3.2.Binding Forces Between Atoms 29 4 :: Si : FIGURE 3.4.(a)Two-dimensional and (b)three-dimensional representations (a) of the covalent bond as for silicon or carbon(diamond cubic structure). The charge distribution between the individual atoms is not uniform but cone-shaped.The angle between the bond axes,called the valence angle,is (b) 10928'.(See also Figure 16.4(a).) cause of the filled electron shells,covalently bound materials are hard and brittle.Typical representatives are diamond,silicon, germanium,silicate ceramics,glasses,stone,and pottery con- stituents. In many materials a mixture of covalent and ionic bonds ex- ists.As an example,in GaAs,an average of 46%of the bonds oc- cur through electron transfer between Ga and As,whereas the remainder is by electron sharing.A range of binding energies is given in Table 3.1. Metallic Bond The outermost (that is,the valence)electrons for most metals are only loosely bound to their nuclei because of their relative re- moteness from their positively charged cores.All valence elec- trons of a given metal combine to form a "sea"of electrons that move freely between the atom cores.The positively charged cores are held together by these negatively charged electrons.In other words,the free electrons act as the bond (or,as it is often said, as a "glue")between the positively charged ions;see Figure 3.5. Metallic bonds are nondirectional.As a consequence,the bonds do not break when a metal is deformed.This is one of the rea- sons for the high ductility of metals. Examples for materials having metallic bonds are most metals such as Cu,Al,Au,Ag,etc.Transition metals(Fe,Ni,etc.)form mixed bonds that are comprised of covalent bonds (involving their 3d-electrons;see Appendix I)and metallic bonds.This is one of the reasons why they are less ductile than Cu,Ag,and Au. A range of binding energies is listed in Table 3.1.cause of the filled electron shells, covalently bound materials are hard and brittle. Typical representatives are diamond, silicon, germanium, silicate ceramics, glasses, stone, and pottery con￾stituents. In many materials a mixture of covalent and ionic bonds ex￾ists. As an example, in GaAs, an average of 46% of the bonds oc￾cur through electron transfer between Ga and As, whereas the remainder is by electron sharing. A range of binding energies is given in Table 3.1. The outermost (that is, the valence) electrons for most metals are only loosely bound to their nuclei because of their relative re￾moteness from their positively charged cores. All valence elec￾trons of a given metal combine to form a “sea” of electrons that move freely between the atom cores. The positively charged cores are held together by these negatively charged electrons. In other words, the free electrons act as the bond (or, as it is often said, as a “glue”) between the positively charged ions; see Figure 3.5. Metallic bonds are nondirectional. As a consequence, the bonds do not break when a metal is deformed. This is one of the rea￾sons for the high ductility of metals. Examples for materials having metallic bonds are most metals such as Cu, Al, Au, Ag, etc. Transition metals (Fe, Ni, etc.) form mixed bonds that are comprised of covalent bonds (involving their 3d-electrons; see Appendix I) and metallic bonds. This is one of the reasons why they are less ductile than Cu, Ag, and Au. A range of binding energies is listed in Table 3.1. Metallic Bond 3.2 • Binding Forces Between Atoms 29 (b) (a) Si Si Si Si Si Si Si Si Si FIGURE 3.4. (a) Two-dimensional and (b) three-dimensional representations of the covalent bond as for silicon or carbon (diamond cubic structure). The charge distribution between the individual atoms is not uniform but cone-shaped. The angle between the bond axes, called the valence angle, is 109°28. (See also Figure 16.4(a).)