Figure 1 presents the diagram of properties (scores plot), then figures (2a, 2b) show the relationships of variables (loading plot) based on experimental data [31]. These results allow us to detect the correlations between the twenty-one physical properties of the elements, renamed by [var1, var2 …var21] to get better visibility of the diagram. It notices some correlations and anti-correlations; some correlations are simple to explain, and others reflect intrinsic physical principles and relationships. Hence, the relationships between the properties are as follows:
Var1 correlated to var2:
The atomic number and mass are correlated as long as the atom mass includes the sum of the neutrons and protons masses.
Var1 and var2 correlated to var16:
The heat capacity, atomic number, and atomic mass are correlated, which can explain as follows: The heat capacity expresses the ability of the material to assimilate heat. The principal mode of heat energy assimilation is the phonons or networks (lattices) vibrations.
Var21 and var19 are correlated:
Melting the boiling temperature have a physical relationship which axiomatic as long as boiling occurs after the melting.
Var19 and var21 have a relationship with var20: The melting and boiling temperatures correlate to the change in enthalpy at melting. This last quantity expresses the energy supplied so that the material passes from the solid to the liquid state (phases behaviors).
Var13 and var14 correlated to var9: The elastic constants C11 and C12 and the young modulus have relationships. The two constants define the material response to deformation on the atomic scale.
The Young modulus is the macroscopic response of the material to tensile deformation; unquestionably, macroscopic mechanical behavior properties are expressions of the displacement of atoms on a smaller scale upon applying external stress.
Var4 correlated to var5:
Electronegativity and the energy of the first ionization are correlated; an electronegative material tends to attract electrons from other atoms in a bond. For stronger atomic binding, the electrons of the last orbit are strongly linked and are very difficult to exit, expressed by high ionization energy.
Var6 correlated to var8:
The lattice parameter and the molar volume are correlated, which is logical since the interatomic spacing is a function of molar volume.
Var17, var6, and var8 are correlated: The entropy has a relationship with the lattice parameter and the molar volume; it implies that the increase in molar volume grows the disorder in the system.
Var10 correlated to var11 and var12: The elasticity constants S11, S12, and S44 have a relationship; this is consistent as long as all these quantities are related to how the structure varies when the external stress is applied. In other words, they all arise from the interatomic bond.
On the other hand, the anti-correlations between some variables are the following:
Var14 has an inverse correlation to var6 and var8: Young's module has an inverse correlation to the lattice parameter and the molar volume; it is known from experience that Young's module is proportional to the compression module that measures the lattice compressibility. It is difficult to compress the atomic volume when the lattice parameter and the molar volume decrease, and the volume per atom, also decreases; consequently, the atom's possibility of bringing closer together decreases. It explains why the network parameter decreases the compression module as much and why Young's module increases.
Consequently, the decrease of electrons implied less energy required to tear them away (first ionization energy) decreases. Also, when the number of electrons increases, the electronegativity decreases, and its' nucleus doesn't attract electrons from adjacent atoms more strongly.