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This study explored diffusion rates along a crystal lattice for multiple dimensions. We focused our attention on particle movement through a crystal lattice to determine how the diffusion rate for a crystalline solid depends on the number of spatial dimensions and the probability between diagonal and axis lattice site movement. We used a Monte Carlo approach to simulate the random walk of a particle confined to move between sites along a crystal lattice. The simulation predicted how the diffusion trajectory differed depending on dimensionality and movement probability. From the results obtained, we concluded that the largest diffusive growth for a particle occurred when the particle was confined to one dimension or to movement along the axis of the crystal lattice. During these conditions, the particle traveled the farthest final distance during the random walk.
Alperstein, Hannah, "Multidimensional Diffusion In Crystalline Solids" (2021). Physics. 1.