The rate of cooling of a mineral does effect the crystal size of mineral.
Step-by-step explanation:
Crystal size and the nature of the crystals are mainly affected by the rate of cooling of a liquid. When a liquid cools very quickly, the crystals are very fine and very small in size. But when the crystals form due to slow cooling of the liquid, the crystal is coarse grained but is big in size.
This is very evident from the igneous rocks. The igneous rocks like basalt which forms by cooling of lava after it comes out of the Earth's interior, do have very small and fine crystals. This is because the lava cools very rapidly in presence of atmospheric air.
But the igneous rocks like granite which is formed by cooling of magma inside Earth's surface, do have large and coarse crystals. This is because the lava cools below the Earth's surface in absence of air slowly.