A general expression for the statistical error in a diffusion coefficient obtained from a solid-state molecular-dynamics simulation.

Analysis of the mean squared displacement of species k $$ k $$ , r k 2 $$ \left\langle {r}_k^2\right\rangle $$ , as a function of simulation time t $$ t $$ constitutes a powerful method for extracting, from a molecular-dynamics (MD) simulation, the tracer diffusion coefficient, D k * $$ {D}_k^{\ast } $$ . The statistical error in D k * $$ {D}_k^{\ast } $$ is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of r k 2 t $$ \left\langle {r}_k^2\right\rangle (t) $$ curves generated by solid-state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in D k * $$ {D}_k^{\ast } $$ depends, in a strongly interrelated way, on the simulation time, the cell size, and the number of relevant point defects in the simulation cell. Reducing our results to one key quantity-the number of k $$ k $$ particles that have jumped at least once-we derive a closed-form expression for the relative uncertainty in D k * $$ {D}_k^{\ast } $$ . We confirm the accuracy of our expression through comparisons with self-generated MD diffusion data. With the expression, we formulate a set of simple rules that encourage the efficient use of computational resources for MD simulations.