Wolfgang Baumann

Kinetics of the allotropic hcp-fcc phase transformation in cobalt.

The allotropic, martensitic phase transformation (hcpu2009→u2009fcc) in cobalt was investigated by differential scanning calorimetry (DSC) upon isochronal annealing at heating rates in the range from 10u2009Ku2009min−1 to 40u2009Ku2009min−1. The microstructural evolution was traced by optical microscopy and X-ray diffractometry. The kinetics of the phase transformation from hcp to fcc Co upon isochronal annealing was described on the basis of a modular phase transformation model. Appropriate model descriptions for athermal nucleation and thermally activated, anisotropic interface controlled growth tailored to the martensitic phase transformation of Co were implemented into the modular model. Fitting of this model of phase transformation kinetics to simultaneously all isochronal DSC runs yielded values for the energy of the interface separating the hcp and fcc Co phase and the activation energy for growth.

Layer-stacking irregularities in C36-type Nb–Cr and Ti–Cr Laves phases and their relation with polytypic phase transformations

Specific layer-stacking irregularities have been identified in C36 (4H) Nb–Cr and Ti–Cr Laves phases on the basis of X-ray diffraction line-profile analysis and high-resolution transmission electron microscopy. Domain boundaries and transformation errors within domains could be distinguished. The layer-stacking irregularities in both C36-NbCr2 and C36-TiCr2 can be associated with a preceding C14 (2H) → C36 (4H) phase transformation carried out by glide of mobile synchro-Shockley partial dislocation dipoles in an ordered fashion. The stacking irregularities observed can be interpreted as deviations from such perfect “ordered glide”. The interpretation is supported by the observation that, in the case of C36-NbCo2, where no preceding C14 → C36 transformation occurs, different layer-stacking irregularities are observed.

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 4u2005µm) were determined by employing X-ray diffraction stress measurements at constant information depths in the range between 200 and about 1500u2005nm. 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 Cuu2005Kα 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.

Mechanical stress gradients in thin films analyzed employing X-ray diffraction measurements at constant penetration/information depths

Stress gradients have been investigated employing a measurement strategy for diffraction measurements at constant penetration/information depths. Two examples have been considered: (i) sputter-deposited copper thin films on silicon wafers and (ii) γ’-Fe4N1-x layers on α-Fe substrates obtained by gaseous nitriding. In the Cu thin films rather low tensile stresses, increasing in magnitude with increasing penetration/information depth have been found. An evaluation of the measured lattice strains has been performed on the basis of the f(ψ) method, where the X-ray elastic constants (XEC’s) have been calculated as weighed averages of the corresponding Voigt and Reuss XEC’s and the weighing parameter has been taken as a fitting parameter. This evaluation reveals that the grain interaction changes with increasing penetration/information depth from near-Reuss type towards Neerfeld-Hill type. In the γ’-Fe4N1-x layers stress gradients occur due to surface relaxation near the surface and deeper in the layer due to a nitrogen concentration gradient which is built up during nitriding. First measurements in a laboratory diffractometer show the effect of surface relaxation on the stress-depth profile near the surface. As no single-crystal elastic constants are available for γ’-Fe4N1-x, the mechanical elastic constants have been employed in diffraction stress analysis. The results indicated that single-crystal elastic anisotropy occurs. From the measured data also a concentration – depth profile has been deduced.

An X-ray diffraction method to determine stress at constant penetration/information depths

A rigorous strategy for (X-ray) diffraction stress measurements at fixed penetration/information depths is described. Thereby errors caused by lack of penetration-depth control in traditional (X-ray) diffraction (sin2ψ) measurements are annulled. The ranges of accessible penetration/information depths and experimental aspects are briefly discussed. The power of the method is illustrated by the analysis of an only small stress gradient in a sputter-deposited nickel layer.