Describes something large in scale or bulk, or coarse rather than fine in texture or granularity. Very common in 粗大ごみ, meaning bulky waste.
Bulky waste is collected only once a month.
Coarse particles were mixed into the sample.
粗い focuses on roughness or coarseness of texture or grain, whereas 粗大 adds the sense of largeness or bulk on top of that coarseness.
微細 describes something minute or finely detailed, the direct opposite of 粗大's sense of being coarse or bulky.
A Sino-Japanese compound written with 粗, associated with coarseness or roughness, and 大, associated with largeness.