What symmetries are found in water molecules

The wonderful physics of the snowflake

This story is about a material that could hardly be more contradicting. Omnipresent, almost banal, and at the same time of immense importance and symbolic radiance. It forms the basis of all life on this planet, and it is also able to unleash destructive forces that are looking for their equal.

Although it consists of two of the three most common elements in the universe, pure, liquid water is an immensely precious commodity and, in terms of its physical properties, water is downright exotic! Water is a small molecule that occurs on earth in solid, liquid, and gaseous states. This is remarkable because similarly small molecules appear exclusively in gaseous form under Earth-like conditions. The decisive factors as to whether a substance occurs as a gas, liquid or solid are primarily temperature and pressure. If the temperatures drop below 0 ° C at typical earth pressure, the rules for the interaction of water particles change dramatically: If the liquid state can be depicted as the wild dancing around of the molecules, in which connected groups are only of short duration, then the solid state must be Remaining in tight formation can be described.

If we take a closer look at snowflakes, we first notice that they all come from a certain "Sixfold" are shaped. But to say they are hexagonal would do them an injustice, as they have many, many more corners. Around "Sixfold" to describe, we use the term symmetry, and mean in the case of a sixfold (rotational) symmetry of the snowflake that after a sixth of a turn it looks the same as in its starting position. This symmetry of a whole snowflake is visible to the naked eye, and yet it manifests the interaction of individual water molecules, which measure just a fifth of a billionth of a meter.

This sixfold symmetry provides the pattern according to which snowflakes can theoretically unfold in an almost infinite variety of shapes. Depending on the pressure and temperature, water molecules come together in different formations. In fact, there are more than fifteen different types of ice, and they all differ in their molecular formations. Most of these types of ice are only formed under special pressure conditions or at special temperatures. Snow, and almost every other form of ice on earth are made up of the so-called Ice cream I.H, in which water molecules come together in hexagonal formations and thus form a crystal lattice.

In contrast to liquid water, where the angle between the two hydrogen atoms is 105 °, the structure of the water molecule in the crystal lattice of the ice is stretched a little to fit better into the formation, and the angle becomes 109.5 °. That is why water molecules need more space in ice than in a liquid state, and that is why ice has a higher density than liquid water. The expansion when cooling down is a property that is found only in a few substances, and we owe it to us that life on earth is possible at all. If ice - as usual - had a lower density than water in its liquid state, it would not float and water would freeze over from bottom to top. But since ice floats, ice forms a good insulating layer, and aquatic life can spend cold periods, even in the Antarctic, under a layer of ice in liquid water. Whether ice or snow forms is not a question of the crystal lattice, but rather depends on the conditions under which water freezes. Snowflakes are formed from tiny drops of undercooled water. Water droplets that do not contain any impurities can be cooled to well below freezing point (-18 ° C) and still remain liquid. You kind of forget to freeze. However, if you come across a speck of dust, everything goes very quickly: The speck of dust helps the water molecules to find the correct six-digit formation. If the surrounding air is full of small droplets of supercooled water, the snowflake can now grow. Trillions (a one followed by eighteen zeros, or 10 for short18) of water molecules arrange themselves into the formation as quickly as possible. A water molecule can adopt six different orientations in the crystal lattice. Since the crystallization from supercooled water droplets takes place particularly quickly, each water molecule settles in the most easily accessible position, and rays are formed at the tips of which the water molecules can easily arrange themselves. Since it is a matter of chance where a water molecule is located, it is also chance that determines the shape of the hexagonal grid. Small differences at the beginning eventually turn into big ones. The snowflake begins to fall, but it keeps growing. On its journey to the ground, each snowflake encounters different atmospheric conditions - sometimes it encounters a little more water, sometimes it is a little warmer, sometimes the pressure is a little higher. All these properties mean that the shape of a snowflake itself ultimately represents a small symphony of its own existence, which pressure and temperature have written into the crystal lattice.

So it is hardly surprising when you hear everywhere that every snowflake is unique! Because compared to the number of theoretically possible snowflakes (a number that is difficult to put into words and even less easy to write down, since it has about a trillion digits; the answer is astronomical in the truest sense, namely it exceeds Number of all atoms in the universe. *) Is itself the number of snowflakes that are estimated to fall in one year, namely about one quadrillion ** (1024), tiny. Nevertheless, folk wisdom can be enjoyed with a pinch of salt: The number of possible shapes for large snowflakes is many times greater than for small ones. Accordingly, it is also more likely to find two small snowflakes that are alike.

But even this small rebuff to a romantic idea should not detract from the magic that emanates from snowflakes. It is the variety of small, differently sized areas in diverse orientations that gives the snow that soothing quality that covers a freshly snowed-in landscape with the silence that is sung about in many a Christmas carol. It is also the reason why snowflakes, which are gathered by the millions in an ordinary pile of snow, shine in the purest white, even though each snowflake is completely transparent in itself. Snowflakes and snow compacted into ice in their multifaceted nature almost completely reflect white light and influence how well our planet reflects incident sunlight. As part of the so-called albedo, they are not only a form of the climate, but also have a decisive influence on it. As the polar ice caps melt, the Earth's ability to reflect sunlight and stay cool also decreases ...

The fable of the speck of dust, which has become the epitome of purity, is as rich in facets as the snowflake itself; a journey of epic scale that took us from the dance of almost invisible particles to processes of global scale. And it ends on a bittersweet note: Despite all the beauty it contains, this story of the snowflake in all its complexity and fragility ultimately serves as a memorial to a threatening climate catastrophe.

Further reading:

  • Philip Ball - H2O biography of water, 2001, ISBN: 3492041566
  • Kenneth G. Libbrecht - snowcrystals.com The website on the subject from the world's leading expert in snowflakes.
  • Ryo Kobayashi"Modeling and numerical simulations of dendritic crystal growth." Physica D: Nonlinear Phenomena 63.3-4 (1993): 410-423. - Technical article that forms the basis for our simulations of snowflake growth.
  • Roberto Maffulli - iSeeing - Github repository with Python code to recreate our simulations

* To estimate the number of possible snowflake shapes, we can imagine a crazy bicycle lock where there is a separate wheel for each of our trillion water molecules in a snowflake. The numbers one to six are shown on each wheel and they describe the orientation of a particular water molecule. Now all we have to do is calculate how many different combinations this bike lock would have. This number of combinations increases sixfold with each wheel of our bicycle lock. In our case, it increases sixfold by a trillion times (in short: 61018).

** Approximately one million billion (1015 kg) kg of snow. With an average weight of around one billionth of a kilogram (10-9 kg), that roughly equates to one quadrillion snowflakes per year (1024).

About the authors

Lukas Hutter studied chemistry in Graz and systems biology in Oxford. He is one of the co-founders of Biotop and currently works as a teacher in Villach.

Roberto Maffulli is a specialist in flow theory and currently works as a lecturer at Balliol College, Oxford University.