Hello, everyone. In this lecture, we are going to talk about the several physical property change, which is related with the zero-dimensional point defect. So electrical conduction, can be expressed by the summation of electronic contribution by holes and electrons, and ionic contribution by anion, cation, and proton. So the total electrical conductivity Sigma, is given by the summation of hole and electron conductivity and ionic conductivity. Basically, the electric conductivity of a material is ruled by this equation: e mu n. In this equation, e is charge of carrier, mu is the mobility of the carrier, and n is the concentration of a carrier. The electrical conductivity of material is also dependent on oxygen partial pressure. The first step. Let's make the oxygen vacancies in perovskite structure oxide, lanthanum gallium oxide. The oxygen vacancies can be generated by putting atom at lanthanum and gallium site. The left side, the figure shows the crystal structure of lanthanum gallium oxide. You can find eight lanthanum atoms at the corner of unit cell, and the one gallium atom is located at the center of unit cell. You can also find six oxygen ion at each phase. By doping of barium at lanthanum site. Barium has always 2 plus charge and lanthanum has always 3 plus charge. So barium substituted at lanthanum site has minus 1 charge. In order to make charge in neutrality, 1 over 2 oxygen vacancy with 2 plus charge should be formed. Also by substitution of magnesium at gallium site. Magnesium has always 2 plus charge and gallium has always 3 plus charge. So magnesium substituted at gallium site has minus 1 charge. In order to make charge neutrality, 1 over 2 oxygen vacancy with 2 plus charge should be formed. Then let's think about the p-type and n-type electronic conduction in the presence of oxygen vacancies. If we increase the oxygen partial pressure, this oxygen can be incorporated into oxygen vacancies and then they makes oxygen at oxygen site with charge neutrality and 2 plus charge of oxygen vacancy makes two holes. In this case, electronic conduction by hole is proportional to oxygen partial pressure to the 1 over 4. At higher oxygen partial pressure, oxygen can also be incorporated into inter-cell site. So inter-cell oxygen with minus 2 charge can be formed, and this make two holes. In this case, the electronic conduction by hole is proportional to oxygen partial pressure to the 1 over 6. Then, if we reduce the oxygen partial pressure, the interstitial oxygen can be diffused out from the lattice then makes 1 over 2 oxygen an interstitial vacancy and the 2 minus charges of interstitial oxygen makes two electrons. In this case, electronic conduction by electron is proportional to oxygen partial pressure to the minus 1 over 4. And at lower oxygen partial pressure, the oxygen at oxygen site can be diffused out from the lattice and makes 1 over 2 oxygen and oxygen vacancy with 2 plus charge and makes two electrons. In this case, electronic conduction by electron is proportional to oxygen partial pressure to the minus 1 over 6. So the total electrical conductivity of a material is given by oxide ion conductivity and contribution by holes and contribution by electrons. And you know, the electronic conduction of materials is dependent on oxygen partial pressure. This equation is rewritten by oxide ion conductivity plus Sigma_0 times oxygen partial pressure_a plus Sigma_0 - times oxygen partial_b. So you can find this for different the dependence of oxygen partial pressure with or without p-type and n-type conduction. Then let's think about the oxide ion conduction in the presence of oxygen vacancies. Basically, oxide ion conductivity is given by this equation, A exponential minus the activation energy over KT. Also, oxygen transferred in oxide material is ruled by the transport of oxygen to oxygen vacancy. So in perovskite structured material, the important the factor to decide the oxygen transport is set at point which is defined by the critical radius between two A site atoms and one B site atom. Also oxide ion conduction is ruled by the diffusion coefficient. As you know, the diffusion coefficient show that arrhenius plot as a function of 1 over T. So the oxide ion conduction showed also this arrhenius type relationship to the 1 over T. The other type of ionic conduction is proton conduction. The first step to induce the proton conduction is the formation of protonic defect. You already know the formation of oxygen vacancy. Then, if we increase the water vapor pressure, so water vapor can be decomposed into one hydroxyl ion and one proton, and hydroxyl ion can be incorporated into oxygen vacancy and remained proton can be bonded with another oxygen. These makes two protonic defect. The protonic effect is the OH at oxygen site with 1 plus charge. Then the transport of proton conduction is diffuse along the oxygen lattice as shown here. The proton conduction in perovskite oxide is ruled by hop and turn mechanism with the state change it between ground state and barrier state of proton which is related with the bonding with the neighboring oxygen. So calcium, magnesium, scandium, yttrium-dobed zirconia , samarium, gadolinium, yttria-doped ceria , and calcium, strontium, barium, gadolinium. yttria-doped bismuth oxide and strontium magnesium doped gallium oxide are oxide ion conductors in the presence of oxygen vacancies. Strontium zirconate doped barium cerate is a proton conductor. Another physical property change by the formation zero-dimensional point defect is the change in electronic structure. For example, we induce the resonant state formation by point defect. As shown here, the top band has this bound state that there is no change in density of states of a matrix material. The OLS, the top band has this virtual bound state. The density of states of matrix material that can be changed and they form this resonant state. So as shown here, this material can have the enlarged density of state build formidable. Sometimes this can be rejected in enlarged Seebeck equation value which is important to carrier transport to properties of inorganic material. Finally, the point defect is also affect the thermal conductivity of material because the total thermal conductivity of material is given by the summation of electronic contribution and lattice contribution. If we introduced the point defect as shown here, then we can reduce the lattice on the conductivity of a material to 2D intensified always scattering. In this lecture we've talked about the several property changes which is induced by the generation of zero-dimensional pointed effect. In the next, we're going to talk about the one-dimensional defect structure. It's dislocation. Thank you.