Axial misfit stress relaxation in core–shell nanowires with polyhedral cores through the nucleation of misfit prismatic dislocation loops

Misfit Stress in Radial Core-Shell Nanowires with Diffuse Interface Boundaries

“…It is proportional to the eigenstrain function ( ) f t according to the Eq. (11). Therefore, the stress in NW with sharp interface is homogenous in core and shell, while the ones in NW with diffuse interface are inhomogeneous in core and shell.…”

“…The stress tensor components in core-shell NWs with the Heaviside theta eigenstrain profile attributed to the sharp interfaces are well-known (see, for example, Ref. [11]):…”

“…To date, the theoretical models describing the stressstrain state in axial NWs with a diffuse interface have been developed [6][7][8], while an elastic model of radial NWs have not been suggested yet. Besides, the available theoretical model of misfit stress relaxation in core-shell heterostructures [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] employs the analytical expressions of the elastic stress induced by eigenstrain defined by Heaviside theta function.…”

The dilatation line in an elastic wedge

“…To validate their general formulation, they obtained analytical solutions for three typical cases: (1) a circular domain containing a triangular inclusion; (2) an inclusion of shape similar to a crescent; and (3) a Pascal's Limac xon containing a squared inclusion. Recently, Krasnitckii et al [44][45][46][47][48] have solved analytically some boundary-value problems in the theory of elasticity for faceted cores in cylindrical core-shell nanowires. In particular, nanowires with axial prismatic cores of square [44][45][46], triangular [45,46] and hexagonal [45][46][47] cross sections, and eccentric prismatic cores of rectangular [48] and trapezoidal [45] cross sections have been studied in detail and used for comparative analysis of critical conditions for nucleation of small rectangular prismatic dislocation loops [45][46][47]49] and straight misfit dislocations [50] at the initial stages of misfit stress relaxation in core-shell nanowires.…”

“…Recently, Krasnitckii et al [44][45][46][47][48] have solved analytically some boundary-value problems in the theory of elasticity for faceted cores in cylindrical core-shell nanowires. In particular, nanowires with axial prismatic cores of square [44][45][46], triangular [45,46] and hexagonal [45][46][47] cross sections, and eccentric prismatic cores of rectangular [48] and trapezoidal [45] cross sections have been studied in detail and used for comparative analysis of critical conditions for nucleation of small rectangular prismatic dislocation loops [45][46][47]49] and straight misfit dislocations [50] at the initial stages of misfit stress relaxation in core-shell nanowires. Thus, the problem of faceted interfaces in core-shell nanowires has been solved, at least for elastically homogeneous nanowires.…”