What was the first written account about snowflake shapes and when did physicists start to study the reasons why the form appears and how snowflakes form in the air?
Is there any old book that mentions these aspects?
There is a very nice site SnowCrystals.com run by Kenneth Libbrecht, a professor of physics at Caltech, which covers both physics and history, and hosts many captivating images, videos and more.
According to Libbrecht's Snowflake History, the first written mention is by Han Yin c. 135-150 BC: "Flowers of plants and trees are generally five-pointed, but those of snow, which are called ying, are always six-pointed". In the 6th century AD Chinese poet Hsiao Tung seconded the observation:“The ruddy clouds float in the four quarters of the cerulean sky. And the white snowflakes show forth their six-petaled flowers.”
Kepler was not quite the first in Europe. Scandinavian bishop Olaus Magnus described snowflakes in 1555, although according to him their shapes included crescents, arrows, and even a human hand (Libbrecht has an image). English astronomer Thomas Harriot identified the characteristic hexagonal shape symmetry in 1591. But Kepler's Six-Cornered Snowflake (1611) was much more systematic, and regarding snowflake shapes, as in astronomy, he rejected the medieval mode of explanation a la Molieres "opium puts you to sleep because it has sleep-inducing power".
"Each single plant has a single animating principle of its own, since each instance of a plant exists separately, and there is no cause to wonder that each should be equipped with its own peculiar shape. But to imagine an individual soul for each and any starlet of snow is utterly absurd, and therefore the shapes of snowflakes are by no means to be deduced from the operation of soul in the same way as with plants."
But even Kepler was still mostly contemplative and speculative. On the other hand, Descartes in Les Météores (1637) reported some "remarkably thorough" empirical naked-eye observations of snow crystals, including the rarer forms like capped columns.
According to Libbrecht, "not all snowflakes look like six pointed stars. Many do, but there are also quite a few odd-looking crystals falling from the winter clouds". In particular, there are dodecagonal crystals, but there are no human handed or octogonal ones, Olaus Magnus and Google's Doodle notwithstanding. The hexagonal shape is predominant, and Francis' Why Are Snowflakes Always Six-Sided? explains the formation process:
"The hydrogen bonding dictates the shape of the ice crystals. You’ve learned that each water molecule is linked to four other water molecules in a tetrahedral arrangement. As the water freezes, these tetrahedrons come closer together and crystallize into a six-ring or hexagonal structure... Each point on the hexagon is an oxygen atom, and each side is a hydrogen bonded to one oxygen. As the water approaches freezing temperature, the water molecules continue to crystallize in this tetrahedral arrangement.
But water does something unlike most substances. As it nears freezing, instead of continuing to contract, it expands slightly from about 4 degrees to 0 degrees Celsius as the motion of the molecules slows with the cold, and the hydrogen bonds extend the molecules to their fullest distance from each other. It’s like a ring of people holding hands, elbows bent, and then gradually straightening their arms to the fullest extension so that they’re at the greatest distance from each other. When water molecules do this, the hexagonal structure expands into a larger and larger hexagonal structure. The snowflake, with its six sides, is what results from this process..."