Atomistic calculations of dislocation core energy in aluminium

A robust molecular-dynamics simulation method for calculating dislocation core energies has been developed. This method has unique advantages: It does not require artificial boundary conditions, is applicable for mixed dislocations, and can yield converged results regardless of the atomistic system size. Utilizing a high-fidelity bond order potential, we have applied this method in aluminium to calculate the dislocation core energy as a function of the angle $\beta$ between the dislocation line and the Burgers vector. These calculations show that, for the face-centered-cubic aluminium explored, the dislocation core energy follows the same functional dependence on $\beta$ as the dislocation elastic energy: $E_c=A{sin}^2\beta +B{cos}^2\beta$, and this dependence is independent of temperature between 100 and 300 K. By further analyzing the energetics of an extended dislocation core, we elucidate the relationship between the core energy and the core radius of a perfect versus an extended dislocation. With our methodology, the dislocation core energy can accurately be accounted for in models of dislocation-mediated plasticity.

Figure 1

Geometry for $\beta ={90}^{\circ }$ (edge) dislocation dipoles (dislocation spacing $S_{\mathrm{x}}$ equals system dimension $L_{\mathrm{x}})$.

Figure 2

Geometry for screw and mixed dislocations: (a) Three-dimensional configuration, (b) top view of $\beta =0^{\circ }$ (screw) and $\beta ={60}^{\circ }$ (mixed) dislocation slip plane, and (c) top view of $\beta ={30}^{\circ }$ dislocation slip plane.

Figure 3

Edge dislocation line energy as a function of (a) dislocation dipole distance $d$ and (b) dislocation spacing $S_{\mathrm{x}}(=L_{\mathrm{x}})$. Error bars represent the standard deviation of MD data. Note that in (a), the solid and dashed lines differ only by the constant core energy.

Figure 4

Line energies as a function of dislocation spacing $S_{\mathrm{x}}$ for (a) ${30}^{\circ }$ and ${60}^{\circ }$, (b) $10.{89}^{\circ },19.{11}^{\circ },40.{89}^{\circ },49.{11}^{\circ },70.{89}^{\circ }$, and $79.{11}^{\circ }$, and (c) $0^{\circ }$ dislocations. Error bars represent the standard deviation of MD data.

Figure 5

Dislocation core energies as a function of dislocation angle $\beta$ at different core radii $r_0$.

Figure 6

Dissociated core configuration of a $\beta ={90}^{\circ }$ (edge) dislocation. (a) Front view of the MD configuration, (b) schematic of the perfect dislocation, (c) schematic of the two partials separated by $r_{pt}^{min}$, and (d) schematic of the two partials separated by $\lambda$.