Surface Stress Anisotropy

Mirzamaani et al. [74, 75] point out that the earlier studies of the interrelationships between structure and magnetics have examined films substantially thicker than those now being used in thin-film disks. These authors have examined very thin CoP films and have studied the relative roles of shape anisotropy, stress anisotropy, and crystal anisotropy in determining the magnetic properties. For their CoP-deposition system, shape anisotropy dominated the other factors in determining the film magnetic properties. The shape anisotropy of a particular deposit was determined by the surface condition of the substrate on which the CoP was deposited. 

Next, the step-mobilityof Si(OOl) is estimated at lower temperatures, T 500°C, from the experiments of Webb et al. [25] on the relaxation kinetics of non-equilibrium step-spacings. In this experiment, the average terrace size was large, and therefore, due to the stress anisotropy of the 2 x 1 surface reconstruction, a long range interaction of the form... 

Surface sizing can induce structural changes in the paper sheet185 due to the interaction of water sorption (which causes a relaxation of internal stresses) and machine direction tension (which increases anisotropy and creates additional stresses). Anisotropy can be lowered by reducing tension on the web during sheet passage... 

Abstract Some aspects of self-assembly of quantum dots in thin solid films are considered. Nonlinear evolution equations describing the dynamics of the fihn instability that results in various surface nanostructures are analyzed. Two instability mechanisms are considered the one associated with the epitaxial stress and the other caused by the surface-energy anisotropy. It is shown that wetting interactions between the film and the substrate transform the instability spectrum from the long- to the short-wave type, thus yielding the possibility of the formation of spatiaUy-regular, stable arrays of quantum dots that do not coarsen in time. Pattern formation is analyzed by means of ampbtude equations near the insta-bibty threshold and by numerical solution of the strongly nonlinear evolution equations in the small-slope approximation. 

In this section, situations are considered for which the surface of a stressed solid is initially flat, or nearly so, and for which the slope of the evolving surface is everywhere small in magnitude throughout the evolution process. Chemical potential for a one-dimensional sinusoidal surface shape was developed in Section 8.4.1, for a two-dimensional sinusoidal shape in Section 8.5.3, and for a general small amplitude surface profile in Section 8.5.2. These results are used to examine surface evolution by either the mechanism of surface diffusion or condensation, as described in Section 9.1. In all cases considered in this section, surface energy is assumed to have the constant value 70, independent of surface orientation and surface strain. Implications of surface energy anisotropy and strain dependence are examined subsequently. 

In the literature, high coercivity values closer to the theoretical ones have been found in a few cases for dispersed y-Fe20s particles, but the mechanisms of such coercivities are still not clear. Several arguments have been reported to explain the coercivity enhancement, such as surface anisotropy [37] or stress anisotropy induced either by the presence of a Fe304-y-Fe203 solid solution, whose differences in lattice constants produce stress [38] or, in thin films, by the differences in thermal expansion coefficients between the film and the substrate [39]. 

The residual film stress anisotropy can be very sensitive to geometry and gas pressure during sputter deposition. This is due to the anisotropic distribution of sputtered atom flux, anisotropic bombardment by high energy reflected neutrals, and the effect of gas phase and surface collisions at higher pressures. Figure 10.11 shows the effect of gas pressure on residual film stress in post cathode magnetron sputter deposition of molybdenum,... 

Material parameters defined by Equations (1.11) and (1.12) arise from anisotropy (i.e. direction dependency) of the microstructure of long-chain polymers subjected to liigh shear deformations. Generalized Newtonian constitutive equations cannot predict any normal stress acting along the direction perpendicular to the shearing surface in a viscometric flow. Thus the primary and secondary normal stress coefficients are only used in conjunction with viscoelastic constitutive models. 

Theories of the oxidation of tantalum in the presence of suboxide have been developed by Stringer. By means of single-crystal studies he has been able to show that a rate anisotropy stems from the orientation of the suboxide which is precipitated in the form of thin plates. Their influence on the oxidation rate is least when they lie parallel to the metal interface, since the stresses set up by their oxidation to the pentoxide are most easily accommodated. By contrast, when the plates are at 45° to the surface, complex stresses are established which create characteristic chevron markings and cracks in the oxide. The cracks in this case follow lines of pores generated by oxidation of the plates. This behaviour is also found with niobium, but surprisingly, these pores are not formed when Ta-Nb alloys are oxidised, and the rate anisotropy disappears. However, the rate remains linear it seems that this is another case in which molecular oxygen travels by sub-microscopic routes. 

Real differences between the tensile and the compressive yield stresses of a material may cause the stress distribution within the test specimen to become very asymmetric at high strain levels. This cause the neutral axis to move from the center of the specimen toward the surface which is in compression. This effect, along with specimen anisotropy due to processing, may cause the shape of the stress-strain curve obtained in flexure to dif-... 

---