Narrow Results

The surfactant structures are approximately given by the zero-potential surfaces of A⁺ and B^- atoms in circle or sphere packings. The Dirichlet domains of A atoms are connected by T₁ channels to neighboring A domains in rod like structures with T₁ = 2, or layered structures at increased T₁ values. Micelles are usually isolated with T₁ = 0 or 1 channels. Layered or rod like structures are formed at A–A attraction while isolated micelles are formed at repulsive A–A interactions. The rod like structures are similar to polymer chains of A = carbon atoms with T₁ = 2 neighbors. The ordered micelle structures are observed for charged colloid particles A⁺.

A large number of homogeneous particles A with different A–A interactions like carbon atoms in diamond, CO₃ ions in CaCO₃, S₆ molecules in rhombic sulphur, colloid or micelle particles are ordered in such a way that the bulk structure can be characterized by the self-coordination numbers T_i, i =1-3 of nearest, second and third neighbors. There are about 500 sets with increased T_i values (aristotypes) and about 500 sets with reduced T_i values, which are obtained from characteristic lattice complexes. The number k=1,2,3, etc. of the (T₁ T₂ T₃) aristotype is added to the Wyckoff letters of standardized structures like 167-b9a9 or 148-a4 for the Ca(CO₃) or (S₆) structures with the centers of (CO₃) or (S₆) groups. Two or more particles A, B, etc. can belong to the same aristotype like Na and Cl atoms in NaCl or Li, Ag and Sb atoms in Li₂AgSb. All possible structures of an aristotype are within certain limits of T_i values in a T_i, i = 1-3 coordinate system, the structure map. The location of A, B, etc. positions on structure maps can be related with repulsive or attractive interactions at high or low T₂ values. The plate- or rod-like habit of single crystals can frequently be related to layered or rod-like packings (T₁ T₂ T₃) of the constituents.