Stress In Thin Layers Research Articles

Stochastic Model of Pore Nucleation when the Sample is Irradiates with Inert Gas Ions

Abstract—Non-point vacancy-gas defects (VGD) (pores, blisters) in the crystal lattice arise as a result of its irradiation with an inert gas Xe++, the process is considered as the formation of first-order phase transition nuclei by means of computational mathematics, kinetic theory, and the theory of stochastic dynamic variables and Wiener random processes. The characteristics of disordered porosity in samples consisting of layers (“dielectric/metal”) at various layer thicknesses are calculated. The formation of spherical shape defects in materials at times of the order of 10–4 s, when the porosity of the material nucleates, is preceded or accompanied by the appearance of microcracks. Irradiation of surfaces with an inert gas with ion energies of 5–10 keV refers to low-temperature blistering; in the model, the constancy of the influence of radiation fluxes stimulating a phase transition creates the condition of an “open” physical system in which it is possible to combine lattice defects into structures that cause local stresses, and the constancy of the temperature of the sample, the pressure of the implantable “monomers” of the gas, and supersaturation (similar to the parameters of vapor condensation) are characteristic of the fluctuation unstable stage of the phase transition move. Partial kinetic equations with nonlinear coefficients (Kolmogorov–Feller and Einstein–Smoluchowski) are solved by the method of stochastic molecular dynamics, which establishes a connection between the solution of Ito stochastic equations in the sense of Stratonovich and kinetic equations; stable numerical methods are used. The conditions for the formation of VGD are determined taking into account the influence of the elastic properties of the lattice, and the porosity and local stresses in thin layers of irradiated materials are calculated.

Yield stress in thin layers of ferrofluids

We present results of theoretical study of quasielastic behavior of ferrofluid filling a thin flat gap, placed into perpendicular magnetic field. When the field exceeds a certain critical magnitude, magnetic particles form dense discrete domains, elongated along the field, and linking the gap boundaries. Due to these bridges between the gap boundaries, the ferrofluid exhibits quasielastic properties with respect to shear strain in the plane of the gap. We estimated the elastic modules as well as the yield stress of the system, depending on magnetic field and concentration of magnetic particles in the ferrofluid. Analysis shows that there are at least two microscopical mechanisms of transition from the elastic to fluid behavior of the ferrofluid. The first one is connected with the loss of the mechanical equilibrium of the domains, slopped, under the shear stress, with respect to applied magnetic field. The second mechanism is connected with breakup of the “bridge” into two separate drops, when the shear strain exceeds some critical magnitude. Estimates show that for real ferrofluids the second mechanism is more probable.

Determination of thermal stresses using grazing incidence X-ray diffraction

The residual stress field in a titanium nitride coating was determined using the X-ray diffraction method based on grazing incident angle geometry. The first order stress components were determined in TiN coating on WC and on steel substrates. The diffraction elastic constants calculated by the self-consistent method were used for the interpretation of the results. The advantages of the grazing incidence geometry are pointed out in the case of the examination of heterogeneous residual stresses in thin layers.

Stress in Thin Layers; Grain Interaction, Elastic Constants and Diffraction Response

The well known models for the description of the macroscopic elastic behaviour of polycrystalline specimens, as for instance those due to Voigt, Reuss, Neerfeld-Hill and Eshelby-Kroner, predict macroscopic isotropy of the body in the absence of texture, and transverse isotropy when fibre texture is present. A thin film is usually only transversely isotropic, even in the absence of crystallographic texture. A recently re-examined and elaborated alternative model for grain interaction in thin films based on an approach by Vook and Witt is able to predict this transversely isotropic behaviour. An overview of results on the application of the various grain interaction models has been given here: in particular, simulations of X-ray diffraction experiments and calculations of macroscopic elastic constants were performed for untextured and fibre textured thin films of nickel.

A model for stress in thin layers induced by misfitting particles: An origin for growth stress

The stress caused by misfitting particles in thin layers adherent to substrates is modelled. The model assumes an elastically isotropic matrix with holes in which the misfitting particles are introduced. The stress field generated in the matrix consists of a hydrostatic stress resulting directly from the misfitting particles and a biaxial state of stress resulting from the condition that the layer should remain attached to its substrate. The model and its implications for diffraction stress measurements are illustrated using magnetron sputtered TiN layers.

The rise and fall of stress in thin layers; the γ’-Fe4N1-x layer as a model

A γ’-ironnitride (Fe4N1-x) layer on an α-iron substrate, prepared by gaseous nitriding of pure α-iron, can be conceived as a model system for layer-substrate assemblies characterized by a thermal misfit at the layer-substrate interface and a compositional misfit within the layer due to a composition-depth profile. It also exhibits the effect of porosity on misfit accommodation in surface layers. The analyzing technique for the determination of residual stress used in this work is x-ray diffractometry. The simultaneous determination of residual stress-depth and composition-depth profiles in γ’ layers (γ’ has a small homogeneity range of only about 0.4 at% N) by x-ray diffractometry implies unraveling of spacing gradients due to both stress and compositional variations. Unique results can be attained: simultaneous changes in nitrogen content and stress of only 0.02 at% N and 50 MPa on a depth change of less than 1.5 μm have been determined. Porosity occurs in γ’-Fe4N1-x as a consequence of the metastability of γ’ with respect to nitrogen gas at normal pressures. Such porosity brings about “relaxation” of the residual stresses. Phase transformations can cause stress relaxation. During annealing of a γ’ layer at a temperature below the nitriding temperature, the composition of the γ’ phase changes, leading to development of α-iron precipitates in the layer. Simultaneous with this phase transformation, stress relaxation occurs in the γ’-layer/α-substrate assembly.

A new method for measuring the yield stress in thin layers of sedimenting blood

A new method is presented to describe the low shear rate behavior of blood. We observed the response of a thin layer of sedimenting blood to a graded shear stress in a wedge-shaped chamber. The method allows quantitation of the degree of phase separation between red cells and plasma, and extracts the yield stress of the cell phase as a function of hematocrit. Our studies showed that the behavior of normal human blood underwent a transition from a solid-like gel to a Casson fluid. This transition began at the Casson predicted yield stress. The viscoelastic properties of blood were examined at shear stresses below the yield stress. The measured Young's elastic moduli were in good agreement with published data. The yield stress of blood showed a linear dependence on hematocrit up to 60%, and increased more rapidly at higher hematocrit.