Determination of Displacement Fields at the Sub-Nanometric Scale

Area of Science:

• Materials Science
• Solid Mechanics
• Nanotechnology

Background:

• Material properties at the macroscopic level are governed by atomic and molecular interactions at the nanoscale.
• Experimental mechanics (EM) provides a bridge between macroscopic observations and the atomic realm.
• Theoretical models at the nanoscale require validation through experimental techniques.

Purpose of the Study:

• To apply EM techniques to analyze high-resolution transmission electron microscopy (HRTEM) patterns.
• To determine displacements, their derivatives, and stresses in deformed crystals using atomic positions.
• To verify the Cauchy-Born conjecture within observed deformation ranges.

Main Methods:

• Analysis of HRTEM patterns of crystalline arrays containing dislocations.
• Utilizing atomic positions to track displacements between undeformed and deformed states.
• Employing two distinct approaches: strain gage rosette analogy and displacement field reconstruction from three directional data.

Main Results:

• Displacements, their derivatives, and stresses were successfully obtained in an Eulerian description of the deformed crystal.
• The first approach established an analogy between crystalline structure and a strain gage rosette.
• The second approach demonstrated the reconstruction of the displacement field from directional displacement information.

Conclusions:

• The study successfully applied EM techniques to quantify nanoscale deformation in crystalline materials.
• The Cauchy-Born conjecture was validated for the observed deformation range, confirming its applicability.
• The developed methods offer a pathway for deriving comprehensive material models from experimental data.