11.2.Conduction in Alloys 193 concentration near the bottom of the valence band,as shown in Figure 11.6(b).As a consequence,the electron population near the Fermi energy is small(Figure 11.7),which leads to a com- paratively low conductivity.Finally,insulators have completely filled(and completely empty)electron bands,which results in a virtually zero population density,as shown in Figure 11.7.Thus, the conductivity in insulators is virtually zero (if one disregards, for example,ionic conduction;see Section 11.6).These explana- tions are admittedly quite sketchy.The interested reader is re- ferred to the specialized books listed at the end of this chapter. 11.2.Conduction in Alloys The residual resistivity of alloys increases with increasing amount of solute content as seen in Figures 11.3 and 11.8.The slopes of the individual p versus T lines remain,however,essentially con- stant(Figure 11.3).Small additions of solute cause a linear shift of the p versus T curves to higher resistivity values in accordance with the Matthiessen rule;see Eq.(11.8)and Figure 11.8.Vari- ous solute elements might alter the resistivity of the host mate- rial to different degrees.This is depicted in Figure 11.8 for sil- ver,which demonstrates that the residual resistivity increases with increasing atomic number of the solute.For its interpreta- tion,one may reasonably assume that the likelihood for interac- tions between electrons and impurity atoms increases when the solute has a larger atomic size,as is encountered by proceeding from cadmium to antimony. The resistivity of two-phase alloys is,in many instances,the sum of the resistivity of each of the components,taking the vol- ume fractions of each phase into consideration.However,addi- tional factors,such as the crystal structure and the kind of dis- tribution of the phases in each other,also have to be considered. Sb Sn n FIGURE 11.8.Resistivity change Cd of various dilute silver alloys (schematic).Solvent and solute are all from the fifth Ag at.Solute period.11.2 • Conduction in Alloys 193 concentration near the bottom of the valence band, as shown in Figure 11.6(b). As a consequence, the electron population near the Fermi energy is small (Figure 11.7), which leads to a com￾paratively low conductivity. Finally, insulators have completely filled (and completely empty) electron bands, which results in a virtually zero population density, as shown in Figure 11.7. Thus, the conductivity in insulators is virtually zero (if one disregards, for example, ionic conduction; see Section 11.6). These explana￾tions are admittedly quite sketchy. The interested reader is re￾ferred to the specialized books listed at the end of this chapter. The residual resistivity of alloys increases with increasing amount of solute content as seen in Figures 11.3 and 11.8. The slopes of the individual  versus T lines remain, however, essentially con￾stant (Figure 11.3). Small additions of solute cause a linear shift of the  versus T curves to higher resistivity values in accordance with the Matthiessen rule; see Eq. (11.8) and Figure 11.8. Vari￾ous solute elements might alter the resistivity of the host mate￾rial to different degrees. This is depicted in Figure 11.8 for sil￾ver, which demonstrates that the residual resistivity increases with increasing atomic number of the solute. For its interpreta￾tion, one may reasonably assume that the likelihood for interac￾tions between electrons and impurity atoms increases when the solute has a larger atomic size, as is encountered by proceeding from cadmium to antimony. The resistivity of two-phase alloys is, in many instances, the sum of the resistivity of each of the components, taking the vol￾ume fractions of each phase into consideration. However, addi￾tional factors, such as the crystal structure and the kind of dis￾tribution of the phases in each other, also have to be considered. 11.2 • Conduction in Alloys Ag Sb Sn In Cd  at. % Solute FIGURE 11.8. Resistivity change of various dilute silver alloys (schematic). Solvent and solute are all from the fifth period