INTERACTIONS FROM SELF-COORDINATION NUMBERS – A PHYSICAL RELATION WITHOUT FORMULA

Abstract

A large number of homogeneous particles A with different A–A interactions like carbon atoms in diamond, CO 3 ions in CaCO 3, S 6 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 Ti, i =1-3 of nearest, second and third neighbors. There are about 500 sets with increased Ti values (aristotypes) and about 500 sets with reduced Ti 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 ( CO 3) or ( S 6) structures with the centers of ( CO 3) or ( S 6) 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 Li 2 AgSb . All possible structures of an aristotype are within certain limits of Ti values in a Ti, 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.