Quite a few higher-level spells require x GP of gemstone or gemstone dust in order to cast — I will not bother listing them here, as it'd just take up space in the question.
However, the value of a gem is primarily determined by Cut, Color, and Clarity (or lack of imperfections), not its size. Considering that the same base material can vary widely in these regards from industrial-grade stones that are practically worthless to a jeweler, but still useful for their material properties up to the finest gemstones money can buy, what minimum standards are required of a gem in order to be usable as a spellcasting material component?
Must it be cut before it can be used, or can uncut (raw) gems be used for casting, straight out of the ground? Could a wizard cast a spell that say called for a sapphire or a ruby with a crystalline lump of industrial corundum (synthetic sapphire) instead of a natural gem? Would a large shard of bort be useful for spellcasting in lieu of a gem-grade diamond?
Citations strongly preferred here, by the way — if you need to dig back into the archives, that's OK, but right now, this is something that I would not even know how to consider from a DM or player perspective.
Best Answer
You're suffering a misconception.
In the real world, gem size is an extremely important marker of value: the 4th 'C' that you missed, Carat. Unusually large gems are worth exponentially more than smaller ones of comparable quality.
However, in D&D, all gems are measured by a single universal standard: their GP value. No version of D&D has ever gone into the specific qualities of a gem, because very few players would care for that much extra book keeping. Gems are simply abstracted into a condensed form of currency.
It would certainly be possible to extrapolate some system of evaluating gems into the 4 C's, but in the end this will provide a great deal of bookwork, and after all that the players won't care: "Yea, but how much is it worth?"
That level of detail is simply below most players' level of concern. Further, unless you plan to give lessons in gemology, much of it would be meaningless to most players, and you will spend an inordinate amount of time re-explaining how to evaluate the gems. After all that, they're just going to ask again: "Yea, but how much is it worth?"
Gems have 3 basic purposes in D&D.
Bort is really poor quality Diamond. If such a thing existed in a given D&D world, then it would just be Diamond, and you would still need the same GP value worth of the material.
In 'regular' D&D, there is no way to produce artificial gems or similar items with high intrinsic value (the money metals, for instance).
The typical response would likely be "They aren't real gems, so they don't work."
Some DM's would happily let you try it, and then have fun messing with the outcome of the spell.
In the end it would be up to each DM to make a ruling on artificial gems.
As discussed above, gem qualities are either ignored, or assumed to be of a fairly standard type. Common gems would be assumed to be cut, though likely not expertly. As spell components, this is all largely irrelevant. Again, the only measurement the spell is concerned with is how much the lump of material you are presenting is worth. Absolute value only, you cannot haggle with your Spell. Many spells also do not care if you use one or many gems, as long as the total value is achieved.
I would like to have been able to present citations for all of this, but I have never seen anything in any of the 5 editions (and multiple subsets) of D&D that I have played. This is in relation to both gem quality, and even more so to the idea of artificial gems.
D&D is intended to be a game of fun. For the majority of players, going into this level of detail reduces the game to 'crunch', bogging it down with bookkeeping and trivial details. Very few would find this to be an enjoyable way to play.
My recommendation is that the best way to consider this is to consider it a poor investment of time which will cost you far more enjoyment than it provides.