Lect3 Tinh thể

Solids

crystalline

amorphous

well defined structures

no orderly structure glass

quartz

SiO2

crystal lattice system of pointsdescribes arrangement of particles

unit cell repeating structural unit lattice

7 unit cells

simple cubic

formed from packing spheres

unit cells

crystalline solids

hexagonal closest packing

“abab” layers “abca” layers

cubic packing

“aaa” layers

in 3 dimensions

hexagonal closest pack cubic closest pack

“abab” layers

simple cubic body centered cubic

Three-Dimensional Cubic Lattices

Simple cubic

Face-centered cubic

Body-centered cubic

1/8x 8 =1 particle

(1/8 )x 8 + 1 = 2 particles

(1/8 )x 8 (1/2 )x 6+ = 4 particles

cubic closest pack

a a a

a b a b

a b c a b c

coordination number = 6

coordination number = 8

coordination number = 12

Calculation of atomic radii

Cu faced-centered cubic

density = 8.92 g/cm3

mass = 63.546 g/mol

63.546 gmol

1 mol6.022 x 1023 atoms

4 atomsunit cell 8.92 g

cm3

4.732 x 10-23 cm3 / unit cell( )1/3

= 3.617 x 10-8 cm

(3.617 x 10-8)2 + (3.617 x 10-8)2 = (4r)2

r = 1.279 x 10-8 cm1 cm1 x 10-2 m

1 x 10-12 m1 pm = 127 pm

r+2r+r

lattice parameter, a

X-Ray Diffraction by Crystals

Bragg Equation n = 2d sin

diffraction interference between waves caused byobject in their pathconstructive or destructive

d

Types of Crystalline Solids

Covalent Ionic Molecular atoms in lattice ions in lattice molecules in lattice

m.p. depends on bonding forces

Cdiamond 3550oC NaCl 800OC H2O 0oC

covalent ionic H-bonding

Covalent solidsatoms in lattice

carbon

sp3 sp2 sp2

hardest material known conduct electricity - e-

diamond

doesn’t conduct electricity

graphite buckminsterfullerene

Covalent solidsatoms in lattice

metals every lattice point - atom of 1 metal

body-centered cubicface-centered cubichexagonal close packed

brass substitutional alloy

steel interstitial alloy

share valence e- e- “sea”

melting pointNa 97oCCr 1890oC

good conductors

Ionic Solids

trigonal hole tetrahedral hole octahedral holetoo small r = 0.225 R r = 0.414 R

composed of charged species –

anions and cationseach unit cell -

anions at lattice points cations in “holes”NaCl face-centered cubicCsCl simple cubic

unit cell neutralstoichiometry of compound

different in size

Molecular Solids molecules in lattice

hemoglobin reaction center

19881962Perutz and Kendrew Deisenhofer, Huber and Michel