ldhair

1840-O Liberty Seated half dollar, PCGS graded XF 40:


Photos courtesy of Stacks Bowers Galleries.

So, I was able to do it again! I found an 1805 C-4 (R.1) in XF40 with a rim clip. I didn't have the variety, and the rim clip makes it a little cool. This coin was a little more expensive than the Sushi dinner, but at $550... it's certainly an achievable coin for a collector that wants to squirrel a few dollars away for something cool.
This coin is not the example in my date set, but an accent piece. I just got it in hand, and I LOVE it. The surfaces are smooth and hard. There are no overly distracting marks to speak of. IMO it is pretty darn hard to find an XF40 half cent that looks as good as this - the clip is what makes it cool (and gives me an excuse to upgrade the variety one day).
I will include the dealer pics, and the PCGS TrueView:

Definitely a 56-n, also known as a camel head variety.  This is one of if not the most common NJ varieties, and as Just Bob stated is usually struck over other coins.  While it is very common, it is a popular variety for collectors and the value is enhanced if the undertype can be identified.

Your New Jersey copper appears to be variety W-5310, also known as Maris 56-n. Bowers states that most of these were overstruck on other coins, including Connecticut, Machin’s Mills, Nova Constellatio, Vermont, and others. It is one of the varieties often referred to as a “camel head.” Rarity is URS-13, meaning there are 2000-3999 examples known to exist.

This coin is likely counterfeit, though apparently modeled from a genuine O-102. The odd surface texture and uneven wear are suspicious.
    What does the edge of the coin look like?  A 1795 half dollar should have "FIFTY CENTS OR HALF A DOLLAR" with decorations between the words as shown on this image from NGC VarietyPlus:
    

For starters, try watching episodes of “The Curse of Oak Island”. The XRF device they use in their science center should be instructive for you. Here’s the problem. They are less than useful for plated and clad coins. There are no “magic tools” to cover all situations.

Welcome to the NGC chat board.
    Anything that looks green on a clad quarter (or most other coins) is either residue of a foreign substance or a corrosion product, neither of which is desirable. (Some uncirculated copper and some silver coins may develop a greenish toning that can be attractive, but that's not what is going on here.)  Based on your photos, both of your circulated 1976 Bicentennial quarter appear to have been coated with glue and/or other foreign substances. (Soaking them in acetone might soften or remove this residue.)  Even without the residue, they would have no numismatic value. Over 809 million were struck, and millions were saved in uncirculated grades.     
     Only coins of significant value (at least several hundred dollars) are worth the cost of submitting to third-party grading services. Many still enjoy collecting lower value--and even higher value--coins in albums, hard plastic holders, or other appropriate holders.  Knowledgeable collectors can grade and otherwise evaluate coins without having them encapsulated in bulky grading service holders. Even for those who collect only certified coins, knowledge of grading is important.  For those who want to submit coins to grading services, it is essential.

1882 Shield nickel, PCGS graded MS 64:


Photos courtesy of Stacks Bowers Galleries.

I don't think the coin will grade no matter what is done to it. It's not an UNC.