清华大学：《材料科学基础》课程教学资源（PPT课件讲稿）Chapter 2.3 Crystal Structure and Complex Lattice

32.3 Crystal Structure and Complex Lattice I Crystal structure is the rea l arrangement of atom in crystals Crystal structure= Space lattice Basis or structure unit

◆Ⅰ.Crystal structure is the real arrangement of atom in crystals Crystal structure ＝ Space lattice + Basis or structure unit §2.3 Crystal Structure and Complex Lattice

+ =

The difference between space lattice and crystal structure Fe Fe:A|=1:1 A

Fe : Al = 1 : 1 Fe Al The difference between space lattice and crystal structure

2×3 atoms/cell

2×3 atoms / cell

◆川. Typical crystal structures of metals 1. BCC O EXample: a-Fe, V, Nb Ta. Cr Mo, W alkali metals 2 n=2 atoms/cell 8CN=8 4 The number of nearest neighbours around each atom is called Coordination Number

1. BCC  Example: α-Fe , V, Nb, Ta, Cr, Mo, W, alkali metals  n = 2 atoms/cell  CN=8  The number of nearest neighbours around each atom is called —— Coordination Number. ◆Ⅱ.Typical crystal structures of metals

4 Packing fraction Volume of atoms/cell Volume of unit cell To determines, The atom is looked as a hard sphere, and the nearest neighbours touch each other 2 For BCC, 5 34 0.68

 Packing fraction ＝ To determineξ, The atom is looked as a hard sphere, and the nearest neighbours touch each other. ∴ For BCC, 0.68 ) 4 3 ( 3 4 2 3 3 =  = a  a  Volume of atoms / cell Volume of unit cell 

2. FCC O EXample: Y-Fe, Al, Ni, Pb, Cu Ag,Au, stainless steal°t。 ②n=8×1/8+6×12=4 atoms/cel 3 CN=12 4√2 4×-丌 34 0.74

2. FCC  Example: γ-Fe , Al , Ni , Pb , Cu , Ag , Au , stainless steal  n= 8×1/8+6×1/2=4 atoms/cell  CN=12  0.74 ) 4 2 ( 3 4 4 3 3 =  = a  

3. HCP O Example: Be, Mg, Zn, Cd, Zr, Hf Ti( low temperature) 2n=×12+×2+3=6 2 CN=12 a5=0.74 32 =1.633 CN=12=0.74

3. HCP CN 12 0.74 1.633 3 8 2 3 3 2 ) 2 ( 2 2 2 = =  = =       = +   a c a c a • • • • • • • • • • • • • • • • •  Example: Be, Mg, Zn, Cd, Zr, Hf Ti( low temperature)  n＝  CN＝12  ξ＝0.74 2 3 6 2 1 12 6 1  +  + =

4. Summary Structure ao vs r Atoms Coordination Packing Examples per cell Number factor Polonium SC ao=2r 6 0.52 (Po), a-Mn 4 Fe.Ti.W Mo BCC 2 8 0.68 Nb, Ta, K,Na VZr. cr 4 FCC 4 12 0.74 Fe, Cu, Au, Pt Ag, Pb, Ni HCP 0.74Ti, Mg Zn, Be Co≈1.633a Co Zr. Cd

Structure a0 vs. r Atoms per cell Coordination Number Packing factor Examples SC 1 6 0.52 Polonium (Po),α-Mn BCC 2 8 0.68 Fe,Ti,W,Mo, Nb,Ta,K,Na, V,Zr,Cr FCC 4 12 0.74 Fe,Cu,Au,Pt ,Ag,Pb,Ni HCP 2 12 0.74 Ti,Mg,Zn,Be ,Co,Zr,Cd a 2r 0 = a r 3 4 0 = a r 2 4 0 = 0 0 0 1.633 2 c a a r  = 4. Summary

82 4 Interstices in typica crystals Of metals Definition In any of the crystal structures, there are small holes between the usual atoms into which smaller atoms may be placed. These locations are called .I. Two types of Interstitials in typical crystals Octahedral interstitial Tetrahedral interstitial

§2.4 Interstices in typical crystals of metals ◆Ⅰ.Two types of Interstitials in typical crystals Octahedral interstitial Tetrahedral interstitial Definition: In any of the crystal structures, there are small holes between the usual atoms into which smaller atoms may be placed. These locations are called interstitial sites