This thought came from researching a previous question. In the spirit of our get-rich-quick scheming, I looked up element densities and prices near gold.
| Element | Density ($g/cm^3$) | Value ($\$/kg$) |
|---|---|---|
| Uranium | $18.95$ | $40$ |
| Tungsten | $19.25$ | $24$ |
| Gold | $19.282$ | $53 000$ |
| Roentgenium | $19.282$ | No market |
| Plutonium | $19.84$ | $4 000 000$ |
| Neptunium | $20.25$ | $660 000$ |
| Rhenium | $21.02$ | $5 000$ |
| Platinum | $21.46$ | $54 000$ |
| Darmstadtium | $21.46$ | No market |
| Osmium | $22.61$ | $77 000$ |
| Iridium | $22.65$ | $42 000$ |
It would be so easy if we could just substitute some of the gold for a cheaper metal, but it seems that gold is well-protected from this kind of forgery (which is perhaps part of the reason it's so special, to begin with). Almost all of the elements denser are vastly more expensive, or only producible in small quantities in a lab.
There is a very thin market for Rhenium, so we could buy some at a price lower than gold, but any more and we'll risk either bumping up the Remarket price or being foiled by the authorities. As thrifty criminals, we would like to go with Tungsten instead.
Can an allow increase the density of a metal? Qualitatively, I imagine that a lighter element could take up interstitial sites, and allow a higher density. But is there any known Tungsten compound that fits this, or any known method of alloying that would increase its density by that ever-so-slight amount?
Best Answer
I'm not sure whether this counts as an answer since it is just one more idea for a fraud, but your question is about the physics of alloying.
Actually there's no need to alloy to scam. You make up the filler mostly with tungsten, but add a little pellet of platinum. Neither of these materials will rouse the authorities' suspicion, since both have legitimate industrial uses in big quantities. At your quoted prices, the relative proportions of Pt and W needed to give gold density is 0,98552 : 0,0144796. This mixture, at your prices, would cost $806 a kilogram: far better than Rhenium. Of course an alloy could be more unseeable (to ultrasonic tomography and the like).
The method could be refined to a pseudo allow: you could distribute little pellets of Pt.
Alloying would likely still work, since there is quite a difference between the densities of W and Pt, but the proportions would likely change, for the very reasons you are asking about (physics of alloying). So you'd need to do some experimenting.
Even though Pt's price is quite volatile, the costing of this method would be very robust, since most of the cost of your filler is Pt itself and the filler's price per kg is much less than Au's (Pt would have to become outlandishly in demand and Au much, much cheaper than at present to upset the profit).
Lastly, once you have worked out the alloying, you would want to develop an acoustic matching multilayer to match the Au to the filler. You would need to find materials with acoustic refractive indices such that the layers would minimize ultrasound reflexions in the frequency bands most used by authorities. THis is the acoustic analogue of anti-reflexion coatings on optical instruments.
Since the matching layers also change the pverall density, you now have to change the proportions of Pt and W in your original mixture yet again to achieve the same overall density as Au. You now have some serious analysis and experimenting to do to find the right proportions of W and Pt. And that's before you work out a disposal scheme so that you won't get caught.