Thin film example, elastic

Suppose that a thin film of elastic-plastic material bonded to an elastic substrate is subjected to temperature cycling, as in the example discussed in Section 7.5.2. Furthermore, suppose that the film material has precisely the same uniaxial stress-strain response under monotonic loading as does the material considered there. However, in the present context, the film is assumed to strain harden according to the kinematic hardening idealization. Under these circumstances of temperature cycling, with the conditions... 

Frankel and Acrivos11 have obtained models with well-defined hydrodynamics for very high concentrations of rigid and elastic particles. Here the solvent forms thin films and we enter the region of lubrication theory. The expressions describing the flow do bear some similarities to the semi-empirical expressions developed at lower concentrations. For example Frankel and Acrivos give... 

Besides the inelastic component, always a certain number of He atoms are elastically scattered in directions lying between the coherent diffraction peaks. We will refer to this scattering as diffuse elastic scattering. This diffuse intensity is attributed to scattering from defects and impurities. Accordingly, it provides information on the degree and nature of surface disorder. It can be used for example to study the growth of thin films or to deduce information on the size, nature and orientation of surface defects Very recently from the analysis of the diffuse elastic peak width, information on the diffusive motion of surface atoms has been obtained. ... 

Figure 9.40 shows another example of residual strain effects on the Raman spectrum. The Si stretching vibration changes its frequency when Si is in the form of a thin film on sapphire. We can compare the Raman band positions between the strain-free sample and strained sample to evaluate the bond length change, which can be converted to residual strain. The residual strain is commonly elastic in nature. Thus, the residual stress in materials can be determined with the linear elastic relationship between strain and stress. 

It follows then that as the electrical field intensity increases across a dielectric, the stiffness or the elastance of the dielectric increases. This comes about by physical compaction of the particles in the diffuse layer and by strong orientation of the dipoles or the polarization of charges in the compact layer. Hence, as the electrical field intensity is increased by compression of DDL, the capacitance of the system decreases due to polarization. An example of a similar behavior has been shown in thin electrolyte films between silica surfaces, where the dielectric permitiv-ity decreases with increasing electrolyte concentration, resulting in increasing field strength across the thin film (Israelachvili and Adams, 1978 Pashley, 1981 Basu, 1993). 

In general, one should not suppose that the properties of bulk materials will apply to materials at the nanoscale level. With respect to the mechanical properties of small-scale solids, it is known that the elastic behaviour, due to bond stretching and twisting, does not vary significantly in nanoparticles compared with that in the bulk. Other properties are more sensitive. For example, the rate of diffusion creep (Nabarro-Herring and Coble creep) is dependent on grain size. Hence, creep will be enhanced in compacts of nanoparticles and in thin films. 

The nuclear resonant inelastic and quasi-elastic scattering method has distinct features favorable for studies concerning the microscopic dynamics (i.e., lattice vibration, diffusion, and molecular rotation) of materials. One advantageous feature is the ability to measure the element-specific dynamics of condensed matter. For example, in solids the partial phonon density of states can be measured. Furthermore, measurements under exotic conditions -such as high pressure, small samples, and thin films - are possible because of the high brilliance of synchrotron radiation. (For the definition of brilliance, see O Sect. 50.3.4.5 of Chap. 50, Vol. 5, on Particle Accelerators. ) This method is applicable not only to solids but also to liquids and gases, and there is no limitation concerning the sample temperature. 

Oflier applications Other applications of thin films include pyroelectric detectors and surface acoustic wave (SAW) substrates. The latter devices consist of a piezoelectric substrate onto which interdigital electrodes are deposited, for example by screen printing. An elastic wave generated at the input interdigital transducer (IDT) travels along the surface and is detected by the output interdigital transducer (OIT). These devices are mainly used as delay lines and filters in microwave and television communications (see also Chilla et al., 2003). 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

Interface delamination and film fracture induced by residual stress in the thin film were the focus of discussion in the preceding chapter where models were developed within the framework of linear elastic fracture mechanics. Such analyses did not account for the actual separation of the film from its substrate. However, there are delamination processes for which transverse deflection of the film away from the substrate becomes an important consideration in a variety of practical applications. Examples include ... 

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