The Haven Ratio in Terms of the Self-Diffusion of Charge
The discrepancy between the measured electrical conductivity of ionic materials and that calculated from the Nernst-Einstein (N-E) equation has been known for a long time. In glasses the discrepancy was perhaps first documented by Fitzgerald1 and has been confirmed by many subsequent works.2 Le Claire suggested that the ratio of the ionic conductivity calculated from N-E and that actually determined be called the Haven Ratio, HR. This terminology is widely accepted in the discussion of glassy as well as crystalline materials. The appropriateness of the choice relates to Haven’s pioneering work in the understanding of the serial correlation of atomic jumps.3 For crystalline materials with well-specified diffusion mechanisms, it is now routine to calculate the Haven Ratio based on the difference between the serial correlation of the jumps of lattice atoms and that of ionic defects.4 Here the goal is to review the procedure and generalize it to apply to noncrystalline solids.
KeywordsSerial Correlation Measured Electrical Conductivity Average Waiting Time Jump Distance Mobile Cation
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