Example Cubic thin film with

Example Cubic thin film with a (111) orientation... 

The transparency of thin films is often slightly worse than that of bulk materials. For example, bulk single crystals of cubic ZnS have an absorption coefficient k5i5 of between 4.3x1 O 6 and 1.2x1 O 5 [209], whereas for evaporated films a value of 2.7x10 4 is obtained. Deposition experiments in high vacuum with ZnS showed that the absorption coefficient k, determined by a calorimetric method [210], does not de-... 

It can be observed that an infinite channel with a square cross section is obtained from Eq. (10.9) when m oo. Prisms and layered cavities have been used, for example, in structural studies of clays [Joshi et al., 1998 Consolati et al 2002], A discussion of pore-size distributions in low-dielectric thin films [Gidley et al 2000] was based on cubic structures. Of course, other geometries are possible For example, ellipsoidal holes were also considered [Jean and Shi, 1994], in an interesting attempt to frame free-volume holes in semicrystalline polymers subjected to tensile deformation. 

In thin films, the picture of the film thickness influence on lattice constants is more complex than that in the powders and/or ceramics. First of all, this is related to the influence of mismatch between the film and substrate parameters, which leads to appearance of compressive or tensile mechanical strain normal to the film surface, similarly to the discussion in Sect. 2.1. This means, that parameter of a film tetragonality c/a l even in cubic phase. Moreover, the substrates, which induce large enough compressive strain, essentially impede thickness induced phase transition from ferroelectric to paraelectric phase, so that ferroelectricity can be conserved even in ultrathin films deposited on such substrates. As an example of such behavior, we show on Fig. 2.5 the ratio c/a measured for PbTiOs film on SrTi03 Nb substrate at r= 300 K [20]. It is seen, that similarly to the powders and ceramics, c/a ratio diminishes with the size (film thickness) decrease. However, up to the thickness 4 nm the ferroelectricity is retained and c/a remains to be more than the value 1.3, corresponding to the disappearance of ferroelectricity with respect to mechanical strain. 

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. 

At normal conditions, bulk forms of all rare earth monoselenides have a cubic NaCl structure, space group Fm3m-0 (No. 225) Z = 4, see for example, landelli [1]. Thin films of MSe, M = Sm, Tb, Dy, and Yb, when prepared from Se/M diffusion couples, have a hexagonal ZnS (wurtzite) structure with space group PSamc-C v (No. 186) Z = 4, Singh, Srivastava [2]. 

The required sensitivity of the analytical procedure is indicated, for example, by the following considerations. Under the extractability test conditions proposed by the British Plastics Federation on thin films (<0.5 mm) of polymer containing 0.03% wiv of additive, each cubic centimetre volume of plastic is contacted with 20 cm of the extraction liquid. Thus, if all the additive present in the original polymer film migrates during the extraction test into the extraction liquid, at the end of the test this liquid will contain only approximately 15 ppm of additive. Consequently it was necessary to devise a procedure for determining extracted polymer additive in each of the extractants in amounts down to 3 ppm. 

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