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Fractal conduction pathways governing ionic transport in a glass

J. L. Iguain, F. O. Sanchez-Varreti, M. A. Frechero

Abstract

We present a systematic characterization of the fractal conduction pathways governing ionic transport in a non-crystalline solid below the glass-transition temperature. Using classical molecular dynamics simulations of lithium metasilicate, we combine mobility-resolved dynamical analysis with a real-space description of the regions explored by lithium ions. Ensemble-averaged velocity autocorrelation functions rapidly decorrelate and do not resolve the pronounced dynamic heterogeneity of the system, whereas single-ion analysis reveals short-lived episodes of nearly collinear motion. By mapping active-site clusters over increasing time windows, we show that ion-conducting pathways are quasi one-dimensional at short times and evolve into larger, branched structures characterized by a robust fractal dimension $d_f\simeq1.7$. This geometry persists while the silicate backbone remains structurally arrested, whereas near the glass-transition temperature the loss of structural memory leads to the reappearance of small clusters. These results provide a real-space structural interpretation of ionic transport in non-crystalline solids and support fractal pathway models of high-frequency ionic response.

Fractal conduction pathways governing ionic transport in a glass

Abstract

We present a systematic characterization of the fractal conduction pathways governing ionic transport in a non-crystalline solid below the glass-transition temperature. Using classical molecular dynamics simulations of lithium metasilicate, we combine mobility-resolved dynamical analysis with a real-space description of the regions explored by lithium ions. Ensemble-averaged velocity autocorrelation functions rapidly decorrelate and do not resolve the pronounced dynamic heterogeneity of the system, whereas single-ion analysis reveals short-lived episodes of nearly collinear motion. By mapping active-site clusters over increasing time windows, we show that ion-conducting pathways are quasi one-dimensional at short times and evolve into larger, branched structures characterized by a robust fractal dimension . This geometry persists while the silicate backbone remains structurally arrested, whereas near the glass-transition temperature the loss of structural memory leads to the reappearance of small clusters. These results provide a real-space structural interpretation of ionic transport in non-crystalline solids and support fractal pathway models of high-frequency ionic response.
Paper Structure (2 equations, 4 figures)

This paper contains 2 equations, 4 figures.

Figures (4)

  • Figure 1: (color online) Lithium velocity autocorrelation function as a function of time fot two temperatures: 1000 K (top) and 700 K (bottom). In each panel, the dashed (red) line corresponds to fast ions, the dash-dotted (green) line to slow ions and solid (blue) line to the ensemble average
  • Figure 2: (color online) Clusters containing more than $300$ active sites at three different times. From top to bottom: $t=$ 5, 10, and 15 ps. The system temperature is $T=700$ K. Cluster size is indicated by grey (color) scale
  • Figure 3: (color online) Cluster properties at $T=700$ K. Top panel: box-counting fractal dimension as a function of cluster length for all clusters at different times: $t=$1 (violet plus), 2 (green cross), 4 (light-blue star), 6 (orange empty square), 10 (yellow filled square), 15 (blue empty-circle), 20 (red filled circle ), 30 (black empty triangle) ps. The horizontal line indicates $d_f=1.7$. Bottom panel: cluster size versus cluster length for the same times. The lines with slopes 1 (left) and 1.7 (right) are shown as guides to the eye.
  • Figure 4: (color online) Cluster properties at $T=1100K$. Top panel: box-counting fractal dimension as a function of cluster length for times $t=$ 0.10 (plus violet), 0.15 (cross green), 0.40 (star light-blue), 0.80 (empty-square orange), 1.20 (filled-square yellow), 2.50 (empty-circle blue), 5.00 (filled circle red), and 7.50 (empty triangle black) ps. The horizontal line indicates $d_f=1.7$. Bottom panel; cluster size versus cluster length for the same times. Straight lines with slopes slopes 1 (left) and 1.7 (right) are shown as guides to the eye.