Material Science Assignment Solution Class Activity Crystal Structure 1

CRYSTAL STRUCTURE

[CLASS ACTIVITY] ACTIVITY]

1. The density of potassium, which has the BCC structure and one 3 atom per lattice point, is 0.855g/cm . The atomic weight of  potassium is 39.09g/mol. 39.09g/mol. Calculate: Calculate: (a) The lattice parameter;

(b)

The atomic radius of potassium;

(c)

The atomic packing factor APF =

4 / 3( r 3 ) V c

3

2. A metal having a cubic c ubic structure has a density of 1.892g/cm 1 .892g/cm , an atomic weight of 132.91g/mol, and a lattice parameter of 6.13A. One atom is associated with each lattice point. Determine the crystal structure of the metal. solution

   

n

nA V C  N  A   V C  N  A  A

3. Beryllium has a hexagon h exagonal al crystal structure, with a 0.22858 nm and c 0.35842 nm. The atomic radius is 0.1143 nm, the 3 density is 1.848 g/cm , and the atomic weight is 9.01 g/mol. Determine; =

=

(a)

The number of atoms in each unit cell

CRYSTAL STRUCTURE

(b)

[CLASS ACTIVITY]

The packing factor in the unit cell.

4. Determine the indices for the direction in the hexagonal lattice  below using both the three-digit and four-digit systems.

Point 2 (a1 a2 z) Point 1 (a1 a2 z) Subtract Clear fraction Enclosed [u’v’w’] u = 1/3(2u’-v) v = 1/3(2v’ – u) t = -(u+v) w = w’

2 3

A 1 0 0 0 0 1 1 0 -1 ] [10 1 ] [10 1 2/3 -1/3 -1/3 -1

clear fraction

(x3) 2 -1 -1 -3

[uvtw]

1 3 ] [2 1

B -1/2 0 -1/2 -1  [1 2  [1 2 0 -1 1 0

-1 0 -1 -2 0] 0]

-

  1 0] [0 1

1

5. Sketch the following directions and planes within a cubic unit cell. (a) 0 1 0 , 2 1 3, 301

0 0 0 0

C 1 1 0 0 1 1 [1 1 [1 1 1/3 1/3 -2/3 1

1 0 1 1] 1]

(x3) 1 1 -2 3

  3] [1 1 2

CRYSTAL STRUCTURE

[CLASS ACTIVITY]

5-Miller Indices 4-Clear Fraction 3-Substracting 2-Point 1 1-Point 2

011 ,

(b)

102 ,

1 bar1 0 No clr. fraction 0 bar1 0 0 1 0 0 0 0

5-Miller Indices 4-Clear Fraction (x3) 3-Substracting 2-Point 1 1-Point 2

2 bar1 3 2 bar1 3 2/3 -1/3 1 0 1 0 2/3 2/3 1

5-Miller Indices 4-Clear Fraction (x3) 3-Substracting 2-Point 1 1-Point 2

3 0 3 0 1 0 0 0 1 0

1 1 1/3 0 1/3

212 

6. Sketch the following directions and planes within a hexagonal unit cell.





(a) 1120  , 01 1 0

01 1 0

1120 

CRYSTAL STRUCTURE

[CLASS ACTIVITY]

(b) 0003

(0003)

7. A diffracted x-ray beam is observed from the (220) planes of iron at a 2  angle of 99.1o  When x-rays of 0.15418 nm wavelength and the order of reflection is one are used. Calculate the lattice parameter a. Solution,