Surface morphological stabilization of stressed crystalline solids by simultaneous action of applied electric and thermal fields
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(a) Dispersion relations for increasing values of Ξ eff giving the dependence of the evolution rate, ω, of a shape perturbation from the planar surface morphology on the dimensionless wave number, , of the perturbation. (1) Ξ eff = 0.85 Ξ eff,c , (2) Ξ eff = Ξ eff,c , (3) Ξ eff = 1.15 Ξ eff,c , and (4) Ξ eff = 2.5 Ξ eff,c . The inset gives the dispersion relation for Ξ eff = 0, indicating an ATG surface instability. (b) Dependence on Ξ E of the range of unstable wave numbers, , for different combinations of thermal and electric field orientations. (1) and with β = 0.1; (2) and with β = 1.2; (3) and with β = 0.5; (4) and with β = 0.5; and (5) and , i.e., in the absence of a surface TM flux. The horizontal arrow indicates the beneficial effect of surface TM in case (4) in reducing the electric-field strength requirement for surface stabilization in case (5). The parameters used in both (a) and (b) are m = 3, A = 10, and φ = −15°.
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Dependence of Ξ eff , c at φ = φopt on the anisotropy strength A. The inset shows the dependence of Ξ E,c on the misorientation angle, φ, for m = 3, A = 10, and β = 0 and 0.5; the minimum corresponds to the optimal orientation of the thermal and the electric field, .
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