Soft gold, hard rings
Pure gold is astonishingly soft. A bar of it can be dented with a fingernail, a coin of pure gold wears smooth in a few years of handling, and gold can be beaten into leaf so thin that light shines through it. A wedding ring made of pure gold, 24 carat, slowly bends out of round and scuffs every time it knocks against something.
Most gold jewellery is not pure. 18-carat gold is 18 parts gold in 24 by weight, and the other quarter is usually copper and silver. That small change makes it several times harder: an 18-carat ring keeps its shape and its polish for decades. A metal made by mixing a metal with other elements is an alloy, and almost every metal object you use is one: steel, brass, bronze, solder, the aluminium in a drinks can, the coins in your pocket.
The puzzle is that copper on its own is not much harder than gold. Mixing two soft metals gives a hard one. To see why, you have to look at what happens to the atoms when a metal bends.
Metals bend by slipping
In a solid metal the atoms are packed in a regular crystal. In gold, copper, silver and aluminium they are stacked in close-packed layers, like oranges on a greengrocer’s tray, each layer nestled into the hollows of the one below. Each atom touches twelve neighbours. The electrons that hold the atoms together are shared by the whole crystal rather than tied to particular pairs, so the bond does not care much exactly where its neighbours sit.
That is why metals bend instead of shattering. Push hard enough sideways and one layer of atoms can slide over the next, dropping from one set of hollows into the next. The plane where this happens is a slip plane. A small push only leans the layers a little, and they spring back when you let go: the metal is behaving elastically. The push at which the layers start to slide for good is the yield strength. Beyond it the metal changes shape permanently.
Real metals do not slide a whole layer at once. The slip runs through the crystal a row at a time, carried by a flaw in the stacking called a dislocation, the way you can move a large rug by pushing a ruck along it instead of dragging the whole thing. That is why a pure metal yields at a stress far below what it would take to shear a perfect crystal in one go.
Try it: with Gold content at 24 ct (pure gold), drag Push slowly up from zero. Up to about 30 MPa the block only leans; past it the readings switch from “Holds” to “Slips” and the top half of the block slides along the slip plane by whole atom spacings. Even 50 MPa is enough to move pure gold.
Odd-sized atoms get in the way
In pure gold every atom is the same size, so the slip plane is smooth: a sliding layer meets the same hollows and the same bumps everywhere. Now swap some of the gold atoms for copper. A copper atom is about 11% smaller than a gold atom, so the atoms around it are pulled slightly towards it and the layers buckle. The slip plane is no longer smooth. A row of atoms sliding over it keeps meeting places where the fit is wrong, and a dislocation running through the crystal gets snagged on the strained patches around each copper atom. More push is needed to drag it past them.
This is solid-solution strengthening: the added atoms sit in the crystal in place of the host’s, mixed in like sugar dissolved in water, and the mismatch they bring makes slip harder. It is why 18-carat gold, which is about half copper atoms, is roughly ten times stronger than pure gold in this model.
Try it: set Gold content to 18 ct with Push at 150 MPa. The block that slipped as pure gold now holds and only leans. Then choose Slip plane under Slip the layers and look at the ringed atoms: each one is an odd size, a bump that a sliding layer has to climb over. At 18 ct there are slightly more copper atoms than gold ones, so it is the gold atoms that are ringed: in a mix this even, each kind is the odd size out among the other. At 22 ct the rings move to the copper.
The readings beside the Scene show two things worth comparing. By weight, 18-carat gold is three quarters gold. By atoms, it is only about half, because a copper atom weighs less than a third as much as a gold atom. It is the atoms that do the work in the crystal, so the strengthening is larger than the weight suggests. In this simple rule the hardening is largest when the two kinds of atom are close to equal in number, which is why moving Gold content from 18 ct to 9 ct makes the alloy weaker again.
Why silver hardly helps
Silver is a soft metal like gold, and its atoms are almost exactly the same size: 144.5 picometres in radius against gold’s 144. Mixed into gold it slots into the crystal without straining it, so the slip plane stays flat. An 18-carat gold–silver alloy is stronger than pure gold, but only by a little.
Try it: switch Mixed with from Copper to Silver at 18 ct, with Push at 150 MPa. The layers stay flat, no atoms are ringed on the slip plane, and the block slips almost as easily as pure gold.
Jewellers use this. Silver mostly changes the colour, making gold paler and greener, and copper both hardens it and warms the colour towards red: rose gold is gold with a lot of copper. Most yellow gold is a balance of the two. The same idea, a few foreign atoms that do not fit, is behind the hardness of bronze (tin in copper), brass (zinc in copper) and sterling silver (copper in silver). Steel works a little differently: the carbon atoms are so small that they squeeze into the gaps between the iron atoms instead of replacing them, and strain the crystal even more.
What this model leaves out
The block is tiny: ten atoms by six by six. A real piece of metal has billions of atoms along every row, is made of many small crystals pointing different ways, and has slip planes running in several directions, so it can bend in any direction. Slip is drawn as the whole top half moving by whole atom spacings as a front crosses the block; in a real metal dislocations run through on many planes at once. Lowering the push puts the block back so settings can be compared; real metal keeps its new shape, and grows harder as dislocations tangle, which is why a bent wire is harder to bend back.
The yield strengths are rough values for soft, annealed metal from a simple rule fitted to a few points, not measured data for each alloy. Real carat golds usually contain copper, silver and often zinc together, and gold–copper alloys can arrange their atoms into ordered patterns when heated, which hardens them further. How far each atom is nudged by its neighbours is a simple estimate, drawn three times larger, and the elastic lean is drawn many times larger than real, since a real crystal leans by about a thousandth before it yields.