Effects of analyser deformation in scanning x-ray interferometry

Mana, Giovanni; Palmisano, Carlo; Zosi, G.

doi:10.1088/0026-1394/41/4/003

Cited by 30 publications

(10 citation statements)

References 23 publications

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“…Additionally, the figures exemplify that peak shifts, and consequently Á, are independent of the surface geometry (flat or cylindrical, concave or convex), but they depend only on the entrance-surface strain Ád=d. This confirms that the flat-surface approximation used by Mana et al (2004a) was admissible. To check further our numerical computations, we also examined two auxiliary cases, when the Bragg planes are simply either contracted or expanded and when the Bragg planes are not distorted.…”

Section: Figuresupporting

confidence: 77%

“…We have studied X-and -ray propagation in flat and cylindrically bent crystals. We have used the relevant results to describe the operation of a Laue-Laue diffractometer consisting of a flat collimating crystal and a bent analyzer crystal and we have extended the results of a previous investigation of ours (Mana et al, 2004a). We have described the distortion characterized by a constant strain gradient in crystals having flat or cylindrical surfaces.…”

Section: Discussionmentioning

confidence: 96%

“…We shall consider two distortions, u fan;1 ðx; zÞ and u fan;2 ðx; zÞ, describing cylindrically bent crystals according to the finiteelement simulation (Mana et al, 2004a). If we exclude the term u fan;i z ðx; zÞẑ z, which is orthogonal to h 0 , we have two pure displacements in the x direction: fan-down,…”

Section: Lattice Distortionmentioning

confidence: 99%

“…The profiles obtained numerically, without any approximation as we shall shortly discuss in x5, are symmetric and validate the above approximation. Mana et al (2004a) report that, in the presence of a constant strain gradient in the analyzer, the Laue-Laue rocking curve is shifted by ðÁd=dÞ tan B , where the lattice strain is evaluated on the crystal surface. However, this peak shift is not easily measurable.…”

Section: Research Papersmentioning

confidence: 99%

“…The expression in (45) can be found in Authier & Simon (1968). In the numerical simulation we considered the two sets of parameters shown in Table 1; the lower-energy value refers to the experimental set-up described by Mana et al (2004a), the upper by Massa et al (2005). We have considered silicon (220) Bragg planes and have taken the values of the dielectric susceptibilities from Sergey Stepanov's X-ray Server (http://sergey.gmca.aps.anl.gov/).…”

Section: Numerical Simulationmentioning

confidence: 99%

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X-ray and γ-ray propagation in bent crystals with flat and cylindrical surfaces

et al. 2008

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In this paper we investigate x-ray and γ-ray propagation in crystals having a constant strain gradient and flat or cylindrical surfaces. When a displacement field is present, we solve the Takagi-Taupin equations either by the Riemann-Green method or by a numerical method. We apply the results to study the operation of a doublecrystal Laue-Laue diffractometer having a flat collimating crystal followed by a bent analyzer crystal. In particular, we examine the effect of the analyzer strain on the location of the diffraction peaks in the dispersive and non-dispersive setup, thus confirming our previously reported peak-location as being set only by the diffracting plane spacing on the analyzer entrance surface.

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Section: Figuresupporting

confidence: 77%

Section: Discussionmentioning

confidence: 96%

Section: Lattice Distortionmentioning

confidence: 99%

Section: Research Papersmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

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X-ray and γ-ray propagation in bent crystals with flat and cylindrical surfaces

et al. 2008

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Influence of surface stress in the determination of the (2 2 0) lattice spacing of silicon

Ferroglio¹,

Mana²,

Palmisano³

et al. 2008

Metrologia

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We have examined the influence of surface stress in the measurement of the (2 2 0) lattice plane spacing of a Si crystal by combined x-ray and optical interferometry. By means of a finite element simulation we have obtained first a quantitative description of various non-linear displacement fields of the diffracting planes; the simulation indicates that surface stress does not cause a significant difference between bulk and surface lattice spacing. Subsequently, to quantify the effect of the above fields on the period of the interference fringes, we have solved numerically the perturbed Takagi–Taupin equations; these results indicate that the fringe period is determined by the atom spacing on the crystal entrance surface, whereas, intuitively, we might have expected this period to be a kind of average of the (2 2 0) lattice plane spacing. To corroborate our numerical calculations, we have found analytical expressions which allow us to isolate the contribution of the non-linear superficial terms on the measurement of the plane spacing.

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Dynamical Theory of X-Ray Diffraction

Authier

2003

394

658

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X-ray diffraction is a major tool for the study of crystal structures and the characterization of crystal perfection. Since the discovery of X-ray diffraction by von Laue, Friedrich, and Knipping in 1912 two basic theories have been used to describe this diffraction. One is the approximate geometrical, or kinematical theory, applicable to small or highly imperfect crystals; it is used for the determination of crystal structures and the study of powders and polycrystalline materials. The other one is the rigorous dynamical theory, applicable to perfect or nearly perfect crystals and, for that reason, is the one used for the assessment of the structural properties of high technology materials. It has witnessed exciting developments since the advent of synchrotron radiation. This book provides an account of the dynamical theory of diffraction and of its applications. The first part serves as an introduction to the subject, presenting early developments, Ewald's theory of dispersion and the basic results of Laue's dynamical theory. This is followed in the second part by a detailed development of the diffraction and propagation properties of X-rays in perfect crystals, including the study of anomalous absorption, Pendellösung, grazing incidence diffraction (GID) and n-beam or multiple-beam diffraction. The third part constitutes an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchrotron radiation, location of atoms at surfaces and interfaces and X-ray diffraction topography.

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Effects of analyser deformation in scanning x-ray interferometry

Cited by 30 publications

References 23 publications

X-ray and γ-ray propagation in bent crystals with flat and cylindrical surfaces

X-ray and γ-ray propagation in bent crystals with flat and cylindrical surfaces

Influence of surface stress in the determination of the (2 2 0) lattice spacing of silicon

Dynamical Theory of X-Ray Diffraction

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