P. Lamparter

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.

Structure of amorphous Al2O3

Abstract The structure of amorphous Al 2 O 3 samples, prepared by anodic oxidation of aluminium foils, was investigated by X-ray and neutron diffraction. The partial pair correlation functions were determined from computer simulation of the structure using the Reverse Monte Carlo method with the result that amorphous Al 2 O 3 is built up by AlO 4 tetrahedra with corner sharing oxygen atoms. Pores in the material were characterized by neutron small-angle scattering.

Diffraction analysis of internal strain-stress fields in textured, transversely isotropic thin films: Theoretical basis and simulation

Abstract Polycrystalline films produced via physical vapour deposition often possess a microstructure composed of columnar oriented grains. From the mechanical point of view, they cannot be treated as isotropic bulk solids; rather their elastic macroscopic behaviour is only transversely isotropic. In this context, the effect of texture on the elastic response of such films has been investigated for different grain interaction models. In particular, the determination of macroscopic stress by X-ray diffraction methods has been analysed. Traditional grain interaction models such as those due to Voigt and to Reuss have been compared with that proposed by Vook and Witt, compatible with the presence of only transverse isotropy of the body (even in the absence of crystallographic texture). By simulation, it has been demonstrated that, although texture only moderately affects the values of the macroscopic mechanical elastic constants of the transversely isotropic body, it can pronouncedly influence the results from the X-ray diffraction measurements. This effect is shown to depend strongly on the type of grain interaction.

Small angle x-ray and neutron scattering for the investigation of the medium-range structure of metallic glasses

Abstract A review is presented on the application of small angle X-ray (SAXS) and neutron (SANS) scattering to the investigation of the medium-range structure in metallic glasses in the as-quenched state as well as after thermal treatments. Scattering experiments revealed that the medium-range structure is characterized by compositional inhomogeneities occurring on a very extended size scale from some ten up to at least some thousand Angstroms. Various types of inhomogeneities are discussed as possible sources for the observed small angle scattering effects. The development of a uniform picture for the medium-range structure and consequently also for the atomic scale structure is complicated by the indications that in fact different inhomogeneities coexist in metallic glasses. Scale invariance of the scattering suggests dilation symmetry of the medium-range structure with fractally rough surfaces.

Diffraction studies of liquid and amorphous alloys

Abstract X-ray, neutron, and electron diffraction experiments permit the evaluation of the total structure factor S as a function of the momentum transfer Q, which yield important information about the structure of liquid and amorphous alloys. A rise of S (Q) at small values of Q, i.e., small-angle-scattering, indicates a tendency for segregation. A premaximum below the first peak in S (Q) is usually a sign for the tendency of compound formation. Detailed structural information is obtained from the so-called partial structure factors S ij (Q).

Uptake of iron, oxygen and nitrogen in molybdenum during ball milling

Abstract Molybdenum powder was ball milled in a steel vessel with hardened steel balls under Ar, O 2 and N 2 atmosphere, respectively. The milling products were examined by chemical analysis, X-ray diffraction and neutron diffraction. During milling under Ar or O 2 the iron as well as the oxygen content of the samples increases dependent on the number of interruptions of the milling process. The presence of dissolved oxygen seems to facilitate the solubility of iron in the molybdenum powder. Milling in a nitrogen gas atmosphere results in the formation of a nanocrystalline cubic γ-Mo 2 N phase and a Mo-rich amorphous-like grain boundary phase. The microstructural imperfection was characterised by X-ray diffraction-line profile analysis. A method was proposed for the evaluation of the crystallite size and the microstrain in nanocrystalline materials, as well as the amount and structure of disordered grain boundaries from the reduced pair correlation function.

An X-ray and neutron scattering investigation of precursor derived Si24C43N33 ceramics

Abstract X-ray and neutron wide angle scattering studies of amorphous Si 24 C 43 N 33 ceramics, annealed at different temperatures, were performed using contrast variation by isotopic substitution ( nat N ⇔ 15 N). The total pair correlation functions exhibit distinct peaks, which can be correlated with two phases, namely amorphous Si 3 N 4 and amorphous carbon. Peaks due to Si–C and C–N bonds were not observed. Reverse Monte Carlo simulation yields partial pair correlation functions which are consistent with the phase separation model.

Structure of binary metallic glasses

Abstract The short range atomic structure of binary amorphous alloys is described by the interatomic distances and the partial coordination numbers. These quantities are deduced from partial structure factors via pair correlation functions. Some methods to determine these partial functions are described. A review of experimental results obtained with metal-metalloid as well as metal-metal alloys is given. The amorphous alloys from the NiNb system are treated more in detail. Some special topics such as the dependence of the amorphous structure on the production process, refractory metallic glasses, hydrogen in metallic glasses, modelling, and triplet correlation functions are discussed.

Study of the Atomic Structure and Phase Separation in Amorphous Si-C-N Ceramics by X-Ray and Neutron Diffraction

Abstract Amorphous Si37C32N31 and Si37C29N34 ceramics were produced by pyrolysis of a polyhy-dromethylsilazane precursor. Their structure was investigated by X-ray and neutron diffraction. Wide angle diffraction showed that the Si-atoms are preferentially bonded to nitrogen atoms, but also bonding to carbon atoms was found. This suggests that the excess carbon atoms form an amorphous graphite-like phase. Small angle scattering revealed that the ceramics are inhomogeneous. The evolution of the phase separation during annealing was investigated and it was concluded that amorphous Si3N4 precipitates grow in the Si-C-N materials. The results are compared with previous results for amorphous Si24C43N33 produced from a polysilylcarbodiimide precursor [1 - 3].

Structure and Density of Gold-Cesium-Melts. II. Neutron Diffraction with Molten Gold-Cesium-alloys

Recently with Au-Cs-melts measurements of some physical properties were done such as electrical conductivity,1 thermoelectric power,1 electromigration,2 and magnetic susceptibility.3 According to t...