On Triangles

FIG. 3-53 Trial functions for Galerldn finite element method linear polynomial on triangle. 

Figure20.7 The Mulliken excess charge (in units leads, that is, Au(Ll) and Au(Rl), respectively, of electron charge) on each atom (or atom The data for the Au(LH) and Au(RH) denoting average) as a function of Vb- The filled and open the Au atoms of the left and right electrodes on triangles denote S(L) and S(R), respectively. The the first layer are plotted as filled and open filled and open circles denote the average of the squares, respectively.

Click once on triangle icon or select mesh/initialize mesh ... 

Figure 5. Thickness profiles of steady-state films on (triangles) a 1-cm strip and (circles) a 1.78-mm-diameter cylinder. The strip is well fit hy a square-root function h xJ/2> whereas the cylinder, being near the needlelike geometric limit, is better fit by h In(x-xo).

We only consider first-nearest neighbor interactions with vacancies and we do not include any order correction on triangle and tetrahedron configurations containing at least one vacancy, i.e. = 0 where i, j, eind k are any of the species Al, Zr,... 

So as to study the influence on kinetics of energy corrections due to order on triangles and tetrahedrons, we fit another set of kinetic parameters corresponding to a thermodynamic description of Al-Zr binary with only pair interactions (i.e. J3 = J4 = 0, or equivalently = ejjy = 0). This other set of kinetic parameters presented in table 5 reproduces as well coefficients for Al self-diffusion and for Zr impurity diffusion, the only difference being that these kinetic parameters correspond to a simpler thermodynamic description of Al-Zr binary. 

Figure 2 Onsager coefficients Laiai and LzrZr- Squares and solid lines correspond toT = 1000 K and circles and dashed lines to T = 900 K. The vertical lines indicate the corresponding solubility limit obtained from CVM calculations. Full symbols correspond to the set of parameters with order corrections on triangles and tetrahedrons and open symbols to the set without order corrections. 

Order corrections mainly affect LzrZr- This coefficient is sHghtly lower when one considers energy corrections due to order on triangles and tetrahedrons. The difference increases with Zr concentration and thus in the metastable solid solution these order corrections lead to a slight slowdown of Zr diffusion. The two thermodsmamic models are equivalent at these temperatures (c/. phase diagram on Fig. 1 (a)). As a consequence kinetic behaviors obtained from them are really close. 

Figure 4 Evolution of second nearest neighbor short range order of Zr atoms, a at T = 1000 K and four different nominal concentrations Full and dotted lines are respectively for the set of parameters with and without order corrections on triangles and tetrahedrons.

Figure 7 Evolution of the steady-state nucleation rate J with the nominal concentration for T = 1000 K. Pull and open symbols are respectively for the set of parameters with and without order corrections on triangles and tetrahedrons. The full line corresponds to the nucleation rate predicted by classical theory of nucleation with a a = 64.1 meV and the dotted line with o

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