Influence of x-ray beam spatial coherence on the diffuse scattering from multilayer mirrors

Abstract

The improved spatial coherence of a synchrotron radiation beam was shown experimentally to stimulate additional diffuse scattering of x rays diffracted from x-ray multilayer mirrors. Although the large-scale (tens of microns) roughness does not affect Bragg diffraction from multilayers, its presence causes phase shifts at the wave packet front. This leads to partial decay of the coherent wave packet and creates additional diffuse scattering. Additional scattering from this mechanism was observed at angles of incidence corresponding to the Bragg and Kiessig maximum angles. The properties of this scattering caused by large-scale roughness, observed due to improved x-ray beam spatial coherence, were shown experimentally to be different from those of diffuse scattering previously reported when the incoming or outgoing angle is equal to the Bragg angle. Typical breaks in the diffuse scattering intensity due to the standing-wave effect are absent, and there is obvious asymmetry of the diffuse scattering cross section around the incoming and outgoing angles. Due to the small angle of incidence, the coherently irradiated area has very different dimensions parallel and perpendicular to the beam, which leads to the observed scattering being concentrated in the specular diffraction plane defined by the incident and reflected wave vectors.

Decoherence phenomenon in X-ray diffraction and scattering from rough multilayers

“…Nevertheless, in the experiment we have repeatedly observed the violation of the reciprocity principle [3][4][5]. The main reason of this violation can be well illustrated by the following.…”

“…[4] we have studied in detail the origin of the ''incoming'' streaks by an example of the firstorder Bragg reflection from a W/Si multilayer mirror including the direct measurements depend upon the spatial coherence of incident X-ray beam. The data obtained allow us to conclude as deposited (upper); at 710 K (lower).…”

Resonant soft x-ray reflectivity of organic thin films

“…Hence, the measured roughness will depend on the transverse coherence length and the instrumental geometry. 40 For the instruments used in this work, we derived the following coherence lengths: XR at X10B, NSLS, had a transverse coherence length t of ϳ1 m; NR at NG7, NIST, had a transverse coherence length of ϳ20 m; and RSoXR at ALS BL6.3.2 had a transverse coherence length of ϳ80 m. Due to the various degrees by which the in-plane coherence length changes during the data acquisition on account of the sample rotation and possible slit width changes, a rigorous, direct and quantitative comparison of this parameter between the different tools is presently not possible. However, for many studies these systematic differences are not very important since it is often the differences measured between a set of samples analyzed with the same instrument that is most relevant.…”

The fine structure of X-ray diffuse scattering in the vicinity of high-angle superlattice Bragg reflections

“…It is not so clear as in the previous case that the second and third terms in (5) generate another type of resonant diffuse scattering. It is quasi-specular diffuse scattering (Chernov et al, 2002). 1 Indeed, in spite of the fact that, according to the de®nition, hÁVri 0 the amplitude Rz is an approxi-mately linear function of z if the angle of incidence is quite far from the Bragg angle and zÁVrdz T 0.…”

“…For the first time this problem was rose by Sinha et al [21]. In our previous work [20] the high spatial coherence of modern SR sources was shown experimentally to involve the long-range interfacial defects into diffraction. In turn, the longrange defects increase the diffuse scattering cross section drastically [22].…”