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ENGINEERING METALLURGY

HOMEWORK # 2

1.

Within a cubic unit cell, sketch the following directions: [101], [211], ][ 210 ,

][ 313 , ][ 111 , ][ 122 , ][ 213 and [303].

2. Determine the indices for the directions shown in the cubic unit cell shown in

Figure 1

3. Determine the Miller indices for the planes shown in the unit cell of Figure 2.

1.

4.

Sketch within a cubic unit cell the following planes:)( 110,

),(),( 012112 )( 313,

)( 111,

)( 213, (301)

5. Calculate and compare the linear densities of the [100], [110] and [111] directions

for FCC

6. Calculate the planar densities of the planes (100), (110) and (111) in both BCC and

FCC structures.

7. Sketch the array of atoms in the (122) plane in a BCC crystal.

8. Find the density of atomic packing in this plane

9.

Indicate and name in terms of Miller indices, the most close-packed direction in

this plane.

Figure 1

Figure 2

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8. Determine the Miller-Bravais indices for the planes and directions shown in

the following figures.

9. Sketch the )1101( and )0112( planes in a hexagonal unit cell.

10.

What are the directions of the family or form for a unit cube?

11.

Determine the Miller indices of the cubic crystal plane which intersects the

following position coordinates: (1,0,0); (1/2,0,1/2); (0,1/4,1/2).

12.

Calculate the value of the density of FCC lead in grams per cubic centimeter

from its lattice constant aof 0.495 nm and its atomic mass of 207.19 g/mol.

13.What is polymorphism with respect to metals?

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14.Calculate the linear atomic density in atoms per millimeter for the following

directions in FCC aluminum, which has the lattice constant of 0.4049 nm;

a. [100]

b.

[110]

c.

[111]

15.X-rays of an unknown wavelength are diffracted by a silver sample. The angle

of diffraction was 19.9940 for the {200} planes. What is the wavelength of the

X-rays used? (The lattice constant of silver = 0.4086 nm. Assume first order

diffraction; n=1).

16.

An X-ray diffractometer recorder chart for an element which has either the

BCC or the FCC structure showed diffraction peaks at the following

diffraction angles: 44.3900, 64.5780, 81.7170, and 98.1410. (Wavelength of the

incoming radiation was 0.1541 nm.)

a. Determine the crystal structure of the element.

b. Determine the lattice constant of the element.

c. Identify the element.

17.Calculate the equilibrium number of vacancies per cubic meter for copper at

1000 0C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight

and density (at 1000 0C) for copper are 63.5 g/mol and 8.4 g/cm3, respectively.