Surface energy density

Figure 10.11 shows the theoretical dependence of the domain radius on the applied voltage, which was compared to an experimental data obtained in lithium niobate. This calculation was performed in the range of voltages between 0 and 1.4 kV, using Ps = 75/xC/cm2, ec = 30, ea = 84. The surface energy density aw was obtained by a fitting procedure where it was a free parameter as expected, the obtained value aw = 4 mJ/m2 was relatively small. 

Figure 10.11 Theoretical dependence of the domain radius on the applied voltage obtained by taking of the surface energy density as a free parameter and adjustment to the experimental results.

A characteristic of these expanding wave fronts is that the acoustical energy of subsequent wave fronts is decreasing because each subsequent wave front is slightly larger than its predecessor. Thus, the surface energy density [W/cm2] of such expanding wave fronts becomes lower as the distance is increased from the transducer face or horn tip. 

A closer view of the ZnO surface (see Fig. 6.7) reveals that the pyramids have nonregular facets, and are actually made up of a multitude of micro-steps. We can explain these steps as the successive stacking-up of (1120) and (0002) atomic planes, which are perpendicular to each other. Indeed, these planes possess the minimum surface energy density, which... 

Here Y represents the Young s modulus of the solid and F represents the surface energy density of the solid, measured by the extra energy required to create unit surface area within the bulk of the solid. 

This approximate two state model of water with bonded OH (which may have an angular partition around 6 = o) and "free" OH is basis for calculations of heat enthalpies, heat of vaporization, specific heat, surface energy, density and T-dependences under... 

The definition of a invariant with respect to positioning of the dividing surface can be worked out, if one analyzes trends in the/z)-pc(z) function within the discontinuity surface. The specified quantity has the same value in the bulk of both phases, equal to the negative external pressure (Fig. 1-4). Within the discontinuity surface, pressure p has a tensor nature, making Pascal s law invalid. Meanwhile, the concentration and pressure dependence of the surface energy density,/ given by eq. (1.1), is valid only in the regions where Pascal s law holds, i.e., where pressure is a scalar quantity (direct summation of a scalar and a tensor within the same equation is not permitted). 

Classical nucleation theory assumes that the surface energy density, a, is independent of the size of the nucleus. This is probably not true when the nucleus is very small and consists of just a few molecules. Also, the theory assumes that the interface between the nucleus and the amorphous phase is sharp. On a microscopic scale, the interface is probably diftuse with a width that could be comparable with the nucleus size at high supercooling. 

Figure 2. The surface energy density in the liquid as a function of depth.

In the context of the discussion in Section 1.3.3, C7s might represent 7s or 7f. It follows that surface stress is derivable from the strain dependent surface energy density according to... 

The local change in area from the undeformed configuration to the strained configuration represented by efj is the trace of the surface strain tensor e j,. It follows that the surface energy per unit area in the deformed configuration is C s(l + e j.) = Ug. In terms of this measure of surface energy density, (1.6) becomes... 

If the surface energy density per unit deformed surface area remains constant, then the surface stress is an isotropic second rank tensor with components numerically equal to 11. On the other hand, if the surface energy density per unit undeformed surface area remains constant, the surface stress vanishes. 

If the surface of interest is a bonded interface between two materials, rather than a free surface, surface stress analogous to ffj arises. This interface surface stress fjj is related to the interface surface energy density according to... 

A surface with sinusoidal pertubartion of its nearly flat surface with wavelength that is less (greater) than Acr is stable (unstable) against spontane-sous growth of the perturbation amplitude. For a surface energy density of Us = I J/m, a plane strain modulus of A = 10 N/m and an applied stress of cjui = 10 N / m, this critical wavelength Acr is approximately 300 nm. 

For a constant surface energy density Us = 7, the surface chemical potential X = U — jK is nonuniform in this configuration. The objective is to identify nearby shapes for which the chemical potential is again uniform. 

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