Automatic X-ray crystallographic phasing at LNLS S.L. Morelha ˜o a, * , L.H. Avanci a , S. Kycia b a Instituto de Fı ´sica, Universidade de Sa ˜o Paulo, CP 66318, 05315-970 Sa ˜oPaulo, SP, Brazil b Laborato ´ ria Nacional de Luz Sı ´ncrotron, LNLS, CP 6192, 13084-971 Campinas, SP, Brazil Available online 1 August 2005 Abstract Phase invariants are important pieces of information about the atomic structures of crystals. Several mathematical methods in X-ray crystallography are used to estimate phase invariant values. Multiwave diffraction experiments offers a unique opportunity for physically measuring phase invariants. In this work, the underneath principals for developing an automatic procedure to measure phase-invariant values are described. A general systematic procedure is demon- strated, in practice, by analyzing intensity data from a KDP crystal. Ó 2005 Elsevier B.V. All rights reserved. PACS: 61.10.Nz Keywords: Three-beam X-ray diffraction; Triplet phase invariants; Physical-phasing crystallography 1. Introduction In X-ray crystallography, the phases of the dif- fracted waves are estimated by mathematical methods, generally known as Direct Methods [1], for analyzing intensity data sets composed of a large number of reflections. These methods exploit algebraic or probabilistic relationships among the phase values, some of which are the triplet phase invariants. Physical measurements of such phase invariants are of great interest since, in principle, they could improve or extend the efficiency of the Direct Methods to complex structures such as proteins. It would have to be compared to other procedures that are actually used to the same pur- poses, such as Multiple Anomalous Dispersion and Multiple Isomorphous Replacement [2]. Triplet phase invariants (or just phase unless specified) are physical quantities accessible via three-beam diffraction (3BD) experiments [3,4] where the interference of simultaneously diffracted wavefields provide information on phase values. Experimental and analytical difficulties are still in- volved in phase determination, such as the reduce 0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.06.044 * Corresponding author. Address: Depto. de Fı ´sica Aplicada, Universidade de Sa ˜o Paulo – USP, Rua do Mata ˜o, Travessa R, 187, 05508-970 Sa ˜o Paulo, SP, Brazil. Tel.: +55 11 3091 6807; fax: +55 11 3091 6749/6807. E-mail address: morelhao@if.usp.br (S.L. Morelha ˜o). Nuclear Instruments and Methods in Physics Research B 238 (2005) 180–184 www.elsevier.com/locate/nimb