Reflection of X-rays from a rough surface at extremely small grazing angles.

Peculiarities of X-ray diffraction from a rough surface at an extremely small grazing angle of an incident beam are theoretically studied. The interrelation of four diffraction channels (coherent reflectance, coherent transmittance, diffuse scattering in vacuum, and scattering into the matter depth) is analyzed for different limiting cases (large and small correlation length of roughness and large and extremely small grazing angle of incident radiation). Both the Debye-Waller and the Nevot-Croce factors are demonstrated to describe improperly the features of X-ray diffraction at extremely small grazing angles. More appropriate simple analytic expressions for the specular reflectivity and total integrated scattering in vacuum are obtained instead. Transformation of one limiting diffraction regime into another one with variation in the correlation length of roughness is discussed.