there are not more than 4 ways of arranging spheres in any shape of unit cell
DESCRIPTION
There are not more than 4 ways of arranging spheres in any shape of unit cell. These are Primit ive , Body Centered, Face Centered & End Centered. Primitive Cubic. Unit Cell shape view. Simple Cubic. 1. 3. 2. 4. 5. 7. 6. 8. Unit Cell arrangement view. a = 2r. - PowerPoint PPT PresentationTRANSCRIPT
There are not more than 4 ways of arranging spheres in any shape of unit cell
These are Primitive, Body Centered, Face Centered & End Centered
a = 2r
1
2
4
3
5
67
8
Unit Cell shape view
Unit Cell arrangement view
Layer arrangement view
Volume occupied by a sphere in the unit cell
V81
Total volume occupied by all the spheres in the unit cell
VV 1881
Packing Fraction
Fraction of the Unit cell’s volume occupied by the spheres
cellunitofvolumecellunittheinsidespheresthebyoccupiedVolume
3
334
a
r
3
3
234
r
r
52.0
Coordination number
6
Unit Cell shape view
Unit Cell arrangement view
Layer arrangement view
ar 34
232 ar a
a >
2r
Packing Fraction
3
3
34342
r
r
68.0
Volume occupied by a corner sphere in the unit cell
V81
Volume occupied by the central sphere in the unit cell
V1
Total Volume occupied by the spheres in the unit cell
V2
Packing Fraction
Coordination number
8
Unit Cell shape view
Unit Cell arrangement view
a
ar 24
22 ar a
r2
Packing Fraction
3
3
24344
r
r
74.0
Volume occupied by a corner sphere in the unit cell
V81
Volume occupied by a face centered sphere in the unit cell
V21
Total Volume occupied by the spheres in the unit cell 42
16818
Packing Fraction Highest Packing Fraction of all
shapes and of all arrangements
Coordination number
x y
z
y-z plane
x-z plane
x-y plane
Coordination number
a/2 a/
2
2a
Minimum rc/ra for various coordination numbers
2ra
B
O
A
3230sec
a
ac
rrr
ABOA
155.0132
a
c
rr
30o
Coordination number - 3
43
444222 aaaarrAB ac
ara 42
Coordination number - 4
z-axis
A
B
(0,0,0)
(a/4, a/4,a/4)
24
43 a
acrrr
aac rrr 23
231
a
c
rr 225.012
3
a
c
rr
Coordination number - 4 (square planar) or 6 (octahedron)
B
A 2arrAB ac
ara 2
aa
ac rrrr 222
414.012 a
c
rr
Coordination number - 8 (cube)
ac rra2
3
ara 2
aca rrr 223
732.013 a
c
rr
Final Radius Ratios
Radius Ratio, rc/ra Co-ordination No.
<0.155 2
[0.155, 0.225) 2 or 3
[0.225, 0.414) 2 or 3 or 4 Td
[0.414, 0.732) 2 or 3 or 4 Td, 4 sq. pl or 6 Oh
[0.732, 0.99) 2 or 3 or 4 Td, 4 sq. pl or 6 Oh
or 8