1.

1 (a) Face cantered cubic,

8 corner atoms*1/8 =1 atoms

6 face atoms*1/2 =3 atoms

Total numbers of atoms per unit cell =3 atoms+1 atoms=4 atoms

(b) Body centred cubic,

8 corner atoms*1/8 =1 atoms

1 enclosed atoms=1 atoms

Total numbers of atoms per unit cell =1atoms+1 atoms=2 atoms

(c) Diamond Lattice,

8 corner atoms*1/8 =1 atoms

6 face atoms*1/2 =3 atoms

4 enclosed atoms=4 atoms

Total numbers of atoms per unit cell =1atoms+3 atoms+4 atoms =8 atoms

1.2 (a) Simple cubic Lattice,

A=2r
Unit Cell volume=a 3=( 2 r )3=8 r 3
3
1∗4 π r
Atom volume=
3
3
4πr
Ratio= 3
3
∗100=52.4 %
8r

(b) Face Centred cubic Lattice,

d=4 r =a √ 2

d
a= =2 √ 2 r
√2
 3
Unit Cell volume=a 3=( 2 √ 2 r ) =16 √ 2 r 3
3
4∗4 π r
Atom volume=
3
3
4∗4 π r
Ratio= 3
∗100=7 4 %
16 √ 2 r
3

(c ) Body centred cubic lattice,

d=4 r =a √ 3

4
a= r
√3

( )
3
3 4
Unit Cell volume=a = r
√3
3
2∗4 π r
Atom volume=
3
2∗4 π r 3
3
Ratio= ∗100=68 %
( )
4 3
√3
r

(d) Diamond lattice,

d=8 r=a √3

8
a= r
√3

( )
3
3 8
Unit Cell volume=a = r
√3
3
8∗4 π r
Atom volume=
3
3
8∗4 π r
3
Ratio= ∗100=34 %
( )
3
8
r
√3
1.3 (a) Given, a=5.43 A °

8
a= r
√3
a √ 3 5.43∗ √ 3
r= = =1.176 A °
8 8
Centre of one silicon atom to centre of nearest neighbour=2r=2*1.176 A °=2.35 A °

8 22 3
(b)Number density = −8 3
=5∗10 c m
( 5.43∗10 )
N ( At .Wt .) 5∗1022∗28.09 3
(c ) Mass density= = 23
=2.33 gram/c m
NA 6.02∗10

1.7 (a) Simple cubic

a=2 r=2∗1.95 A ° =3.9 0 A °

(b) fcc

4 r 4∗1.95
a= = =5.51 A °
√2 √2
(c ) bcc

4 r 4∗1.95
a= = =4 .5 0 A °
√3 √3
(d) Diamond

2∗4 r 2∗4∗1.95
a= = =9.0 A °
√3 √3

1.8 (a) Radius of atom B=r A ( √ 2−1 )=1.035∗( √ 2−1 )=0.4287 A °

(b) Lattice constant,

a=2 r A =2∗1.035=2.04 A °

(c ) For atom A:

No. of atoms=8*1/8 =1

1 23 3
Desnity= −8 3
=1.13∗10 c m
( 2.07∗10 )
For atom B:

No. of atoms=6*1/2 =3

3 23 3
Desnity= −8 3
=3.38∗10 c m
( 2.07∗10 )
1.11 (a) NaCl atoms in a 100 plane:
(b) a=r Na +r Cl =1+1.8=2.8 A °

(c) Na:

1 /2 22 3
Desnity= −8 3
=2 . 28∗10 c m
( 2.07∗10 )
Cl:

1 /2 22 3
Desnity= −8 3
=2 .28∗10 c m
( 2.07∗10 )

1 1
∗22.99+ ∗35.45
(d)Mass per unit Cell= 2 2
23
=4.85∗10−23
6.02∗10
−23
4.85∗10 3
Mass density= =2.21 gram/c m
−8 3
( 2.8∗10 )
1.15

(a)(i) (110)

(ii) (111)
(iii)(220)

(iV) (321)

(b)

(a)(i) (110)
(ii) (111)

(iii)(220)

(iV) (321)