上海交通大学：《材料与文明》课程教学资源（参考资料）Understanding Mater_Chapter 3 - Mechanisms

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).)

30 3·Mechanisms FIGURE 3.5.Schematic representation of metallic bonding.The valence electrons become disassociated with "their" atomic core and form an electron "sea" that acts as the binding medium be- tween the positively charged ions. Van der Compared to the three above-mentioned bonding mechanisms, Waals Bond van der Waals bonds!are quite weak and are therefore called secondary bonds.They involve the mutual attraction of dipoles. This needs some explanation.An atom can be represented by a positively charged core and a surrounding negatively charged electron cloud [Figure 3.6(a)].Statistically,it is conceivable that the nucleus and its electron cloud are momentarily displaced with respect to each other.This configuration constitutes an electric dipole,as schematically depicted in Figure 3.6(b).A neighboring atom senses this electric dipole and responds to it with a simi- lar charge redistribution.The two adjacent dipoles then attract each other. FiGURE 3.6.(a)An atom is represented by a (a) positively charged core and a surrounding B negatively charged electron cloud.(b)The electron cloud of atom'A'is thought to be displaced,thus forming a dipole.This in- duces a similar dipole in a second atom,'B'.Both dipoles are then mutually attracted,as proposed by van der Waals. (b) IJohannes Diederik van der Waals (1837-1923),Dutch physicist,re- ceived in 1910 the Nobel Prize in physics for his research on the math- ematical equation describing the gaseous and liquid states of matter.He postulated in 1873 weak intermolecular forces that were subsequently named after him

Compared to the three above-mentioned bonding mechanisms, van der Waals bonds1 are quite weak and are therefore called secondary bonds. They involve the mutual attraction of dipoles. This needs some explanation. An atom can be represented by a positively charged core and a surrounding negatively charged electron cloud [Figure 3.6(a)]. Statistically, it is conceivable that the nucleus and its electron cloud are momentarily displaced with respect to each other. This configuration constitutes an electric dipole, as schematically depicted in Figure 3.6(b). A neighboring atom senses this electric dipole and responds to it with a simi￾lar charge redistribution. The two adjacent dipoles then attract each other. FIGURE 3.5. Schematic representation of metallic bonding. The valence electrons become disassociated with “their” atomic core and form an electron “sea” that acts as the binding medium be￾tween the positively charged ions. 30 3 • Mechanisms 1Johannes Diederik van der Waals (1837–1923), Dutch physicist, re￾ceived in 1910 the Nobel Prize in physics for his research on the math￾ematical equation describing the gaseous and liquid states of matter. He postulated in 1873 weak intermolecular forces that were subsequently named after him. + – – – – – – – – A B (a) (b) + + FIGURE 3.6. (a) An atom is represented by a positively charged core and a surrounding negatively charged electron cloud. (b) The electron cloud of atom ‘A’ is thought to be displaced, thus forming a dipole. This in￾duces a similar dipole in a second atom,‘B’. Both dipoles are then mutually attracted, as proposed by van der Waals. Van der Waals Bond

3.3.Arrangement of Atoms(Crystallography) 31 FIGURE 3.7.Two polymer chains are mutually at- tracted by van der Waals forces.An applied exter- nal stress can easily slide the chains past each other. Many polymeric chains which consist of covalently bonded atoms contain areas that are permanently polarized.The cova- lent bonding within the chains is quite strong.In contrast to this, the individual chains are mutually attracted by weak van der Waals forces (Figure 3.7).As a consequence,many polymers can be deformed permanently since the chains slide effortlessly past each other when a force is applied.(We will return to this topic in Section 16.4.) One more example may be given.Ice crystals consist of strongly bonded H2O molecules that are electrostatically attracted to each other by weak van der Waals forces.At the melting point of ice, or under pressure,the van der Waals bonds break and water is formed. Mixed As already mentioned above,many materials possess atomic Bonding bonding involving more than one type.This is,for example,true in compound semiconductors (e.g.,GaAs),which are bonded by a mixture of covalent and ionic bonds,or in some transition met- als,such as iron or nickel,which form metallic and covalent bonds. 3.3.Arrangement of Atoms (Crystallography) The strength and ductility of materials depend not only on the binding forces between the atoms,as discussed in Section 3.2, but also on the arrangements of the atoms in relationship to each other.This needs some extensive explanations. The atoms in crystalline materials are positioned in a periodic

Many polymeric chains which consist of covalently bonded atoms contain areas that are permanently polarized. The cova￾lent bonding within the chains is quite strong. In contrast to this, the individual chains are mutually attracted by weak van der Waals forces (Figure 3.7). As a consequence, many polymers can be deformed permanently since the chains slide effortlessly past each other when a force is applied. (We will return to this topic in Section 16.4.) One more example may be given. Ice crystals consist of strongly bonded H2O molecules that are electrostatically attracted to each other by weak van der Waals forces. At the melting point of ice, or under pressure, the van der Waals bonds break and water is formed. As already mentioned above, many materials possess atomic bonding involving more than one type. This is, for example, true in compound semiconductors (e.g., GaAs), which are bonded by a mixture of covalent and ionic bonds, or in some transition met￾als, such as iron or nickel, which form metallic and covalent bonds. 3.3 • Arrangement of Atoms (Crystallography) 31 FIGURE 3.7. Two polymer chains are mutually at￾tracted by van der Waals forces. An applied exter￾nal stress can easily slide the chains past each other. 3.3 • Arrangement of Atoms (Crystallography) Mixed Bonding The strength and ductility of materials depend not only on the binding forces between the atoms, as discussed in Section 3.2, but also on the arrangements of the atoms in relationship to each other. This needs some extensive explanations. The atoms in crystalline materials are positioned in a periodic

32 3·Mechanisms that is,repetitive,pattern which forms a three-dimensional grid called a lattice.The smallest unit of such a lattice that still pos- sesses the characteristic symmetry of the entire lattice is called a conventional unit cell.(Occasionally smaller or larger unit cells are used to better demonstrate the particular symmetry of a unit.) The entire lattice can be generated by translating the unit cell into three-dimensional space. Bravais Bravais!has identified 14 fundamental unit cells,often referred Lattice to as Bravais lattices or translation lattices,as depicted in Figure 3.8.They vary in the lengths of their sides (called lattice constants, a,b,and c)and the angles between the axes (a,B,y).The char- acteristic lengths and angles of a unit cell are termed lattice pa- rameters.The arrangement of atoms into a regular,repeatable lat- tice is called a crystal structure. The most important crystal structures for metals are the face- centered cubic(FCC)structure,which is typically found in the case of soft (ductile)materials,the body-centered cubic (BCC) structure,which is common for strong materials,and the hexag- onal close-packed (HCP)structure,which often is found in brit- tle materials.It should be emphasized at this point that the HCP structure is not identical with the simple hexagonal structure shown in Figure 3.8 and is not one of the 14 Bravais lattices since HCP has three extra atoms inside the hexagon.The unit cell for HCP is the shaded portion of the conventional cell shown in Fig- ure 3.9.It contains another "base"atom within the cell in con- trast to the hexagonal cell shown in Figure 3.8. The lattice points shown as filled circles in Figure 3.8 are not necessarily occupied by only one atom.Indeed,in some materi- als,several atoms may be associated with a given lattice point; this is particularly true in the case of ceramics,polymers,and chemical compounds.Each lattice point is equivalent.For ex- ample,the center atom in a BCC structure may serve as the cor- ner of another cube. We now need to define a few parameters that are linked to the mechanical properties of solids. cla Ratio The separation between the basal planes,co,divided by the length of the lattice parameter,ao,in HCP metals(Figure 3.9),is theoret- ically V8/3 =1.633,assuming that the atoms are completely spherical in shape.(See Problem 3.6.)Deviations from this ideal ratio result from mixed bondings and from nonspherical atom shapes.The c/a ratio influences the hardness and ductility of ma- terials;see Section 3.4. See Section 3.1

that is, repetitive, pattern which forms a three-dimensional grid called a lattice. The smallest unit of such a lattice that still pos￾sesses the characteristic symmetry of the entire lattice is called a conventional unit cell. (Occasionally smaller or larger unit cells are used to better demonstrate the particular symmetry of a unit.) The entire lattice can be generated by translating the unit cell into three-dimensional space. Bravais1 has identified 14 fundamental unit cells, often referred to as Bravais lattices or translation lattices, as depicted in Figure 3.8. They vary in the lengths of their sides (called lattice constants, a, b, and c) and the angles between the axes (, , ). The char￾acteristic lengths and angles of a unit cell are termed lattice pa￾rameters. The arrangement of atoms into a regular, repeatable lat￾tice is called a crystal structure. The most important crystal structures for metals are the face￾centered cubic (FCC) structure, which is typically found in the case of soft (ductile) materials, the body-centered cubic (BCC) structure, which is common for strong materials, and the hexag￾onal close-packed (HCP) structure, which often is found in brit￾tle materials. It should be emphasized at this point that the HCP structure is not identical with the simple hexagonal structure shown in Figure 3.8 and is not one of the 14 Bravais lattices since HCP has three extra atoms inside the hexagon. The unit cell for HCP is the shaded portion of the conventional cell shown in Fig￾ure 3.9. It contains another “base” atom within the cell in con￾trast to the hexagonal cell shown in Figure 3.8. The lattice points shown as filled circles in Figure 3.8 are not necessarily occupied by only one atom. Indeed, in some materi￾als, several atoms may be associated with a given lattice point; this is particularly true in the case of ceramics, polymers, and chemical compounds. Each lattice point is equivalent. For ex￾ample, the center atom in a BCC structure may serve as the cor￾ner of another cube. We now need to define a few parameters that are linked to the mechanical properties of solids. The separation between the basal planes, c0, divided by the length of the lattice parameter, a0, in HCP metals (Figure 3.9), is theoret￾ically 8/3
1.633, assuming that the atoms are completely spherical in shape. (See Problem 3.6.) Deviations from this ideal ratio result from mixed bondings and from nonspherical atom shapes. The c/a ratio influences the hardness and ductility of ma￾terials; see Section 3.4. Bravais Lattice 32 3 • Mechanisms 1See Section 3.1. c/a Ratio

3.3.Arrangement of Atoms (Crystallography) 33 Simple Cubic Face-Centered Body-Centered (SC) Cubic (FCC) Cubic (BCC) Simple Body-Centered Tetragonal Tetragonal Simple Body-Centered Base-Centered Face-Centered Orthorhombic Orthorhombic Orthorhombic Orthorhombic Simple Base-Centered Hexagonal Rhombohedral Monoclinic Triclinic Monoclinic FIGURE 3.8.The 14 Bravais lattices grouped into seven crystal systems: First row:a=b=c,a=B=y=90(cubic); Second row:a=b≠c,a=B=y=90°(tetragonal); Third row:a≠b≠c,a=B=y=90°(orthorhombic: Fourth row:at least one angle is 90.Specifically: Hexagonal:a=B=90°，y=120°a=b≠c(the unit cell is the shaded part of the structure); Rhombohedral:a=b=c,a=B=y≠90°≠60°≠109.5°； Monoclinic:a=y=90°，B≠90°，a≠b≠c; Triclinic:a≠B≠y≠90°，a≠b≠c

FIGURE 3.8. The 14 Bravais lattices grouped into seven crystal systems: First row: a
b
c, 


90° (cubic); Second row: a
b  c, 


90° (tetragonal); Third row: a  b  c, 


90° (orthorhombic); Fourth row: at least one angle is  90°. Specifically: Hexagonal: 

90°, 
120° a
b  c (the unit cell is the shaded part of the structure); Rhombohedral: a
b
c, 

  90°  60°  109.5°; Monoclinic: 

90°,   90°, a  b  c; Triclinic:       90°, a  b  c. 3.3 • Arrangement of Atoms (Crystallography) 33 Simple Cubic (SC) Face-Centered Cubic (FCC) Body-Centered Cubic (BCC) Simple Tetragonal Body-Centered Tetragonal Simple Orthorhombic Body-Centered Orthorhombic Base-Centered Orthorhombic Face-Centered Orthorhombic Hexagonal Rhombohedral Simple Monoclinic Base-Centered Monoclinic Triclinic