That's an excellent question and the short answer is yes. There are many kinds of crystals, and each has a favorite range of temperature and pressure under which it will grow. Many crystals, such as garnets, amphiboles, or pyroxenes, are melted only at the very high temperatures or pressures found in the interior of the earth, and so will only form by the cooling-down of molten rock.
There are a lot of substances, however, that crystallize at fairly low temperatures and pressures. Many of these crystals form when water moves through rocks: the water can dissolve the minerals in one section of rock, and later, when the water becomes saturated, re-precipitate its solutes in another part of the earth. This process of dissolution and re-precipitation causes the growth of new crystals. Some crystals commonly grown this way include calcite (CaCO3) and quartz (SiO2).
Calcite and quartz dont just grow in rocks. The shells of most invertebrates are made from calcite and aragonite (two crystalline forms of CaCO3) or silica (another name for quartz). Crystal formations will also grow in very saline lakes, as they dry out and become more and more chemically concentrated. The strange formations found at Mono Lake were formed by this process. What are the formations at Mono Lake are made of?
There's one very common crystal that definitely never forms in molten rock. I spent five years in New England, and so got to see it a lot but I dont see it often in sunny Santa Barbara! See if you can think of it
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