10.1 10.2 10.3 10.4 10.1 (1) ( ) (2) (3) (anisotropy) anisotropy)(isotropy) isotropy) http://www.its.caltech caltech.edu/~atomic/ /~atomic/snowcrystals/ photos/photos.htm htm (Left) Quartz is a crystalline form of silica, SiO 2, with the atoms in an orderly network, represented here in two dimensions. (Right) When molten silica solidifies, it becomes glass. Now the atoms form a disorderly network. 17 17Steno a b b cac ( ) (19 Bravais, ëopob, Shoenflies 20Laue,, BraggX ) ( ) (c) (c) 1
(unit cell) 3 a, b, cbc, ca, ab 3 α, β, γ6 (Cubic) (Tetragonal) (Rhombic) (Rhombohedral) Rhombohedral)* (Hexagonal) (Monoclinic) (Triclinic) 7* a = b = c a = b c a b c a = b = c a = b c a = b c a b c a b c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ 90 α = β = 90 γ =120 α = β = 90 γ =120 α = γ =90 β 90 α β γ 90 Cu Sn I 2 Bi Al 2 O 3 Mg NaCl SnO 2 HgCl 2 AgI S KClO 3 CuSO 4 5H 2 O * 3 3 90 90 120 14 14Bravias 7 (1) (2) (3) 3 (4) (4) (5) 2(6) (6) (7) (7)(8)(9) 4 (10) (10) (11) (11) 1 (12, 14) (13) (13)2 14 14 Bravias Bravias1866 Bravias Bravias (6) (12) (1) (2) (3) (4) (5) (7) (8) (9) (10) (11) (13) (14) Cu a = b = c = 0.356 nm, α = β = γ = 90 o 8 61Cu 8 1/8 81Cu 1/2 1/263 4Cu Cu r a 2 1 r = a = a 4 2 2 r = 0.126 nm 4r Shared by 8 unit cells Shared by 2 unit cells 2
X Bragg λx dθ θ Bragg λx θ nλ nλ/2 2d sinθ = nλ (Bragg ) NaCl Al 2 O 3 CuSO 4 H 2 O 20 30 40 50 2θ X 10.2 1 2 3 4 1 2/3 2/3 12 128 6 nucleus & inner shell e mobile sea of e (1) a) (2) b) 6 6 a 3
6 6 1 52% 52% α- Po 8 2 4 π(a/2) 3 3 100% = = 52% a 3 2 4 π( 3 a/4) 3 3 100% = 68% a 3 Li, Na, K, Rb,, Cs V, Nb,, Ta, Cr, Mn,, Fe20 20 12 124 74% ar a = 2 2r A face-centered centered cubic unit cell for the cubic closest packing of spheres Ca, Sr,, Pt, Pd, Cu, Ag 50 50 12 12274% 74% The hexagonal closest packed crystal structure A unit cell is highlighted in heavy black. The atoms that are part of that cell are in solid color. Note that the unit cell l is Be, Mg, Sc, Ti, a parallelepiped, but not a cube. Three adjoining unit cells are Zn, Cd also shown. The highlighted unit cell and broken-line regions together show the layering (ABA). The hexagonal prism showing parts of the shared spheres at the corners and the single sphere at the center of the unit cell. Closest packed structures Spheres in layer A are red. Those in layer B are yellow, and in layer C, blue. The holes in closest packed structures. The trigonal hole is formed by three spheres in one of the layers. The tetrahedral hole is formed when n sphere in the upper layer sits in the dimple of the lower layer. The octahedral l hole is formed between two groups of three spheres in two layers. 4
Coordination Number (( ) I 6 8 12 12 % 52 68 74 74 2 (I) Billions of unit cells stack together to recreate the smooth faces of the crystal of sodium chloride seen in this micrograph. The first inset shows some of the stacked unit cells. The second inset identifies the individual ions. The third inset (lower right) illustrates the coordination of an anion to its six cation neighbors. ( ) ( ) Cross section of an octahedral hole 5
(CsCl) AB AB 88:81 1) NaCl 6 6:64 The cesium chloride unit cell The Cs + is in the center of the cube, with Cl ions at the corners. In reality, each Cl is in contact with the Cs + ion. An alternative unit cell has Cl at the center and Cs + at the corners. The sodium chloride unit cell For clarity, only the centers of the ions are shown. Oppositely charged ions are actually in contact. We can think of this structure as an fcc lattice of Cl ions, with Na + ions filling the octahedral holes. 2) ZnS ZnS 4 4 AB r + /r - NaCl NaCl 6 4(r + + r - ) 2 = 2(2r - ) 2 r - r - r + /r - = 0.414 r - + r - I AB AB CsCl NaCl ZnS 8:8 6:6 4:4 r+/r- 0.732-1 0.225-0.414 0.414-0.732 CaCl, CsBr, CsI, TlCl,, NH 4 Cl () ZnS,, ZnO, HgS, MgTe, BeO, BeS r + /r - AB r + /r - = 0.414 0.732 NaCl r + /r - > 0.732 CsCl r + /r - < 0.414 ZnS ZnS AB AB ZnS AB 2 CaF 2 (TiO 2 )ABX 3 CaTiO 3 ()CaCO 3 ()AB 2 X 4 MgAl 2 O 4 ( )MgFe 2 O 4 () 6
3 12 12 HCl, HBr,, HI H 2 S, CH 4 C60 O C O 1985 H. W. Kroto,, R. E. Smalley B. Curl 60 C60 C60 1996 C60R. E. Smalley C60 C604 C60 CO 2 CO 2 8 (c) CO 2 CO 2 CO 2 H 2 O O 4O4H 2H 2H 7
4 The structure of diamond. Each dot represents the location of the e center of a carbon atom. Each atom forms an sp 3 hybrid covalent bond to each of its four neighbors. 4 34% The diamond structure (3750 C) C) A portion of the Lewis structure. Crystal structure. Each carbon atom is bonded to four others in a tetrahedral fashion. The segment of the entire crystal shown here is a unit cell. (SiO 2 )SiO Si Si4O Si Si-O O SiO 2 Si Si Ο O ( 344) 4) 400 kj mol 1 GeSi Si ( ) 6 r+/ +/r- (),, ( ) ( ) () 8
10.3 1 9
/ C / C NaCl 801 Na 2 O 920 MgCl 2 714 MgO 2802 AlCl 3 193 Al 2 O 3 2027 * PCl 5 [PCl + 4 ][PCl 6 ] SiCl 4 68 * SiO 2 1700 PCl 5 166 P 2 O 3 24 SO 3 16.9 (SF 6 ) 56 Cl 2 O 7 91.5 2 + + + + ()) (( ) ) (( ) ) (( ) Z/r 2 Z r (pm) pm)z/r 2,, Li+ 0.034 (2.78) Na 2+ (1.11) K + 0.923 (0.565) Rb + 1.56 (0.457) Cs + 2.69 (0.35) Be 2+ (20.8) Mg 2+ (4.73) Ca 2+ 0.52 (2.04) Si 2+ 096 (1.57) Ba 2+ 1.72 (1.10) B 3+ 0.0033 (75) Al 3+ (12) Sc 3+ 0.318 (4.57) Y 3+ 0.61 (3.47) La 2+ 1.16 (2.27) () Si 4+ (23.8) Ti 4+ 0.206 (8.65) Zr 4+ --- (6.25) Ce 4+ (3.92) O 2 4.32 (1.02) S 2 (0.591) Se 2 11.7 (0.51) Te 2+ (0.409) F 1.16 (0.541) Cl (0.305) Br 5.31 (0.263) I (0.214) 10
( ) d n d n d n d 10 Ag +, Cu +, Zn 2+, Hg 2+ r 0 /pm (r + +r - )*/pm AgX AgX AgF 246 246 NaCl AgCl 277 289 294 309 NaCl AgBr AgI 281 333 ZnS Ag + d 10 I 6NaCl 4ZnS ZnS AgF AgFAgIr o X A X X 0.2 0.4 0.6 0.8 1.0 % 1 4 9 15 22 X A X X 1.2 1.4 1.6 1.8 2.0 % 30 39 47 55 63 X A X X 2.2 2.4 2.6 2.8 3.0 3.2 % 1.7 1.750% 50% 1.7 1.7 70 76 82 86 89 92 Percent Ionic Character Percent ionic character of a chemical bond as a function of electronegativity difference 3 () 10.4 11
1 (1) (2) (c) AgBr 2() M 3 M 2 M 1 γ-al 2 O 3 (c) a) b)(c) c) X 3 12