Defocusing for the Schulz Technique of Determining Preferred Orientation

Abstract

During measurement of preferred crystallographic orientation with the Schulz x-ray diffraction technique, several factors can cause defocusing. Earlier investigations showed that tilt of the specimen in Φ, the angle between the normal to the sample surface and the normal to the diffracting plane, is the most severe limitation for the Schulz reflection technique. The present study shows that this defocusing effect is strongly dependent on the size of the Bragg diffraction angle θ: The greater the Bragg angle, the smaller the decrease in intensity for a given tilt angle of Φ. On the other hand, the absorption coefficient μ of the sample has no influence on the decrease in intensity with increasing tilt in Φ, and its effect is negligibly small for most metals. Correction factors for the loss of intensity can be derived and have a general analytic form, but different coefficients are required for each goniometer setting.

Defocusing effects in the reflexion technique for the determination of preferred orientation

“…2). When the diffracted X-ray beam is no longer completely detected by the receiving slit, the measured intensity will be lower than the actual inten- gives the broadening of the Bragg peak (Tenckhof, 1970).…”

“…In practice, however, the beam is always more or less a divergent one and its angular width is controlled by the collimator and/or the main slits. Therefore, starting from a divergent beam, Tenckhof (1970) derived an expression for the broadening of the diffraction peak due to specimen tilt:…”

Correcting intensity loss errors in the absence of texture-free reference samples during pole figure measurement

“…The limitations of the X-ray optics meant that defocusing errors were highly sensitive to: (i) variations in the irradiated area and broadening of the diffracted peaks with increasing tilt angle, (ii) the Bragg angle, (iii) the inaccurate positioning of the sample in the Eulerian cradle and/or, (iv) the incorrect alignment of the goniometer itself [3][4][5][6][7]. The conventional method to eliminate defocusing errors is via a correction function (UI) involving the pole figure scanning of a texture-free reference sample with a peak position and width close to that of the sample under investigation 1 [1].…”

“…The conventional method to eliminate defocusing errors is via a correction function (UI) involving the pole figure scanning of a texture-free reference sample with a peak position and width close to that of the sample under investigation 1 [1]. Thus, for a given Bragg angle, the correction function is a measure of the change in the normalised intensity (UI = Iα=0-85°/ Iα=0°) with tilt angle [1,3,8]. Alternatively, analytical methods that correct for defocusing in the classical Schultz reflection geometry with incident crossed slits have also been developed by a number of authors [3,[9][10][11].…”

“…While the measured intensities (Imeas) are a function of both α and β angles, the background intensities (IBG) are mainly affected by the α-angle. Since the background intensities tend to remain stable for a given α-angle, they are typically measured on either side of a Bragg peak, averaged and subtracted from the measured intensities [1,3].…”