A method based on the Green’s function technique for calculating strain in quantum dot (QD) structures has been developed. An analytical formula in the form of a Fourier series has been obtained for the strain tensor for arrays of QDs of arbitrary shape taking into account the anisotropy of elastic properties. Strain distributions using the anisotropic model for semiconductor QDs are compared to results of a simplified model in which the elastic properties are assumed to be isotropic. It is demonstrated that, in contrast to quantum wells, both anisotropic and isotropic models give similar results if the symmetry of the QD shape is less than or equal to the cubic symmetry of the crystal. The strain distribution for QDs in the shape of a sphere, cube, pyramid, hemisphere, truncated pyramid, and flat cylinder are calculated and analyzed. It is shown that the strain distributions in the major part of the QD structure are very similar for different shapes and that the characteristic value of the hydrostatic strain component depends only weakly on the QD shape. Application of the method can considerably simplify electronic structure calculations based on the envelope function method and plane wave expansion techniques.
Molecular dynamics simulations of fully hydrated and dehydrated Na + -zeolite-4A with a mobile zeolite framework at 298 K and a steepest descent energy minimization simulation on the dehydrated zeolite have been performed. The optimized structure yields bond lengths, bond angles, and positions of sodium ions in very good agreement with published X-ray data. The simulations at 298 K confirm that the Na(1) and Na (3) ions oscillate about their mean positions and that migration is slow. The Na(2) ions, located in the oxygen eight-rings, are much more mobile and move out of the plane of the ring as well as within the plane. Most water molecules in the R-cages are found to migrate between preferred sites on the inside of the cage. The preferred sites form a polyhedron with 44 vertices, differing from the interpretation of experiment. On average, 2.5 water molecules are found up to 3 Å from the R-cage center, with the remaining 21.75 water molecules at sites on the inside of the cage. Water molecules in the -cages remain in the cages for 300 ps at 298 K and occupy six octahedral preferred sites. The water molecules in -cages containing exactly four molecules are found to occupy planar sites.
The first systematic and quantitative experimental study of the influences on lateral drying in colloidal films is reported. The time until water recedes from the edge of a drying thick film of a waterborne colloidal dispersion, called the open time, was measured as a function of several controllable parameters. Magnetic resonance microscopy, using a specially designed probe, noninvasively provides a direct and quantitative measurement of the concentration of water as a function of vertical and lateral position. Images were obtained from drying films of latices with known values of thickness, particle size, and surface tension, which are neatly encapsulated in an expression for the reduced capillary pressure, p c. A strong increase in the open time was found over a relatively narrow range of p c values. Larger particles, slower evaporation rates, and thinner films encourage more uniform lateral drying with a delay in drying from the edges. This observation is consistent with a recent model (Routh, A. F.; Russel, W. B. AIChE J. 1998, 44, 2088) based on the lubrication approximation. The experiments and the modeling point to a way of achieving control over the lateral drying processes of waterborne colloids.
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