Chapter 3 - Crystalline Structure

Question 1

Crystalline materials are often structures found in…

Answer 1

metals, ceramics, and some polymers

Question 2

What are noncrystalline materials?

Answer 2

atoms that have no periodic packing.

Question 3

What is another term for Noncrystalline?

Answer 3

Amorphous

Question 4

What is a unit cell?

Answer 4

the smallest repeat unit of a crystal structure

Question 5

How many atoms make up a simple cubic, FCC and BCC?

Answer 5

simple → 1 (8 corners)
BCC → 2 (8 corners & one in the middle)
FCC → 4 (6 halves, 8 corners)

Question 6

What is the Atomic packing factor?

Answer 6

The volume of atoms/volume of a unit cell

Question 7

What is the atomic packing factor for simple cubic

Answer 7

π / 6

Question 8

What is the atomic packing factor for BCC?

Answer 8

π / (3 root(3))

Question 9

What is the atomic packing factor for FCC?

Answer 9

3π / 8root(3)

Question 10

to find the a to r value in a simple cubic unit cell

Answer 10

one side length (a) is 2 r

Question 11

to find the a to r value in a BCC unit cell

Answer 11

find the length from one corner, to the farthest corner away (note across the x & y axis is a root(2)

Question 12

to find the a to r value in an FCC unit cell

Answer 12

use the two side lengths b across the face and calculate the hypotenuse using r and a

Question 13

What does this formula mean? what do each of the variables represent?
𝜌 = 𝑛𝐴 / 𝑉 _C 𝑁 _A

Answer 13

n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= 6.022 x 1023 atoms/mol

Question 14

List the densities of metals, ceramics, and Polymers from highest to lowest density.

Answer 14

Metals > ceramics > polymers

Question 15

What are single crystals?

Answer 15

When the periodic arrangement of atoms (crystal structure) extends without interruption throughout the entire specimen.

Question 16

What are polycrystals

Answer 16

Composed of many small crystals
or grains

Question 17

What are the four different steps in the solidification of a polycrystalline material?

Answer 17

1. small crystalline nuclei develop
2. growth of crystallites
3. formation of grains of irregular shapes
4. grain boundaries

Question 18

define Anisotropy?

Answer 18

A given property value depends on the crystallographic direction of measurement.

Question 19

Are polycrystals isotropic or anisotropic when the grains are randomly oriented or if they are textured (preferential crystallographic orientation)?

Answer 19

isotropic, and anisotropic respectively

Question 20

What is Polymorphism?

Answer 20

a material that can have multiple different crystal structures depending on the
conditions it is in (temperature, pressure etc.).

Question 21

What temperatures and crystal structures form in iorn in particular temperatures

Answer 21

> 1538 °C → liquid

1538 - 1394 °C → BCC (δ -Fe)

1394 - 912 °C → FCC (γ -Fe)

< 912 °C → BCC (α -Fe)

oya

Question 22

How to solve a crystallographic Direction problem (5 steps)

Answer 22

1. Determine the coordinates of the vector tail and vector head
2. Take the head coordinates and subtract the tail from them
3. Normalize coordinate differences in terms of lattice parameters a, b, and c:
4. Reduce to integer answers
5. Enclose in square brackets, no commas

Question 23

What is the formula for Linear Density?

Answer 23

number of atoms/unit length of direction vector

Question 24

What is the algorithm used to find the crystallographic planes?

Answer 24

1. Read off intercepts (x, y, z) of plane
2. Take reciprocals of intercepts
3. Reduce to smallest integer values
4. Enclose in parentheses, no commas i.e., (hkl)

Question 25

What is the equation for Planar Density?

Answer 25

atoms centers in a 2D plane / area of a 2D repeat unit

Question 26

What does directional equivalency mean?

Answer 26

that every equivalent direction and plane have the same planar and linear densities.

Question 27

What is the unit cell edge length for a face-centered cubic in terms of R?

Answer 27

a = 4R / root(2)

Question 28

What is the unit cell edge length for a body-centred cubic in terms of R?

Answer 28

a = 4R / Root(3)

Question 29

What is this formula?
p = N A / (V_C N_A

What are the terms in it?

Answer 29

p = density
n = number of equivalent atoms in a unit cell
A - atomic wieght
V_C = Volume of a unit cell (always a³)
N_A = Avogadro’s number 6.022 * 10²³

Question 30

How can you tell if something is isotropic or anisotropic?

Answer 30

if they have particular grains that run across the structure in an organized way (anisotropic) or are made of just one material (anisotropic). If the grains are random, or there is a ton of different metals inside, it is more likely to be isotropic.

Question 31

Would a polycrystal or single crystal have more isotropic properties? Why?

Answer 31

A polycrystal would have more isotropic properties because of the random orientation of the ton of anisotropic grains. Whereas different loads on the same unit cells (which are mostly not isotropic) in a single crystal would not balance out, but magnify instead.

Question 32

How would a material being a polycrystal change its real density compared to its theoretical
density?

Answer 32

the theoretical density would be higher, as the crystals are not as closely packed together on the grain boundaries.

Question 33

Rate the following structures from most to least ordered (Crystalline, polycrystalline, and Amorphous)

Answer 33

Crystalline, polycrystalline, and Amorphous.

Question 34

Describe what type of notation is nessesary around the indices of these following terms: Point, direction, family of directions, plane, and family of planes

Answer 34

point → 123
direction → [123]
family of directions → <123>
plane (123)
family of planes {123}

Question 35

When counting atoms centred in a plane which atoms do you count?

Answer 35

How many atoms are in the plane,

Question 36

When counting equivalent atoms centred in a plane which atoms do you count?

Answer 36

The portion of the atom inside the plane, excluding the part that would be cut off at the edges

Question 37

Define a maximally dense (or close-packed) plane/direction.

Answer 37

Plane/direction has no void space.

Question 38

Does it matter what side you draw the arrow in a direction?

Answer 38

no, while they might have different directions their magnitudes are the same.

Question 39

What is the Volume of a sphere?

Answer 39

4/3 π r^3