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1 (1) ( ) (2) (3) (anisotropy) anisotropy)(isotropy) isotropy) 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 Steno a b b cac ( ) (19 Bravais, ëopob, Shoenflies 20Laue,, BraggX ) ( ) (c) (c) 1

htm htm (Left) Quartz is a crystalline form of silica, SiO 2, with the atoms in an orderly network, represented here in

2 (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 * Bravias 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) Bravias Bravias1866 Bravias Bravias (6) (12) (1) (2) (3) (4) (5) (7) (8) (9) (10) (11) (13) (14) Cu a = b = c = 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 r = nm 4r Shared by 8 unit cells Shared by 2 unit cells 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)

3 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 θ X /3 2/ nucleus & inner shell e mobile sea of e (1) a) (2) b) 6 6 a 3

4 % 52% α- Po π(a/2) % = = 52% a π( 3 a/4) % = 68% a 3 Li, Na, K, Rb,, Cs V, Nb,, Ta, Cr, Mn,, Fe % ar a = 2 2r A face-centered centered cubic unit cell for the cubic closest packing of spheres Ca, Sr,, Pt, Pd, Cu, Ag % 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

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.

5 Coordination Number (( ) I % (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

The first inset shows some of the stacked unit cells. The second inset identifies the individual ions.

6 (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 - = r - + r - I AB AB CsCl NaCl ZnS 8:8 6:6 4:4 r+/r CaCl, CsBr, CsI, TlCl,, NH 4 Cl () ZnS,, ZnO, HgS, MgTe, BeO, BeS r + /r - AB r + /r - = NaCl r + /r - > CsCl r + /r - < 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

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.

7 HCl, HBr,, HI H 2 S, CH 4 C60 O C O 1985 H. W. Kroto,, R. E. Smalley B. Curl 60 C60 C 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

8 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

4 34% The diamond structure (3750 C) C) A portion of the Lewis structure. Crystal structure.

10 / C / C NaCl 801 Na 2 O 920 MgCl MgO 2802 AlCl Al 2 O * PCl 5 [PCl + 4 ][PCl 6 ] SiCl 4 68 * SiO PCl P 2 O 3 24 SO (SF 6 ) 56 Cl 2 O ()) (( ) ) (( ) ) (( ) Z/r 2 Z r (pm) pm)z/r 2,, Li (2.78) Na 2+ (1.11) K (0.565) Rb (0.457) Cs (0.35) Be 2+ (20.8) Mg 2+ (4.73) Ca (2.04) Si (1.57) Ba (1.10) B (75) Al 3+ (12) Sc (4.57) Y (3.47) La (2.27) () Si 4+ (23.8) Ti (8.65) Zr (6.25) Ce 4+ (3.92) O (1.02) S 2 (0.591) Se (0.51) Te 2+ (0.409) F 1.16 (0.541) Cl (0.305) Br 5.31 (0.263) I (0.214) 10

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.

11 ( ) d n d n d n d 10 Ag +, Cu +, Zn 2+, Hg 2+ r 0 /pm (r + +r - )*/pm AgX AgX AgF NaCl AgCl NaCl AgBr AgI ZnS Ag + d 10 I 6NaCl 4ZnS ZnS AgF AgFAgIr o X A X X % X A X X % X A X X % % 50% Percent Ionic Character Percent ionic character of a chemical bond as a function of electronegativity difference 3 ()

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.

12 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

99710b45zw.PDF

99710b45zw.PDF 1 2 1 4 C && Zn H H H H H Cl H O H N H H H CH C H C H 3 2 5 3 7 H H H H CH 3 C2H 5 H H H O H H O K K O NO 2 H O NO 2 NO O 2 C2H5 H O C2H5 C H O C2H3 2 5 H H H O H H O 1826 O