A discussion group is now available on Yahoo Groups

“Our group includes Eric Scerri, among others. A number of our subscribers took part in the action on David Bradley’s Rebuilding the Periodic Table thread on Sciencebase.com.

Periodic Discussion

Fundamentally, there is, with current chemical understanding, no resolution to the debate to be had, it seems, despite the best efforts of each party to argue their case for the status quo, staggers and steps, relocations and the spiralling of the PT into 3D.

GAME OVER

(Please don’t try and put any more coins in the slot, you will lose your money).

Inevitably, a parent must step in to take charge of the situation before someone gets hurt. The kids are asked to “play nicely”. If they continue with the bad behaviour, the ball is usually confiscated and in extreme cases they are sent to bed with no supper…

I’d always been bothered by the fact that we had to double up elements to make a regular tetrahedron. Now with equal-count and -distribution real estate one could re-assort and have all elements get one sphere each.

A remaining problem was that this inverse Adomah set, which intercalated the first one, broke up the continuity of subperiods- that is, one edge would get, say, all the s1 electrons, and its opposite s2. In addition one still had to deal with the numerical lopsidedness of putting Z=1 on one vertex and Z=2 on another, but not 3 and 4 on the remaining two vertices (though one COULD do this and I tried it too).

As I explored this virgin territory, I found that a number of different ways to rationally distribute the quantum numbers on vertices, edges, faces, and the tetrahedral body existed that would give symmetrical results- some were just more aesthetically pleasing than others. One particular set took the center-point of two opposing edges as the place around which to put H, He, and then 119 and 120 on the other edge. This system gave one a very symmetrical result, with all Cartesian coordinates, straight lines, and right angles for the locations of subperiods. But it still broke things up in ways I found displeasing.

It was at that moment that, serendipitously, I realized suddenly that by switching the constructional assignment of two of the quantum numbers I could get around these subperiod discontinuities. But I was dubious- I’d already built an Adomah-style tetrahedron from wooden spheres (my young nephews built others for themselves from the remaining pile of balls). I physically counted, one by one, the spheres on the outer edge of the 120-sphere tetrahedron (which wasn’t THAT easy since I’d constructed the thing from slices and it would fall apart unless deliberately held together) and to my delight and astonishment I found that the outer ring contained exactly 28 spheres, enough for the full f block.

So, did this carry over to the other orbital types? The next ring held 20 spheres, but there were TWO of these. The next inward had 12 spheres- it took a bit of doing to visualize that there were three of these rings, since nothing was colored, or labeled, and the slices didn’t lend themselves easily to the counts. Well, if there were THREE, then the innermost rings would be 4 spheres apiece, and there should be four of them- as there turned out to be.

Note that the differences in sphere counts for the rings were consistently 8 different: 28, 20, 12, and 4, reflecting the fact that each ring represents two full subperiods of the same type. Having to multiply these by 1, 2, 3 and 4 respectively shows the relation to the symmetrically disposed flat Adomah system as adapted from the LSPT, and the Madelung table.

The s-block elements directly surround a rotational axis that extends from the center of one edge to the center of the opposing edge at right angles to it. In my model the counts still increase along this axis, so there is still ‘lopsidedness’ numerically (but then this seems to be a fault of all periodic depictions). A 120-sphere tetrahedron has a continuous outer ‘jacket’ of 100 spheres surrounding a core of 20 (and as discussed over on the Yahoo Group (http://tech.groups.yahoo.com/group/tetrahedronT3) everything up to Z=20 seems much more regular), so I’ve wondered whether one could actually start in the middle and move outward instead.

Just as an aside the rule for constructing these jackets is to sum successive squares of even numbers: The core has 2 sq + 4 sq, and the outer jacket has 6 sq + 8 sq, which are oriented the same way. One can also get inverted tetrahedra by summing intermediately, so 0 sq + 2 sq gives the first four elements which can be hidden inside the 20-sphere tet. What the significance of the next sum, 4 sq + 6 sq (=52), may be, I haven’t any clue. Takers?

I’ve also constructed periodic systems out of 4-sphere tetrahedra. Two such sets turned out to have been discovered first (to my chagrin, but then one has to take as well as one gives…) by Pierre Demers in Quebec some years ago.

All of these models have the advantage of assigning one element to one sphere, though they otherwise vary wildly in terms of symmetry and continuity of elements from the original periodic string.

One can also get symmetrical models utilizing the 4 vertices for symmetry, but the results are far uglier to the mind of someone used to 3D. Perhaps someone from Flatland would find such aesthetic reactions superfluous…

Because of kinships beyond primary, secondary, tertiary and some quaternary, I still think that extra dimensions might be likely, but now made up for by ‘hidden’ dimensional quality as an offset, so no NET increase on the surface- the figure folds back on itself, negating any increase in numbers of spheres (though this would possibly mean that all elements and their properties would be combinatoric in nature from contributions from higher dimensions (i.e. extra spheres), then reduced by the back-folding (so fewer spheres). Hard to wrap one’s mind around, and I can’t find any references to such a thing. But if good enough for subatomic physics, why wouldn’t it work for us?

Jess Tauber

I have never built sliced up tetrahedron myself in real world. I built computer model of it using 2×7, 4×5, 6×3, 8×1 and 9×0 blocks. It surely works on computer. The last pair yields edge of the tetrahedron (line thickness of 0) with zero area and zero corresponding elements. I am not sure about irregular tetrahedron that you suggested. I have never tried that. I am sure that Alex will enjoy that. Jess told me once that he actually built physical model around 1979.

I find it amazing, though, that in order to make regular tetrahedron work, quantum number “ms” values have to be +/-1/2 as guessed by Pauli and later confirmed by Dirac. So, the relationship between the quantum numbers “n”, “l”, “ml” and “ms” has tetrahedral character.

I had a lot of fun while making 3D Madelung rule diagram using red and green spheres. Each red sphere has to be marked with two consecutive elements: H-He, Li-Be, B-C, N-O…. Green spheres stay unmarked. Than 3D Madelung rule diagram is built like this:

Put first red sphere (H-He) on top of a table; then put two green spheres next to the red to form triangle and put second red sphere (Li-Be) on top of the triangle. Then put three red spheres (B…Ne) on top of table so they interlock with two green spheres, put two green spheres on top of three red and next to one red and then red sphere (Na-Mg) at the very top. Start fourth layer with 4 green spheres on top of the table next to three red. Put three red (Al….Ar) on top of four green, then two green on top of three red and then one red for K and Ca. Proceed in the same manner, alternating red and green spheres to build up bi-color tetrahedral stack of spheres of any size. The tetrahedron does not have to stop, it can grow infinitely, just like 2D Madelung rule diagram. You will notice that Janet’s dyads occure due to the presence of two types of spheres, red and green (protons and neutrons?). Jess suggested once that it could be electrons and neutrinos.

I was amazed at first that such simple procedure of constructing bi-color stack of spheres mimics Madelung rule diagram in 3D so precisely and third dimension corresponds to number of “ml” values for each subshell exactly. I think that Alex will enjoy that!

Valery.

The thinking was more fun than being a pair of hands, but mostly this was quashed by superiors. Because of this that last firm missed out on getting in on wound glues, at a time when they were focussed on clipping fractions off cents per pound costwise. Shortsighted would be putting it mildly. I remember telling them about the tetrahedral PT configuration too- the only response was derision.

Jess Tauber