Uncle George was never one for meekly accepting the established point of view. Show him a majority opinion and he'll do his utmost to disagree. So when not one but three Nobel prize winning research chemists told him that carbon has only four valence electrons he refused to believe it. "Carbon," he said, "has six electrons." Every authority he could find told him that carbon could only sustain a maximum of four bonds — a tetrahedral arrangement of sp³ orbitals — but that only convinced him that so far nobody had thought things through with an open mind.

As he remarked to Gaye and me, six is not four. "No, but in an infinite universe it could be," argued Gaye. "Twice infinity is still only infinity." Sometimes Gaye's a lot like Uncle George. As for me, I suppose I take more after my mother. We never really knew her, of course — our parents died when we were only infants — but sometimes Uncle George talks about them. Father was Uncle George's brother.

"I need more bonds," he said.

This was when he was having trouble with his first magnene design, (C₆S)_n>138, in which a looped chain of sulphur atoms was threaded with dehydrogenated benzene rings. It wasn't really the bonds that were the problem, it was getting enough magnetic flux through the loops, but he reckoned it would be easier if he could synthesise a magnene out of a single atomic species. What he had in mind was C_n>56 with the carbons linked by triple bonds on either side, which would give him more conduction electrons to play around with after orbital delocalisation.

If you remember Gaye's true teeth — I'm pretty sure I've mentioned them before — you'll realise that Uncle George managed to solve his flux problem without having to rewrite the laws of chemistry. Still, it got him thinking.

It was Christmas that was the trigger. Christmas … and Christmas decorations. Incited and encouraged by Gaye, Uncle George had the scintillating notion of making decorations out of nanoscale artificial diamond. The snag, as they soon discovered, was that their diamond kept coming out black.

"Looks more like soot to me," said Gaye, after the latest failure.

It was soot.

More accurately, fragments of graphene sheet. Conjoined aromatic rings which as everyone knows form the constituent layers of graphite.

"No problem," said Uncle George. "We'll make clean soot instead."

That's not as daft as it sounds. Pure graphene oxide, if I remember correctly, is white, and I dare say you could get other colours with suitable substituents. But Uncle George had a better idea.

"What we really want," he said, rolling marbles onto the snooker table and trapping them inside the triangular thing you use to set the balls out with, "is a hexagonally close-packed layer."

Gaye calls it a tring. The snooker thing, I mean. I don't know what it's supposed to be called. I like tring. It has a good ring. And that's the thing. It makes you sing.

Where was I? … Oh, yes. Hexagonally close-packed carbon sheets. Well, as you'll appreciate, that only works if each carbon atom can form chemical bonds with all six of its nearest neighbours. And, Gaye notwithstanding, six is not four. 

Not surprisingly, those pesky carbon atoms refused to cooperate. Uncle George would lay them down in order, and Gaye would try to hold them in position, and they'd slip right back out again. Rather like those three silly springs that hold the chuck in place in a hand drill and which are the very devil to put back when you accidentally screw the head off. It takes hours, and then, just when you think you've got it, one of the springs goes sprung! off into the middle distance, and you spend another couple of hours looking for it before you give up and toddle off to the ironmongers for another one, which turns out to be too short or too long or too stiff or something. At least the carbon atoms matched.

It was Gaye who turned out to be Uncle's Diamond. You know the story, I suppose? How Isaac Newton had a dog who ate all his sums, so he took him on his knee and said, "Oh Diamond, Diamond, thou little knowest what thou hast done!"

When yet another close-packing attempt went poof! into soot, Gaye got mad and hit the atomic thingy they were moving the atoms with. It went bang! and blew a fuse.

"Don't get excited," said Uncle George, hunting in his fuse box for a replacement. "Science is one percent inspiration, ninety percent perspiration, and ninety-nine percent total failure." Which shows it was getting to him too. He can usually add up better than that. Even I can. "What I don't understand is how a box of fuses can attract so much lint," he added plaintively, picking off another piece and blowing it away.

Suddenly he sat up. "Excited!" he said. "You got excited."

"Sorry," Gaye apologised.

"Don't apologise," he said. "That's the answer. We need to get the carbon atoms excited first."

Come to think of it, I've got it wrong. Diamond was a disaster, and that's usually Gaye to a T, but for once she wasn't catastrophic, she was serendipitous. By the way, did you know that the island of Ceylon was once called Serendip? Just thought I'd mention it.

"See here," said Uncle George. "Carbon has two electrons in the K shell, the lowest, and four in the L shell. Normally, only those four can take part in chemical bonds. But suppose we excite the inner electrons into the outer shell. Then there'll be six valence electrons, enough to sustain our hexagonal close-packing. I can calculate the energy levels easily enough."

"Won't the excited state be unstable?" Gaye asked.

"Probably," he said. "Definitely, or the excited state would be the ground state. But not as much as you'd think. The new L shell will get to see the full nuclear charge of six protons instead of four, so the orbitals will be that much more compact and the energy levels lower. With any luck, hybridising them into six single bonds will release enough energy to stabilise them."

I must admit I blurred out somewhere in there, and found myself gazing with deep concentration at a robin de-earthing a worm on the lawn outside. No, I tell a lie. It was a blue tit. Recondite discussions on the possibility of s³p³ versus sp³d² orbitals are a bit beyond me. To tell the truth, I think they were a bit beyond Gaye and Uncle George too, but they're both good bluffers.

"If we can get deep bonding to work," mused Uncle George, "it will revolutionise all sorts of things."

Ever the optimist, Gaye said, "I don't see why it shouldn't. I'm not sure we should be starting with deep graphene, though. Wouldn't we get less steric hindrance in 3D?"

"You could be right," Uncle George admitted. "We could try for a deep diamond with a simple cubic lattice — six nearest neighbours again. Bond length about 0.1nm. Should be pretty hard and dense."

"Twenty tonnes per cubic metre," said Gaye, calculating with incredible rapidity. I blinked. Only later, when she laboriously explained it to me, did I realise that it was actually a rather fortuitously easy sum. Like one of those tricks Sherlock Holmes uses to show up Dr Watson. Sometimes I can understand how he felt. Dr Watson, I mean. Not Sherlock Holmes. I leave understanding Sherlock Holmes to Gaye. And Uncle George, I suppose.

"Or two interpenetrating cubic lattices," he said. "Nearly twice as dense, probably."

The trouble with this story is that there doesn't seem to be much of a story. Sorry about that. It was never going to be on a par with Greek tragedy — thank heavens — but I suppose a Dick Francis or Captain W. E. Johns could have done better. It's all so technical. But then, in the real world, some things are. That's life.

When my teacher asked me to tell the story of the discovery of deep bonding I thought it would be easy. After all, I was there. But she wanted me to tell it without using words like electrons and orbitals, and that's plain impossible. It's like gardening without plants. Or Formula One racing without cars or gears.

Well, anyway, Uncle George got his deep graphene, and his deep diamonds too, though not in time for Christmas. We had to dig out the old decorations from the attic and buy some new ones from B&Q. Not that deep graphene is particularly decorative. It comes as a very thin, transparent ribbon of enormous tensile strength. Or in a block like mica. That one's fun. It's so subatomically smooth that you can exfoliate it layer by layer just by flicking it between your fingers. Graphite does the same, but not as well. This stuff's slipperier than soap and lots better than a banana skin. Practically invisible, too. When Gaye and I stuck a kilo-layer film over the white-board, teacher went absolutely nuts trying to write on it. Every time she tried another layer would come off and wrap itself all round her arm.

On the other hand, deep diamond is decorative. A faceted deep diamond gives ordinary diamonds an inferiority complex. And talk about hard. It treats ordinary diamonds as if they were talcum powder. You wouldn't believe the prices Uncle George was able to charge for them. Gem quality or industrial grit, it was all the same to him. "Pity I'm not married," he said. "Think how many points I'd score giving my wife deep diamond jewellery."

Gaye's eyes lit up. "Even better. Think how many girls you'll be able to pick up now. You'll be more popular than an Arab sheikh. Rudolf Valentino the Second."

She wasn't far wrong. Uncle George had more fun that year than … well … than ever really. Call it … deep bonding …

But that was only the beginning.

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