What accounts for the ductility and malleability of metals?

The ductility and malleability of metals are primarily due to the unique arrangement of atoms within the metallic structure. Metals consist of a lattice of positively charged metal ions surrounded by a 'sea' of delocalized electrons. This arrangement allows the metal atoms to be organized in layers, which can slide over one another when force is applied.

When a metal is deformed, the layers can move while maintaining the overall metallic bonding provided by the delocalized electrons, which holds the layers together. This property is what enables metals to be drawn into wires (ductility) or hammered into thin sheets (malleability) without breaking. The ability to withstand deformation without fracturing is a hallmark of metallic materials and is a direct consequence of this atomic structure.

Other options do not capture this fundamental characteristic of metals. Rigid structures would not allow for deformation, non-metallic elements do not exhibit metallic properties, and the existence of metals in solid mineral form does not explain their ductility or malleability.