Physiscs of Snow Crystals

Physics of Snow Crystals

Snow crystals, also called snowflakes, are single crystals of ice that grow from water vapour. They form in copious numbers in the atmosphere and are well known for their elaborate, symmetrical patterns. The physics of snow crystal formation is a specific example of the more general problem of how crystals grow and develop, creating complex structures on many length scales in the process. Because crystallization is a basic phase transition and crystals make up the foundation of several major industries, much effort has been expended toward developing a detailed understanding of the physics of crystal nucleation and growth. There is also a considerable literature on pattern formation during solidification. Beyond the intrinsic scientific merit of these problems, the burgeoning commercial interest in the self-assembly of nano-scale devices has reinvigorated our desire to understand just how solidification produces ordered, and sometimes complex, structures from disordered precursors. Structure formation during crystal growth is a rich many-body problem, for which there are few overarching theories and perhaps even fewer uncomplicated experimental systems. In part this reflects the fact that many factors contribute to crystal growth, including both largescale phenomena (e.g. particle and heat transport) and microscopic dynamics (e.g. surface diffusion and chemistry). Different crystals grown under different conditions exhibit a broad

range of morphologies, growth rates and other characteristics, reflecting the variety of physical mechanisms that influence crystal growth. The inherent complexity of the physics has resulted in a rather large gap between the basic tenants of crystal growth theory and the phenomenology

of growing practical crystals.

1.1. Ice as a case study

In many ways, the formation of ice crystals from the vapour phase is an excellent case

study of crystal growth dynamics and pattern formation during solidification. Although

it appears to be a relatively simple monomolecular physical system, the growth of snow

crystals exhibits a surprisingly rich behaviour as a function of temperature, supersaturation and other external parameters. As we will see below, a great deal of this behaviour remains unexplained, even at a qualitative level. Thus there is much to be learned, and ample potential that a better understanding of ice will contribute to our overall understanding of crystal growth and solidification. Taking the next step beyond the monomolecular system, ice crystal growth from water vapour is known to be quite sensitive to chemical influences at the growing surface, so again ice is an excellent case study for the more general, and exceptionally diverse, problem

of chemically mediated crystal growth.

While the physics of snow crystal formation is an excellent crystal growth problem,

it also touches on several environmental and meteorological issues, simply because ice

crystals often play major roles in atmospheric phenomena. For example, ice crystals are

important in cloud electrification and lightning, via charging mechanisms that involve collisions between ice particles. These mechanisms depend on details of the ice surface structure that are still not well understood [1Ð'-3]. Also, chemical processes in the upper atmosphere frequently require the surfaces of ice crystals to boost their reaction rates [4,

5]. Most meteorological phenomena involving ice particles, like the growth of snow crystals, are

influenced to some degree by the structure and dynamics of the ice surface. Thus we

expect they will share some common physics at a fundamental level. A better picture of

the dynamics of the ice crystal surface during growth may also shed light on some of the

many remaining mysteries surrounding the dynamics of the different solid and liquid states of water [6]. 858 K G Libbrecht

1.2. Natural snow crystals

Since snowcrystals fall from the sky in symmetrical, patterned forms, they have been the source of considerable curiosity and scientific study for centuries (for detailed historical accounts see [7Ð'-11]). Johannes Kepler was apparently the first person to look at snow crystals with a scientific eye, writing a short treatise devoted to the subject in 1611, in which he describes the possible origins of snowcrystal symmetry [12]. RenÐ'Ò'e Descartes penned an account of many different forms of natural snow crystals in 1637 as part of his famous treatise on weather phenomena,

Les MÐ'Ò'etÐ'Ò'eores (see [7]). These early investigations were followed by numerous accounts

that described, in words and with sketches, the great variety of snow crystal morphologies found