M. Wohlschlögel

Local, submicron, strain gradients as the cause of Sn whisker growth.

It has been shown experimentally that local in-plane residual strain gradients occur around the root of spontaneously growing Sn whiskers on the surface of Sn coatings deposited on Cu. The strain distribution has been determined with synchrotron white beam micro Laue diffraction measurements. The observed in-plane residual strain gradients in combination with recently revealed out-of-plane residual strain-depth gradients [M. Sobiech et al., Appl. Phys. Lett. 93, 011906 (2008)] provide the driving forces for whisker growth.

Crystallite size dependence of the coefficient of thermal expansion of metals

The coefficients of thermal expansion (CTEs) of polycrystalline Ni and Cu thin films have been investigated by employing temperature-dependent x-ray diffraction measurements of lattice parameters. Great care has been taken to exclude effects of, in particular, microstructural relaxation and mechanical stresses on the dependences of the lattice parameters on temperature. The CTEs determined in the as-deposited condition, characterized by grain sizes in the range of 25–35nm, are considerably (about 10%) larger than the corresponding literature values of bulk materials. Heat treating the specimens at moderate temperatures induced grain growth and decrease of the crystalline imperfection. After the heat treatment, the CTEs determined for the thin films had reduced considerably and had become equal to (Ni) or approached (Cu) the corresponding literature data for bulk materials.

Large excess volume in grain boundaries of stressed, nanocrystalline metallic thin films: Its effect on grain-growth kinetics

The excess volumes per unit grain-boundary area of nanocrystalline Pd and Ni thin films were measured by an efficacious method based on real time in situ x-ray diffraction measurements. The obtained large values for the grain-boundary excess volume reveal the background of surprising, yet unexplained observations of grain growth in nanocrystalline materials.

Application of a single-reflection collimating multilayer optic for x-ray diffraction experiments employing parallel-beam geometry

Instrumental aberrations of a parallel-beam diffractometer equipped with a rotating anode X-ray source, a single-reflection collimating multilayer optic and a parallel-plate collimator in front of the detector have been investigated on the basis of standard measurements (i.e. employing stress- and texture-free isotropic powder specimens exhibiting small or negligible structural diffraction line broadening). It has been shown that a defocusing correction, which is a major instrumental aberration for diffraction patterns collected with divergent-beam (focusing) geometries, is unnecessary for this diffractometer. The performance of the diffractometer equipped with the single-reflection collimating multilayer optic (single-reflection mirror) is compared with the performance of the diffractometer equipped with a Kirkpatrick–Baez optic (cross-coupled Gobel mirror) on the basis of experimental standard measurements and ray-tracing calculations. The results indicate that the use of the single-reflection mirror provides a significant gain in photon flux and brilliance. A high photon flux, high brilliance and minimal divergence of the incident beam make the setup based on the single-reflection mirror particularly suitable for grazing-incidence diffraction, and thus for the investigation of very thin films (yielding low diffracted intensities) and of stress and texture (requiring the acquisition of large measured data sets, corresponding to the variation of the orientation of the diffraction vector with respect to the specimen frame of reference). A comparative discussion of primary optics which can be used to realise parallel-beam geometry shows the range of possible applications of parallel-beam diffractometers and indicates the virtues and disadvantages of the different optics.

Calibration of a heating/cooling chamber for X-ray diffraction measurements of mechanical stress and crystallographic texture

Methods have been developed for the calibration of specimen temperature and of specimen displacement caused by the thermal expansion of the specimen holder in a heating/cooling chamber equipped with a strip or plate heater mounted on an X-ray diffractometer. For the temperature calibration two methods were proposed. One method relies on X-ray diffraction measurements of thermal lattice strains, whereas the other method is based on resistance thermometry. The method proposed for the determination of the temperature-dependent specimen displacement is based on the measurement of diffraction-line positions of the specimen employing two diffraction geometries, one being sensitive to the specimen displacement and the other being insensitive to the specimen displacement. The thermal displacement of the specimen due to thermal expansion of the specimen holder is significant and was determined as about 38 μm per 100 K.

Unexpected formation of ε iron nitride by gas nitriding of nanocrystalline α-Fe films

Polycrystalline iron thin films exhibiting different crystallite sizes, which were deposited on α-Al2O3 substrates by molecular beam epitaxy, were nitrided in a NH3∕H2 gas mixture. After different nitriding treatments the specimens were prepared and analyzed by focused ion beam microscopy and x-ray diffraction. It was found that formation of e-Fe3N1+x occurs upon nitriding of specimens exhibiting a small crystallite size at values of the thermodynamic nitriding parameters for which pure γ′-Fe4N1−x is predicted to form according to bulk thermodynamics. This unexpected phenomenon is explained as a consequence of the nanocrystalline nature on the thermodynamics of the binary system iron-nitrogen.

Determination of depth gradients of grain interaction and stress in Cu thin films.

Grain-interaction and residual stress depth gradients in a sputter-deposited Cu thin film (thickness 4 µm) were determined by employing X-ray diffraction stress measurements at constant information depths in the range between 200 and about 1500 nm. A novel procedure, which allows the determination of an effective grain-interaction parameter on the basis of the f(ψ, hkl) method and the Voigt and Reuss models of elastic grain interaction, was used. The range of accessible penetration depths was maximized by employing different photon energies using a laboratory diffractometer with Cu Kα radiation and a diffractometer at a synchrotron beamline. The variation of grain interaction with depth could be successfully related to the microstructure of the specimen. The tensile residual stress in the film parallel to its surface decreases with decreasing depth. By measuring the lattice spacing for several reflections at one penetration depth with two different photon energies (i.e. using small and large incident beam angles) it was found that the surface roughness of the specimen counteracts the effect of beam refraction to some degree. As a consequence, irrespective of whether a refraction correction is applied or neglected for the low-incidence angle measurement, erroneous results are obtained for lattice spacings derived from reflections at small incidence angles; reliable grain-interaction and stress analysis requires measurements at high incidence angle.

Residual stress and strain-free lattice-parameter depth profiles in a γ’-Fe4N1-x layer on an α-Fe substrate measured by X-ray diffraction stress analysis at constant information depth

The residual stress and lattice-parameter depth profiles in a γ′-Fe 4 N 1- x layer (6-μm thickness) grown on top of an α-Fe substrate were investigated using x-ray diffraction stress analysis at constant penetration depths. Three different reflections (220, 311, and 222) were recorded at six different penetration depths using three different wavelengths. At each penetration depth, x-ray diffraction stress analysis was performed on the basis of the sin 2 ψ method. As a result, the residual-stress depth profile was obtained from the measured lattice strains. The lattice spacings measured in the strain-free direction were used to determine the (strain-free) lattice-parameter depth profile. The nitrogen-concentration depth profile in the layer was calculated by applying a relationship between the (strain-free) γ′ lattice parameter and the nitrogen concentration. It was found that the strain-free lattice-parameter depth profile as derived from the 311 reflections is best compatible with nitrogen concentrations at the surface and at the γ′/α interface as predicted on the basis of local thermodynamic equilibrium. It could be shown that the 311 reflection is most suitable for the analysis of lattice-parameter and residual stress depth profiles because the corresponding x-ray elastic constants exhibit the least sensitivity to the type of and changes in grain interaction. The depth-dependence of the grain interaction could be revealed. It was found that the grain interaction changes from Voigt-type near the surface to Reuss-type at the layer/substrate interface.

Grain growth in nanocrystalline copper thin films investigated by non-ambient X-ray diffraction measurements

The microstructure evolution (crystallite size and microstrain) as well as the residual stress of Cu thin films of various thicknesses (250 nm, 500 nm, and 1 μm) on passivated Si substrates during isochronal annealing was investigated by in situ X-ray diffraction measurements in the temperature range between 25 °C and 250 °C. Before annealing, the thermoelastic behavior was investigated excluding the occurrence of thermally activated relaxation processes occurring above ambient temperature by in situ stress measurements below ambient temperature. On this basis, above ambient temperature, effects of stress relaxation and emerging secondary stresses (due to grain growth and annihilation of crystal defects, giving rise to a considerable tensile stress contribution development) could be identified for all three layers in the temperature regime between ambient temperature and 250 °C. Grain growth in the nanocrystalline thin films started at much lower temperatures as compared to coarse-grained materials. The results were discussed in terms of the effects of different driving forces and grain-boundary mobilities acting in nanocrystalline materials.