The breaking of a mineral along irregular surfaces is called fracture.

Here's why:

* Cleavage refers to the tendency of a mineral to break along specific, smooth planes of weakness.

* Fracture describes any break that doesn't follow a specific cleavage plane.

There are different types of fractures, including:

* Conchoidal: Smooth, curved surfaces, like a seashell (e.g., quartz)

* Hackly: Jagged, sharp edges (e.g., metals)

* Uneven: Rough, irregular surfaces (e.g., most minerals)

* Splintery: Thin, elongated fragments (e.g., asbestos)

* Fibrous: Like fibers or threads (e.g., gypsum)

Let me know if you'd like more details about any specific type of fracture!