How fascinating are snowflakes?Why is that?Eight | xian said

2022-05-07 0 By

Snow is one of the small-scale solid forms of water.Snowflakes are hexagonal and have A D6 symmetry, but each snowflake is unique.How snowflakes can vary in shape while maintaining the symmetry of D6 has long been a puzzle.The first person to study the formation mechanism of snowflakes was Kepler, who proposed the three laws of planetary motion, and brought about the sphere-dense accumulation model of solids.Writing | cao xian (institute of physics, Chinese Academy of Sciences) source | back to park the earth different from other planets a remarkable feature is 70% of its surface is covered by water.If the earth’s surface were uniformly covered with water, the average depth would be 2,700 meters.The physical conditions on the earth’s surface are just right for the three phases of water, solid, liquid, and gas to coexist in one corner.This feature is of Paramount importance for understanding the origin of life on Earth, as well as the physics of human creation (Figure 1).Remember, all the properties of water are abnormal and cannot be reasoned with.Of the sixteen crystalline phases known of water, as far as ice is concerned, three are actually lighter than liquid water.Thankfully, nature’s common ice, Ih phase, is lighter than water — otherwise you wouldn’t be able to skate on a river unless it froze completely from the bottom up.By the way, the homogeneous nucleation temperature of water is about 232 K.So when you see water freezing at 0 degrees Celsius, it’s because the water is dirty, it’s in contact with something else, or it’s turbulent.The solid phase of water also has small pieces that do not crystallize well, including frost, rime, snow, rime, hail, graupel, sleet and so on.Among them, snow is the most beautiful, and there is a Chinese word for snow.Swirl of snow, caused how many people reverie?Figure 1. A common scenario on the surface: three-phase coexistence of water, liquid, and gas in a small area snowflakes are generally flaky, millimeters in size, and visible to the naked eye.One of the things about snowflakes is that different snowflakes are generally hexagonal.Han Ying, in the Western Han Dynasty, said in his Biography of Korean Poetry that “there are five flowers on every plant and six snowflakes alone”. The first half of this sentence is not correct, but the second half is correct.In the later literature, the statement of six snowflakes can be found everywhere, but the statement of six snowflakes is actually very vague.Six out? What kind of a six out?Further we can ask, why?The earliest recorded study of the shape of snowflakes and how they form was by Johannes Kepler (1571-1630), a German scientist who gave us the three laws of planetary motion as a peek into the mysteries of God by declaring: “I am better than you men.”As early as 1611, Kepler published a 24-page pamphlet de Nive Sexangula (FIG. 2), which attempted to explain the hexagonal shape of snowflakes using a model of the stacking of spheres.Of course, ball packing is not enough to explain the hexagonal shape of snowflakes, but Kepler’s book was the first to use the ball packing model to understand the atomic structure of matter, especially crystals.Kepler’s work sowed the seeds of crystallography: the geometry of crystals could be explained by the way the pellets stacked up.In addition, Kepler’s work raised an important mathematical problem, known today as the Kepler conjecture, namely that hexagonal packing is the densest form of packing for identical spheres.Kepler’s influence on crystallography was so great,So much so that in 1981 someone wrote a classic paper on the hexagonal Snowflake called “Pentagonal Snowflake” (Alan L. Mackay, De Nive Quinquangula, Krystallografiya, Vol. 26, 910-919 (1981)).In 1984, quasicrystal with quintic symmetry was discovered.Figure 2 Kepler’s Hexagonal Snowflake and his ball-packing model One prerequisite for understanding the shape of snowflakes and how they form is to know what a snowflake actually looks like.However, even in cold northern China, it is difficult to observe and record the shape of snowflakes, which are small (millimeters in size) and melt quickly.Therefore, although there is a saying of “six snowflakes appear” in the literature of our ancestors, it is difficult to communicate with others about what snowflakes really look like.To talk about snowflakes, you first have to draw and photograph them.The first photograph of a snowflake is believed to have been taken by German Johann Heinrich Ludwig Flogel (1834-1918) in 1879 (FIG. 3).Wilson Alwyn Bentley (1865-1931), an American, took snowflake photography seriously as a career (FIG. 4).Bentley was born in 1865 in the small town of Jericho, vermont, which is famous for its snow belt, with annual snowfall of up to 300cm.When Bentley was 15, he received a small microscope as a birthday present from his mother. It was an ordinary family gesture that turned into a scientific event.Bentley loves photography, and his curiosity was sparked by the constant snow in his hometown.I do not know when, he had a fervent desire to take a picture of snow.In 1885, at the age of 19, Bentley attached a microscope to a camera and got his first picture of a snowflake on January 15 (FIG. 5).Bentley’s snowflake photo was clearly of much higher quality than flog’s.One of the significance of Bentley’s photographs of snowflakes was that he pioneered photomicrography, which today has achieved the ability to distinguish atomic images, greatly promoting the development of modern science and technology.5. Bentley’s first photo of a snowflake Success in getting his first photo of a snowflake made Bentley even more interested in taking pictures of snowflakes.Bentley is often seen standing in the snow, using feathers or flaps to catch falling snow, carefully placing samples under the microscope of a camera that is also kept outside.Bentley acquired more than 5,000 photographs of snowflakes, perfecting his technique in the process.The second thing Bentley did with his snowflake photographs was to stimulate interest in snowflakes.In his 1931 book Snow Crystals, he showcased more than 2,500 lacy photographs of snowflakes, mesmerising people with their hexagonal symmetry and varying shapes (Figure 6).Figure 6. Bentley’s Book Snow Crystal and his photographs of snowflakes of various shapes.Bentley noticed from his photographs that although the snowflakes were generally hexagonal, he had never photographed two of them — Every single snowflake is unique.The idea that every snowflake is different may not convince everyone, given the limited number of snowflakes photographed and the vague definition of “different.”But it is remarkable that a snowflake can take on so many different forms that are known while maintaining hexagonal symmetry.”Under the microscope,” Bentley wrote, “I found snowflakes to be stunningly beautiful, and it would be a shame if that beauty could not be seen and shared.Each crystal is a masterpiece of design, and none of it is repetitive.Once the snow melts, the design is gone forever.”Imagine how many snowflakes have fallen on the earth, and only a few have been recorded. It’s a shame.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 techniques (Figure 7).If you still don’t like it, please use the words snowflake, snowflake, snow crystal, etc.Now let’s see what snowflake six means.Snowflakes are centrosymmetric, always made up of six identical, left-right branches.In scientific terms, snowflakes have D6 symmetry.However, this striking feature may be sufficient to describe microcrystals of materials such as ZnO, which are barely changeable, but not enough to describe snowflakes.Snowflakes are always doing new things while maintaining an overall D6 symmetry.B: Why?Leaving aside the fact that a snowflake is a solid of water, even when it comes to mathematically constructing snowflake patterns — patterns that maintain D6 symmetry but differ from one another — you find that people’s imaginations are limited.Compared with the reality of nature, human imagination is too pale.How snowflakes form and how they look is still a topic that baffles scientists today.With clearer, more beautiful photographs of snowflakes, we expected to have a deeper understanding of how snowflakes form. Instead, we were more puzzled by the atomic processes and thermodynamics of snowflake growth.It has now been established that snowflakes have generally uniform distinctive shapes in different regions of the plane of temperature and water vapor supersaturation (FIG. 8), but exhibit different shapes in regions far apart.For water to freeze, a few water molecules must first form micron-sized ice cores, which requires a pre-nucleation process.The formation of snowflakes should involve two processes of droplet nucleation and growth, and the final shape of snowflakes can be classified as dendrite.Currently, the so-called structure-dependent attachment kinetics model of snowflake growth mechanism is only an improvement on the previous crystal growth kinematic model, which is far from enough to answer the question of snowflake morphology.FIG. 8. The phase diagram of snow crystal morphology in the temperature-water vapor supersaturation plane shows that the key to understanding the shape of snowflakes is the nucleation process rather than the subsequent dendrite growth process.It would have been a phase transition (and volumetric expansion) of supercooled droplets of sufficient size, rather than a growth process from scratch.To do this, three questions need to be clearly answered: 1. Why do three-dimensional droplets become flaky when they become solid?2. Why is the chip hexagonal?3. How to create such varied shapes while maintaining the symmetry of D6?Of these three questions, probably the second is the best.Hexagonal configurations are common in nature. The hexagonal motif is the most appropriate element for the requirement of a paved plane (FIG. 9), because its topological charge is defined by the author as its V-E+F (V, number of vertices;E, the number of edges;F, number of faces, is always zero.Of course, this fact is not a hard limit on the water droplets becoming hexagonal wafers.FIG. 9. Honeycomb.Hexagonal grid is nature’s favorite.After all, there is no convincing answer to why snowflakes are so fascinating and yet each one is unique.Don’t blame scientists. There are very few problems that scientists really understand — scientists themselves are in a hurry.Finally, as a consolation, here’s a tip for photographing snowflakes.The worst thing about taking a snowflake is that it will melt before it’s done.In order to get beautiful snowflakes, choose very poor thermal conductivity, cool enough sweaters, silk and other items to undertake snowflakes, to take pictures in cold outdoor, with several times the magnification of macro photography can be.Of course, melting snow is also beautiful (Figure 10).As a reverse problem, maybe the melting of snowflakes will give us some insight into how they form.[1] Cao Zexian, Yi Nifan Fei, 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).