Crystallographic direct methods for surfaces

A brief review is given of the status of crystallographic direct methods for solving surface structure problems. The basic concepts of using the a priori information that the scattering comes from atoms to generate self-consistent equations and statistical constraints upon the phases are described. The use of a genetic algorithm to perform a search over possible phases is then discussed. Finally, solved cases in projection as well as the status of three-dimensional solutions for surfaces with a representative example are detailed.

[1]  C. Giacovazzo.  Direct Methods in Crystallography , 1980 .

[2]  D. Sayre.  The squaring method: a new method for phase determination , 1952 .

[3]  Ferrer,et al.  Study of C60/Au(110)-p(6x5) reconstruction from In-plane X-Ray diffraction data , 2000, Physical review letters.

[4]  L. Marks,et al.  STRUCTURE DETERMINATION OF THE Ge(111)-(3×1)Ag SURFACE RECONSTRUCTION , 1999 .

[5]  L. Marks.  GENERAL SOLUTION FOR THREE-DIMENSIONAL SURFACE STRUCTURES USING DIRECT METHODS , 1999 .

[6]  L. Marks,et al.  A feasible set approach to the crystallographic phase problem. , 1999, Acta crystallographica. Section A, Foundations of crystallography.

[7]  S. Ferrer,et al.  Application of the ‘direct methods’ difference sum function to the solution of reconstructed surfaces , 1999 .

[8]  L. Marks,et al.  Determination and refinement of the Ag/Si(111)−(3×1) surface structure , 1998 .

[9]  L. Marks,et al.  IMAGING SURFACE STRUCTURES BY DIRECT PHASING , 1997 .

[10]  Laurence Marks,et al.  Multi-Solution Genetic Algorithm Approach to Surface Structure Determination Using Direct Methods , 1997 .

[11]  M. Woolfson,et al.  Physical and Non-Physical Methods of Solving Crystal Structures , 1995 .

[12]  L. Marks,et al.  CYCLIC OZONE IDENTIFIED IN MAGNESIUM OXIDE (111) SURFACE RECONSTRUCTIONS , 1998 .

[13]  L. Marks,et al.  Direct solutions of the Si(111) 7 × 7 structure , 1997 .

[14]  L. Marks,et al.  Structural investigations of metal–semiconductor surfaces , 1999 .

[15]  A. Wilson,et al.  Determination of Absolute from Relative X-Ray Intensity Data , 1942, Nature.

[16]  A. Wilson,et al.  The probability distribution of X-ray intensities , 1949 .

[17]  Laurence Marks,et al.  DIRECT METHODS FOR SURFACES , 1998 .

[18]  S. Heun,et al.  Application of x-ray direct methods to surface reconstructions: The solution of projected superstructures , 1998 .

[19]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[20]  L. Marks,et al.  Structure of the TiO2−x(100)-1×3 surface by direct methods , 1998 .

[21]  O. Bunk,et al.  Subsurface dimerization in III-V semiconductor (001) surfaces. , 2001, Physical review letters.

[22]  M. Woolfson.  Direct Methods from Birth to Maturity , 1987 .

[23]  Jordi Rius,et al.  In-Plane X-Ray Diffraction Study of the C60/Au(110) p(65) Reconstructed Surface by Direct Methods , 1999 .

[24]  N. Erdman,et al.  Solution of the p(2 2) NiO(1 1 1) surface structure using direct methods , 2000 .

[25]  L. Marks,et al.  A minimum-entropy algorithm for surface phasing problems , 1998 .

[26]  L. Marks,et al.  Direct methods determination of the Si(111)-(6 × 6)Au surface structure , 1998 .

[27]  L. Marks,et al.  Solution of Ge(111)-(4×4)-Ag structure using direct methods applied to X-ray diffraction data , 1998 .

[28]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[29]  L. Marks,et al.  Au 6 × 6 on Si(111):. Evidence for a 2D Pseudoglass , 1998 .