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Schematic drawing of phonon reflection and transmission at the interface between a grain and the grain boundary.
The curves of scaling functions varying with the grain sizes for different dimensional position coordinates of and . (a) vs the grain diameter; (b) vs the grain-boundary thickness. Here , .
Comparison of scaling function with others and , which varies in the diameter region of . Here , , , and .
The semilogarithmic curves of reduction ratio of bulk thermal conductivity vs the grain diameter for the materials of Si and CoSb3 when , , , and for Si and for CoSb3.
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