Exploring the link between crystal defects and nonaffine displacement fluctuations

Area of Science:

• Solid-state physics
• Materials science
• Crystallography

Background:

• Thermal fluctuations cause atomic displacements in crystals.
• These displacements can be decomposed into affine (strain/rotation) and nonaffine (localized) components.
• Understanding these modes is crucial for predicting material properties and defect formation.

Purpose of the Study:

• To generalize and apply a formalism for studying thermal fluctuations of atomic displacements.
• To analyze both compact and open crystals with multiatom bases in various dimensions.
• To investigate the nature and behavior of affine and nonaffine displacement modes.

Main Methods:

• Generalization of a recently introduced formalism.
• Coarse-graining analysis of atomic displacement fluctuations.
• Computation of thermodynamic averages and correlation functions within harmonic theory.

Main Results:

• Compact crystals exhibit a dominant, gapped nonaffine mode linked to defect precursors.
• Open crystals lack a prominent gap, showing soft nonaffine modes associated with localized defects.
• Higher-order coupling between affine and nonaffine modes is significantly larger in open lattices.

Conclusions:

• The study provides a unified framework for understanding crystal deformation mechanisms like slips and stacking faults.
• Nonaffine modes play a critical role in lattice stability and defect formation.
• The findings are expected to be general, independent of specific atomic interactions.