Study of the temperature dependence of the symmetrical grain boundary energies on the plane (110) in aluminum

In this work the energy of symmetric tilt and twist grain boundaries in the range of grain misorientation angles from 0 to 180$^{\circ}$ and temperatures from 100 to 700 K in pure aluminum is investigated. The bicrystal systems with different grain tilt/twist angles are maintained at constant temperatures of 100, 400, or 700 K by molecular dynamic method and the energy of each grain boundary is calculated. The results show that the minimum grain boundary energy decreases as the temperature increases from 100 to 400 K; but the energy may decrease, remain practically unchanged, or even increase with further heating to 700 K. The average grain boundary energy obtained by averaging the energies of the resulting grain boundary structure variations at constant temperature grows with increasing temperature from 100 to 700 K for random boundaries with initially high energies. In the case of special grain boundaries with small $\Sigma$ values, the average energy will be practically unchanged. To describe the continuous energy dependence of symmetric tilt and twist boundaries on temperature, an approximation by an forward propagation of artificial neural network is proposed. The neural network is trained and tested on atomistic simulation data and shows high predictive ability on test data and to describe the boundary energy in the temperature range from 100 to 700 K.