High-resolution X-ray diffraction imaging of non-Bragg diffracting materials using phase retrieval X-ray diffractometry (PRXRD) technique

X-ray diffraction imaging of Al2O3 nanoparticles embedded in an amorphous matrix

“…The solution is to record the diffracted intensity as a function of the angular ͑momentum transfer͒ space coordinates. 7 Such diffraction data can be recorded using a crystal analyzer ͓Fig. 1͑b͔͒.…”

“…Since the diffraction patterns of objects, measured as a function of the angular direction in momentum transfer space, are virtually immune to sample vibrations there is no need for coherent radiation and unusual stability of the radiation source and/or sample, and there is no need for a beamstop to block the direct beam. 7,8 Use of a single photon counting detector ͑e.g., APD instead of charge coupled device, e.g., CCD͒ allows one to record data within a linear dynamic range of 8-9 orders of magnitude. The crucial central peak of the diffraction pattern is therefore readily measurable in this case.…”

Nanoresolution profiling of metal-metal interfaces from x-ray Fraunhofer diffraction data

“…11,12 The PRXRD technique allows reconstruction of both the phase and the modulus of radiation diffracted from an object using the experimentally recorded intensity distribution profile and thus recovery of the full complex transmission function ͑CTF͒ of the object irradiated by x-radiation. 12 Two sets of samples were prepared for the experiment. One comprised strips of aluminum and steel to create an Al-Fe interface, while the other comprised strips of aluminum and brass to create an Al-Cu/ Zn interface.…”

“…It is important to note that the method does not require a priori information for the reconstruction of the CTF, except analyticity of the complex diffraction amplitude. 11,12 The data analysis yields the product of the complex refractive index and the sample thickness in the direction of x-ray propagation from the reconstructed profile of the CTF. 12 Hence, use of a priori knowledge of the sample thickness allows the retrieval of profiles of the real and imaginary parts of the complex refractive index from the reconstructed phase and modulus of the CTF, respectively.…”

“…11,12 The data analysis yields the product of the complex refractive index and the sample thickness in the direction of x-ray propagation from the reconstructed profile of the CTF. 12 Hence, use of a priori knowledge of the sample thickness allows the retrieval of profiles of the real and imaginary parts of the complex refractive index from the reconstructed phase and modulus of the CTF, respectively. In the analysis of data collected at one radiation energy, as it was the case in this experiment, a priori knowledge of at least one of the refractive indices of materials forming the interface is required to choose the most plausible solution.…”