Phase Separation of Crystal Surfaces: A Lattice Gas Approach

We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic crystal with nearest--neighbor attractive interactions and weak next--nearest--neighbor repulsive interactions. It is likely applicable to alkali halides with the sodium chloride structure. Emphasis is placed on the fact that the equilibrium crystal shape can be interpreted as a phase diagram and that the details of its structure tell us into which surface orientations an unstable surface will decompose. We find that, depending on the temperature and growth conditions, a number of interesting behaviors are expected. For a crystal in equilibrium with its vapor, these include a low temperature regime with logarithmically--slow separation into three symmetrically--equivalent facets, and a higher temperature regime where separation proceeds as a power law in time into an entire one--parameter family of surface orientations. For a crystal slightly out of equilibrium with its vapor (slow crystal growth or etching), power--law growth should be the rule at late enough times. However, in the low temperature regime, the rate of separation rapidly decreases as the chemical potential difference between crystal and vapor phases goes to zero.Comment: 16 pages (RevTex 3.0); 12 postscript figures available on request ([email protected]). Submitted to Physical Review E. SFU-JDSDJB-94-0

Effects of Low-Level Long-Term Ozone Fumigation and Acid Mist on Photosynthesis and Stomata of Clonal Norway Spruce (Picea abies (L.) Karst.).

Four clones of 3-year-old Norway spruce (Picea abies (L.) Karst.), grown on two soils, were from July 1986 to September 1987 exposed to ozone fumigation (50 μg m−3 as a control, 100 μg m−3 plus peaks between 130 and 360 μg m−3 as treatment) and acid mist of pH 3·0 (versus mist pH 5·6 in the control). Climatic conditions, identical for both control and treatment, followed a diurnal and seasonal pattern characteristic of medium high altitudes of the Bavarian Forest, an area affected by the new-type forest decline. Gas-exchange measurements were carried out on the plants from December 1986 until the end of the 14-month's exposure using a series of climate-controlled minicuvettes. ANOVA of the four clones investigated towards the end of the experiment gave hints of a treatment-related depression of the photosynthetic capacity of the previous year's needles (age-class 1986). Within this age-class only one of the clones (11) showed a significant treatment effect, indicating an age-class dependence and a genetic influence of the treatment-related depression of the photosynthetic capacity. The current year's flush was not impaired through the ozone and acid mist exposure. Analysis also revealed clear effects of soil, clone and needle age on photosynthetic parameters