Chapter 3 Problems

Question 1

everything on Simple Cubic (SC)

Answer 1

number of atoms: 1
coordination #: 6
side length: 2R
Vc: 8R^3
Vs: (4/3) Pi R^3
Atomic Density: 1/ (8R^3)
APF: 0.5235
Void Fraction: 0.4765

Question 2

everything on Body Centered Cubic (BCC)

Answer 2

number of atoms: 2
coordination #: 8
side length: 4R/√3
Vc: (64/3√3) R^3
Vs: (8/3) Pi R^3
Atomic Density: 3√3/32R^3
APF: 0.6802
Void Fraction: 0.3198

Question 3

everything on Face Centered Cubic (FCC)

Answer 3

number of atoms: 4
coordination #: 12
side length: 4R/√2
Vc: 16√2R^3
Vs: (16/3) Pi R^3
Atomic Density: 1/ (4√2R^3)
APF: 0.7405
Void Fraction: 0.2595

Question 4

APF Forumla

Answer 4

Volume of atoms in
Unit Cell
APF= ——————————-
Volume of unit
Cell

example: (FCC)
(4)(4/3 PI (R)^3)
APF = ————————
(a)^3

Question 5

Void Fraction Forumla

Answer 5

1-APF

Question 6

Density Variables

Answer 6

n = number of atoms
A = atomic weight
Vc = a^3
Na = Avogadro’s Number

Question 7

Isotropy

Answer 7

independent of direction of measurement

Question 8

Anisotropy

Answer 8

Direction Dependent of properties

Question 9

Direction

Answer 9

• Use head - tail
• square brackets

Question 10

Planes

Answer 10

• read off intercepts
• take reciprocal
• curved brackets

Question 11

Polycrystals

Answer 11

• why theoretical and actual density are different
• where grain boundaries come from

Question 12

Linear Density Forumla

Answer 12

Number of atoms on vector
LD= ———————————
length of vector
(length of vector: 4R = √2a, only use √2a)

Question 13

Planar Density Forumla

Answer 13

Number of atoms on plane
PD = ——————————-
(a)^2