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I see both terms refereing to fractures on crystals or minerals, so I wonder if they could be considered synonymous.

If no, what's the difference between both terms?

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They are not synonymous.

Cleavage means breaking along planes defined by crystallographic directions. For example, cubic crystals like halite, NaCl, often cleave along directions that follow the cubic form. However, with a different bond strength, like fluorite $\ce{CaF2}$, the crystals cleave most easily along octahedral directions, similar to two pyramids sharing a base.

Fracture is when the break does not form along the crystallographic directions. It then can be grainy or conchoidal (like breaking glass).

Fracture is also used to describe the breaking of rocks as opposed to single crystals. In this case planar fracture follows the direction of forces that formed the rock.

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