Transcript Crystal structure - mrnicholsscience

Crystal structure
Unit Cells, density, and
3-dimensional geometry.
Cubic crystal structures
1) Simple cubic (sc)
2) Body-centered cubic (bcc)
3) Face-centered cubic (fcc)
How many atoms/cell?
• A corner atom has 1/8 atom inside the
cube.
• A body-centered atom is entirely within
the cube
• A face-centered atom has ½ atom inside
the cube
Cubic crystal structures
SC
BCC
FCC
SC
(8 x 1/8)=1 atom/cell
BCC (8 x 1/8)+1=2 atoms/cell
FCC (8 x 1/8)+ (6 x ½)=4 atoms/cell
a=edge of a cell, r=radius of atom
• SC
a=2r
a=edge of a cell, r=radius of atom
• BCC
(√3)a=4r
a=edge of a cell, r=radius of atom
• FCC
(√2)a=4r
A word about volume
• r is usually expressed in picometers(10-12m)
• V (cube)= a3
• Your best bet is to convert: mm3Lml
Conversion factors
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L=6.02 x 1023 atoms/mol
D=__g/ml
FM=___g/mol
V=___ml/cell
1m3=1000L
1L=1000ml
Tasks
• What is the crystal structure?
• What is the radius of the atom?
• What is the volume of the unit cell?
• What is the density?
Tasks
• What is the crystal structure?
Find atoms/cell
• What is the radius of the atom?
Find r
• What is the volume of the unit cell?
Find a3
• What is the density?
Find g/ml
Ex:
• What is the crystal structure?
Find atoms/cell
Manganese has a density of 7.4 g/ml, the
length of the unit cell is 291 pm.
Ex:
• What is the radius of the atom?
Find r
Chromium has a BCC structure and a
density of 7.19 g/ml
Ex:
• What is the volume of the unit cell?
Find a3
Copper has a FCC structure and a density
of 8.96 g/ml
Ex:
• What is the density?
Find g/ml
Strontium has BCC structure and r=215 pm
Ex:
• What is the crystal structure?
Find atoms/cell
Nickel has a density of 8.9 g/ml. Its atomic
radius is 125 pm