Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilattice

Area of Science:

• Crystallography
• Materials Science
• Mathematical Physics

Background:

• Redundant basis vector systems are common in crystallography and materials science.
• Indexing these systems can be ambiguous, necessitating robust methods.
• The least path criterion offers a potential solution for unambiguous indexing.

Purpose of the Study:

• To mathematically prove the uniqueness of indices obtained via the least path criterion.
• To apply and analyze the least path criterion within the context of a two-dimensional decagonal lattice.
• To explore the concept of redundancy order in indexing sets.

Main Methods:

• Mathematical proof of the least path criterion's uniqueness.
• Application of the criterion to a two-dimensional decagonal lattice.
• Analysis of redundancy order in basis vector systems.

Main Results:

• A rigorous mathematical proof demonstrates the uniqueness of indices derived from the least path criterion.
• The study confirms the applicability of the least path criterion to the two-dimensional decagonal lattice.
• Insights into the order of redundancy in indexing sets are provided.

Conclusions:

• The least path criterion provides a unique and reliable method for indexing in redundant basis vector systems.
• This method shows promise for applications in crystallography and related fields.
• Further research can correlate redundancy order with other desirable indexing sets.