The Diamonds of Winter

Would you like to take a walk with me through the chemical winter wonderland of snowflakes? Well, we chemists know that the stunning six-sided symmetry of snowflakes (Figure 1) results from repeated arrangement of water molecules into a hexagonal crystal structure (Figure 2). Further, we are aware that this hexagonal crystal is possible because of hydrogen bonding that occurs between the water molecules in solid ice.

Figure 1: Photographs of snowflakes captured by the author. For details, about how I was able to take photographs of snowflakes, see my YouTube video: See Snowflakes and Crystals Up Close!

Figure 2: A model of the crystal structure of ice. Red spheres represent O atoms, white spheres represent H atoms, and lavender spokes represent hydrogen bonds.

Bond angles in ice

However, snowflakes still hold a few surprises – even for us chemists! For example, did you know that the H-O-H bond angle in ice is 109.5°, and not 104.5° as is commonly taught in introductory chemistry classes? First, I should note that it is indeed true that water molecules in the gas phase have H-O-H bond angles of 104.5°¹ as predicted by VSEPR theory. In the gas phase, molecules have little interaction with other molecules. Because of this, the structure of each gaseous water molecule is influenced only by itself: by forces within each individual water molecule. As such, the tetrahedral electronic geometry of water becomes slightly distorted as the two lone pairs exert slightly stronger repulsive pressure on each O-H bond pair. This forces the H-O-H bond angles down from 109.5° to the well-known 104.5° (Figure 3). 

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Figure 3: The bond angle of a water molecule in the gas phase is 104.5°.

In the solid phase (ice), however, each water molecule is hydrogen bonded to four other water molecules. These hydrogen bonding interactions point to the corners of a near perfect tetrahedron with H-O-H bond angles very close to 109.5°.¹

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Figure 4: A water molecule in the crystal structure of ice that is tetrahedrally connected to four other water molecules through hydrogen bonding interactions. Red spheres represent O atoms, white spheres represent H atoms, and lavender spokes represent hydrogen bonds.

The Diamonds of Winter

Like ice, tetrahedral bonding occurs between the carbon atoms in diamond (Figure 5).² In fact, the positioning of carbon atoms in diamond is the same as the arrangement of oxygen atoms in ice! And sure enough, because of this similar arrangement, hexagons can be seen in the crystal structure of diamond (Figure 6).²

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Figure 5: Crystal structure of diamond. White spheroids represent carbon atoms. The tetrahedral arrangement is evident by noting that the top carbon sits at the top of a tetrahedron. Image credit: see reference 2.

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Figure 6: Crystal structure of diamond. White spheroids represent carbon atoms. The red lines are present to guide the reader to see the hexagonal structure.

Conclusion

Thinking about the connections between ice and diamond inspired me to make a short video that explores the connection between these two fascinating materials. You can watch it below and let me know what you think (Video 1). Happy winter, everyone!

Video 1: How Are Snowflakes Like Diamonds? Tommy Technetium YouTube Channel. December 2024.

References

1. Kuhs. W. F.; Lehmann, M. S. Bond-length, bond angles and transition barrier in ice Ih by neutron scattering. Nature, 1981, 294, 432-434.
2. Diamond lattice - Diamond cubic - Wikipedia The reader is strongly encouraged to click on this link to manipulate the model for 3-dimensional viewing. The original image has been altered by the author in Figure 6 (addition of red lines).