Grain Size of Ceramics: Why Larger is Smaller for Diffusivity

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Why is it that the larger the grain size, the smaller the grain-boundary contribution to diffusivity?
 
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The larger the grain size, the less grain boundaries and the less grain boundary surface area.

One method of determining grain size in polycrystalline materials is the linear intercept method. On can draw a straight line and determine how many grain boundaries are intercepted. This has been correlated with a mean grain size.
 
The grain-boundary has higher entropy, because it has a mixture of different type of atoms, is that correct?