Measurement of Residual Strains with High Depth Resolution by Energy-Variable Diffraction on Synchrotron Beam Lines

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Measurement of Residual Strains with High Depth Resolution by Energy-Variable Diffraction on Synchrotron Beam Lines E. Zolotoyabko, B. Pokroy, and J. P. Quintana1 Department of Materials Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel. 1 Northwestern University, DND-CAT, APS/ANL Sector 5, Building 432A, 9700 South Cass Avenue, Argonne, IL 60439-4857, U.S.A.

ABSTRACT An energy-variable synchrotron diffraction technique is established as a novel method for depth-resolved measurements of d-spacings and residual strains in polycrystalline structures. The depth sensitivity is achieved by the controlled changing the x-ray energy and, hence, the x-ray penetration into the sample. Quasi-parallel synchrotron radiation being diffracted at different depths deviates differently from the detector axis. As a result, the maximum diffraction intensity recorded in the detector is coming from a certain depth, which is energy dependent. This finding opens a way for strain measurements with high depth resolution by changing the x-ray energy in small enough steps. The developed technique is applied to characterize the electrodeposited Cu/Ni multilayers.

INTRODUCTION Characterization of the microstructure of materials with high spatial resolution is one of key issues of nano-science and nano-technology. Despite recent achievements of x-ray microscopy (see Ref. [1] and references therein), high depth resolution in x-ray diffraction measurements is still a problem since x-rays interact much weaker with materials, as compared to electrons, and their penetration depths are much larger. As partial solution, we are developing novel x-ray diffraction technique for synchrotron beam lines – energy-variable diffraction (EVD) [2-6]. An initial idea behind this method is rather simple, viz. to precisely change an energy of synchrotron radiation by double-crystal monochromator and, thus, to accurately control the x-ray penetration depth. Detailed analysis [6] of the x-ray trajectories, including the initial misalignment of the diffraction instrument as well as the energydependent changes in the x-ray penetration depth and in the height of the x-ray beam issuing from the double-crystal monochromator, showed that x-rays diffracted at different depths enter the detecting system at slightly different angles with respect to its axis. As a result, these x-rays are registered in the detector with different probabilities. Taking into account the exponential attenuation of the x-ray beams in depth, allowed us to conclude that maximum diffraction intensity recorded in the detector is coming from a certain depth, which is energy dependent (see next section). This finding opens a way for strain analysis with high depth resolution by precise measurements of the diffraction peak positions at different x-ray energies varied in small enough steps. Recently, by using this approach we were able to extract residual strains across the alumina/zirconia bilayer and found significant strain modifications near the alumina/zirconia interfa