Monoclinic sphere packings. II. Trivariant lattice complexes with mirror symmetry

Area of Science:

• Crystallography
• Materials Science
• Geometry

Background:

• Sphere packing is fundamental to understanding crystal structures and material properties.
• Monoclinic lattice complexes with mirror symmetry provide a specific framework for exploring packing arrangements.
• Investigating the inherent symmetry of sphere packings is crucial for classifying crystal structures.

Purpose of the Study:

• To systematically derive all homogeneous sphere packings associated with three specific trivariant monoclinic lattice complexes.
• To determine and classify the inherent symmetries of the discovered sphere packings.
• To provide a comprehensive catalog of sphere packing types within the specified crystallographic constraints.

Main Methods:

• Derivation of sphere packings based on the geometric constraints of monoclinic lattice complexes.
• Analysis of the maximal inherent symmetry for each identified sphere packing.
• Classification of packings according to their symmetry groups (monoclinic, orthorhombic, tetragonal, hexagonal, cubic).

Main Results:

• A total of 29 distinct types of homogeneous sphere packings were identified.
• Only three of these packings possess maximal inherent monoclinic symmetry.
• The majority of the packings exhibit higher symmetries: 13 orthorhombic, 8 tetragonal, 4 hexagonal, and 1 cubic.

Conclusions:

• The study reveals a diverse range of symmetries within sphere packings derived from monoclinic lattice complexes.
• Homogeneous sphere packings in this context frequently exhibit symmetries higher than the parent lattice.
• This classification contributes to a deeper understanding of crystallographic structures and their potential packing arrangements.