Solids
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Solids. Ch.13. Solids. Fixed, immobile (so to speak) Symmetry Crystals So what’s the inner order?. Unit Cells. Unit cell = smallest repeating unit containing all symmetry characteristics Unit cell reflects stoichiometry of solid

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Solids

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Solids

Solids

Ch.13


Solids1

Solids

  • Fixed, immobile (so to speak)

  • Symmetry

  • Crystals

  • So what’s the inner order?


Unit cells

Unit Cells

  • Unit cell = smallest repeating unit containing all symmetry characteristics

  • Unit cell reflects stoichiometry of solid

  • Several unit cell types possible, but atoms or ions placed at lattice points or corners of geometric object


Crystal lattices

Crystal Lattices

  • 3D unit cells built like legos 

  • Crystal Lattice = arrangement of units cells

  • seven 3D units cells found

  • Simplest = Cubic Unit Cell (equal length edges meeting at 90° angles)

  • Each face part of 2 cubes

  • Each edge part of 4 cubes

  • Each corner part of 8 cubes


Cubic unit cell

Cubic Unit Cell

  • 3 types:

  • 1)Primitive or Simple Cubic (SC)

  • 2) Body-Centered Cubic (BCC)

  • 3) Face-Centered Cubic (FCC)


Cubic unit cell cont

Cubic Unit Cell (cont.)

  • Similarity:

  • Same ions/atoms/molecules at each corner

  • Difference:

  • BCC/FCC have more items at other locations

  • BCC has same item in center of cube

  • FCC has same item centered on each side of cube


What do they look like

SC:

What do they look like?

  • BCC:

  • FCC:


Which metals have which crystal lattices

Which metals have which crystal lattices?

  • Simple cubic: Po

  • BCC: GI, 3B, 4B, Ba, Ra, Fe

  • FCC: VIIIB, IB, Al, In, Pb


How many atoms per unit cell

How many atoms per unit cell?

  • SC: each atom shared by 8 cubes

  • 8 corners of cube  1/8 of each corner atom w/in unit cell = 1 net atom/unit cell


More on sc

More on SC

  • Each atom touches one another along edge

  • Thus, each edge = 2r

  • Coordination number (# of atoms with which each atom is in direct contact) = 6

  • Packing efficiency = fraction of volume occupied = 52%


How many atoms per unit cell cont

How many atoms per unit cell? (cont.)

  • BCC: 2 net atoms w/in unit cell (SC + 1 in center)

  • FCC: 6 faces of cube  ½ atom w/in unit cell = 3 atoms + 1 atom (SC) = 4 net


More on bcc

More on BCC

  • Each atom does not touch another along edge

  • However, atoms touch along internal diagonal

  • Thus, each edge length = 4r/3

  • Let’s derive this…

  • Coordination number (# of atoms with which each atom is in direct contact) = 8

    • Central atom touches 8 atoms

  • Packing efficiency = fraction of volume occupied = 68%


More on fcc

More on FCC

  • Each atom does not touch another along edge

  • However, atoms touch along face diagonal

  • Thus, each edge length = (22)r

  • Let’s derive this…

  • Coordination number (# of atoms with which each atom is in direct contact) = 12

  • Packing efficiency = fraction of volume occupied = 74%


Problems

Problems

  • Eu is used in TV screens. Eu has a BCC structure. Calculate the radius of a europium atom given a MW = 151.964 g/mol, a density of 5.264 g/cm3.

  • Iron has a BCC unit cell with a cell dimension of 286.65 pm. The density of iron is 7.874 g/cm3 and its MW = 55.847 g/mol. Calculate Avogadro’s number.


Ccp and hcp efficiency in stacking

CCP and HCP: Efficiency in Stacking

  • CCP = Cubic Close-Packing (it’s FCC)

  • HCP = Hexagonal Close-Packing

  • 74% packing efficiency


Structures of ionic solids

Structures of ionic solids

  • Take a SC or FCC lattice of larger ions

  • Place smaller ions in holes w/in lattice

  • Smallest repeating unit = unit cell


Solids

CsCl

  • SC unit cell

  • Cs+ in center of cube  Cubic hole

  • Surrounded by 1 Cl- (in 8 parts)

    • 1 Cs+ : 1 Cl-

  • Coordination # = 8

  • Why SC and not BCC?

  • Because ion in center different from lattice pt ions


Solids

LiCl

  • Notice: Li+ has octahedral geometry

  • Thus, cation in octahedral hole (between 6 ions)

    • Coordination # = 6

  • FCC


Solids

NaCl

  • FCC

  • Lattice has net 4 Cl-/unit cell

    • (8x1/8)+(6x1/2) = 4

  • 1 Na+ in center of unit cell

  • 3 Na+ along edges of unit cell

    • (12x1/4) = 3

    • Thus, net total of 4 Na+ ions

  • Total 4 Cl- : 4 Na+  1:1


Tetrahedral holes

Tetrahedral holes

  • Each ion surrounded by 4 other oppositely-charged ions

  • Unit cell: 4 of each ion  total 8 ions

  • Coordination # = 4

  • 8 tetrahedral holes in FCC unit cell

    • 4 by Zn2+ and 4 by S2-

  • Zn2+ occupies ½ of tetrahedral holes and surrounded by 4 S2-

  • S2- forms FCC unit cell


Solids

ZnS


Solids

ZnS


Other types of solids network solids

Other Types of Solids: Network Solids

  • Array of covalently bonded atoms

  • Graphite, diamond, and silicon

  • The latter two  sturdy, hard, & high m.p.’s


Graphite and diamond

Graphite and diamond


Other types of solids amorphous solids

Other Types of Solids: Amorphous Solids

  • Glass & plastics

  • No regular structure

    • Break in all sorts of shapes

  • Long range of m.p.’s


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