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By the guidelines from colonialjohn, both coins are genuine and from the same mint but one is an official strike and the other a debased specimen. That's my conclusion.
In this case, what is proven is that the coins were made of silver refined (likely from Mexico or South America) no later than the first half of the 19th century. However, the SG also shows in one case that the coin is NOT solid silver.
Remember one fact - Class 2 counterfeits were made in the first half of the 19th century and they do contain essentially perfect silver if they were made using Mexican silver. These Class 2 counterfeits can often be identified visually - the XRF tests proves the age and means they are NOT Class 3. But the XRF test does NOT mean they are GENUINE.
I believe as I said before that you are likely dealing with two varieties of Class 2 counterfeits one made to a lower standard than the other. The real question was when they were made. So they are unlikely modern.
They were unlikely made for interior China because they are not Carolus issues, but I have very recently discovered a clue (unsupported as yet) that would indicate that Ferdinand coins were also made for other markets to take advantage of a lower premium over silver melt that was present in other areas. That is a different story one too new to go into here. It is in the working theory phase. I have been pursuing this line of research because I have several coins that appear to be Class 2 silver types but which are Ferdinand designs.
To return to my theory that both coins actually fall into a counterfeit category we need to be clearer about what XRF tests provide.
XRF does not penetrate into the core of the coin so the coin may have been made using a technique that leaves good silver at the surface.
There are two primary methods.
The Sheffield process is one such method. The core of a Sheffield coin (usually nearly pure copper) is covered with thin layers of silver. That surface layer is coin silver of the era and will test properly if Mexican silver was used. (If Mexican silver was used at a secondary location, this postulates conditions similar to the Mexican mints when melting and rolling the silver so as not to remove volatile elements).
The second and more likely method that could have been used is a debased silver alloy which is pickled AFTER the coin is struck to raise the surface % of silver. Pickling removes the surface copper from the coin and alters the color and composition of the upper layers. That is the same part of the coin that XRF measures. The heavy trace contaminants are unaffected by pickling resulting in a test showing a shift in Ag and Cu ratios but not the contaminants. Pickling can of course be overdone removing too much silver and resulting in an underweight coin which also will look sea salvaged because of loss of metal.
So that means XRF can be fooled and is worthless. Right? WRONG.
What I did not see in the XRF test results you posted are any other trace contaminants like Tin or Yttrium or Cadmium. The test results of coin A add up to 99.08% and for coin B 99.09 %. Therefore something is missing from both coins - almost 1%. XRF can be done to different levels and can detect major as well as VERY MINOR components.
XRF tests are also limited by other factors and some lightweight metals and all non-metals are not detectable.
This is where the high tech science comes in.
Were there any trace contaminants in the 20 - 80 ppm range? These are the ones that tend to identify modern silver in the mix. They are what is left in the 0.001 part of the 0.999 fine silver bars from present day refineries.
This inability to see into the core is remedied if the coin has a test cut. The readings in the test cut are often totally different than XRF tests of the surface. Worn areas at the high points are also great to look deeper into the coin. They often show completely different percentages.
This is why I have wondered if it would not be advisable to core drill every coin tested to get a sample of the interior metal BEFORE it is encapsulated as genuine. The drill hole in the edge would permanently mark a coin and prove it was authenticated. IT would prevent re-holdering and the fraud that goes with it. The hole could be very small - exactly like museums do with all ancient statues to prove authenticity. The core sample would be more accurate and could be tested in several different ways. SEM analysis of the crystals provides a lot of good information.
XRF surface tests only go so far, but they can still be used to exclude the majority of Modern fakes by the very minor trace contaminants.
The principle is that to make a fake today you need to measure elements at XRF levels of accuracy to get the alloy right. If a forger takes "pure" silver and "pure" copper the trace contaminants will be different today than they were in 1800. Pure silver in 1800 meant 95-98% silver 2-5% other metal. By the second half of the 19th century it meant 99% silver with 1% other metal. By the turn of the 20th century 99.9%.
Today if you pay extra you can get 99.999% fine silver BUT what do you mix with it? Who produces 99.999% fine copper? The answer is NO ONE DOES. Most copper today has nearly 1% trace contaminants. What those are varies and they do not match elements seen in 1800 refined Mexican copper.
If the modern silver used by our theoretical forger was produced from silver salvaged from electronics components there are a couple rare earth elements used to increase conductivity that are VERY difficult to refine out of the silver. They are usually seen even in the 0.0001 remainder of the purest silver available.
So today there is a problem even in the best metal labs which precludes cheaply manufacturing an identical alloy. The more it costs our forger to make his coins the fewer he will make. Mass production of coins will be discoverable by XRF testing.
I know many people are now thinking just melt old coins. Perfect source right? WRONG AGAIN.
Melting the coins will in fact alter the alloy by driving off the volitile elements that are always seen in the originals. Also depending on the crucible composition and even furnace linings there are contaminants that can re-enter the alloy in the refining and melting process.
To make an 1800 coin precisely would require using all of the melting and processing methods of the time period. This gets very costly and would slow the process to a trickle.
In this discussion, I am getting ahead of the present capabilities of XRF because of the small data base. However, if you view this as the beginning step in a long process - it will not be to long before a good database exists - then if core sampling ever catches on and lighter elements not now picked up by XRF can be included - a whole new range of trace contaminants including carbon will be available.
I see this as just the start of bringing counterfeit identification into the 21st century. It is also the only way we will be able to exclude counterfeit coins in the future. As digital engraving improves, I can see a day when an absolutely perfect die can be re-created digitally. If that is done all the visual clues will disappear and we will have only the metalurgy left for positive proof.
I am very optomistic that
Counterfeit Detection can stay one step away from the technology of forgery. Sometimes we are one step ahead, sometimes one step behind but always close.
That is the real "fun" of doing this.