Calculate the radius of vanadium atom

Engineering Materials

Homework Ch 3

1. If the atomic radius of chromium is 0.125 nm, calculate the volume of its unit cell in cubic

meters.

2. Show for the face-centered cubic crystal structure that the unit cell edge length (a) and the

atomic radius (R) are related through a = 4R/(2) 1/2

.

3. Show that the atomic packing factor for the simple cubic structure is 0.52.

4. Tungsten has a BCC crystal structure, an atomic radius of 0.137 nm, and an atomic weight of

183.84 g/mol. Calculate and compare its theoretical density with the experimental value found

inside the front cover of your text book.

5. Calculate the radius of an iridium atom, given that Ir has an FCC crystal structure, a density of

22.4 g/cm 3 , and an atomic weight of 192.2 g/mol.

6. Calculate the radius of a vanadium atom, given that vanadium has a BCC crystal structure, a

density of 5.96 g/cm 3 , and an atomic weight of 50.9 g/mol.

7. Some hypothetical metal has the simple cubic crystal structure shown in Figure 3.23. If its

atomic weight is 70.4 g/mol and the atomic radius is 0.126 nm, calculate its density.

8. Below are listed the atomic weight, density, and atomic radius for three hypothetical alloys.

For each determine whether its crystal structure is FCC, BCC, or simple cubic and then justify

your answer.

Alloy Atomic weight Density Atomic radius

(g/mol) (g/cm 3 ) (nm)

A 195.08 21.45 0.139

B 209 9.32 0.335

C 55.85 7.87 0.124

9. What are the indices for the directions indicated by the two vectors in the following sketch?

10. Within a cubic unit cell, sketch the following directions:

(a)



[1 10], (e)



[1 1 1] ,

(b)



[1 2 1], (f)



[1 22],

(c)



[01 2], (g)



[12 3 ],

(d)



[13 3], (h)



[1 03].

11. Determine the indices for the directions shown in the following cubic unit cell:

12. Determine the indices for the directions shown in the following cubic unit cell:

13. Sketch within a cubic unit cell the following planes:

(a)



(01 1 ) , (e)



(1 11 ) ,

(b)



(112 ) , (f)



(12 2 ) ,

(c)



(102 ) , (g)



(1 23 ),

(d)



(13 1) , (h)



(01 3 )

14. Determine the Miller indices for the planes shown in the following unit cell:

15. Determine the Miller indices for the planes shown in the following unit cell:

16. Determine the Miller indices for the planes shown in the following unit cell: