Department Microstructure and Residual Stress Analysis

Offered thesis

Master thesis (in materials science or physics) on the topic: "Compensation of mechanical residual stresses in technological semiconducting metallic layers" at Helmholtz-Zentrum Berlin for Materials and Energy (HZB) and Leibniz Institute for Innovative Mikroelectronic (IHP)  Please read here further details - in German -

Current theses

“Sin²Psi-based high spatial resolution residual stress gradient analysis by energy-dispersive synchrotron diffraction”

Application of very small gauge volume dimensions

(a) for the local analysis of steep in-plane residual

stress depth gradients (b) using sin²ψ-based energy-

dispersive Synchrotron X-ray diffraction (c)

considering the absorption of the material and the

gauge volume geometry in a 2D fit.

Matthias Meixner

X-ray diffraction carried out in reflection geometry is a powerful tool to reveal near surface residual stresses of polycrystalline materials. The application of the sin²ψ-measuring-technique in combination with evaluation methods that offer the possibility to reconstruct depth gradients, like the multiwavelength- or the universal-plot-approach for instance, yields reliable results. However, for intensity reasons in many cases large beam cross-sections are used for the experiments, resulting in large gauge volumes and thus the lateral resolution available is poor. For investigations being focused on the local analysis of residual stresses it is necessary therefore, to decrease the gauge volume dimensions. Consequently the lateral resolution is improved, but, as an ancillary effect, the height of the gauge volume may be in the range of the natural information depth τ of the X-rays. Hence, the effective information depth , to which the diffraction signal has to be assigned to, is determined by the material’s absorption as well as by the shape and the size of the gauge volume, while only absorption is relevant if conventional large measuring probes are implemented. Therefore, the influence of the gauge volume geometry on the analysis of steep near surface residual stress gradients by means of energy-dispersive synchrotron diffraction is studied. It is shown that the ratio between τ and the part of the gauge volume height which is immersed into the sample h^GV represents the crucial parameter shaping the d_ψ^hkl-sin²ψ distributions obtained in the Ψ-mode of X-ray stress analysis. Because the superposition of absorption and gauge volume geometry can lead to ambiguities in the conventional plot of the LAPLACE stresses vs. the information depth , a modified mathematical treatment based on a two dimensional least squares fit procedure is proposed for evaluating near surface residual stress depth gradients. The validity of this approach is demonstrated by simulations as well as by the experimental analysis of the very steep in-plane residual stress depth gradient in a shot-peened Al₂O₃ ceramic sample.

"Local structural changes in cathode materials for rechargeable Li-ion batteries studied using X-ray Absorption Spectroscopy"

Jatinkumar K. Rana

Local structural changes in the Li₂MnO₃, LiMn_0.4Ni_0.4Co_0.2O₂, 0.5 Li₂MnO₃ · 0.5 LiCoO₂ and 0.5 Li₂MnO₃ · 0.5 LiMn_0.4Ni_0.4Co_0.2O₂ cathodes are investigated using the X-ray ab­sorption spectroscopy (XAS). Qualitative information about the average valence state of the absorbing atom and changes in the local coordination symmetry are estimated from the near-edge region (XANES) of the absorption spectra, while geometrical changes in the local structure around the absorbing atom are quantified by fitting the extended region of the absorption spectra (EXAFS) with theoretical models. By fitting the EXAFS data, I provide direct evidence for the charge compensation by each of the transition metal (TM) ions upon lithium extraction and/or re-insertion and associated structural changes. The electrochemical processes in the Li₂MnO₃ cathode are complex and non-conventional. Both oxygen-loss and ion-exchange mechanisms play a significant role during the activa­tion of the cathode. Lithium extraction occurs with the concurrent removal of oxygen, giving rise to the formation of MnO₂-type structure (R-3m), while the presence of protons in the interslab region, as a result of Li⁺-H⁺ exchange, alters the stacking sequence of oxygen layers from O3-type to P3-type. Lithium re-insertion reverts the P3-type stacking sequence back to the O3-type, giving rise to formation of Li₂MnO₃-type structure which is oxygen deficient. Oxygen removal occurs only during the activation of material and at slower rates. Upon subsequent cycling, charge compensation occurs by the Li⁺ ↔ H⁺ exchange only, with the structural flip-over between P3-type ↔ O3-type. The repetitive changes in the stacking sequence during each cycle are responsible for the structural degradation, and in turn fading electrochemical performance of Li₂MnO₃ upon cycling. Lithium extraction/re-insertion from/into the LiMn_0.4Ni_0.4Co_0.2O₂ cathode occurs in the conventional way via oxidation/reduction of its TM ions. However, deep delithiation re­sults in an irreversible transition of the O3 structure to the O1-type structure. There is no solubility between the two components of the composite 0.5 Li₂MnO₃ · 0.5 LiCoO₂ cathode. However, there are some indications of solubility between two components of the 0.5 Li₂MnO₃ · 0.5 LiMn_0.4Ni_0.4Co_0.2O₂ cathode. Both components of the composite cathode respond to the electrochemical activation in their own unique ways. Li₂MnO₃ domains act as a source of excess lithium above 4.4 V and protects LiMO₂ (M=Mn, Ni or Co) component from complete delithiation and deteriorating structural changes.

"Analysis of diffraction line-broadening and diffraction-line shifts by RIETVELD refinement of energy-dispersive synchrotron diffraction patterns"

Fig.: Result of the Rietveld-refinement of
an energy-dispersive diffraction pattern of a
CeO₂ powder sample, recorded under 2θ = 10°.

Daniel Apel

The energy-dispersive diffraction patterns contain a variety of information about the structural material properties. However, until now the wealth of information included in energy-dispersive diffraction patterns has not been fully accessed. To exploit the amount of provided information and also to use the essential advantage of the method compared with angle-dispersive diffraction, which lies in the fast measurement of complete diffraction patterns in well-defined but arbitrary scattering directions, a Rietveld refinement program code has been developed to analyze energy-dispersive diffraction data. The aim of this project is to handle energy-dispersive diffraction data sets measured in various orientations (j,y) in such a way that models describing the depth dependence of the phase specific residual stresses, of domain size as well as of microstrain can be refined simultaneously. To analyze line-broadening observed in the energy-dispersive diffraction patterns, evaluation procedures applied so far in angle-dispersive diffraction were adapted to the energy-dispersive case. A model to separate size and strain broadening is introduced. It is shown that even though the instrumental resolution of the energy-dispersive diffraction is inferior compared to the most angle-dispersive diffraction instruments, line-broadening assignable to microstructural effects can still be observed. Concerning the evaluation of macro residual stress depth gradients in the near-surface region of quasi-isotropic polycrystalline materials by means of Rietveld refinement, the formalism is applied to mechanically surface treated samples with well-defined in-plane residual stress distributions within the accessible information depth of the X-rays. The results are compared with those obtained by means of the “real space” and the conventional “Laplace space” methods.

Skalen- und methodenübergreifende Analyse randschichtnaher Eigenspannungsverteilungen in vielkristallinen Werkstoffen und Bauteilen

Tillman Fuß