Evaluating the effect of grain size distribution on thermal conductivity of thermoelectric materials

The influence of grain size (d) on the thermal conductivity (k) of thermoelectric (TE) materials has been well established through experimental studies. However, the effect of grain size distribution, described by S ( n ), on k has not been reported before. Since thermal conductivity is a key contributor to the figure of merit (ZT) for thermoelectric materials, studying the effect of grain size distribution, an important microstructural descriptor, on k is necessary. In the current study we are evaluating the effect of S ( n ) on the k of thermoelectric materials by using data reported in literature on bismuth telluride (Bi2Te3) and lead telluride (PbTe). We first check for correlations between k and d. In literature, mathematical correlations between lattice thermal conductivity (k ( l )) and d have already been reported but the same is missing for electronic thermal conductivity (k ( e )) and d. By analysing literature data for bismuth telluride and lead telluride at 300 K, we identified a linear correlation between k ( e ) and d, wherein an increase in d leads to an increase in k ( e ). This dependence of k ( e ) on d was combined with the dependence of k ( l ) on d to establish the overall dependence of k on d. Subsequently, the grain size distribution effect was imposed by using a log normal distribution. The analysis revealed that for a given grain size, an increase in S ( n ) leads to lowering of the thermal conductivity of the material. The analysis was also extended to bimodal grain size distributions wherein the microstructure was designed in a way to contain a mixture of both nanocrystalline and microcrystalline grains.