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