The value of mining smoky quartz depends on the quality and size of the crystals, as well as market demand. Smoky quartz is popular for its unique color and metaphysical properties, making it sought after by collectors and healers. Conducting research on current market trends and consulting with local mineral experts can help determine if mining smoky quartz is a worthwhile venture for you.

Amethyst is a precious stone much like but not as popular as diamonds. It is used in jewelry such as rings, necklaces and bracelets.

you find it almost everywhere in the world
quarts is located on the earths surface

No. Quartz is insoluble in water and contains no sodium ions. It is a giant covalent structure of silicon and oxygen.

Some are, some aren't.

No. It is very common and easy to find.

I can't tell if you mean "crystal" as in "made of a crystalline material" or "crystal" as in "made of lead crystal, which is not technically a crystal at all".

Take it to a jeweler. There's not any simple foolproof way a layman could tell.

No. In minerology, cleavage is a feature, not a physical thing. Regardless, quartz does not possess the feature known as cleavage, meaning that it has no parallel broken surfaces. Rather, the feature that quartz can possess is called "fracture."

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