Impact of grain boundary characteristics on lattice thermal conductivity: A kinetic theory study on ZnO

Grain boundaries are natural interfaces present in polycrystalline materials and have an important role in transport properties. In this work, the impact of grain boundary crystallographic mismatch, local impurity modulation, and spacing on lattice thermal conductivity is examined from the kinetic theory approach, with ZnO as a case study. We employ a dislocation-based model to describe the grain boundary scatterings of phonons, in which structural characteristics of grain boundaries are explicitly built-in and grain boundary scattering time depends on phonon frequency. This is in contrast to the gray model or the commonly used Casimir limit, which is blind to both grain boundary features and phonon frequency. We show that the lattice thermal conductivity generally decreases with grain boundary misorientation angle, and this dependence is significant for small grain boundary spacing while it tends to diminish for a large one. Intriguingly, our results show that local grain boundary chemistry can affect even more substantially than the crystallographic misfit on phonon relaxation time and interfacial thermal (Kapitza) resistance. Our results suggest new opportunities in tuning lattice thermal conductivity besides the nanostructure engineering approach, and demonstrates the synergetic effects of grain boundary characteristics on phonon conduction in polycrystals.

Figure 1

(a) Calculated room temperature ZnO thermal conductivity and (b) the derived grain boundary Kapitza resistance as a function of grain boundary misorientation angle for grain boundary spacing ranging from 10 nm to 10 μm. The corresponding linear dislocation density along grain boundary is indicated on the top axis. The intrinsic thermal conductivity of ZnO is also superimposed on the figure.

Figure 2

(a) Calculated room temperature ZnO thermal conductivity as a function of impurity concentration for Pr (open square) and Bi (open circle) elements, respectively. The thermal conductivity data consist of two sets: the ZnO with all impurity atoms segregate on GBs (red symbols) and ZnO solid solutions with “clean” GBs (blue symbols). To show the contrast between the effects of point defect and GB impurity segregation on phonon scattering, hypothetical ZnO solid solutions with impurity concentration beyond the solid solubility limit is also presented (gray symbols). All calculations are performed on a GB spacing of 500 nm with a misorientation angle of ${15}^{\circ }$. (b) Derived Kapitza resistance as a function of impurity segregation concentration at ZnO GBs.

Figure 3

(a) Frequency dependence of phonon relaxation time and (b) spectral thermal conductivity for ZnO with various grain boundary characteristics: “clean” GBs with misorientation angle of 1, 15, and ${30}^{\circ }$ and $\left[\mathrm{Pr}\right]=\left[\mathrm{Bi}\right]=0.10$ segregated GBs with misorientation angle of ${15}^{\circ }$. Calculations are performed for room temperature and grain size of 100 nm. Also shown are the Casimir model and anharmonic scattering for comparison.

Figure 4

(a) Cumulative thermal conductivity and (b) thermal conductivity accumulation function versus phonon MFP for different grain boundary spacing. All GBs are impurity-free and have a misorientation angle of ${15}^{\circ }$. Anharmonic scattering is considered in all calculations. Also shown is the intrinsic behavior where phonon conduction is solely governed by anharmonic scattering.