Absolute measurement of refractive index and structure factor in polycrystalline and crystalline wedges using anomalous X-ray transmission in perfect crystals

Abstract

Bragg and Laue diffraction methods can be combined to study the refractive index and structure factor of polycrystalline and crystalline thin metal wedges, within 1%, using anomalous transmission of travelling X-ray waves in a thick perfect single crystal of silicon {110}. Anomalous transmission occurs in a thick defect free absorbing crystal when the diameter point on the alpha branch is excited by a parallel beam of monochromatic X-rays. Travelling wave of σ polarisation connected to this point and the nearby Laue point has antinodes between the diffracting lattice planes and suffers much smaller absorption than in the normal case (μ ₀ t = 15), in going through a thick silicon perfect crystal. This method shows how by introduction of a thin wedge one can produce and measure (in absolute units) the shift in the position of Bragg and Laue diffracted Mo K(α) (17.4 keV) X-rays. Using Mo K(α) which has a low Bragg angle and a Si {220} symmetrical reflection, thin wedges can be sampled. The position of Bragg and Laue peaks from the centre of the rocking curve and the introduced change (in arcsec) gives refractive index and structure factor valueF ₀ of the test wedge. The index of refraction parameter 1−n of a 21.2° aluminium wedge was determined experimentally as 1.7×10⁻⁶.