Molecular dynamics simulation of fast-ion conduction in SrCl2. I. Self-diffusion

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.

Investigating finite-size effects in molecular dynamics simulations of ion diffusion, heat transport, and thermal motion in superionic materials

The effects of the finite size of the simulation box in equilibrium molecular dynamics simulations are investigated for prototypical superionic conductors of different types, namely, the fluorite-structure materials PbF₂, CaF₂, and UO₂ (type II), and the α phase of AgI (type I). Largely validated empirical force-fields are employed to run ns-long simulations and extract general trends for several properties, at increasing size and in a wide temperature range. This work shows that, for the considered type-II superionic conductors, the diffusivity dramatically depends on the system size and that the superionic regime is shifted to larger temperatures in smaller cells. Furthermore, only simulations of several hundred atoms are able to capture the experimentally observed, characteristic change in the activation energy of the diffusion process, occurring at the order-disorder transition to the superionic regime. Finite-size effects on ion diffusion are instead much weaker in α-AgI. The thermal conductivity is found generally smaller for smaller cells, where the temperature-independent (Allen-Feldman) regime is also reached at significantly lower temperatures. The finite-size effects on the thermal motion of the non-mobile ions composing the solid matrix follow the simple law that holds for solids.

Neutron powder diffraction and molecular dynamics study of superionic SrBr2

The nature of the dynamic ionic disorder within the high-temperature superionic phase of strontium bromide, β-SrBr2, has been investigated using reverse Monte Carlo (RMC) modelling of neutron powder diffraction data and complementary ab initio molecular dynamics (MD) simulations. The RMC and MD results are in good agreement and indicate the presence of extensive dynamic disorder within the Br(-) sublattice of the cubic fluorite structure. Rapid anion diffusion predominantly occurs as hops between nearest neighbour sites in the 〈100〉 directions, though the trajectories are markedly curved and pass through the peripheries of the octahedral voids in the cation sublattice. In addition, there are extensive correlations between the motions of individual Br(-), often leading to the formation of a short-lived square antiprism co-ordination environment around the Sr(2+). Such polyhedra are observed within the (ambient temperature) ordered tetragonal crystal structure of α-SrBr2. The nature of the ionic disorder in SrBr2 is of particular interest because it is the only known example of a Br(-)-ion superionic. Owing to the large size of this anion, a comparison with the behaviour of other superionic phases gives an insight into the role of ionic size on the conducting properties within these materials.

Computer simulation of defect motion in model normal and ‘fast ion’ conductors II. SrCl 2

The molecular dynamics method has been applied to the simulation of the fast-ion conductor SrCl 2 . Calculations have been done at increasing temperatures from low temperatures through the normal and high-conductivity regions into the melt. Because of the periodic boundary conditions imposed and the size of the simulation sample (324 ions), the minimum defect concentration of anion Frenkel defects that can exist in the steady state is 1/216 defects per anion lattice site. At low temperatures Frenkel defects introduced into the initial configuration are eliminated, but at higher temperatures Frenkel defects form spontaneously on the anion sublattice. Anions move primarily in <1 0 0> directions by the vacancy mechanism, although more rarely <1 1 0> jumps also occur. At intermediate temperatures interstitials were observed to make non-collinear interstitialcy jumps, but at higher temperatures the motion of interstitials makes little contribution to mass transport. The vacancies appear to be very mobile and interstitials have little or no chance to move before being annihilated by a wandering vacancy. The picture is thus one of a highly dynamic system in which individual defects do not survive for long. However, it must be recognized that the rigid-ion potential used has its limitations and may overemphasize to some extent the vacancy mobility. There is so much motion on the anion sublattice at temperatures close to melting that various indicators such as the anion–anion radial distribution function, the individual ion displacements in a fixed time, and the anion self-correlation function are quite similar below and above the melting temperature. In this sense therefore, the applied description of sublattice melting does not seem to be inappropriate. However, periodic structure is still recognizable on the anion sublattice until it also disappears on the cation sublattice. The small sample molecular dynamics simulation does not predict defect clustering; this is probably because of limitations of the method and so our results are not necessarily in conflict with recent quasi-elastic neutron scattering results.

A model for the onset of fast-ion conduction in fluorites

The quasielastic neutron scattering from fast-ion conductors with the fluorite structure has been interpreted alternatively as being due to either clusters of defects or to the motion of defects and their associated strain field. In this paper, we examine the hypothesis that the sharp rise in ionic conductivity that occurs in fluorites near the transition temperature ( T c ) from normal to superionic conductivity, is associated with defect clustering. By using lattice simulation techniques it is shown that a wide variety of clusters are stable in SrCl 2 , CaF 2 , SrF 2 , BaF 2 and β-PbF 2 . A cluster consisting of two vacancies, two relaxed lattice ions and three interstitials (which we shall designate 2| 2| 3) is particularly stable. It is shown that the formation of 2| 2| 3 clusters results in an increase in the concentration of vacancies and that this increase can account quantita­tively for the rise in conductivity near T c . Our concern is thus with the possible connection of the onset of superionic conduction with defect clustering and we do not attempt, in this paper, any interpretation of the quasielastic neutron scattering.