Within a cubic unit cell sketch the following directions

Homework Set 2

Chapter 3: [1pt each problem]

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

image1.wmf

[

1

10

]

,
image2.wmf

[

1

2

1

]

,
image3.wmf

[

0

1

2

]

,
image4.wmf

[

1

2

3

]

,
image5.wmf

[

1

03

]

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

image6.png

3. What are the indices for the two planes in the following sketch?

image7.png

4. Within a cubic unit cell, sketch the following planes:

image8.wmf

(

0

1

1

)

,
image9.wmf

(

1

1

1

)

,
image10.wmf

(

11

2

)

,
image11.wmf

(

1

2

2

)

,
image12.wmf

(

10

2

)

image13.wmf

(

1

2

3

)

,
image14.wmf

(

1

3

1

)

,
image15.wmf

(

0

1

3

)

5. Determine the Miller indices for the planes in the following cubic unit cells.

image16.png image17.png

Plane A = (403) Plane A =

image18.emf
€

(32 4)

(32 4)

Plane B =

image19.emf
€

(1 1 2)

(1 1 2)

Plane B = (221)
6. Sketch the planar cross section for the following planes in the FCC structure (label the edge lengths in terms of a and R):

a. (001)

b. (011)

c. (111)

Now calculate the planar densities for the three planes above (do so in terms of both atoms/nm2 AND the dimensionless quantity)

7. Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. Compute and compare its theoretical density with the experimental value found inside the front cover of the book.

8. On the basis of ionic charge and ionic radii given in Table 3.4, predict crystal structures for the following materials:

a. CsI

b. NiO

c. KI

d. NiS

9. Compute the atomic packing factor for the rock salt crystal structure in which rC/rA = 0.414.

10. Magnesium oxide has the rock salt crystal structure and a density of 3.58 g/cm3.

e. Determine the unit cell edge length.

f. How does this result compare with the edge length as determined from the radii in Table 3.4, assuming that the Mg2+ and O2- ions just touch each other along the edges?

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