ON THE PYRAMIDAL DIAGRAM OF THE CHEMICAL ELEMENTS
dipl. eng. Thomas Kombai Zerkov, 2000, 2016

The present work introduces a new arrangement of the chemical elements. Unlike the most popular existing arrangements, which are two-dimensional, this new arrangement is three-dimensional. It organizes the elements in a pyramidal structure of four levels, giving a clear spatial expression of different relations between the chemical elements. Since the three-dimensional structures are harder to perceive than the two-dimensional ones, the present work also suggests a two-dimensional table representation of the three-dimensional pyramidal diagram, where the four levels are all placed in a single plane, instead of one above the other.

KEYWORDS: chemical, elements, arrangement, pyramid, table.

The subject of the present work is not only the 3D pyramidal diagram definition, but also the comparison of its 2D table representation with the most popular nowadays arrangement of chemical elements - the modern version of the periodic table.

The elements are structured in the form of a pyramid, which consists of four levels for the time being, numbered from 0 (the highest level) to 3 (the lowest one). Each level with number N represents a square matrix of 4x(N+1)2 elements. Thus the zero level comprises 4 elements, the first one - 16 elements, the second one - 36 elements, and the third one - 64 elements. The square matrices are positioned exactly one under another, forming a regular discrete pyramid with a square base. The centres of the four squares lie on a straight line, which is perpendicular to the planes of the different levels and represents the pyramid axis.

Every level with number N consists of two periods - the period with number 2xN and the period with number 2xN+1, each of them comprising 2x(N+1)2 elements. Thus the zero level consists of the singular zero period and the first one, holding 2 elements each, the first level consists of the second period and the third one, holding 8 elements each, the second level consists of the fourth period and the fifth one, holding 18 elements each, and the third level consists of the sixth period and the seventh one, holding 32 elements each. Both periods making up a level are centrally symmetric to each other, where the centre of symmetry is the centre of the square matrix, representing the level. In this way each element with a sequential number within one of the periods is centrally symmetric to the element with the same sequential number within the other period.

The color convention used in the present work and in the table is as follows:

• The color for the zero level is grey, and
• the color for the singular zero period is light grey
• the color for the first period is dark-grey
• The color for the first level is red, and
• the color for the second period is light red
• the color for the third period is dark-red
• The color for the second level is green, and
• the color for the fourth period is light green
• the color for the fifth period is dark-green
• The color for the third level is blue, and
• the color for the sixth period is light blue
• the color for the seventh period is dark-blue

Within every level each two elements with successive atomic numbers are positioned at adjacent places, i.e. they are in one and the same row or column of the square matrix, representing the level, and there are no elements between them: The elements are arranged in such a way, that each column of the pyramid includes elements of one and the same group. All the elements of a certain group are distributed in two columns of the pyramid, parallel to its axis and axially symmetric to each other, where the axis of symmetry is the pyramid axis. In this way the elements are grouped into periods within the planes of the four levels, and into groups by the third dimension, given by the pyramid axis.

The singular zero period comprises of two singular entities, that obey the inner logic and symmetry of the following ordinary elements, ordered by their atomic numbers. Its first element belongs to the first group; its atomic number is equal to -1 and represents the electron. It marks the beginning of the elements sequence. Each element of the pyramid column, containing this special element, is the beginning of the sequence for the respective level. The second element of the zero period belongs to group 18; its atomic number is equal to zero and represents the neutron.

The pyramidal diagram of the chemical elements reflects the structure of their atoms electron shell. The elements, for which a s subshell or a p subshell is being filled up, are positioned either by the pyramid axis (groups 1 and 18), or in the periphery of the first level and under it (group 2 and groups 13 to 17). The elements of groups 3 to 12, where a d subshell is being filled up, are positioned in the periphery of the second level and under it. Lanthanides (without lanthanum) and actinides (without actinium), where a f subshell is being filled up, are positioned in the periphery of the third level.

The 2D representation of the 3D pyramidal diagram (PD) places the square matrices, representing the four levels of the pyramid, all in a single plane, instead of one above the other. It is represented in the figure.

The periodic table (PT) of the elements in its modern version exists in two modifications, conventionally called here PT1 and PT2. PT1 arranges the elements in nine rows: the elements of a period numbered from one to seven (without lanthanides and actinides) are placed in the row with the corresponding number, lanthanides are placed in the eighth row, and actinides are placed in the ninth row. PT2 arranges the elements in seven rows: the elements of a period numbered from one to seven are placed in the row with the corresponding number, lanthanides being incorporated in the sixth row, and actinides being incorporated in the seventh row.

Both systems (PD and PT) are compared by two indicators.

1. Compactness. PD arranges the elements within a rectangular table of 140 cells, distributed in 10 rows and 14 columns: PT1 arranges the elements within a rectangular table of 162 cells, distributed in 9 rows and 18 columns: PT2 arranges the elements within a rectangular table of 224 cells, distributed in 7 rows and 32 columns: The ratio of the number of rows to the number of columns is the closest to 1 for PD. The number of cells that make up the rectangular table is the smallest for PD. Therefore PD is more compact than PT1 and PT2.

2. Uninterruptedness. Subject of consideration here is the number of instances, where two elements with successive atomic numbers are not ajacently positioned. There are three such instances in PD (these are the transitions from one pyramid level to another - He - Li, Ar - K, Xe - Cs). There are thirteen such instances in PT1 (H - He, He - Li, Be - B, Ne - Na, Mg - Al, Ar - K, Kr - Rb, Xe - Cs, La - Ce, Lu - Hf, Rn - Fr, Ac - Th, Lr - Rf). There are eleven such instances in PT2 (H - He, He - Li, Be - B, Ne - Na, Mg - Al, Ar - K, Sc - Ti, Kr - Rb, Y - Zr, Xe - Cs, Rn - Fr). Therefore PD is more uninterrupted than PT1 and PT2.

The pyramidal diagram is a better arrangement of the chemical elements, because it is more compact and more uninterrupted. In PD the elements of a given period are all grouped together, unlike PT1, where they are split into two sets for periods 1, 2, 3, 6, and 7, and unlike PT2, where they are split into two sets for periods 1, 2, 3, 4, and 5. A disadvantage to PD in comparison with PT is the relatively harder tracing of elements of a given group in the 2D representation of the 3D pyramidal diagram (unlike the tracing in the pyramidal structure itself).

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