spiral diagram of elements

This is an alternative version of the standard chemistry Periodic Table of the Elements that I developed. In high school I learned the basic concept of element families and how they were arranged into columns to show the periodicity in their electrical properties. I was fascinated with the idea, but immediately wondered whether there might be better ways of graphically showing those relationships.

In case you don't know the principles, they are quite simple: By far the most distinguishing thing between one atom and another is simply the number of protons their nuclei contain (called their atomic numbers). All Hydrogen atoms contain exactly one proton. That's what defines it as Hydrogen. If you add a second proton to it, it becomes a Helium atom. From this perspective then, it would make the most sense to arrange the hundred or so atom types (called elements) into a simple linear list according to their atomic number. Within that list there is a lot of regularity. Elements fall into families which share similar chemical properties with each other. For example, copper, silver and gold have many similar properties. It turns out that zinc, the element with one more proton than copper, is likewise similar to cadmium, which has one more proton than silver, and is also similar to mercury, which has one more proton than gold. This pattern repeats for all atomic families. The standard chart is arranged into columns to show this regularity which is why it is called periodic, and table because of the neat rows and columns.

Two things about the standard table bothered me. The first was that it was broken into rows even though the relation between the element at the end of one row to the one at the beginning of the next row is the same as that between any two elements that are next to each other. That suggested to me that the chart might at least be better displayed on a cylinder so that it's not split artificially between any rows.

The second thing that bothered me were the gaps between some elements near the top of the table (lower atomic numbers). That was done so that the middle rows of the table would clearly show that for those elements, the period of repetition was 18. That choice tends to hide the linear nature of the list. Worse, it also hides the fact that there is a repeated section of length 8 before it. That choice also hid the repetition of period 32 which follows it.

You might have noticed that the standard table contains two rows of elements floating off by themselves almost as an afterthought at the bottom of the chart. Those rows are supposed to be wedged between a couple pairs of elements in the last two rows of the main section. They are drawn separately because it would mess up the nice straight columns if they were to be wedged in. If you look at the standard table, you'll see that each element's box contains it's atomic number. If you look closely, you'll notice that the box following Lanthanum, which has the atomic number 57, doesn't have atomic number 58 like you would expect. Instead, it is number 72. The missing 14 numbers are in the first row of those strange ones at the bottom. Likewise, the second row of 14 elements should logically be inserted into the gap below where the first extra 14 belong.

<>If the above description is at all confusing, that's because that's about the best you can do if you insist on making the rows and columns line up at perfect 90 degree angles. To create my chart, I threw out that restriction and added the restriction that the linear list of atomic numbers not be broken, but I kept the restriction that elements in the same families must still line up so that those relationships are easily seen. I then worked to stretch the resulting figure onto a flat plane with as little distortion as possible. The linear progression of the atomic numbers is now obvious. It starts with Hydrogen in the center and spirals out from there. All the element families become equally obvious, but now they follow radial arcs instead of straight columns. Just for fun, Hop David created a beautiful painting based on this diagram.

The greatest benefit of my approach is that now, all the periodicity becomes clear. One of the first things you notice about the chart are the forks (bulbs) that are introduced where the periods of length 8, 18 and 32 begin. What also becomes apparent is the self-similarity in the way these periods appear which is impossible to see in the standard chart. This self-similarity is the reason that I call this chart the periodic fractal of the elements. Of the many alternate diagrams I've seen, only other one that I feel clearly shows the periodicity of the elements is Emil Zmaczynski's triangular form.

At the following page you can see yet another spiral treatment of the table of elements by Professor Thoedor Benfey. It's clear from his diagram that he predicts that the next shell beyond the currently discovered elements should branch off between the new element in the family of Ra and the one in the family of Ac. Simply according to the pattern discernible in my diagram, he seems to be off by two elements and the fork should come between new elements related to Th and Pa. Zmaczynski's triangular form appears to make yet another prediction for the position of the next fork though I find it surprising that it didn't follow it's own clear pattern and put it between Th and Pa, exactly where I would also place it. Perhaps it's impossible to ever create these elements, but if it's ever done it will be interesting to see who's right. On the other hand it may be possible to predict from what's currently known about particle physics who's right, I simply don't know. It's also interesting to note that he seems to have missed the very first fork between Be and F - understandable since the spiral is so tightly curled near the origin, but fits well in my diagram once you see what's going on. The easiest way to see that something is missing from his diagram is that Hydrogen appears to be in eight families simultaneously or no families whereas in my version it's clearly in the alkali metals family.

A very early attempt at a spiral treatment was done by  J. F. Hyde of Dow Corning Corporation in 1975. See also the closeup of  the low atomic number elements shows that his chart is missing the first fork in my chart. (Images courtesy of Andrew Cakebread.)

Perhaps the cleverest treatment I've seen is pTable3D in which P. Fraundorf used a molecular modeling package to relax a 3D model of the graph of atomic relations into what he calls the periodic "T-Shirt of the Elements". I had considered doing something similar to automatically generate an optimized version of my 2D spiral form but his idea is much more natural and the results are striking.

Not long ago I participated in a fascinating discussion on Sciencebase.com titled Rebuilding the Periodic Table, regarding the pros and cons of the various alternate representations with their most ardent proponents. I don't think that we resolved anything but the discussion was educational and became surprisingly philosophical.

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