Fragment, n.
Etymology: [L. fragmentum, fr. frangere to break: cf. F. fragment. See Break, v. t.]
A part broken off; a small, detached portion; an imperfect part; as, a fragment of an ancient writing. Gather up the fragments that remain. John vi. 12.
Shades of meaning
Fernald has no entry of its own for fragment; he lists it under part.
Where he writes about it:
A fragment is the result of breaking, rending, or disruption of some kind, while a piece may be smoothly or evenly separated and have a certain completeness in itself. — from part
A piece is often taken for a sample; a fragment scarcely would be. — from part