Basis functions of the backprojection operator

Cluster self-organization of inorganic crystal-forming systems: Templated nanocluster precursors and self-assembly of framework MT structures of A/B,Zr silicates (A = Na, K; B = Ca, Sr)

“…These compounds have compositions V(SO4)(H 2 O) 5 and V(SO4)(H 2 O) 3 . The three com pounds in the V-S-O-H system are chemical and structural analogs of minerals [21].…”

“…The nanocluster precursor (it was introduced in [1][2][3]), which is universal for all crystal structures, is a new concept in the simulation of the behavior of self orga nizing systems [1][2][3][14][15][16][17][18][19][20].…”

“…PRECURSORS B OF INORGANIC COMPOUNDS The difference between the precursors of crystal structures-molecules (in inorganic or organic molecular structures) and nanoclusters (in inorganic structures)-is in the nature of particle-particle bonds at the transition of the chemical system from the zero level to and higher self organization levels [1][2][3].…”

“…A С 60 cluster is formed in four stages according to the mechanism of assembly of self folding nets com posed of very simple 5 atom cyclic clusters [1][2][3]. С 60 and С 70 clusters cannot be obtained according to the mechanism of random association of individual C atoms with a growing cluster or random attachment of 5 and/or 6 atom clusters [1][2][3].…”

“…It is difficult to unambiguously predict the occurrence of the simplest (1D) or more complex (2D and 3D) periodicity (as a reflection of the fundamental nature of crystalline state) in different stages of evolu tion of a chemical system. In particular, the establish ment of long range order in the arrangement of nano particles is far from obvious in an analysis of their local interactions at the lower levels of self organization of a chemical system [1][2][3].…”