Bismuth!!!! Pt III

This is the last post on Bismuth hopefully. I am not satisfied with my crystal growth, but unwilling to procure vast amounts of material and equipment to improve further.

 

These are the best crystals that I made apart from my geode method. If you look closely, you can see the stair-step pattern of hopper crystal growth in several places.

The latest geode is more interesting. This time I let my bath of molten Bi cool for 15 minutes inside a blanket of kaowool refractory insulation. Honestly, I thought it would never cool down. After plunking the above from the top of the melt, I poured the remaining liquid out and had a thick geode that still had relatively small but fairly interesting crystal growth. So as to see inside better, I used pliers to break the top edges and overburden off. This exposed an interesting simultaneous view of the silver (unoxidized) crystallized metal. Finally I sanded the top smooth. Here is what it looks like:

Here is a close up view of the floor of the geode:

I especially like the largest formation where the crystal obviously grew up and out in a spiral pattern, like a nautilus shell (which grows according to Fibonacci's mathematical sequence).

Note that even the edges are not completely parallel at 90 degree angles. The crystal lattice itself is rhombohedric and is known as pseudo-cubic because it is not exactly cubic. I wish I could explain the shape and pattern in great detail but I can't get from the unit cell of Bismuth to this in a fully logical way.

What I can explain is that the hoppered nature is clearly evident in almost every crystal. The edges grow faster than the crystal can fill in the middle. Halite (salt) is another mineral that is famous for hoppered crystals. The Bismuth cools slowly enough to form large crystals easily, but they still grow so fast (think in geological terms) that they don't have a chance to fully form inside the edges.

Fibonacci's Sequence is x(n)=x(n-1)+x(n-2). This is not a math blog but the pattern is 0,1,1,2,3,5,8,13 and so on...

Does the largest crystal obey this sequence?  No, not quite. I can see evidence of 1,1,2,3 when blown up and measured, but it falls apart before and after these four edges. That being said, I googled it and there are numerous cases of Bismuth crystals being referenced as following Fibonacci's Sequence. I think, though, that it may be an assumption to describe a given crystal. I am not sure a scientist would make this claim. But nature does have its patterns, and crystals are at least related in this sense.

The unit cell for Bismuth, the smallest pattern that replicates, has two axes the same length, and the third in-between two and three times that length. Atoms are so small that these distances are measured in Angstroms. Still, that could help explain ratios that may look similar to 1,1,2,3...

Now, there may be something else intriguing related to the unit cell. There are three angles in the symmetry of the Bismuth unit cell, between the axes whose lengths are discussed above. Two are 90 degrees and the third is 120 degrees. I definitely see angles close to if not exactly 120 angles in numerous crystals towards the center as the edges formed. I am not sure if they are related, but it seems more than a random coincidence as it is frequent and far from "cubic."

If anyone can shed more light on these patterns, I would appreciate a comment.

Thanks for reading,

Paul