The phenomenon of water freezing at 0°C that you see is because the water is dirty, the water is in contact with something else, or because the water is turbulent.
Written by | Zexian Cao (Institute of Physics, Chinese Academy of Sciences)
One distinctive feature that distinguishes Earth from other planets is that 70% of its surface is covered with water. Assuming that the Earth's surface is evenly covered with water, the average water depth can reach 2700 meters. The physical conditions of the earth's surface are precisely the ones that allow the solid-liquid-gas phases of water to coexist in one corner (that is, the temperature-pressure conditions on the earth's surface are exactly near the three-phase point of water!). This feature is of second to none to understanding the origin of life on Earth, as well as to understanding the physics created by humans (Figure 1). Remember that all the properties of water are abnormal and cannot be normalized. The solid phase of water, as far as large pieces of ice are concerned, there are 16 known crystal phases, of which 3 are actually lighter than liquid water. Thankfully, the ice common in nature, the Ih phase, is lighter than water— and if it weren't, you wouldn't have a chance to skate on the river unless it freezes completely from the bottom up. Incidentally, the homogeneous nuclei of water have a temperature of about 232 K (minus 41°C). That is to say, the phenomenon of water freezing at 0°C that 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 is also small and less crystalline, including frost (rime), snow, rime, hail (hail), soft hail (graupel), sleet (sleet) and so on. Among them, snow is the most beautiful, and there is a saying of snowflakes in Chinese. How many people's reverie have been aroused by the snowflakes that have been raised?
Figure 1. A common scenario on the surface: the coexistence of solid-liquid-gas phases of water in a small area
Snowflakes are generally flaky, millimeter-sized, and visible to the naked eye. One of the characteristics of snowflakes is that different snowflakes are generally hexagonal. During the Western Han Dynasty of the mainland, Han Bao said in the "Biography of Han Poetry" that "where there are five more flowers and flowers, and six snowflakes are unique", the first half of the sentence is not correct, but the second half of the sentence is correct. In later literature, the saying of six snowflakes abounds, but the statement of six out is actually very vague. Six out, what kind of six out of the law? Further, we can ask, why?
The earliest recorded study of the shape of snowflakes and their formation mechanism is the German scientist Johannes Kepler (1571-1630), a man who left us with the three laws of planetary motion as a glimpse into the mysteries of God by declaring, "I am better than you humans." As early as 1611, Kepler published a 24-page pamphlet, de nive sexangula (Figure 2), which attempted to explain the hexagonal morphology of snowflakes using a stacked model of small balls. The accumulation of small balls is certainly not enough to explain the hexagonal appearance of snowflakes, but Kepler's book is a precedent for understanding the atomic structure of matter, especially crystals, using the ball accumulation model. It can be said that Kepler's research sowed the seeds of crystallography - the original geometry of crystals can be explained by the accumulation of small pellets. In addition, Kepler's research raises an important mathematical problem, which is known today as the Kepler conjecture, that is, for all-identical balls, hexagonal dense accumulation is the most dense accumulation method. Kepler's influence on crystallography was so great that in 1981 someone wrote a classic paper modeled after "Hexagonal Snowflakes" (Alan L. Mackay, De Nive Quinquangula, Krystallografiya, Vol. 26, 910-919 (1981)）。 In 1984, quasicrystals with five-fold symmetry were discovered.
Fig. 2 Kepler's book Hexagonal Snowflakes and the model of ball stacking in it
A prerequisite for understanding the shape of snowflakes and how they form is to know what snowflakes really look like. However, even in the cold of northern China, it is difficult to observe and record the shape of snowflakes, which are very small (millimeters in size) and melt quickly. Therefore, although there is a saying in the literature of our ancestors that "snowflakes are six out", it is difficult to communicate with others what snowflakes are like. If you want to talk about snowflakes, you must first paint and take pictures of snowflakes. The first photograph of snowflakes is believed to have been taken in 1879 by the German Johann Heinrich Ludwig Fl gel (1834-1918) (Figure 3).
Figure 3. Frogg's photograph of snowflakes in 1879
The American Wilson Alwyn Bentley (1865-1931) who seriously considered photographing snowflakes as a career (Figure 4). Bentley was born in 1865 in the small town of Jericho, Vermont, usa, which is famous for its snow belt, with an annual snowfall of up to 300 cm. At the age of 15, Bentley received a birthday present from his mother, a small microscope, a mundane family gesture that accomplished something important in the history of science. Bentley loves photography, and the snow in his hometown stimulates his intense curiosity. At some point, he had a fervent desire to take a picture of the snowflakes. In 1885, at the age of 19, Bentley added a microscope to a camera and obtained his first photograph of a snowflake on January 15 (Figure 5). Obviously, Bentley's snowflake photo is of much higher quality than Flogg's previous photo. One of the significances of Bentley's snowflake photos is to open the microphotography technology, which has reached the ability to distinguish atomic images today, which has greatly promoted the development of modern science and technology.
Figure 4. Bentley, an American farmer and photographer, photographs snowflakes
Figure 5. Bentley's first photograph of snowflakes
The success of getting the first snowflake photo made Bentley even more fascinated by taking pictures of snowflakes. Bentley is often seen standing in the snow and wind, using feathers or flannel to pick up falling snowflakes, carefully placing the sample under the microscope head of a camera that is also placed outdoors. Bentley has obtained more than 5,000 snowflake photographs, and in the process Bentley has perfected its snowflake photography techniques. The second significance of Bentley's photographs of snowflakes was that they sparked interest in studying snowflakes. In his 1931 book Snow crystals, he showed more than 2,500 photographs of snowflakes with lace designs, of which there were always hexagonal symmetrical but different styles of snowflakes that fascinated people (Figure 6).
Figure 6. Bentley's book Snow Crystal and the different shapes of snowflakes he photographed.
Bentley noticed from his photographs that although snowflakes were generally hexagonal, he had never taken two of the same pictures—Every single snowflake was unique. The idea that each snowflake is different may not convince everyone, after all, the number of snowflakes being photographed is very limited, and the definition of "different" is also vague. However, it is already incredible that snowflakes can exhibit so many different forms known while maintaining hexagonal symmetry. Bentley wrote emotionally: "Under the microscope, I find snowflakes amazingly beautiful, and it would be a shame if this beauty could not be seen and shared with others." Each crystal is an outstanding design piece, and none of them are repetitive. Once the snowflakes melt, the design disappears forever. Imagine how many snowflakes have fallen on the earth, and only a few have been recorded, which is a pity.
In order to give everyone a more intuitive understanding of the beauty and beauty of snowflakes, you may wish to add a few more photos of snowflakes obtained with modern photography techniques (Figure 7). If you don't think it's too addictive, please search for snowflake, snowflake, snow crystal and other words.
Figure 7. Photos of snowflakes taken with modern technology
The formation process and morphology of snowflakes remain a frontier issue for scientists today. With clearer, more beautiful pictures of snowflakes, I thought I could understand the formation process of snowflakes more deeply, but I was more and more confused about the atomic processes and thermodynamics of snowflake growth. It has now been established that snowflakes have a generally consistent and unique shape in different regions of the plane of the two variables, temperature and water vapor supersaturation (Figure 8), but will exhibit different morphologies in different regions that are far apart. For water to freeze, some water molecules must first form some micron-sized ice cores, that is, a process that requires a preformed nucleus. Snowflake formation should have two processes of droplets being subjected to cold nuclei and growth, and the final shape of the snowflake can be classified as dendrite. The current so-called Structure-dependent attachment kinetics model of snowflake growth mechanism is only an improvement on the previous model of crystal growth kinematics, and is far from enough to answer the question of snowflake morphology.
Figure 8. Temperature-water vapor supersaturation plane of snow crystal morphology
For the requirement of a paved plane, the hexagon is most appropriate as a unit (motif) (Figure 9) because its topological charge, i.e., the value of its V-E+F (V, number of vertices; E, number of edges; F, number of faces) defined by the author in the laying, is always 0. Of course, this fact is not a hard restriction that requires water droplets to become hexagonal symmetrical wafers.
Figure 9. beehive. Hexagonal lattice paving is nature's favorite.
After half a day of talking, there is no convincing answer to why snowflakes are so charming, but each snowflake is unique. Don't blame the scientists, there are very few problems that scientists really understand – scientists themselves are in a hurry. Finally, as a consolation, give you a hint to shoot snowflakes. The most frightening thing about shooting snowflakes is that the snowflakes will melt before they are filmed. In order to shoot beautiful snowflakes, choose sweaters, silk cloths and other items with very poor thermal conductivity and cool enough to undertake snowflakes, shoot outdoors in the cold, and shoot macro with several times the magnification. Of course, the melting snowflakes are also beautiful (Figure 10). As a reverse problem, perhaps the melting process of snowflakes will give us enlightenment about the formation mechanism of snowflakes.
Figure 10. Snowflakes that start to melt
exegesis
[1] Cao Zexian, An Extraordinary Thought, 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 mention
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