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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 (g/cm^3) (dollars/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 its so special to begin with). Almost all of the elements more dense 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 Rh market 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?

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There's a listed market value for plutonium??? –  Chris White Jul 19 '13 at 20:31
1  
@ChrisWhite Yes! Of course there is. This is from the study of nuclear fuel cycle. It's extremely well established, because Plutonium can't be produced in its elemental form - only within fuel material. The Pu price is so much higher than U because of those multi-billion dollar reprocessing facilities. Advanced fuel cycles are often taken to be economic around $1,000/kg U price, but Pu burns maybe x50 times more thoroughly. That still doesn't get me to their price, so maybe it's the "lab" price. Of course virtually no one is allowed to buy it... –  Alan Rominger Jul 19 '13 at 20:44
    
Depleted uranium price must be low enough. Otherwise they would not be shooting it at people or their vehicles. The only problem is that it remains slightly radioactive, which would probably betray you. –  babou Jul 19 '13 at 20:56
    
Interestingly, with its fission yielding $84\mathrm{TJ\,kg^{-1}}$, Pu's "market" price is way, way above any energy value, which would be of the order of tens of thousands of dollars. This number bespeaks a demand comprising almost wholly some other use (no prizes for guessing what). –  WetSavannaAnimal aka Rod Vance Jul 20 '13 at 7:04
    
@WetSavannaAnimalakaRodVance Looks to me like your comment could be turned into an answer. –  joshphysics Jul 26 '13 at 21:20

2 Answers 2

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.

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Nobody would expect gold to be very pure so they would not attempt to distinguish it from tungsten by density which is very close. Pure tungsten would be obviously different from gold by colour, hardness, acid test etc., but tungsten embedded inside gold bars is harder to detect.

One way used to tell the difference relies on the slightly diamagnetic properties of gold compared to tungsten which is slightly feromagnetic. You can tell the difference with a strong magnet and sensitive scales e.g. see this video.

http://www.youtube.com/watch?v=foELQ7T8_90

Another method is ultrasound because tungsten is harder and so has a different speed of sound, see

http://www.youtube.com/watch?v=5FvM_4B7Pkc

Here is a video to show that using tungsten to replace gold really happens

http://www.youtube.com/watch?v=ZKczs-7BFRI

Here is another news story on the subject

http://buying-gold.goldprice.org/2012/03/detecting-fake-gold-bars.html

Google is your friend

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Btw, I'm not sure if the first video would actually work with Tungsten, since he is using a paperclip and those are made out of steel. I have asked a related question: physics.stackexchange.com/questions/102463/… –  Roland Mar 7 at 17:15

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