Hidekazu Ido

Wellchemie Laboratory

wellchemlab(atmark)yahoo.co.jp

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 　　　　　Public technical report　2021-500018

The periodic table of elements is the basic table in science. It has evolved since Russian chemist Dmitri Mendeleev published the prototype of periodic table in 1869.  The long periodic table is useful and most popular in various periodic tables¹. It is a table in which the elements are arranged in order of atomic number, which well represents the chemical properties based on the electron configuration of the atoms (figure 1).

However it may not be able to fully express the similarity of chemical properties, the arrangement of main group elements and transition elements, and the stability of nuclei.

 Here we show that the element table with a fractal structure greatly improves the above problems and expands the function of the periodic table. In the periodic table, the elements are arranged mainly focusing on the seven rows (periods) corresponding to the periodicity of chemical properties. That is, the elements are arranged by focusing mainly on the seven rows called the period. On the other hand, in the fractal table of elements, we focused on the fact that the group of elements has similar chemical properties, and clarified a new relationship between the elements and nuclei by forming a fractal structure with the group as the basic unit.

We expect that the fractal table of elements contributes the development of chemistry, physics, biology and other sciences. 

In the long periodic table, the elements are arranged in order of atomic number in periodic units, and elements with similar chemical properties are arranged vertically in the table. It is very useful, but there are some problems. The elements are classified in the order of s, f, d, p blocks from the left of the table, which is different from the order of azimuthal quantum number. Since the table is arranged in periodic units, groups 1 and 18 are separated, and there is no continuity. Main group elements are divided into group 1 〜 2 and group 13 〜 18 by transition elements. Since the positions of main group elements and transition elements with similar valences (for example, group 5 and 15 and group 7 and 17) are separated, their similarity is not expressed. Lanthanoids and actinoides are listed in a separate table. The shell model of atomic nucleus is not considered, and the magic numbers (2, 8, 40, 50, 82, 114) do not appear in the elemental arrangement.

 Therefore, we studied the structure of the element table that can express chemical similarities without division. Approximately fractal figures are found in every aspect of nature and seem to be related to the essence of nature, so we decided to apply the fractal structure to the element table.

 A group with similar chemical properties was defined as a basic structure (cell) consisting of 9 squares. Figure 2 shows the cell in the fractal element table. In the cell, the elements of each group are arranged in the order of the numbers listed in the cells from the one with the smallest atomic number. The cells were then arranged to form a fractal structure to create a fractal element table.

 Figure 3 shows a fractal table of elements. It consists of the 0th to 3rd layers. The 0th layer (central part) is hadron, the 1st layer is an element close to hadron, the 2nd layer is s, p block element, main group element, and the 3rd layer (peripheral part) is d, f, g block element, transition element. Hydrogen and helium in the 1st layer are the simplest and closest elements to hadrons with the fewest electrons. Hydrogen symbolizes odd-numbered electrons and helium symbolizes even-numbered electrons. Main group elements and transition elements with similar valences are close to each other.  Main group elements are gathered in the 1st and 2nd layers without being separated by transition elements. Since the alkali metal cell and the rare gas cell are in contact with each other, each period is continuous. Lanthanoids and actinoids are listed in the same table as other elements.

 In Figure 4, the elements whose stable isotopes with the highest abundance ratio have magic numbers are shown in yellow, and artificial radioactive elements other than transuranium elements are shown in blue. The elements whose stable isotopes with the highest abundance ratio have magic numbers (2, 8, 40, 50, 82, 114) are lined up parallel to the diagonal line connecting the lower left and upper right of the table. Artificial radioactive elements other than transuranium elements are concentrated in the middle right part of the table. There are elements with atomic numbers 126, 146, 160, and 162 in the vicinity of the line passing through Ni parallel to the diagonal line connecting the lower left and upper right of the table, and these numbers may be magic numbers.

 Figure 5 is a table in which elementary particles related to hadrons located in the center (0th layer) of the fractal table of elements are arranged in cells. The left and right columns of the cell are the elementary particles mentioned in the Standard Model². The particles located opposite each other in the cell are related to each other. Hadrons are particles in which quarks are bound by a strong interaction. Neutrons are transformed into protons by a weak interaction. Atomic nuclei consisting of hadrons and electrons form atoms by electromagnetic interaction. Graviton and supersymmetric particles are elementary particles mentioned in superstring theory³.

 The Fractal Table of Elements reflects both the chemical properties of the elements due to the electron configuration and the properties of the nuclei due to the nuclear shell model.

 It is expected to contribute to developing of chemistry, physics, biology and other sciences.

Figure 1 Long periodic table of elements.

Figure 2 The cell in the fractal table of elements.

Figure 3 The fractal table of elements

 　　 　red: 0th layer, orange: 1st layer, yellow: 2nd layer, green: 3rd layer.

Figure 4 The elements whose stable isotopes with the highest abundance ratio have magic numbers are shown in yellow, and artificial radioactive elements other than transuranium elements are shown in blue.

1. Marchese, F. T. The Chemical Table: An Open Dialog between Visualization and Design. 2008 12th International Conference Information Visualisation, London, 75-81. (2008).
2. Beringer et al. (Particle Data Group), Review of Particle Physics. Phys. Rev. D 86, 010001 (2012).