Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. I. Theory

Area of Science:

• Materials Science
• Surface Science
• Crystallography

Background:

• Epitaxial growth of molecular crystals is heavily influenced by the initial monolayer.
• Understanding the relationship between 3D crystal structure and the 2D surface layer is key to controlling crystal formation.

Purpose of the Study:

• To present a theoretical framework for comparing 3D crystal lattices with their corresponding 2D molecular monolayers.
• To derive mathematical relationships between the lattice parameters of 3D crystals and 2D surface unit cells.
• To investigate how monolayer symmetries and orientations influence epitaxial order.

Main Methods:

• Utilizing real-space and reciprocal-space representations for lattice analysis.
• Deriving mathematical expressions to connect 3D lattice parameters to 2D surface unit cell parameters.
• Applying the method to experimental data from grazing-incidence X-ray diffraction (GIXD) measurements.

Main Results:

• Established a method to relate 3D crystal lattices to 2D molecular monolayers based on crystallographic orientation.
• Demonstrated that rotational symmetries in monolayers are mirrored in the epitaxial order.
• Correlated crystallographic plane orientations with the mirror symmetry of surface unit cells.

Conclusions:

• The theoretical approach provides a link between 3D crystal growth and the nucleating 2D monolayer.
• This work enables the study of 3D crystal growth by analyzing the initial ordered monolayer.
• Suggests combining GIXD and low-energy electron diffraction for comprehensive analysis of epitaxial growth.