Dislocations in stacking and commensurate-incommensurate phase transition in bilayer graphene and hexagonal boron nitride

TL;DR

This study models dislocation formation and phase transitions in bilayer graphene and boron nitride under strain, revealing a second-order transition from commensurate to incommensurate phases with detailed phase diagrams.

Contribution

It introduces a combined ab initio and Frenkel-Kontorova model approach to analyze dislocation behavior and phase transitions in strained bilayer 2D materials, highlighting the critical elongation points.

Findings

Dislocations form and evolve with increasing strain.

A second-order phase transition occurs at a critical elongation.

Intermediate states with partial dislocations are identified.

Abstract

Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed depending on the magnitude and direction of elongation. The second-order phase transition from the commensurate phase to the incommensurate one with multiple dislocations is predicted to take place at some critical elongation. The order parameter for this transition corresponds to the density of dislocations, which grows continuously upon increasing the elongation of the bottom layer above the critical value. In graphene and metastable boron nitride with the layers aligned in the same direction, where elementary dislocations are partial, this transition, however, is preceded by formation of the first dislocation at the elongation smaller than the critical one. The phase diagrams including this intermediate state are plotted in coordinates of the magnitude and direction of elongation of the bottom layer.