Topic: I measured the density of my silver/gold coins... (Read 16249 times)

This thread is the second result for me when i google "gold measure density"

I just used the improved density measuring method by minitmark to measure the density of 8 silver coins. Took roughly 20 minutes including setup (found the old C-shaped metal thingy with the thread) and cleanup.

Well I have a method that I think will work and avoid all these problems. It uses magnetically induced eddy currents, and uses no test leads. It measures energy loss in the coin or bar. It tells you thickness - if the conductivity is wrong, the thickness will be out by the same factor. (Typically a factor of 1.5 or 2)  BUT I could really do with a transformer like the one I described to test this. Someone must have one??

You'd also be dealing with measuring a coin who's conductivity is ten times higher than even the multimeter test leads.

On page 10 is a subject called "milliohmmeter" discussing circuits and methodology to measure such low resistances:
http://cds.linear.com/docs/en/application-note/an98f.pdf

Since silver is the best conductor in the world at temperatures ~293K, what you'd be looking for is any resistance higher than a known good reference coin of the same minting. To establish what an expected resistance is, I'm not aware of what software can model electrical resistance @ current vs skin effects etc on various shapes, such a project would likely be PhD-earning material.

I had been wondering about that and indeed couldn't think of a way around that, except for actually having a numerical simulation program in which you fill in the details, and which then simulates the resistance. Then you still have to account for contact point resistance, which you might do by measuring different points on the coin (edge to opposite side edge, middle of face to middle of flipside face, edge to face, etc) and then correcting for the constant factor.

Please note that the shape of an object can affect the conductivity, so a conductivity test isn't a good way to test for purity. This is one of the reasons why Shire Silver has never implemented a method of directly accessing the metal through the plastic. We considered it when we were creating our prototypes, putting holes at each end of the embedded wire to allow probes to be used. For more on this, you might start with http://en.wikipedia.org/wiki/Electrical_conductor and particularly note sections like
and
This last one indicates that a conductivity test would likely be more accurate for Shire Silver than traditional bullion, but it would still not be accurate enough and adding the probe access points would add significant cost to the card production.

And yes, we get our silver and gold from a well known jewelry supply company who has been in the business for a long time. We also try to make our cards contain at least as much metal as they say they have plus a small amount to help account for our production variance. For example, a half gram silver card will have 0.52 +/- 0.02 grams of .999 fine silver.

I suppose I should get around to making a Shire Silver specific thread so I can post stuff like the news that our recent site upgrade has temporarily cut off the ability to accept bitcoins in the shopping cart, which we're trying to fix.

And people following this thread might find this page interesting: https://shiresilver.com/counterfeiting

The (molar) heat capacity might also be useful.  For background, read up on Trouton's rule.  The data you can collect at home is to heat your coin in boiling water, measure the temperature, put the coin into a thermos with a known amount of water, and measure the temperature rise.  You might want to arrange the volume of water so that the start and end temperature are on scale with a digital fever thermometer.

Then make a 2D plot, with density and heat capacity as the two axis. 

Any method that you use will easily detect some problems, and be blind to others.  Your own personal crooks will specialize in the blind spots that you have.  It is a locksmith - thief race.

Very nice testing, molecular I love it!

That's a method that shows eddy currents, but the problem is, eddy currents happen in every metal. Sure, much more in gold or silver (less resistance), but it's hard to make this a quantitative method, suitable for testing if your coin is genuin.

One of the most amazing demos is to hang a gold coin by two threads, so it will swing but not spin.  Place a super magnet just past the place where the coin will rest when it stops.  Lift the coin back, release it, and watch as it swings into the magnet and comes to a dead stop.

This is a variation of the "induced eddy current method" and it's totally cool.

There is a factory in China that makes fake gold coins, so far as I know it has been making them for many years. They are made of tungsten, and gold plated. The density of Gold and Tungsten is nearly exactly the same, far to close to call.

The electrical conductivity is very different, and so too I imagine is the thermal conductivity. Goldmoney.com use a sonar device to check all their bars for suspicious inconsistencies, and I am sure you would see a core of different material, but I am not sure if you would be able to tell if the whole bar was made of Tungsten and gold plated, as seems certain some are.

So far as silver is concerned, there are (I suppose) many alloys that would have the right density, but the right conductivity would be impossible to fake - silver is the best metalic conductor known.

I believe an induced eddy current method could work very well.

Honestly, no clue. Impure silver would conduct both heat and electricity differently, and I'm pretty sure the the lead core/lighter alloy wrapping would throw them off, too... but I'm uncertain in exactly what way.


All my silver is genuine. Right, ShireSilver?

That's very interesting. Gives one a feel for how expensive such accuracy is and what factors have to be taken into account in cases where such accuracy is necessary.

I think for the "detect fake silver coin" application using the described method (and ignoring pressure, temperature, water purity, coin uncleanliness, etc) and just getting a scale that does 0.001 g instead of 0.01 gaccuracy will go a long enough ways to be good enough.

Probably makes more sense to measure other properties in addition to density before scaling accuracy of density measurement, no?

The conductivity ideas (both of them) sound good. Still looking for something simple, though. I have a voltmeter but no thermometer... well, maybe I could build one using an arduino and some semiconductor...

I teach analytical chemistry.  Undergrad analytical labs have balances that read 0.000 1 g.  Well respected manufacturers include Mettler and Sartorius.  Troemmler also comes to mind, though I don't remember if they make balances, or only calibration weights.  I have my students do a very similar lab, and at that sensitivity level we can watch evaporation as it happens.  We need to know the barometric pressure, to account for the buoyancy of the objects in air.

The next level of sensitivity, 0.000 01 g, escalates the cost to about $25,000.

I wish all bitcointalk threads were of this kind.

which of these 2 is harder to fake (by using impure silver or using core of different material(s)).

I'd love to have some fake silver coins. Anyone have any?

Hmm, I have an idea for that too.  But I need something and wondered if anyone has it.  You used to be able to buy a transformer where the core is retangular, and the primary and secondary are on seperate bobins.

So I want to remove the secondary and then cut a 1cm air gap in the core that I can easily fit a coin or even a gold bar into.

This doesnt really work well with the normal "B" shaped transformer core. So if anyone has one of these in their junk box, I would really appreciate it...

Electrical. You probably could do it with thermal, though.

thermal or electric conductivity?

Probable source: https://www.kitcomm.com/showpost.php?p=1619194&postcount=30

Analogous argument:

I don't know how much more accuracy I could expect than the above results, they are very good but probably within the range of what determined counterfeiters might be able to produce with an alloy. This test of pocket scales shows $60 0.01g generic scales are more like +/- 0.09g: http://www.digitalscale.com/Precision.htm. Here's that scale on eBay. www.ebay.com/itm/170625095817

Next the conductivity tests!

Haha! Exactly what I had in mind!!

I am glad it actually worked well :-)

I measured a densitiy of 10.40 g/cm³. Slightly less heavy than silver, as expected.

much better results using mintymarks method:


(click image above for google doc, these are single measurements of 7 individual coins)



As expected, the Casascius 10 BTC round has lower density than silver because of the sticker and space (filled with paper and maybe some air) behind it.

The scale zeroed in much quicker than with my first setup. I conclude that the higher weight of the water cointainer in my first setup (about 150g, scale max is 200g) as opposed to the weight of the frame used here (< 3g) really did add a lot of inaccuracy in the scale.

Repeated measurements had a variation of +/- 0.01g max (resulting already in a ~0.24% jump in resulting "error").

Thanks mintymarks, now I have a much better method at hand.

https://docs.google.com/spreadsheet/ccc?key=0Au-mVSBh0PA4dFRMMTV5RmM5S0ppZDVJSVR6RUROb2c#gid=0

But please note: each row is a seperate coin, so we're talking about 15 distinct coins. I did take multiple measurements for 2 of the coins, but only recorded one.

If you would put the spreadsheet on Google docs I might look at it more.

I notice that one measurement for each coin is in disagreement with the later measurements on the coin.

I would add some other calculations.  From the average density of the coin, calculate the weight of water that you expect for the measured weight of the coin, also, calculate the expected weight of the coin given the measured weight of water.

thanks for these tips, I'll try to do my best.

The variation between measurements was (if I recall correctly) up to 0.03 g. There have even been some outlieres with something like 0.08 if I recall correctly. I tried this on a couple of measurements with 2 of the coins. The variation was present only on the measurements using the container. The simple weighing of the coin showed max of 0.01 g variation.

I'll do the (modified) process on my 10 BTC silver round when I have some time.

The sticker plus the volume (and paper) below it we could probably estimate pretty well. How thick is the hologram and how deep the "inlet" in the coin for the paper with the key? They weight of sticker+paper we can probably neglegt or guesstimate also.

A fake would not be from the claimed mint, though

Yes.  And the evaporation rate of the water.
Those balances cost $5,000.

holy f..k! That is cool! I will try this and see if I can get better accuracy from my scale this way.

Thanks for taking the time to explain (and make that great drawing) for me

Watch for air bubbles when suspending the object into water. Gently tap the thread to get rid of them.

Clean the object, handle with gloves (non-powdered).

Use distilled water, and read the density from the table for the particular temperature.

Repeat several times. What is the variation between measurements? Is it random, or is there a consistent up or down trend?

Make sure the balance is level.

I'm curious to know how a Casascius silver coin would stack up, but the sticker and private key paper would probably throw things off by quite a bit.

Ok, I'll explain the "frame" a bit more. You can make it out of a coathanger, but ideally something a bit flimsier is lighter and so better. It does not have to  be totally rigid, if it moves out of shape, it doesnt matter. I use copper wire because its easy to bend and holds its shape.

Here is a diagram:                                                  .------------.
                                                                           |              |
                                                                     ________        |
     Scales                                                         :::::::::         |
     Table edge     ===========================       |
                                                                                          |
                                                                                          |
     Bent Wire Frame                                                 .-----------.
                                                                            .
     Cotton Thread                                                    .
                                                                            .
                                                                            .
                                                                   |        .        |
     Object                                                      |      |||||     |
                                                                   |                 |
                                                                   |                 |
     Beaker of water                                        |                 |
                                                                   |                 |
                                                                    .__________.

                                                                       
The frame can be C shaped, it doesnt have to be rectangular, the important point is that the object is directly under the place where it rests on the scales so that it balences.  In fact it will pretty much hang that way anyway.

I have drawn a table in here, and you do want the scales to be horizontal and not moving, so this is quite a good way to do it. You take two mass measurements as |I explained, first with no beaker or water, then you raise the beaker and note the loss of weight due to boyancy with the object fully submerged.

Now one problem here is that any airbubbles that stick to the object represent an inaccuracy. Really you would like to use a bit of soap to prevent this, but that might alter the purity of the water. If you use a very small amount this would probably be a good idea. There is an alternative however. You can use any liquid provided that you take its density into account, so if you decided to use say parafin, because you will not get air bubbles in parafin because of the low density. But you probably do not know the density of parifin given thatit may vary quite a bit from sample to sample. So, use a known good coin or other object as a "calibration", that gives you the density acurately, which you can then use in your calculation of the 2nd object. The known good coin in fact can be anything you know the volume of, a freshly minted coin is convienient since you know the mass and the density of the material its made to high accuracy, so you know the volume!! But A 1cc cube or other known volume  of anything that sinks (in parafin) would be just as good.

Yeah, this is probably overkill, the smidgeon of soap method would be much simpler and probably work just fine.

again: I meant error of my measurement. I'm sure these coins are both legit and 99.9+% pure silver.

This is very interesting and I am impressed by your research. But I am sure that such prestigious mints have a very high standard of quality control; I find it hard to believe those margins of error are accurate.

thanks for the clarifications...


Sounds great, I'd love to be able to do that. I understand your point about the accuracy deteriorating with higher weight and I'd like to avoid that.

Can you maybe find or produce a drawing of that frame and the other stuff? I'm still having problems. The setup I come up with in my mind has other problems... I'm probably thinking too complicatedly.


I'm not sure what you mean by "you're displacing water out of the cointainer". No water leaves the container (except after the measurement is complete and I remove the coin some drops stick to the coin of course). I'm weighing the container with the water first (resetting scale to 0), then I'm submersing the coin hanging it from the string (so it doesn't touch either the floor of the container of the top of the water). The scale then shows the weight of the displaced water. (Actually I did it a little differently: For resetting the scale I put the coin (attached to the string but not hanging from it) into the container (so it's laying on the ground of the container). Scale shows zero at that point. Then I lift it up while keeping it submerged to it doesn't touch the ground or surface. That's why the scale show a negative value in my shot (the weight of the displaced water minus the weight of the coin)).

Well, for a start at no point does the weight of the beaker of water go on the scales. Your photograph seems to show the beaker of water on the scales. The point about these small scales is they are very accurate for small masses, less so for larger masses. Especially so as regards repeat readings which of course is what counts. Partly its a percentage thing. So its much better to not weigh large weights as far as you can. My method does involve weighing a wire frame so that you can weigh under the scales (and submerse the dangling object in water, which of itself is never weighed. You could use a 100 ton bucket of watter when weighing a 10g coin, and it would make no difference.

I think you are displacing the water out of the contain. There is an acuracy problem with this, and that is that surface tension may result in inconsistent results. Its inherrently sticky, and a few drips more or less may splut out as you do it. Any amount of grease or detergent on the object may also change the surface tension and that is worse. You may say its a trivial amount, but the point is, its multiplied by the comparatively large area of the top of the beaker. So it ends up as quite a bit.

My method also used the bouyancy principle and find the volume of the coin by "weighing" the displaced water. I also suspend the coin from a thread. I don't see how his method differs at all from what I did, practically. Am I overlooking something?

We're getting closer!: http://en.wikipedia.org/wiki/Spectrum_analyzer

Here's more fun science - remove silver tarnish: http://scifun.chem.wisc.edu/homeexpts/tarnish.html

Both silver sulfide and silver oxide have a lower density than pure silver.

The programming, I think, would be the hardest. Though one could always just use a frequency analyzer and compare each coin against a known good example.

You telling me that with all the high-tech doodads on the market for musicians, there's not one reasonably priced device that can detect the purity of precious metals by sound alone?

If that's the case, then there's money to made by the first person who invents/builds one.

A true Krugerrand has a distinct tone, whereas a fake would have a definite different tone.

How hard could making such a device be?

His test relies on more implied concepts of physics. Mainly Archimedes's bouyancy principles. This helps to get rid of errors in weighing or measuring the volume of the displaced water.

An E1 1mg test weight has a tolerance of ±0.003mg. The scale in the OP likely would not change from 0.00 to 0.01 with several of these weights on it. A slight fingerprint weighs about 0.1mg and an ungloved hand on a beaker can leave behind 1mg. The university chemlab where I work-studied had several scales this accurate just for undergraduate chemistry. Put sample in, close door, wait. (I should add that these weren't generally used for student experiments, they were in the lab where chemicals and glassware were stored).

If you are serious about weighing the coins, washing them first may be in order. You're probably not going to have an ultrasonic cleaner around, but dawn detergent followed by lots of rinsing and gloved handling will remove the contaminants that may contribute to the differences in measurement between coins. A troy ounce is 31.1034768g; all the coins weighed more than this.

While the accuracy of measurements can't be verified without a calibration weight that has not been mishandled, the precision can, by determining repeatability - does one kronwitter always measure 1% more than another?

In ordinary chemistry labs - not true. Mechanical scales for 1/10 of gram with some error.

Um, scales in labs 15 years ago could measure the weight of fingerprints.

Common metals used:
Tungsten: 19.25 g/cm^3
Lead: 11.34 g/cm^3
Iron: 7.874 g/cm^3
Steel: 7.859 g/cm^3
They might also use Uranium: 19.05 g/cm^3

Some people are sneaky, and use a lead core, and lighter alloy on the outside, mimicking the density and weight of silver. There's almost always a plating of real metal in any case, so the surest non-destructive way to tell is ultrasound, or a carefully calibrated electrical test.

Failing that, there's always the ear test. "Ring true," as it were.

Most likely the difference in calculations are caused by impurity or different density of water due to temperature conditions. The error of +/- 2% might be caused by other factors and measurement tolerances. The scale is not laboratory grade but for most purposes even the cheapest 8$ scales are extremely accurate compared to what was available in labs 15 years ago.

Hmm. I think this is what I did, no? What's the difference?

What density could a fake have? What kind of materials/techniques might be used?


I thought about that. I think lowest hanging fruit would be a better scale. I can't use more water, scale can only do 200g.

with error I meant error of my measurement.

I dont think your method is correct. This is the method I used to satisfy myself that a oplatinum ring was truly pure.

a) Weigh Ring.   
b) Weigh ring under water.
    This can be done by suspending the ring on a frame such that it hangs from a thread, and is imersed.
c) As an alternative to b), weigh the difference in weight between b) and a) , many scales can do this automatically.

Either way, you have the in air weight , and the loss of weight from imersion in water, c.

c is also the of mass of water displaced, and so gives the volume of the coin or ring.
If you do this in grams, the volume is in cubic centimeteres.

The density (or specific gravity) is found as normal by dividing the weight in air in grammes by the volume in cubic centimetres.

I found this method pretty accurate.

Main sources of inacuracy, I guess:

 Water not pure - use deionised water.
 Density varies with temperature, both of water and of the metals, corrections could be applied for this.
 Make sure you weight the item before you wet it, you do not want to weigh a wet item.
 Displacement of anything used to hold item, minimal if it is a thread.

I believe that a modern 'cheap' pair of digital scales is more accuracy than you will need. For their price these items give fantastic value. Just bear in mind that the weight of the frame, which can be a bent wire to suspend the item in a beaker of water under the scales should be as low as possible. Although the frame is zeroed out of the calculations, the errors in these types of scales go up when you do this type of thing.

I think you can get better accuracy than you did by using this method.

Still would catch most real fakes as the density would be off by more then 5%.

 A bigger water container could help, and maybe a more accurate scale.  Finally having a consistent amount of string in the water and taking that into the calculation would help.   

There's definitely a good bit of error there, which I really doubt since the coins at minted by respected sources. Those coins are probably either .999 or .9999 and that thousandth or ten thousandth of an percent does not result in a 1-2% error.

I measured the density of my silver/gold coins unsing this setup

EDIT: a better method was suggested by mintymark and yielded better results.



these are the results:



Here's how I did it:

• Weigh the coin itself
• Put container with water and the coin attached to string on scale and reset scale to 0
• pull on string, effectively measuring weight of coin minus weight of displaced water
• calculate density (assuming water density is 1g/cm³) by dividing weight of coin by volume of coin (equals volume of displaced water)

I used a cheap scale I ordered from Hong Kong for around €5. Yet the results seem to be quite reassuring (error margin (EDIT: of my measurements) seems to be around 1%-2%)

Comments?