Research Interests

Are you interested in ordered structures: two-dimensional patterns, gas atoms on metal surfaces, ordered alloys, magnetic ordering, superconducting oxides, colloids, polymers, dendrimers, lipids, proteins, DNA, stable clusters, stable isotopes?

The approach of Dr. Mika and myself is based on the self-coordination numbers T₁ and T₂ of identical nearest and next-nearest particles. The T₁ and T₂ values are plotted in T₁ and T₂ structure maps to analyze for attractive or repulsive interactions between particles or disorder. You can enlarge Fig. 1-3 as examples for two-dimensional and projections of some three-dimensional structures or a jig-saw puzzle. More detailed information can be found in

The last two articles are offered to all who want to analyze other structures like moving adatoms, dancing figures, architecture, ordered structures in biology, bacterial patterns, proteins, languages, music notes, etc.

Fig. 1

Fig. 2

Fig. 3

Figure 1-3:Periodic patterns A_xB_y, which are based on the square or hexagonal net and related nets like honeycomb or kagomé net with T₁ T₂ T₃;y/x values. The unit cell with x A and y B atom positions are indicated by points. The T₁ and T₂ neighbors of A positions are linked by solid or dashed lines, respectively (in 6 6 6;(1) etc. only T₁ neighbors). Some hexagonal layers of the ph system are also included. The structural units can be enlarged and photocopied to obtain a two-dimensional jig-saw puzzle. The blocked positions within the circles can not be occupied.

Figure 4: T₁, T₂ structure maps of the square and hexagonal nets and the primitive hexagonal lattice (ph').

Table 1: Constants a_i, b_i,c_i of different relations between T₁, T₂ values for boundaries B1,..., B7.

Can you find other structures with identical T_i values for all x positions?
Can you determine the different borders T₂ = f(T₁,r) of the structure maps?
Can you determine the structure map of all possible structures of a blocked system?
(The structures 3 6 3;(1) and 4 4 6;(1) are given in [2]).