Simulations of Step Motion During Crystal Evaporation
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Simulations
of Step Motion During Crystal Evaporation A.Peter Jardine Dept. of Material Science and Engineering S.U.N.Y at Stony Brook Stony Brook, NY 11794 Abstract
The rate of decay of a macroscopic sinusoidal grating etched into a clean surface can bc predicted from its surface and volume diffusion coefficients and the partial pressure of the material. The microscopic theory of crystal growth and evaporation of Hirth and Pound has produced an expression for the step velocity for a surface in equilibrium with its own vapor, which was used to simulate the decay of a sinusoidal surface. The macroscopic decay rate was determined from the measured surface diffusion coefficient and the equilibrium vapor pressure of the Ni (100) surface. The rate of decay of a model sinusoidal grating surface using the microscopic step velocities was inconsistent with the observable mnacroscopic results. Reasons for this are discussed. Introduction Curved surfaces or surfaces inclined to a stable low-index crystallographic plane accommodate the imposed macroscopic curvature by splitting into nominally flat terraces seperated by steps of equal height. In response to a thermodynamic driving force generated by changes in the local curvature of the surface, steps will move in order to minimize the total surface energy. The evolution of step positions can result in observable macroscopic changes in crystal shape in a mass-transport process known as capillarity. The path lengths from intrinsic surface diffusion arc typically < 1/.Lm, too small [or macroscopic changes in crystal shape to occur. Steps, considered as a surface defect, effectively increase diffusive path lengths to > 100/•m [1]. Early work on step motion a~cross surfaces in equilibrium with an overpressure of vapor (crystal growth) or an undcrpressure of vapor (crystal evaporation) considered step motion as resulting from the difference in diffusing fluxes from the step to upper and lower terraces. The dependence of step)velocities on local step densities were derived by Burton, Cabrerra and Frank [2] in their continmuumkinematical approach. Hirth and Pound [3] predicted, using the TLK( model, the rate of vaporization of metals using the notion of steps nucleating at corners and propogating across the crystal surface. Further work by Mullins and Hirth [4] produced a microscopic model for growth processes based on individual step dynamics, which is used to predict decay of a sinusoidal step array. This model has been used in simulations of crystal evaporation from crystal edges and emerging screw dislocations (Frank-Read sources) by Surek et al [5,6,7]. Semi-quantitative agreement of step motions on NaCl surfaces was provided by Hoche and Bethge [8]. There was no attempt in these studies to relate these processes to a macroscopically observable process such as capillarity, and so the simulations were at best encouraging though not conclusive confirmation of any particular model. A better test may be to simulate the macroscopic process of capillarity using the models of microsco
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