Assembly of small building blocks such as atoms, molecules and nanoparticles into macroscopic structures-that is, 'bottom up' assembly-is a theme that runs through chemistry, biology and material science. Bacteria 1 , macromolecules 2 and nanoparticles 3 can self-assemble, generating ordered structures with a precision that challenges current lithographic techniques. The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice (BNSL) [3][4][5][6][7] can provide a general and inexpensive path to a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. Maximization of the nanoparticle packing density has been proposed as the driving force for BNSL formation 3,8,9 , and only a few BNSL structures have been predicted to be thermodynamically stable. Recently, colloidal crystals with micrometre-scale lattice spacings have been grown from oppositely charged polymethyl methacrylate spheres 10,11 . Here we demonstrate formation of more than 15 different BNSL structures, using combinations of semiconducting, metallic and magnetic nanoparticle building blocks. At least ten of these colloidal crystalline structures have not been reported previously. We demonstrate that electrical charges on sterically stabilized nanoparticles determine BNSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.Face-centred-cubic (f.c.c.) ordering of monodisperse hard spheres dispersed in a liquid permits larger local free space available for each sphere compared to the unstructured phase, resulting in higher translational entropy of the spheres. When the volume fraction of hard spheres approaches ,55%, this ordering enhances the total entropy of the system and drives the ordering phase transition. Entropy-driven crystallization has been studied in great detail both theoretically 12 and experimentally on monodisperse latex particles, whose behaviour can be approximated by hard spheres 13,14 . In a mixture containing spheres of two different sizes (radii R small and R large ), the packing symmetry depends on the size ratio of the small and large spheres (g ¼ R small /R large ) 3,8 . Calculations show that assembly of hard spheres into binary superlattices isostructural with NaCl, AlB 2 and NaZn 13 can be driven by entropy alone without any specific energetic interactions between the spheres 9,15 . Indeed, NaZn 13 -and AlB 2 -type assemblies of silica particles were found in natural Brazilian opals 16 and can be grown from latex spheres 17 . In a certain g range, the packing density of these structures either exceeds or is very close to the density of the close-packed f.c.c. lattice (0.7405), while structures with lower packing densities are predicted to be unstable 8,15 .Despite these predictions, we observed an amazing variety of BNSLs that self-assemble from colloidal solutions of nearly spherical nanoparticles of different materials (Fig. 1). Coheren...
