Snowflakes are all hexagonal, and each one is unique. Why? | Xian Shuo Ba Dao

The phenomenon of water freezing at 0°C that you see is because the water is dirty, the water has come into contact with other substances, or because the water is turbulent.

Written by Cao Zexian (Institute of Physics, Chinese Academy of Sciences)

One of the most striking features of the Earth that distinguishes it from other planets is that 70% of its surface is covered by water. Assuming that the entire surface of the Earth is uniformly covered by water, the average depth of the water is as much as 2,700 meters. The physical conditions on the Earth's surface are just right for the solid-liquid-gas phases of water to coexist in one corner (that is, the temperature-pressure conditions on the Earth's surface are just near the triple point of water!), which is of paramount importance for understanding the origin of life on Earth and the physics created by humans (Figure 1). Remember that all the properties of water are abnormal and cannot be measured by common sense. The solid phase of water, as far as large blocks of ice are concerned, is known to have 16 crystalline phases, of which 3 are actually lighter than liquid water. Thankfully, the common ice in nature, the Ih phase, is lighter than water - if it were not so, you would not have the opportunity to skate on the surface of a river unless it was completely frozen from the bottom up. By the way, the homogeneous nucleation temperature of water is about 232 K (minus 41°C). That is to say, the freezing of water at 0℃ you see is because the water is dirty, the water is in contact with other substances, or because the water is turbulent. The solid phase of water also has small pieces and poor crystallization, including frost (rime), snow, rime, hail, soft hail (graupel), sleet, etc. Among them, snow is the most beautiful, and Chinese people say "雪花". How many people have been inspired by the falling snowflakes?

Figure 1. Common scene on the Earth’s surface: solid, liquid and gas phases of water coexist in a small area

Snowflakes are generally flake-shaped, millimeter-sized, and visible to the naked eye. One characteristic of snowflakes is that different snowflakes are generally hexagonal. Han Ying of the Western Han Dynasty in my country said in "Han Shi Waizhuan" that "most flowers of plants and trees have five petals, but snowflakes have six petals." The first half of this sentence is wrong, but the second half is correct. In later literature, there are many references to snowflakes having six petals, but the statement of six petals is actually very vague. What is the six-petal method? We can further ask, why?

The earliest person who has a record of studying the shape of snowflakes and their formation mechanism is the German scientist Johannes Kepler (1571-1630), a man who left us the three laws of planetary motion and was considered to have glimpsed the mystery of God because he claimed that "I am better than you humans." As early as 1611, Kepler published a 24-page booklet "De nive sexangula" (Figure 2), trying to use the stacking model of small balls to explain the hexagonal shape of snowflakes. The stacking of small balls is certainly not enough to explain the hexagonal shape of snowflakes, but Kepler's book opened the precedent of using the ball stacking model to understand the atomic structure of matter, especially crystals. It can be said that Kepler's research sowed the seeds of crystallography - it turns out that the geometric shape of crystals can be explained by the stacking of small balls. In addition, Kepler's research raised an important mathematical problem, which is now called Kepler's conjecture, that is, for identical spheres, hexagonal close packing is the densest stacking method. Kepler's influence on crystallography was so great that in 1981, someone wrote a classic paper called "Pentagonal Snowflake" based on the "Hexagonal Snowflake" (Alan L. Mackay, De Nive Quinquangula, Krystallografiya, Vol. 26, 910-919 (1981)). In 1984, quasicrystals with five-fold symmetry were discovered.

Figure 2 Kepler's book "Hexagonal Snowflake" and the sphere stacking model in it

To understand the shape of snowflakes and their formation mechanism, a prerequisite is to know what snowflakes look like. However, even in the cold northern China, it is difficult to observe and record the shape of snowflakes. Snowflakes are very small (millimeter size) and melt quickly. Therefore, although our ancestors' documents say that "six snowflakes" exist, it is difficult to communicate with others what snowflakes look like. To talk about snowflakes, we must first draw and photograph them. It is believed that the first snowflake photo was taken by the German Johann Heinrich Ludwig Flögel (1834-1918) in 1879 (Figure 3).

Figure 3. Photo of snowflakes taken by Frog in 1879

Wilson Alwyn Bentley (1865-1931) (Figure 4) was an American who took snow photography seriously. Bentley was born in 1865 in the small town of Jericho, Vermont, USA, which is a famous snow belt with an annual snowfall of up to 300 cm. When he was 15 years old, Bentley received a birthday gift from his mother - a small microscope. This ordinary family warm gesture made a great event in the history of science. Bentley likes photography, and the heavy snow in his hometown aroused his strong curiosity. At some point, he had an ardent desire to take a picture of snowflakes. In 1885, the 19-year-old Bentley installed a microscope on a camera and took his first personal snowflake photo on January 15 (Figure 5). Obviously, Bentley's snowflake photo is of much higher quality than Frog's previous photos. One of the significances of Bentley's photos of snowflakes is that it opened up the field of microscopic photography. Today, microscopic photography technology has reached the level of being able to resolve atomic images, greatly promoting the development of modern science and technology.

Figure 4. American farmer and photographer Bentley taking pictures of snowflakes

Figure 5. Bentley's first snowflake photo

The success of taking the first snowflake photo made Bentley even more fascinated with photographing snowflakes. People often saw Bentley standing in the snow, using feathers or flannel to catch falling snowflakes, and carefully placing the samples under the microscope of a camera that was also placed outdoors. Bentley obtained more than 5,000 snowflake photos in total, and in the process he perfected the snowflake photography technique. The second significance of Bentley's snowflake photos is that it stimulated people's interest in studying snowflakes. In his book "Snow Crystals" published in 1931, more than 2,500 snowflake photos with lace designs were displayed, among which the snowflake photos that were always hexagonally symmetrical but with different styles really fascinated people (Figure 6).

Figure 6. Bentley’s book Snow Crystal and the snowflakes of various shapes he photographed.

Bentley noticed from his photographs that, although snowflakes are generally hexagonal, he never photographed two alike—every single snowflake is unique. The idea that every snowflake is different may not convince everyone, after all, the number of snowflakes photographed is limited, and the definition of "different" is vague. But it is incredible that snowflakes can show so many different known forms while maintaining hexagonal symmetry. Bentley wrote emotionally: "Under the microscope, I found the snowflakes to be so amazingly beautiful that it would be a pity if this beauty could not be seen and shared with others. Each crystal is a brilliant design, and no two are repeated. Once the snowflake melts, the design is gone forever." Imagine how many snowflakes have fallen on the earth, and it is a pity that only a few have been recorded.

In order to give you a more intuitive understanding of the beauty and diversity of snowflakes, let's add a few more photos of snowflakes obtained using modern photography technology (Figure 7). If you still feel that this is not enough, please search using the words snowflake, snowflake, snow crystal, etc.

Figure 7. Snowflake photos taken using modern technology

The formation process and morphology of snowflakes are still a frontier topic that puzzles scientists today. With clearer and more beautiful snowflake photos, we thought we could have a deeper understanding of the formation process of snowflakes, but the result is that we are more confused about the atomic process and thermodynamics of snowflake growth. Now people have determined that in different regions on the plane formed by the two variables of temperature and water vapor supersaturation, snowflakes have a roughly consistent unique shape (Figure 8), but they will show different morphologies in different regions far away. For water to freeze, some water molecules must first form some micron-sized ice nuclei, which requires a pre-nucleation process. The formation of snowflakes should have two processes: nucleation of droplets by cooling and growth. The shape of the snowflakes obtained in the end can be classified as dendrites. The current so-called Structure-dependent attachment kinetics model of the snowflake growth mechanism is just an improvement on the previous crystal growth kinematics model, which is far from enough to answer the question of snowflake morphology.

Figure 8. Phase diagram of snow crystal morphology in the temperature-water vapor supersaturation plane

For the requirement of paving the entire plane, the hexagon is the most suitable unit (motif) (Figure 9), because its topological charge, that is, the value of V-E+F (V, number of vertices; E, number of edges; F, number of faces) defined by the author in the paving, is always 0. Of course, this fact is not a hard limit for requiring the water droplet to become a hexagonally symmetrical wafer.

Figure 9. Honeycomb. The hexagonal grid is nature’s favorite.

After all this talk, there is still no convincing answer to why snowflakes are so charming, yet each snowflake is unique. Don't blame scientists, there are actually very few problems that scientists truly understand - scientists themselves are also anxious. Finally, as a consolation, here is a tip for taking pictures of snowflakes. The most feared thing about taking pictures of snowflakes is that the snowflakes melt before you take a good picture. In order to take beautiful pictures of snowflakes, choose sweaters, silk cloths and other items with very poor thermal conductivity and sufficient coolness to hold the snowflakes, take pictures outdoors in the cold, and use a few times the magnification for macro photography. Of course, melted snowflakes are also beautiful (Figure 10). As an inverse problem, perhaps the melting process of snowflakes will give us some inspiration about the formation mechanism of snowflakes.

Figure 10. Snowflakes starting to melt

Notes

[1] Cao Zexian, One Thought is Extraordinary, Foreign Language Teaching and Research Press (2016).

[2] Philip ball, On the six-cornered snowflake, Nature 480, 455(2011).

[3]Kenneth G. Libbrecht, The physics of snow crystals, Reports on Progress in Physics 68, 855(2005).

Special Tips

1. Go to the "Featured Column" at the bottom of the menu of the "Fanpu" WeChat public account to read a series of popular science articles on different topics.

2. Fanpu provides a function to search articles by month. Follow the official account and reply with the four-digit year + month, such as "1903", to get the article index for March 2019, and so on.

Copyright statement: Personal forwarding is welcome. Any form of media or organization is not allowed to reprint or excerpt without authorization. For reprint authorization, please contact the backstage of the "Fanpu" WeChat public account.