Al O2 Ta(110), Mo(110), Nb(110) (a) Al deposition and oxidation

#### (b) Preferential oxidation of Al-containing intermetallics

**Figure 4.** Schematic representation of alumina growth by (**a**) Al deposition and oxidation on highmelting-temperature bcc metal (110) surfaces, and (**b**) preferential oxidation of (110) surface of Alcontaining intermetallics having bcc-like structure. **Figure 4.** Schematic representation of alumina growth by (**a**) Al deposition and oxidation on highmelting-temperature bcc metal (110) surfaces, and (**b**) preferential oxidation of (110) surface of Al-containing intermetallics having bcc-like structure.

#### *2.2. Thermoelectric Materials*

The above findings suggest the possibility of using Al-containing alloys that have a crystal plane with sixfold symmetry. The author was successful in finding such alloys that fulfill the conditions and demonstrated the growth of 1–4 nm thick atomically flat alumina films using Cu-9Al(111) as a substrate [26–28]. The key was to expand the search space beyond intermetallic compounds, which rarely have a plane with sixfold symmetry, and consider alloys as candidate materials. *2.2. Thermoelectric Materials*  In thermoelectric materials, a voltage is generated between two edges of a material, which are kept at different temperatures. When the two edges are electrically connected via a load, current flows, which can be used as electric power. The efficiency of power generation is expressed as Z = *S2σ/κ*, where *S* is the Seebeck coefficient, *σ* is the electrical conductivity, and *κ* is the thermal conductivity. In the early stage of intense research on thermoelectric materials around the beginning of the 2010s, the Seebeck coefficient and electrical conductivity were thought to have a trade-off relationship, and therefore most research focused on controlling the thermal conductivity by fabricating nano structures. However, the author demonstrated that the trade-off can be partially avoided [29,30]. By considering the scientific principles of voltage generation by placing samples of the same material at different temperatures in contact (temperature difference causes difference in electron distribution, accordingly the Fermi level difference, but the shape of density of states (DOS) is the same), and of voltage decrease due to current flow, we can draw a diagram of the relationship between *S, σ, κ*, and the quantities that determine *S, σ*, and *κ*, as shown in Figure 5. [31,32]. One reason for the trade-off relationship is doping, which In thermoelectric materials, a voltage is generated between two edges of a material, which are kept at different temperatures. When the two edges are electrically connected via a load, current flows, which can be used as electric power. The efficiency of power generation is expressed as Z = *S <sup>2</sup>σ/κ*, where *S* is the Seebeck coefficient, *σ* is the electrical conductivity, and *κ* is the thermal conductivity. In the early stage of intense research on thermoelectric materials around the beginning of the 2010s, the Seebeck coefficient and electrical conductivity were thought to have a trade-off relationship, and therefore most research focused on controlling the thermal conductivity by fabricating nano structures. However, the author demonstrated that the trade-off can be partially avoided [29,30]. By considering the scientific principles of voltage generation by placing samples of the same material at different temperatures in contact (temperature difference causes difference in electron distribution, accordingly the Fermi level difference, but the shape of density of states (DOS) is the same), and of voltage decrease due to current flow, we can draw a diagram of the relationship between *S, σ, κ*, and the quantities that determine *S, σ*, and *κ*, as shown in Figure 5. [31,32]. One reason for the trade-off relationship is doping, which does not change the main DOS but increases the impurity states (and thus increases *σ*); consequently, the Fermi level changes, decreasing the generated voltage thus *S*. However, this explanation between *S* and *σ* applies only for doping. A comparison of materials with differently shaped DOSs reveals that there is no trade-off relationship [31]. The reason is that the shape of the DOS depends on the carrier mobility, which is determined by the effective mass of electrons. Therefore, a search for materials considering not the DOS but the shape of the DOS would identify materials that have both large Seebeck coefficients and high electrical conductivity.

does not change the main DOS but increases the impurity states (and thus increases *σ*);
