Data-driven holistic view on the materials science fundamentals

§1. Compound formation

The atomic size, electrochemical, valence-electron, and cohesion energy factors determine compound formation. For example, about 30% of all element combinations form no compounds within the binary, ternary, and quaternary systems.

§2. Correlation of the element count and the atomic environment type

The maximal diversity of the atomic environments is achieved within the binary and ternary inorganic compounds. The quaternary, quinary, and other higher-order compounds strongly prefer the atomic environment types with the low coordination number. This is the surprising reduction of geometrical diversity with the increasing element count.

§3. Preferred concentration ranges

There is the systematic occurrence of daltonide inorganic phases for binary, ternary, and quaternary inorganic systems within the certain rather limited preferred concentration ranges.

§4. Preferred stoichiometric ratios

There are highly preferred stoichiometric ratios for the vast majority of daltonide compounds.

§5. Preferred compound simplicity

The vast majority of the inorganic compounds have on average only ten atoms per unit cell, thus showing only three or fewer atomic environment types within the crystal structures. The nature prefers simplicity.

§6. Preferred symmetry

The 10% of the space groups cover nearly 70% of the inorganic compounds. The most frequent 11 space groups are 12, 62, 63, 139, 166, 191, 194, 216, 221, 225, and 227. As seen, the high symmetry is preferred.

§7. Preferred atomic environments

The 18 out of about 100 possible atomic environment types are highly preferred and were found for 90% of all the PAULING FILE compounds. Namely, the most frequent types of polyhedra are tetrahedron, octahedron, cube, tri-capped trigonal prism, four-capped trigonal prism, icosahedron, cubooctahedron, bi-capped pentagonal pyramid, and anti-cubooctahedron.

§8. Preferred prototypes

Only about 30 structure prototypes have more than 1000 representatives, and the 1000 most populous prototypes and their representatives cover the majority of the PAULING FILE crystalline structures.

§9. Correlation of the structure prototype and the periodic table

On an example of the 1000 most populous prototypes, the vast majority of the crystalline structures show a very strict regularity between the position of the element in the periodic table and its Wyckoff position occupation.

§10. Linking of structure and stability

The atomic size, electrochemical, valence-electron, and atomic number factors determine the crystalline structures of the intermetallic compounds. This is applicable to binary, ternary, and quaternary systems. There are clear patterns for e.g. former or non-former systems, iso-stoichiometric structure stability maps, and complete solid solubility between binary compounds within the same prototype.

§11. Generalized atomic environment type stability

Using the periodic numbers (from Lothar Meyer's periodic table), different atomic environment types can be subdivided into distinct stability domains. The elements with the periodic number more than 54 control the atomic environment types, independently of whether they act as the central or coordinating atoms. Thus, there exists a clear separation between the possible and impossible atomic environment types. Interestingly, the diversity of atomic environment types is very much reduced for quaternaries, as compared to binaries and ternaries.

§12. Complete solid solution stability

The atomic size, electrochemical, and valence-electron factors control the solid solubility. For example, in a ternary system, where two of the binary boundary systems have the same structure prototype, either a complete or limited solid solution formation can be predicted. Similarly, for a given element, either a limited or extended solid solubility can be predicted.

§13. Physical properties and the constituent elements

At least 6 physical properties (isothermal bulk modulus, enthalpy of formation, congruent melting temperature, Debye temperature, energy gap, electrical conductivity) of any compounds are determined by the constituent elements positions in the periodic table.