Foliation refers to the parallel alignment of platy or elongated mineral grains in a rock, giving it a layered, banded, or sheet-like appearance. This texture is typically developed in metamorphic rocks subjected to directed pressure. However, some sedimentary rocks can also exhibit a similar layering, though it's usually referred to as lamination or fissility rather than true metamorphic foliation.
- Shale (option a): Shale is a fine-grained, clastic sedimentary rock composed mainly of mud that is a mix of flakes of clay minerals and tiny fragments (silt-sized particles) of other minerals, especially quartz and calcite. Shale is characterized by its fissility, meaning it splits easily into thin layers or laminae along parallel planes. This fissility is due to the parallel orientation of clay mineral flakes, which aligns during compaction. This characteristic is analogous to foliation in metamorphic rocks, and shale is often described as a "foliated" or, more precisely, "fissile" sedimentary rock.
- Marble (option b): Marble is a non-foliated metamorphic rock formed from the metamorphism of limestone or dolostone. It is composed primarily of calcite and has a crystalline, granular texture.
- Quartz (option c): Quartz is a mineral (silicon dioxide, SiO$_2$), not a rock type in this context. Rocks like quartzite (metamorphic) or sandstone (sedimentary) are composed primarily of quartz. Quartzite is non-foliated.
- Sandstone (option d): Sandstone is a clastic sedimentary rock composed mainly of sand-sized mineral grains (often quartz). It is typically bedded (layered due to deposition) but not usually described as foliated or fissile in the same way as shale. It has a granular texture.
Given the options, shale is the sedimentary rock best known for a layered characteristic (fissility) that resembles foliation. In a broader sense, if "foliated" is used to describe any parallel layering in rocks, shale fits. \[ \boxed{\text{Shale}} \]