### Abstract

The motion of mobile ions in one dimensional ionic conductors is described by stochastic Langevin dynamics. The interactions of the mobile ions with the framework lattice are approximated by a sum of periodic and random potentials, yielding a set of coupled Langevin equations, which are then solved numerically. The parameters in these phenomenological equations of motion include the potential in which the ion moves and the lattice temperature. Correlated motion is considered by including long range (Coulombic) and short range potentials among the mobile ions. Inclusion of these potentials incalculations describing systems with an integral ratio of total sites to mobile ions (commensuratestoichiometry) shifts the frequency dependent conductivity (increase of maximum frequency, decrease of dc conductivity) in a manner indicating that the mobile ions are driven towards their equilibrium positions. The conductivity then decreases with increasing effective charge. However, when the carrier/site ratio is not integral (incommensurate stoichiometry, e.g., potassium hollandite) the long range ion-ion interaction drives the mobile ions into arrays which are distorted near the vacancies. This lowers the effective potential barrier, and therefore is responsible for increasing the calculated diffusion coefficient and conductivity. As the strength of the ion-ion interactions is increased this cooperative behavior is enhanced. The results for potassium hollandite are in good agreement with x-ray scattering data.

Original language | English |
---|---|

Pages (from-to) | 3712-3719 |

Number of pages | 8 |

Journal | Journal of Chemical Physics |

Volume | 72 |

Issue number | 6 |

Publication status | Published - 1980 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*72*(6), 3712-3719.

**A stochastic Langevin dynamics study of correlated ionic motion in one dimensional solid electrolytes.** / Jacobson, S. H.; Nitzan, A.; Ratner, Mark A.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 72, no. 6, pp. 3712-3719.

}

TY - JOUR

T1 - A stochastic Langevin dynamics study of correlated ionic motion in one dimensional solid electrolytes

AU - Jacobson, S. H.

AU - Nitzan, A.

AU - Ratner, Mark A

PY - 1980

Y1 - 1980

N2 - The motion of mobile ions in one dimensional ionic conductors is described by stochastic Langevin dynamics. The interactions of the mobile ions with the framework lattice are approximated by a sum of periodic and random potentials, yielding a set of coupled Langevin equations, which are then solved numerically. The parameters in these phenomenological equations of motion include the potential in which the ion moves and the lattice temperature. Correlated motion is considered by including long range (Coulombic) and short range potentials among the mobile ions. Inclusion of these potentials incalculations describing systems with an integral ratio of total sites to mobile ions (commensuratestoichiometry) shifts the frequency dependent conductivity (increase of maximum frequency, decrease of dc conductivity) in a manner indicating that the mobile ions are driven towards their equilibrium positions. The conductivity then decreases with increasing effective charge. However, when the carrier/site ratio is not integral (incommensurate stoichiometry, e.g., potassium hollandite) the long range ion-ion interaction drives the mobile ions into arrays which are distorted near the vacancies. This lowers the effective potential barrier, and therefore is responsible for increasing the calculated diffusion coefficient and conductivity. As the strength of the ion-ion interactions is increased this cooperative behavior is enhanced. The results for potassium hollandite are in good agreement with x-ray scattering data.

AB - The motion of mobile ions in one dimensional ionic conductors is described by stochastic Langevin dynamics. The interactions of the mobile ions with the framework lattice are approximated by a sum of periodic and random potentials, yielding a set of coupled Langevin equations, which are then solved numerically. The parameters in these phenomenological equations of motion include the potential in which the ion moves and the lattice temperature. Correlated motion is considered by including long range (Coulombic) and short range potentials among the mobile ions. Inclusion of these potentials incalculations describing systems with an integral ratio of total sites to mobile ions (commensuratestoichiometry) shifts the frequency dependent conductivity (increase of maximum frequency, decrease of dc conductivity) in a manner indicating that the mobile ions are driven towards their equilibrium positions. The conductivity then decreases with increasing effective charge. However, when the carrier/site ratio is not integral (incommensurate stoichiometry, e.g., potassium hollandite) the long range ion-ion interaction drives the mobile ions into arrays which are distorted near the vacancies. This lowers the effective potential barrier, and therefore is responsible for increasing the calculated diffusion coefficient and conductivity. As the strength of the ion-ion interactions is increased this cooperative behavior is enhanced. The results for potassium hollandite are in good agreement with x-ray scattering data.

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M3 - Article

VL - 72

SP - 3712

EP - 3719

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

ER -