Abstract: Using the second rank algebraic formulas, the structure seminvariants of six differenttypes of known crystal structure have been estimated. These phases have also been esti-mated with other approaches:the Σ₁, Σ₄ relationships of probabilistic method and the firstrank algebraic formulas. The results show that compared with the probabilistic method, thealgebraic method not only gives results as satisfactory as the probabilistic method does,but also increases the computing rate significantly. From the comparison between the secondand first rank formula, we get a quite unexpected case-the resultss of all the six structureshow unanimously that the first rank formula almost has the same application value as thesecond one. The first rank formula has a great advantage over the second one in reducingthe computing time.

Key words: crystal structure determination, second rank algebraic formula, structure seminvariant, structure factor phase