The spiral form of the Periodic Law is proposed as its fundamental graphic representation. This idea is based on the fact that the spiral is the most appropriate form in description transitions from simple to complicated. The spiral is easily obtained from the linear succession of the elements when they are ranged by growing nuclear charge. The spiral can be simply transformed into many other graphic representations, including tables. This paper suggests the conception of the autonomy of blocks. This autonomy (...) is clearly seen in the variation of the outer electronic shells, in the width and the height of the blocks, as well as the number and properties of elements included therein. The regularities in the changes of element properties are pronounced in certain blocks but actually absent in others. The blocks can be permuted to obtain full-fledged versions of Periodic Table. The new stage of the verification of the blocks autonomy is the use of the total number of the differentiating electrons as an independent variable in describing the properties of the elements and their compounds. Consideration of individual blocks made it possible to deduce the periodic equations valid for all the elements within each block. Formulation of the Periodic Law is advanced: while describing characteristic determining the properties of the elements, the nuclear charge is replaced by the total number of differentiating electrons. Two modifications of the conventional Periodic Table are obtained by minimal changes. The first one shows the secondary and the additional periodicites. Another table shows the total number of differentiating electrons for each element. (shrink)

Demarcation of elements for two subsets appears to be the most fundamental approach to their classification. If one draws a vertical straight line through the middle of each block of elements in the Periodic table, all the elements are divided into two subsets: “early” and “later”. For example, in the d-block, the early ones are Sc–Mn, and the late ones, respectively, are Fe–Zn. Later elements partially repeat the properties of the early ones, and this is defined as the internal periodicity. (...) Another criterion for dividing the elements into two subsets is the evenness and oddness of the sum of n + l, where n is the principal quantum number, and l is the orbital quantum number for the outer electron subshells. Properties of the odd elements are closer to each other than to properties of even elements, and vice versa. This regularity is manifested as the secondary periodicity. The history of concepts, which considered the existence of subsets as well as of inner and secondary periodicities, is discussed. The features of the electronic structure, which underlie the existence of subsets, are considered. The existence of subsets was depicted earlier by dividing the periodic table into two tables or by applying a mirror-symmetric table. Small changes are proposed in the conventional Periodic table, allowing to reflect the existence of the considered subsets. (shrink)

The early Periodic Tables displayed an 8-Group system. Though we now use an 18-Group array, the old versions were based on evidence of similarities between what we now label as Group (n) and the corresponding Group (n + 10). As part of a series on patterns in the Periodic Table, in this contribution, these similarities are explored for the first time in a systematic manner. Pourbaix (Eh–pH) diagrams have been found particularly useful in this context.

As part of a series of contributions on patterns in the periodic table, the relationships among the transition metals are examined here in a systematic manner. It is concluded that the traditional method of categorizing transition elements by group or by period is not as valid as by using combinations thereof. From chemical similarities, it is proposed that the transition metals be considered as the [V–Cr–Mn] triad; the [Fe–Co–Ni–Cu] tetrad; the [Ti–Zr–Hf–Nb–Ta] pentad; the [Mo–W–Tc–Re] tetrad; and the [Ru–Os–Rh–Ir–Pd–Pt–Au] heptad. Silver (...) does not fit neatly in anywhere and is better linked with thallium. (shrink)