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ªñ³êéæ¤ÉÈèCÜ½CñÜ­x©ç¼ÚC\Ê´qð¾é½ßÌV½ÈðÍè@Ì¤à­ÅéB±ÌðàÅÍC\Ê X üñÜÉæé\Ê\¢èÉÂ¢ÄC]Ìªè@CðÍ@ðTÏµ½ãCªèÌ¸
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2. \Ê X üñÜ»ðFig. 1é»ÊÅØfµ½êC»\¢ªÛ½ê½ÜÜÌz\ÊÍêÊÉsÀèÅC\Ê´qzñÌÄ\¬âiqÉað¶¶ÄæèSGlM[ªá­ÀèÈ\¢ðÆéBé¢ÍC´qzReection geometry for (a) out­of­plane, and (b) in­planesurface X­ray diraction. (c) Transmission geometry formore time­eective and precise data acquisition. Gray circles
denote Ewald spheres. Diraction conditions are satised
where either crystal truncation rods (CTRs) or fractional­
order rods (FORs) intersect the Ewald sphere.

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Fig. 2

Calculated intensity of crystal truncation rod (CTR) scatter­ing from a simple cubic crystal with a surface. Blue curve is
CTR intensity from an ideal crystal that surface atoms are in
the same positions as they would be in the bulk. Solid curveshows CTR intensity from a crystal in which the top layer isrelaxed inward by 7÷. The results demonstrate that CTR issensitive to a surface structure.

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Intensity map of in­plane diraction from a Si(111)_7~7.
Fractional­order reections are indicated by solid circles ofwhich area are proportional to the related structure factors.
Green circles denote integer­order reections. An irreduciblearea in symmetry is represented by blue lines. The inset
shows a typical rocking curve of the (6/7 0) in­plane reec­tion obtained in grazing incidence geometry. X­ray energy
used was 15 keV.

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The phase problem and perspectives of surface
X­ray diraction
Hiroo TAJIRI
Toshio TAKAHASHIJapan Synchrotron Radiation Research Institute,
1_1_1, Kouto, Sayo­cho, Sayo­gun, Hyogo 679_5198, Japan
Institute for Solid State Physics, University of Tokyo,
5_1_5, Kashiwanoha, Kashiwa­shi, Chiba 277_8581, Japan

Abstract The emergence of synchrotron radiation sources has accelerated the application of diraction
techniques to surface sciences. Surface X­ray diraction has become the state­of­the­art technique for deter­mining ordered structures of atoms on crystal surfaces. We introduce surface X­ray diraction briey from thehistorical point of view and describe the concept that not only determine constellation of surface atoms but
also view surface atoms as image. The progress in experimental and theoretical studies of surface X­raydiraction including crystallographic direct methods is reviewed.

úËõ May 2009 Vol.22 No.3  141