Final answer:
Asbestos is the silicate material composed of double chains of SiO4 tetrahedra, differing from quartz, mica, and glass which have other structures.
Step-by-step explanation:
The silicate material that is composed of double chains of SiO4 tetrahedra is asbestos. In silicate minerals, SiO4 tetrahedra can be arranged in various forms such as single units, rings, sheets, or three-dimensional frameworks. Asbestos specifically has its silica tetrahedra joined in a double chain structure, where every tetrahedron shares two of its oxygen atoms with adjacent tetrahedra, leading to a silicon to oxygen ratio of 1:3 (SiO3). This is distinct from other silicate materials like quartz, which has a three-dimensional crystal lattice structure with a formula of SiO2, or mica, which has a sheet-like structure and glass, which possesses a random network structure of SiO2.