Snowflake Self-Organization

March 12, 2019 by Danielle Parsons

 

A snowflake is made up of billions of water molecules, each one identical to every other. And yet somehow in a snowflake a single ingredient is able to form endlessly varying, intricate, and symmetrical designs. How do water molecules do it?

The surprising truth is that in order to freeze, water molecules assume a mineral formation. A basic hexagonal ring arrangement of six H2O molecules is repeated millions of times in every direction, creating a crystalline lattice. A snowflake has a crystal structure made of inorganic molecules (containing no carbon), and therefore technically qualifies as a mineral. A temporary status, granted, because once the snowflake melts into liquid or vapor, its constituent H2O molecules degenerate into less orderly configurations.

The hexagonal arrangement is apparent on both the smallest and largest levels of the ice crystal. The overall shape of a snowflake displays its utmost internal organization. But exactly how do H2O molecules transition from the chaotic dance of water vapor in a cloud to the orderly repetition in the crystalline lattice of a snowflake? It’s through one of Nature’s most powerful and prevalent forces — self-organization.

Self-organization is defined as a process through which some form of overall order arises from local interactions between the parts of an initially disordered system. Self-organization occurs across a wide array of disciplines, including physics, chemistry, biology, and, most recently, in human society and computer science. Some examples include flocking in birds, social behavior of certain insects, traffic patterns, pattern formation, swarm robots, optimization algorithms, and the growth of slime molds.

Self-organization is spontaneous and not controlled by any external agent.

Certainly the inside of a cloud is a disorganized system if ever there were one — with water vapor blowing this way and that in the shifting wind, and subject to constant fluctuations in temperature and air pressure. But from this initial chaos emerges a pristine symmetrical snowflake. This tiny miracle is actually due to four main factors: the polarity of H2O, the dynamic growth of the ice lattice, faceting, and branching.

 

1: POLARITY

A frozen water molecule contains three atoms of course: one oxygen atom attached to two Hydrogen atoms. The angle formed by the hydrogen bonds is always 104.5 degrees.

 

 

Consulting the Periodic Table, we can see that an oxygen atom has a larger mass than the hydrogen atom — oxygen is eight times as large. The hulking oxygen nucleus with 8 protons and 8 neutrons exerts a stronger gravitational pull on its 8 electrons, drawing them close. Importantly for snowflake formation, the oxygen nucleus even draws hydrogen’s electrons ever so slightly towards it as well. Not enough to pull the electrons out of orbit around the hydrogen nucleus. This it the polarity of H2O.

 

Electrons are negatively charged particles. The greater proximity of electrons to oxygen than to hydrogen confers an ever-so-slightly slightly negative charge to oxygen, and an ever-so-slightly positive charge to the hydrogen. This polarity determines everything about a snowflake’s shape.

 

2: LATTICE
If you’ve ever played with magnets, you know that like charges repel and opposite charges attract. So when multiple water molecules bond with each other, it’s always between the slightly-negative oxygen of one H2O and the slightly-positive hydrogen of the other H2O. Floating water molecules attach to the growing snowflake only oxygens to hydrogens.

 

Because of that 104.5 degree angle between the hydrogen atoms in each H2O molecule, new bonds between different water molecules happen to form rings of six H2O.

 

 

The ring of six H2O is called the unit cell or the lattice, because it is the smallest unit of organization. As more and more rings of six H2O molecules self-assemble, the ice extends into a crystalline lattice, repeating the one basic molecular unit in all directions. The growth of a lattice is the reason ice is classified as a mineral.

 

 

That’s how the six-sided, hexagonal symmetry of the snowflake begins at the molecular level, 10 million times smaller than the final ice crystal.

But what keeps the snowflake from growing indefinitely as an undifferentiated lattice? How do the six branches form? It’s due to the hexagonal ring shape of its unit cell.

 

3: FACETING
Snowflakes become six-sided as self-organization continues through a process called faceting. Water molecules diffusing through a cloud collide with a growing ice lattice on all sides. Some molecules bounce off. Others attach. Many evaporate. The edge of an ice lattice is a very dynamic region.

 

We recommend you watch the Wonder Science video, Self-Organizing Snowflake, to help visualize faceting. All you need to take away is this: once an initial few water molecules freeze together in ringed unit cells*, the rest of the incoming molecules attach in accordance with that specific pattern. The ice lattice grows into a six-sided prism shape because of the 6 molecule ring unit cell.

A water molecule hitting the lattice attaches when there are available atoms with which to bond. The edges of a growing lattice offer more points of attachment than the top and bottom, so the lattice grows into a flat disc. Furthermore, the lattice grows into a six-sided prism because of the six-ringed unit cell. Smooth edges of the lattice offer fewer points of attachment. The incomplete parts of the lattice grasp incoming water molecules strongly at multiple points of attachment. Hence the rough edges of the lattice grow faster. When the rough edges fill in and become smooth, fewer new water molecules attach, and the growth of that edge naturally slows.

 

4: BRANCHING
The existence of a hexagonal prism triggers a new dynamic: branching. The six corners of the ice prism stick out into the air further than the sides of the prism, causing diffusing water molecules in the cloud to hit the corners sooner and more frequently.

At first it’s only by the tiniest bit. But with every molecule that preferentially bonds to the corners of the prism, the corners grow larger, causing even more diffusing water molecules to attach. This activity becomes a positive feedback loop. The corners grow larger and larger. All the while, the developing ice prism spins inside the cloud, exposing all sides more or less equally to the presence of water vapor. Soon, branching structures form outward from all six corners of the ice prism.

The snowflake is a delightful instance of order emerging out of the simple interactions between identical water molecules. No one is in charge of building a snowflake and yet they. Every six-sided starlet is a triumph of non-engineering.

*A snowflake’s growth always begins around an ice nucleator. For more on this, read the Snowflake Starters blog post and watch the Wonder Science Self-Organizing Snowflake video.