PROBABILITY CORRELATION OF ∑_1 RELATION-SHIPS AND THEIR TABLES OF 230 SPACE GROUPS

In the present paper, using the structure factor algebra method, we discuss the correla-tion and the distinction between thte conventionally used ∑_1 relationships and the probabilityvalue of P_ (h_1) on the basis of the P_ (h_1) of Hauptman's ana Karle's ∑_1 relationship. Theintroduction of conception on equivalent point weight ω of h_1 and degeneracy ω_2 of h_2 makesthe probability P_ (h_1) expressed by ∑_1 relationships become more strict. There are a lot ofinterrelated ∑_1 relationships in all four high symmetry crystal systems. According to theresults of this paper, what we need is noly to retain a few independent ∑_1 relationships. Usingthe principle of linearization, we have completed the tables of the ∑_1 relationships for 156space groups which belong to tetragonal, trigonal, hexagonal and cubic crystal systems.Now, we present the concise and perfect tables of 230 space groups of which 74 wereaccomplished by Hasek.