[MUSIC] Hello, everyone in the previous four lectures we talked about the several defect structures, including general dimensional point defect, one-dimensional the dislocation, and two-dimensional interfaces and three-dimensional precipitates. And in this lecture, we will talk about some defect structure, which is laced with the physical properties of materials. And in this lecture, I will give you one example, the constellations, the [INAUDIBLE] can show us the relationship between defect and thermal transport properties of a material. As you know, the total thermal conductivity is given by the summation of electronic thermal conductivity, kappa electron, and lattice thermal conductivity by phonon, kappa lattice. And electronic thermal conductivity is ruled by Wiedemann-Franz law. The equation is given by kappa electron equals sigma times L times absolute temperature, T. In this equation sigma is the electrical conductivity and L is the Lorenz number. In metallic conductor Lorenz number is given by 2.44x10^-8WΩ/k^2. The rarest in semiconductors, the Lorenz number can be changed so we should calculate the Lorenz number based on this equation. And in this equation, you can find the Lorenz number in semiconductor is determined by the Fermi integral. So from the measured carrier concentration and Seebeck coefficient, we can calculate the relative number of semiconducting material. And then let's think about the lattice thermal conductivity, which is given by this equation 1/3 times specific heat capacity time sound velocity times the phonon mean free path. In this equation specific heat capacity shows this like the temperature dependence based on this equations. Though specific heat capacitance is constant, if the temperature is higher than Debye temperature, whereas the specific heat capacity of the material that shows the T to the three at the lower temperature compared to the Debye temperature. And normally the mean free path of a phonon is decreased with temperature. So the acquired the lattice thermal conductivity of a material shows the dislike temperature-dependent the behavior. The phonons, which is later with the lattice thermal conductivity, are particles derived from the vibrations of atoms in a solid. There are two different types of phonons. The first is acoustic phonon with coherent movement of atoms of the lattice out of their equilibrium positions, including two transverse modes and one longitudinal mode. And the second is optical phonon with out of phase movement of the atoms in the lattice. In optical phonon one atom moving to the left and its neighbor to the right. Phonons can scatter through several mechanisms. These scattering mechanisms are Umklapp phonon-phonon scattering, phonon-impurity scattering, phonon-electron scattering, and phonon-boundary scattering. And can be characterized by a relaxation time, relaxation rate 1/t. Tau is the relaxation time, the characteristic time for a system to reach an equilibrium condition after a disturbance. And lattice thermal conductivity of a material can also be given by this equation, including the three important parameter I1, I2, I3. And as shown here the parameter Is have the relationship between phonon relaxation time Tau. In many cases it is very convenient to use the inverse relaxation time because if we increase inverse relaxation time, that means the reduction in thermal conductivity. So anyway, the inverse relaxation time of a material can be given by this equation. It includes the contribution by phonon process and contribution by Umklapp process. This is the intrinsic component scattering mechanism, which can be found in materials and also contains by the contribution from point defect, boundary, strain, dislocation, precipitate, sometimes bipolaron. So from this equation, we found that any defective structure can affect the phonon scattering of material, including zero-dimensional point defect, one-dimensional dislocation, two-dimensional boundary, and three-dimensional precipitate and trained field generated by defect structure. In detail as shown here, the inverse relaxation time for boundary is given by this equation. So if we decrease the grain size, we can effectively reduce the lattice thermal conductivity of a material. And also from the inverse relaxation time for the precipitate, we can find this like equation. So this equation means that if we increased the interface density between the precipitate and matrix and also by increase of the density of particles, we can effectively reduce the lattice thermal conductivity of materials. And for dislocations, so the effect can include by the core, the screw, and edge and mixed dislocation. And let's think about the relationship between defect and phonon wavelengths. So one important defect structure is zero-dimensional point defect. And by the introduction of phonon atoms, we can generate zero-dimensional point defect and we can obtain the reduced lattice thermal conductivity due to the intensified alloy phonon scattering based on this equation. From this equation we can find that if we increase the fraction of a point defect, and if we use the point defect with the large difference in mass compared to host ions, and if we reduce the lattice disorder by the introduction of a point defect, we can effectively reduce the lattice thermal conductivity. And the right side figure shows the microstructure of a polycrystalline samples with various type of defect structure. You can find one-dimensional dislocation and dislocation strain field and two-dimensional grain boundary and phase boundary, and three-dimensional precipitate and narrow inclusions. As shown here, the short wavelength phonon can be effectively scattered by the one-dimensional dislocation core and also small side three-dimensional precipitate. And also mid to long wavelength phonon can be effectively scattered by the strain field and, large sized, the precipitate. So in order to reduce the lattice thermal conductivity of materials effectively, we should understand the heat carried phonon distribution according to the phonon wavelength. Normally the point defect and dislocation core is very effective phonon scattering center for low wavelengths phonon. And whereas the interfaces and the larger size precipitates are effective phonon scattering center for the high phonon wavelengths of energy. And then let's think about the phonon scattering mechanism by the point defect boundary and nanoparticles. And you can find Rayleigh-type the phonon scattering mechanism in the point defect structure of the material. And whereas you can find the geometrical, the phonon scattering mechanism at the boundary of a material. However, you can find Rayleigh-type phonon scattering and also geometrical type phonon scattering in three-dimensional defect structure, it is nanoparticles. So nanoparticles provide us additional phonon scattering based on the changeover between the Rayleigh and geometrical scatterings. And the indispensability of nanoparticles to scatter phonons that cannot be scattered effectively by either point defect or grain boundaries. So by controlling the size of nanoparticles we can effectively reduce the lattice thermal conductivity of a material. So in this lecture, we talked about the relationship between the thermal transport properties of a material and de facto structure and found that the hierarchical design in the defect structure, according to the phonon mean free path, is required to minimize the lattice thermal conductivity of materials. Thank you.