Premium
The phase problem for two‐dimensional crystals. I. Theory
Author(s) -
Arnal Romain D.,
Millane Rick P.
Publication year - 2017
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273317013687
Subject(s) - phase problem , uniqueness , phaser , a priori and a posteriori , envelope (radar) , diffraction , phase (matter) , crystal (programming language) , series (stratigraphy) , ab initio , set (abstract data type) , crystallography , direct methods , materials science , molecular physics , physics , statistical physics , computational physics , chemistry , computer science , optics , mathematics , mathematical analysis , quantum mechanics , telecommunications , philosophy , radar , paleontology , epistemology , biology , programming language
Properties of the phase problem for two‐dimensional crystals are examined. This problem is relevant to protein structure determination using diffraction from two‐dimensional crystals that has been proposed using new X‐ray free‐electron laser sources. The problem is shown to be better determined than for conventional three‐dimensional crystallography, but there are still a large number of solutions in the absence of additional a priori information. Molecular envelope information reduces the size of the solution set, and for an envelope that deviates sufficiently from the unit cell a unique solution is possible. The effects of various molecular surface features and incomplete data on uniqueness and prospects for ab initio phasing are assessed. Simulations of phase retrieval for two‐dimensional crystal data are described in the second paper in this series.