Evaluating the effect of grain size distribution on thermal conductivity of thermoelectric materials
P. Das, Sivaiah Bathula, Srikant Gollapudi
Abstract
Abstract 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 (Bi 2 Te 3 ) 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.