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In this work, multi-phase field and molecular dynamics simulations have been used to investigate nanoscale grain growth mechanisms. Based on experimental observations, the combination of grain boundary expansion and vacancy diffusion has been considered in the multi-phase field model. The atomistic mechanism of boundary movement and the free volume redistribution during the growth process have been investigated using molecular dynamics simulations. According to the multi-phase field results, linear grain growth in nanostructured materials at low temperature can be explained by vacancy diffusion in the stress field around the grain boundaries. Molecular dynamics simulations confirm the observation of linear grain growth for nanometer-sized grains. The activation energy of grain boundary motion in this regime has been determined to be of the order of one-tenth of the self-diffusion activation energy, which is consistent with experimental data. Based on the simulation results, the transition from linear to normal grain growth is discussed in detail and a criterion for this transition is proposed.