Extinction correction and synchrotron radiation

Abstract

The primary extinction factor y_p is defined as the ratio of the integrated reflection from a coherently diffracting domain to the integrated kinematical reflection from the same domain. When y_p is larger than 0.5 it may be approximated by y_p = exp{−(αδ)2}, where α is about 0.5 andδ the average size of the coherent domain when measured in units of the extinction length A,δ = D/λ.

Transfer equations are applied to symmetrical Laue diffraction, and the reflectivity per unit length, Σ(ε) is solved from the measured reflecting ratio as a function of the rocking angleε =θ− θ_B.

Measurements with conventional x-ray sources are made on single crystal slabs of Be and Si using AgKΒ, MoKα₁ and CuKα radiation. The primary extinction factor y_p(ε) is solved from a point-by-point comparison of two measurements where the extinction length λ is changed by varying the polarization and/or wavelength of the x-ray beam. The results show that primary and secondary extinction are strongly correlated, and that the customary assumption of independent size and orientation distributions of crystal mosaics is unjustified. The structure factors for Be and Si show close agreement with other recent measurements and calculations.

The limitations of the method are discussed in length, particularly the effects of beam divergences and incoherence of the rays in the crystal. It is concluded that under typical experimental conditions the requirements of the theory are met. Practical limitations arising from the use of characteristic wavelengths and unpolarized radiation prohibit the use of the full potential of the method.

The properties of a synchrotron radiation source are compared with a conventional x-ray source, and it is demonstrated that the experimental limitations can be removed by the use of synchrotron radiation. A diffraction experiment with synchrotron radiation is outlined, as well as generalization of the method to small spherical crystals.