The Trypolite Crystal
In my last post “Collapsing a Cylinder-Sphere” I presented a model by which close-packed clusters rotating cylinders collapse into cylindrical crystallites and showed in a simple illustration how these cylindrical crystallites can be compressed into rounded rhombuses. However, for the illustration of a spherical crystallite, I only applied the second-to-last step of collapsed cylinders and left the rhombuses out. The reason for this was that making the rhombus model would be processor heavy, so I needed to leave it for another post. And today is the day: today I present the compressed collapsing a cylinder-sphere, or the trypolite crystal.
But before I do this, let’s recap. In my last post I talked about how to collapse (semi)freely rotating hollow nanotubules into closely packed rhombus lattices and illustrated the principle with figure c) below (both front and side projection shown). I also showed that with this level of collapse, the crystallites would not shrink isotropically, but leaving gaps between the six crystallites that make up the spherical crystal. However, as there is plenty of space between the cylinders, if these cylinders are compressed into rounded rhombuses, the gaps between the crystallites can be closed.
In today’s post I illustrate this concept. However, to do this properly, I can’t (or don’t want to) use solid shapes, because solid shapes are generally not considered compressible. Nor am I suggesting that my lignosphere nanotubules would be solid cylinders. Rather, as the nanotubules are hollow, the model should reflect this.
Surprisingly, making a hollow rounded rhombus was quite easy and it didn’t take too long to get the shape right. The only caveat is that I didn’t make sure that the circumference of the compressed rounded rhombus is identical to the non-compressed cylinder, meaning that the model is still partly qualitative rather than fully quantitative. And I decided that I wouldn’t include the cylinders at the interfaces of crystallites, as doing it right would require more work. I’ll tackle that eventually, as well, but just not today.
So, here’s the final rounded rhombus crystallite:
I call it a trypolite crystal, based on the same root word for a hole that gave us the word trypophobia, or the fear of holes. This isn’t the first holey crystal structure. There’s at least zeolites, that show quite similar holes in electron microscopy. But because zeolite crystal refers to a very specific sort of hole, I can’t use that term
You might be wondering why I’ve omitted the cylinders at the intersection of the zig-zag wedges. The biggest reason is, that these intersections would hold four or six rounded rhombuses at the same location at the point of copying the shape into a full spherical crystal, so I avoid this by not including any. But this will be an issue that I will need to address properly before making this into a proper scientific article.
Also, the color coding is still a bit off. I think I need to use this two-colored coding for alternating layers, but I also need to use the three-colored coding for alternating planes as well. This means that I need to increase the number of colors to six (= 2 x 3) to illustrate both ‘facets’ of the theory.
So, in conclusion, my theory is very nearly ready, but it still requires some finessing at the edges (quite literally). But it’s no longer a matter of if, but when I get it fully ready. Of course there’s still the tiny matter of quantum pressure, but I’ll worry about it when I get there.
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