A short history of observations on the shapes of snow crystals starts in ancient China, summarizes the remarkable but little-known essay by Kepler in 1611, includes contributions by Descartes and Hooke, and ends with the beautiful collections of microphotographs by Bentley and Humphreys (1931) and Nakaya (1954). Modern observations from aircraft and mountain observatories reveal that the dominant crystal habits, hexagonal plates, columns, needles and dendritic stellar forms, and transition from one to another, are strongly correlated with air temperature, with the supersaturation of the vapour having only a secondary influence. There follows a review of laboratory experiments to determine the nature and origin of natural ice-forming nuclei and the properties of artificial nuclei, such as silver iodide, through the study of epitaxial growth of ice crystals on single crystalline substrates. Growth of snow crystals under carefully controlled conditions in laboratory cloud chambers has established that the crystal habit changes sharply six times over the temperature range 0 to -25-degrees-C The author argues that the basic habit is determined in the very early stages of growth by the relative rates of surface diffusion of water molecules across the basal and prism faces. He deduces the average migration distance, x(s), for molecules on the basal face from measurements on the velocity of growth layers and of that on the prism faces from measurements on the axial ratios of small crystals. In both cases, x(s) varies rapidly between 1 and 6 mum with temperature, and the two curves intersect at three temperatures that correspond to transitions between crystal habits. A theory is developed to explain the transition from regular plates to dendritic stellar crystals; the corners sprout when material from the vapour phase arrives at corners more rapidly than it can be carried away by surface diffusion and occurs only when the diameter of the plate exceeds a critical value d(c) is-proportional-to D(s)/D(v) = alphax(p)2/D(v), where D(s), D(v) are the coefficients of surface and volume diffusion and x(p) is the surface migration distance on the (prism) edge of the plate. The predictions of the theory are compared with observations on natural snow crystals. Equations are derived for the growth rates of snow crystals as they fall through the atmosphere. The predicted maximum attainable diameters of the various shapes are in good agreement with observations.
