I'll start this with a couple of axioms.  The first I heard from another dealer, to the effect that EVERY ancient coin has been cleaned.  The second, self-generated, is my personal assertion that any dealer who deals in loose coins has cleaned them on occasion.  These statements offered for amusement only, as many dealers will deny ever doing such a thing.
     One should look upon old coins with suspicion should they completely lack toning.  Example: I have seen a number of bright 18th century Russian coppers.  Their owners swore by them of course, but I could not bring myself closer to their point of view than "maybe."  I have, on the other hand, seen British conders, USA large cents, etc. with full luster, but they were subdued, not bright.  Bright old copper is improbable, but bright old silver does happen, and on silver you can do such a good job that you can't tell.  The fact is modern cleaning techniques are very good and you can be fooled.
 When discussing this subject two categories of state are important:
      A) the condition of the surfaces before the cleaning, and
      B) the material from which the item was made.
     In this exposition I will not go deeply into the chemical interactions which take place.  I will, rather, confine myself to practical considerations: what works with what kind of "dirt," what won't work, what reduces value, what enhances, etc.

 A. Circulated
 B. Uncirculated
 C. Proof
  1. Gold
  2. Platinum & palladium
  3. Silver
  4. Copper & bronze
  5. Brass (including aluminum-bronze)
  6. Iron and ferrous alloys
  7. Zinc, tin, lead, aluminum, nickel

     The basic principle is that the better the grade the more likely the possibility that one can perform an undetectable cleaning job.  On some of the late proofs in precious metal, where all there is is some superficial toning, a "dip" may restore the thing to blazing original perfection.  This will be
less possible with regular issue Uncs, and nothing will restore original luster to a circulated coin.  Details will be discussed below.

     Gold by itself will not tone, but coins are never pure gold, there is always some alloy, and the alloy will be subject to chemical attack.  Old gold will most likely have been buried in earth or water, and will be subject to physical encrustation and abrasion, as well as facing possible attack on the
alloying metal.  Straight out of the ground these things will often have a coating of dirt.  Base specimens may show pitting where the alloy has been leached by acid conditions.
     On good gold there should be no pitting.  The color might be a bit dark. This will more likely be due to dirt than oxidation, so a bath in soapy water would not be amiss.  You want to be careful what you use to scrub your gold with though, because nothing is easier to scratch and abrade than gold.  I'd suggest fingers and perhaps a carefully wielded Q-tip or similar.  No pressure should be applied.  The lightest of touches only.  But look carefully at your old gold.  Probably someone has already tried to clean it, and probably you can see where they tried too hard.
     Biggest problem with gold is not dirt, but jewelry mounting.  Many old coins were so treated.  Many times the evidence has been skillfully removed. Five out of five 18th century Russian gold coins recently examined by me showed ambiguous evidence of having been mounted.  The removal of the traces was skillful enough that the seller was able plausibly to deny that the traces existed.  This kind of tooling is common on old gold and silver, and often is of high enough caliber that you can't tell with naked eye.  20x magnification will usually clear up the ambiguity, but not always.

     Coins made of these metals typically don't get dirty, are not reactive, are hard, and thus are not usually cleaned.  Nevertheless, one often runs into 19th century Russian platinum coins which have been treated with abrasive or polished, the desecrations performed not doubt by idle rich of bygone years with nothing better to do than ruin coins.  As far as the chemistry is concerned, you can dunk these into most anything: acid, base, organic solvent, etc. and it won't hurt the coins.

     Now we get to the real business.  Silver surfaces are chemically responsive, and can develop salt and oxide layers of various colors, depths, and degrees of adherence.  All of these can be removed.  Some are more difficult than others, and with some you'll wish you hadn't.  But by and large, most silver coins will clean nicely, and often the appearance of a coin can be improved considerably without leaving any definite evidence that something has been done.
     I've cleaned a lot of silver coins.  The vast majority had favorable results.  I've done this for so long that I've developed a general routine I follow for silver.  Here's a list of my personal dos and don'ts:
     1.  For dirt and minor toning (brown is oxide, gray and black is sulfide) I carefully place the coins in a jar of straight household ammonia and leave them there for 15 minutes to 3 days or so.  The dirt and most of the toning come off.  The solution always takes on a blue color after a while, sooner with base coins, later with purer alloys.  The blue is copper in solution, but I have never, over 20 years of doing this, created pitting, not even under 20x magnification.
     What you get at the end of this treatment is a dirt free coin, lighter in color than it used to be.  If there were any deep tone spots they will still be present.  Silver coins will pick up black marks from contact with steel staples, such as are used to close 2x2 cardboard/mylar sandwich-type holders.  Ammonia won't touch them.  Green crust on old coins will eventually come off, you just need to be patient.  However, under the green you will often find a red copper oxide adhesion, which is  difficult.  Best result on red crust comes from alternate immersions in ammonia and vinegar or lemon
juice (works just as well as hydrochloric or sulfuric acids).  Patience is required, and occasionally one might consider a little physical help with a sharp tool, if one trusts one's hand.  One can eventually get it all off with no marks.
     One occasionally finds coins from Central Asia and other places with what I call "purple yuck," and more refined people call "horn silver."  The coins have patches of dark encrustation that obscure the designs.  Yuck is a sulfur salt of some kind, but it is acidic, and under the crust the coin's surface has been lost to corrosion.  Ammonia won't touch yuck.  Neither will vinegar or lemon juice.  A long soak in battery acid will take it off, but then you'll have a pitted area.  Whatever you do, your coin will be worth less than when you started.
     2. After the ammonia bath comes the vinegar or lemon juice bath.  (Wash coins in soapy water between baths.)  Why acid?  The deeper sulfate layers will respond to acid where they won't to ammonia, I suppose because they're denser?  At any rate it's true.  Some people don't do the ammonia, start right with the acid.  The problem I see with acid is that its action is a little more vigorous, and if your spots or toning are too deep you will start to visibly erode the surface.  Large areas of deep toning will strip to an off-color matte gray, spots will turn into pits.  You need to know when to stop.  That takes experience, which comes from ruining coins.  So get some cheap coins to practice on.  This kind of problem hardly ever arises with ammonia.
     3. Both ammonia and weak acid will leave a circulated coin with a nice, mildly tony, completely natural looking "old silver" appearance.  High grade coins will have their luster.  Some deeper toning will remain in the recesses, and the overall result will usually be salubrious.  One can go further and
strip the surface completely.  This is done by things like Jeweluster, Tarnex, etc., all of which are basically the same thing: versions of thiosulfate and various secret ingredients.  These will take away all of the toning and leave a bright coin.  The thiosulfate compounds give excellent results with high
grade coins, but deeply toned coins are subject to the overkill mentioned above, and these chemicals will ruin your coin in minutes versus hours for weak acid.  Still, I use Tarnex frequently to brighten up tired proofs. Thiosulfates have limits too.  They often won't work on staple marks, or the heat sealing defects on some Franklin Mint proofs of the 70s and 80s.  They have no effect on crusts of any kind.
     To repeat my progression: ammonia, vinegar, Tarnex.  When all done wash in soap and water.  Handle by edges, carefully dry, place in inert package.  I think that's enough for silver.

     Might as well include billon too, any silver under about .350 fine.  Copper divides into two categories: been buried or hasn't been.  Unburied pieces will either have original red surfaces or will be toned various degrees of brown, but will have no encrustation or patina.  I generally don't mess
with these other than to clean them if they're dirty.  That I do with soapy water or organic solvent.  I don't use ammonia or vinegar on these.  The result will be a mottled surface.  Won't look good.  In fact, I think there's very little to be gained from working on coppers of the 18th century onward.
You can always tell when one's been messed with.  I think it's useless to try to restore mint appearance to toned copper.  Just stick it in an inert capsule and leave it as is.
     On older coins I follow a different policy.  A bunch of late Romans, or Indian dumps, or medieval European billons will most likely end up in the ammonia bath, some pieces staying in for weeks.  The solution becomes very blue.  Many of these coins are very dark or encrusted to the point that they
have no value as is, and must be improved if anything is to be done.  Ammonia works on copper as on silver, except that pitting will happen to some small percentage of the coins.  "Silver wash" on late Roman coins is not disturbed by ammonia.  Usually you will have a cleaner coin with a normal looking surface.  Coins with green patina will lose the entire patina, and are likely to be pitted underneath.
     Red oxide is not touched.  On copper I often end up scraping it.  Sometimes this works, but sometimes there's nothing underneath the red patch.  A couple of times I've actually used a ball peen hammer to percuss patches off large Ptolemaic bronzes with good result.  A heavy duty ultrasonic cleaner might occasionally give similar results.
     By and large I've found ammonia worth applying, as it has turned many pieces of worthless junk into saleable pieces of junk. Use a utensil to get the coins out of the blue solution.  It'll stain your fingers.
     Acid is not nice to copper.  Pitting almost always occurs.  I recommend not to use.
     Tarnex on copper will give bad results to all except proofs and BUs.  It will not yield desirable results with fingerprints, nor will it restore lost lustre.
     I think artificial toners are stupid.  You can always tell.  Wipe the thing with an oily rag and put it in sunlight for a year or so.
     How to stabilize bronze disease (green powder).  This is a carbonate caused by acid conditions.  The easiest way to deal with it is to soak the coin in ammonia until all I mean all the green is gone, neutralize it in soapy water, dry carefully, and tuck it in an inert holder.  If it comes back that means you didn't bathe it long enough.  Do it again.

5. BRASS (including aluminum-bronze)
     The brasses do not clean well.  None of the things described above work.  Ammonia will mess up modern brass and aluminum bronze.  It will leave spots and create a "wrong" color.  Ancient orichalcum will respond more poorly to ammonia than copper or bronze.  Acid is murder on brass, and tarnex is only useful to freshen BUs and proofs.  I admit it, brass has stumped me for 3 decades.

6. IRON and ferrous alloys
     Start with ammonia for the dirt.  For rust you'll need an extended pickling in acid.  If the rust is too bad you'll have pits.  Rust is a fact of life.  Tarnex is useless.

     When you get an Unc piece of zinc or tin you need to put it in an inert holder immediately if not yesterday.  It's probably too late already.  These things suck up oxygen and grow spots in the dark.  You can then clean the spots off with acid, but they ALWAYS leave pits.  You can always tell when
zinc has been cleaned.  Other than soapy water for dirt and organic solvent for pvc scuzz (you're probably too late) I wouldn't bother trying to clean zinc or tin.  As for lead, I wouldn't do anything, no matter what shape it was in, how deep the patina, how ugly it looks.  Old lead coins will be covered in tannish patina.  Strip that and it looks disgusting.  I don't mess with lead.
     Aluminum reacts badly with ammonia, and there's nothing else that works either.  This is not a problem though.  Aluminum doesn't do much other than get dirty and corrode.  Corrosion in the numismatic context usually comes from contact with acid paper envelopes, and is a whitish powder.  This can be removed with acid and stabilized, but you'll be left with a pit.  Either way your coin is ruined.  With aluminum at this point prevention is really your only option.
     Pure nickel will clean in ammonia or vinegar, and responds to tarnex like it should.  Copper-nickel, on the other hand, will quickly develop pitted surfaces in all three solutions.  I still dunk copper-nickel coins when I have to because of unsightly spots, etc., but I get them in and out fast: not more than a few minutes for ammonia and vinegar and not more than a couple of
seconds for thiosulfates.

     Organics come in two varieties: lacquer and scuzz.  Both have to be stripped before any chemical cleaning can be done.

     Lacquer happens.  It can save a coin when the alloy is reactive.  Lodz Ghetto 10 pfennig coins are examples of coins which should be lacquered, anything made of magnesium.  But most lacquer jobs are terrible and you have to strip it.
     All lacquer will come off with acetone.  Use a sealed jar, provide good ventilation, and work patiently with soft rag and Q-tip.  It'll come off.  On some coins, zinc for instance, lacquer may actually be a good idea.  In fact, why shouldn't we consider restoring precious metal coins to circulation with thick coats of lacquer to preserve intrinsic value?
     The term is usually applied to green, adherent, acidic, sticky stuff that gets on coins that have been kept in PVC, a substance that is still in use for coin storage.  PVC scuzz can be removed with most organic solvents. Acetone usually works fine.  The scuzz occasionally ruins proof surfaces, and base metals in any condition can be spoiled, in which case nothing can be done.
    Another kind of scuzz is simple grease or wax.  Use any organic solvent.

 I clean silver coins often, and "dip" them frequently.  I clean copper coins only when their salability in their uncleaned state is severely restrained, which is to say when I have nothing to lose.  Many times I get an improved coin which does not look cleaned, but a decent percentage end up
worse than before.  I usually take the rust off iron.  I don't mess with brass, zinc, tin, aluminum.

 Which metals will be affected by which solution.  Follow normal safety procedures.  Use sealed containers, adequate ventilation, dispose of properly, etc.
SUBSTANCE Ammonia  Acid Thiosulfate
Gold OK OK why?
Platinum OK OK why?
Silver OK OK usually OK
Copper OK no not recommended
Brass no no no
Iron OK OK no effect
Zinc no no no
Tin no no no
Aluminum no no no
Nickel OK OK OK
Copper-nickel act fast act fast very fast

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