No. And also yes.
On a purely physical level, in 1988, researcher Nancy Knight found two virtually identical snowflakes.
The paper is called ‘No two alike?’, and was published in the Bulletin of the American Meteorological Society (Issue 69). Here is the image of the snowflakes taken from the paper:
Image Credit: NCAR
I could just leave it at that and knock off for lunch, but I’d like to think I’m more professional than that, so it’s worth delving into the topic a bit more.
Snowflakes form when very cold water comes into contact with a dust grain or pollen particle. The water coats the particle and freezes into an ice crystal. The newly-formed ice crystal can no longer be held up by the buoyancy of the air, so it falls. As it falls, more water and water vapour freezes onto the crystal, building it up in size. If the air between the cloud and the ground is below freezing, the snowflake will be preserved and continue to grow.
In terms of the crystal structure of snow, there are entire academic papers dedicated to the physics and chemistry of snowflake structures and diversity.
Most snowflakes start as a simple hexagonal structure, but many factors exist which can change how the crystal grows from there. Crystal temperature as the snowflake falls, the altitude at which the snowflake is formed, the speed it falls, the snowflake’s overall trajectory, variations in the diameter of the particle the water condensed onto, differences in the clouds, drop collisions and vapour pressure in the clouds all control how the crystal structures form.
Lower vapour concentrations cause a snowflake to grow more slowly and produce less intricate shapes. The shapes we most associate with snowflakes form more readily in higher vapour concentrations, or in colder conditions (like the ones found in high altitude cirrus clouds). Larger snow crystals can have more diversity in patterns than smaller crystals.
All these factors control how diverse snowflakes can be. Estimates of crystal diversity vary from 500 different types (cited from the paper linked above), to 30,000. A diversity curve for snowflakes, adorably called the mitten curve, is basically impossible to observe.
To get around this problem and determine the likelihood of crystal similarity, an approximation for snowflake uniqueness, called the Feller’s approximation, attempts to calculate the probability all crystals in a snow cloud are unique. In large snowstorms, there are enough crystals so that some crystals stand a good chance of looking like copies.
Taking all the snow that may have ever fallen to Earth, the Feller’s approximation tells us that two indistinguishable crystals almost certainly existed.
The only problem is, this is virtually impossible to disprove.
On a molecular level, the ‘impossible to prove’ problem exists for the opposite reasons. Two molecularly different snowflakes could very easily look alike under a microscope.
Since a typical small snow crystal might contain 1018 water molecules, we see that about 1015 of these molecules will be different from the rest. These unusual molecules will be randomly scattered throughout the snow crystal, giving it a unique design. The probability that two snow crystals would have exactly the same layout of these molecules is very, very, very small. Even with 1024 crystals per year, the odds of it happening within the lifetime of the Universe is indistinguishable from zero.
Thus, at some very pure level, no two snow crystals are exactly alike.
While there’s no way to prove if snowflake doppelgangers exist, snow has many wide reaching impacts on the climate of the entire globe.
Even if there aren’t unique snowflakes, those small crystals are tiny cogs in an amazingly complicated climatological system that affects the entire planet. Perhaps that’s the real magic of snow.
Or maybe it’s just the excuse to stay in with hot drink, or snowball fights in the Peaks.