E. J. Mittemeijer

Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction

The components of the macroscopic mechanical stress tensor of a stressed thin film, coating, multilayer or the region near the surface of a bulk material can in principle be determined by X-ray diffraction. The various analysis methods and measurement strategies, in dependence on specimen and measurement conditions, are summarized and evaluated in this paper. First, different X-ray diffraction geometries (conventional or grazing incidence) are described. Then, the case of macroscopically elastically isotropic, untextured specimens is considered: from the simplest case of a uniaxial state of stress to the most complicated case of a triaxial state of stress. The treatment is organized according to the number of unknowns to be determined (i.e. the state of stress, principal axes known or unknown), the use of one or several values of the rotation angle φ and the tilt angle ψ of the sample, and one or multiple hkl reflections. Next, the focus is on macroscopically elastically anisotropic (e.g. textured) specimens. In this case, the use of diffraction (X-ray) elastic constants is not possible. Instead, diffraction (X-ray) stress factors have to be used. On the basis of examples, it is demonstrated that successful diffraction stress analysis is only possible if an appropriate grain-interaction model is applied.

Analysis of solid state phase transformation kinetics: models and recipes

Abstract The progress of solid-state phase transformations can generally be subdivided into three overlapping mechanisms: nucleation, growth and impingement. These can be modelled separately if hard impingement prevails. On that basis, an overview has been given of recent numerical and analytical methods for determination of the kinetic parameters of a transformation. The treatment focuses on both isothermally and isochronally conducted transformations. To extend the range of transformations that can be described analytically, a number of more or less empirical submodels, which are compatible with experimental results, has been included in the discussion. It has been shown that powerful, flexible, analytical models are possible, once the concept of time or temperature dependent growth exponent and effective activation energy, in agreement with the existing experimental observations, has been adopted. An explicit (numerical) procedure to deduce the operating kinetic processes from experimental transformation-rate data, on the basis of different nucleation, growth and hard impingement mechanisms, has been demonstrated. Without recourse to any specific kinetic model, simple recipes have been given for the determination of the growth exponent and the effective activation energy from the experimental transformation-rate data.

Growth kinetics and mechanisms of aluminum-oxide films formed by thermal oxidation of aluminum

The growth kinetics and mechanisms of thin aluminum-oxide films formed by the dry, thermal oxidation of a bare Al(431) substrate at a partial oxygen pressure of 1.33×10−4 Pa in the temperature range of 373–773 K were studied using x-ray photoelectron spectroscopy. The initial oxidation of the bare Al substrate proceeds by an island-by-layer growth mechanism, involving the lateral diffusion over the bare Al substrate surface of mobile oxygen species. At low temperatures (T⩽573 K), an amorphous oxide film develops that attains a limiting (uniform) thickness. At high temperatures (T>573 K), growth is not impeded at a limiting thickness. Kinetic analysis established the occurrences of two different oxide-film growth regimes: an initial regime of very fast oxide-film growth and a second, much slower oxidation stage that is observed only at T>573 K. These results could be discussed in terms of electric-field controlled, interstitial, outward transport of Al cations through a close packing of O anions in the amo...

Determination and interpretation of isothermal and non-isothermal transformation kinetics; the effective activation energies in terms of nucleation and growth

A general model for the kinetics of solid state phase transformations has been discussed. The model is valid for both isothermal as well as non-isothermal transformations. In certain specific cases, the model can be simplified such that it reduces to so-called Johnson-Mehl-Avrami (JMA) kinetics. The model kinetic parameters are independent of the time-temperature program. In addition, it has been shown that in certain cases where the presented model does not pertain to JMA exactly, the JMA description still holds within practical accuracy. This holds for example, for nucleation of mixed nature. In this case, it is possible to obtain the activation energies for growth and for nucleation, separately, from measurements, if it is possible to vary the nucleation mode, for example by pre-annealing. This determination of the separate activation energies has been tested on a virtual and a real phase transformation: crystallisation of glassy Pd40Cu30P20Ni10.

Structure and morphology of aluminium-oxide films formed by thermal oxidation of aluminium

AbstractThe structure and morphology of thin aluminium-oxide films grown by the dry, thermal oxidation of a bare Al (431) substrateat a partial oxygen pressure of 1.33 =10 Pa in the temperature range of 373–773 K were studied using X-ray photoelectron y4 spectroscopy and high resolution electron microscopy.The initial oxidation of the bare Al substrate proceeds by an island-by-layer growth mechanism, involving the lateral diffusion over the bare Al substrate surface of mobile oxygen species.At lowtemperatures ( T (573 K ), the mobility of the oxygen species is very low, and an amorphous oxide film of relatively uniform,limiting thickness develops.X-ray photoelectron spectroscopic analysis established the occurrence of a surface-oxide species atthe very surface of these films.At higher temperatures( T )573 K ) an initially amorphous oxide film of less uniform thicknessdevelops that gradually transforms into crystalline g-Al O .At these temperatures an amorphous-to- 23 23 g-Al O transition oxidephase occurs. 2002 Elsevier Science B.V. All rights reserved.

The kinetics of the austenite-ferrite phase transformation of Fe-Mn: differential thermal analysis during cooling

Abstract Differential thermal analysis (DTA) has been employed to study the austenite–ferrite phase transformation of Fe-1.89at% Mn upon cooling. The transformation has been shown to occur in two stages. The first stage is not thermally activated; the second stage is thermally activated. A phase transformation model, incorporating a new impingement correction, has been used for the extraction, from the DTA experiments, of data for the velocity of the austenite–ferrite interface. It follows that the interface velocity does not only depend on temperature, but also on transformed fraction. This has been interpreted as the consequence of the (non-neglectable) dissipation of energy by the volume misfit of the austenite and ferrite phases during the transformation. This misfit accommodation Gibbs energy has been assessed quantitatively; it has been shown to be of the same order of magnitude as the chemical Gibbs energy.

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.

Driving force for Sn whisker growth in the system Cu–Sn

The evolution of residual stress gradients in Sn thin films on Cu substrates upon aging at ambient temperature has been investigated, for specimens which do exhibit and which do not exhibit Sn whisker growth, by performing x-ray diffraction stress measurements at constant penetration depths. Comparison of the measured near-surface stress-depth profiles for both types of specimens, as function of aging time at ambient temperature, showed that a significant negative stress gradient from the surface toward the Sn∕Cu interface is decisive for Sn whisker growth in the system Cu–Sn.

The isothermal and isochronal kinetics of the crystallisation of bulk amorphous Pd40Cu30P20Ni10

Abstract The amorphous alloy Pd 40 Cu 30 P 20 Ni 10 has been produced by water quenching the molten alloy. The kinetics of crystallisation has been measured by means of isothermal and isochronal differential scanning calorimetry. The associated microstructural changes have been analysed using scanning electron microscopy. Special interest has been devoted to the influence of isothermal pre-annealing on subsequent isochronal crystallisation kinetics. By applying appropriate isothermal pre-annealing temperatures, nucleation of the crystalline phases takes place to different extents. Accordingly, the initial state for the subsequent isochronal crystallisation could be changed gradually with respect to the number of pre-existing nuclei. This leads to a gradual change of the mode of nucleation from site saturation to continuous nucleation during the crystallisation. The corresponding change of the kinetic parameters has been used to determine the activation energies of nucleation and growth separately.

A method for the non-destructive analysis of gradients of mechanical stresses by X-ray diffraction measurements at fixed penetration/information depths

A rigorous measurement strategy for (X-ray) diffraction stress measurements at fixed penetration/information depths has been developed. Thereby errors caused by lack of penetration-depth control in traditional (X-ray) diffraction (sin2ψ) measurements have been annulled. The range of accessible penetration/information depths and experimental aspects have been discussed. As a practical example, the depth gradient of the state of residual stress in a sputter-deposited nickel layer of 2 µm thickness has been investigated by diffraction stress measurements with uncontrolled penetration/information depth and two controlled penetration/information depths corresponding to about one quarter and one tenth of the layer thickness, respectively. The decrease of the planar tensile stress in the direction towards the surface could be well established quantitatively.