structure factor Fh is defined by…”