Why no two snowflakes are the same

November 14, 2011

Nature forced Washingtonians to contemplate winter earlier than most would have liked this year, as a rare October storm dropped as much as six inches of snow around the region. The early snow was a perfect excuse to ponder an age-old question: Is it true that no two snowflakes are alike?

The answer turns out to be a combination of physics and metaphysics.

Let’s start with an introduction on snowflake formation. As you’re probably aware, evaporation from lakes and rivers, transpiration of plants, and human and animal exhalation send water vapor up into the atmosphere. That water vapor gathers in clouds.

Water molecules in clouds engage in a complex dance of phase changes. Variables such as temperature, pressure and even the presence of dust can affect snow formation. When it gets cold, the gaseous molecules want to enter the liquid phase, but it’s much easier for them to do so if they can find a solid on which to settle. This phenomenon is known as nucleation, and it can be observed right here on Earth.

Try microwaving water in a glass. If your glassware is exceptionally clean, the water will get very hot — hotter than 212 degrees — and still not bubble. But if you place a chopstick or other rough-surfaced item into the water, it will suddenly boil furiously, as the water moves from liquid to gas. In a cloud, dust serves the same purpose: It provides a surface on which water can change phases (in this case, from gas to water).

A cloud is essentially a mass of water vapor molecules that have found dust particles and condensed into water. As a cloud cools, a few of the droplets begin to freeze, while others resist turning to a solid. Some even evaporate back into their water vapor form. When the water vapor molecules come into contact with a frozen droplet, they freeze into a solid. Skipping the liquid phase is crucial to the snowflake process: It’s the difference between getting an ice droplet and a flake.

Infant snowflakes show little variation in their hexagonal design. If the process stopped here, all snowflakes would be visibly indistinguishable, 10-molecule structures. (The word “visibly” has to be understood metaphorically here. You couldn’t see a 10-molecule snowflake, even with standard optical microscope.)

But it doesn’t stop there. Parts of the growing snow crystal have rough edges, or bonds, dangling off their sides, which are better at attracting other water molecules than the smoother parts of the hexagon. As more water vapor molecules settle on these bonds, the rough edges become a relatively large protuberance with its own rough edges, which attract more water molecules. Through this process, the rough edge becomes a branch of the crystal. Eventually the branches develop their own rough edges, which develop into sub-branches of the original branch, and so on.

The temperature and humidity also affect how new water vapor molecules bond to the growing snowflake. Warmer, drier conditions tend to create solid plates and prism shapes — the kinds of snowflakes that look boring to the layperson. As conditions in the cloud get colder and more moist, the beautiful winter-wonderland-type snowflakes become more common. Scientists refer to these shapes as dendrites and sectored plates. The same conditions can also create needles, which are long, thin snow crystals that don’t look like flakes at all.

Okay, we’re ready to get back to the question about no two snowflakes being the same. Kenneth Libbrecht, a professor of physics at the California Institute of Technology and probably the world’s foremost expert on snowflake formation, says, “It really depends on what you mean by snowflake and what you mean by different.”

As mentioned above, newly formed snow crystals with only a handful of molecules would be nearly impossible to distinguish. But that’s not really the issue. We’re talking about real snowflakes, which have something on the order of a quintillion molecules. (That’s the number 1 with 18 zeros.)

Now, it’s not a law of nature that no two snowflakes could be truly identical. So, on a very technical level, it’s possible for two snowflakes to be identical. And it’s entirely possible that two snowflakes have been visibly indistinguishable. But probability dictates that this is incredibly unlikely. Libbrecht draws a helpful visual comparison.

“There are a limited number of ways to arrange a handful of bricks,” he says. “But if you have a lot of bricks, the number of combinations grows very quickly. With enough of them, you can make a driveway, a sidewalk or a house.”

Water molecules in a snowflake are like those bricks. As the number of building blocks increases, the number of possible combinations increases at an incredible rate.

Consider the math, which Libbrecht helps explain using a bookshelf analogy. He points out that, if you have only three books on your bookshelf, there are only six orders in which you can arrange them. (That’s 3 times 2 times 1.) If you have 15 books, there are 1.3 trillion possible arrangements. (Fifteen times 14 times 13, etc.) With 100 books, the number of combinations increases to a number that is far, far greater than the estimated number of atoms in the universe.

An ordinary snowflake has hundreds of branches ribs, and ridges, all arranged in minutely different geometries. To be sure, lots of snowflakes have fallen in the world, but not nearly enough to render two identical snowflakes a reasonable possibility.

If you’re skeptical, you’re more than welcome to undertake your own study. But you might want to block off a pretty big chunk of time. Libbrecht estimates that around a septillion — that’s a 1 with 24 zeros — snowflakes fall every year.

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