The conductivity of materials is primarily determined by their atomic structure and the presence of free electrons. Metals are excellent conductors due to their "sea" of free electrons that can move freely, allowing heat to transfer efficiently. In contrast, non-metals lack free electrons, relying on vibrating ions to transfer heat, making them poor conductors. The type of bonding—metallic, covalent, or ionic—also influences conductivity, with metallic bonds generally leading to higher conductivity compared to covalent and ionic compounds. Ultimately, the atomic arrangement and electron mobility are key factors in determining a material's conductive properties.