Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical...

24
Chapter 3 - Kryptonian Data Crystals 1

Transcript of Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical...

Page 1: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -Kryptonian Data Crystals

1

Page 2: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Crystal System Review

Property SC FCC BCC HCP# atoms/cell 1 4 2 6

Lattice Parameter

a,c

Coordination # 6 12 8 12

APF 0.52 0.74 0.68 0.74

2

Page 3: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

VOLUME DENSITY

3

Page 4: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 4

Theoretical Density, ρ

where n = number of atoms/unit cellA = atomic weight (g/mol) VC = Volume of unit cell = a3 for cubicNA = Avogadro’s number

= 6.022 x 1023 atoms/mol

Density = ρ =

VC

n Aρ =

CellUnitofVolumeTotalCellUnitinAtomsofMass

Book Section 3.5

How much stuffHow much spaceNA

Page 5: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 5

• Ex: CrA = 52.00 g/molR = 0.125 nmn = 2 atoms/unit cell

ρtheoretical

a = 4R/ 3 = 0.2887 nm

ρactual

aR

ρ = a3

52.002atoms

unit cell molg

unit cellvolume atoms

mol

6.022 x 1023

Theoretical Density, ρ

= 7.18 g/cm3

= 7.19 g/cm3

Adapted from Fig. 3.2(a), Callister & Rethwisch 8e.

(BCC)

Book Section 3.5

Table 3.1Back of book

Page 6: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

So what

• When you sinter a ceramic, you have pores, which make it less dense

• You can compare manufactured density to theoretical density for process quality

6http://www.additivalab.com/en/blog/laser-sintering-vs-laser-melting/ DOI: 10.1016/j.matlet.2015.12.042

Page 7: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 7

Densities of Material Classesρmetals > ρceramics > ρpolymers

Why?

Data from Table B.1, Callister & Rethwisch, 8e.

ρ(g

/cm

)3

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

1

2

20

30Based on data in Table B1, Callister

*GFRE, CFRE, & AFRE are Glass,Carbon, & Aramid Fiber-ReinforcedEpoxy composites (values based on60% volume fraction of aligned fibers

in an epoxy matrix).10

345

0.30.40.5

Magnesium

Aluminum

Steels

Titanium

Cu,NiTin, Zinc

Silver, Mo

TantalumGold, WPlatinum

GraphiteSiliconGlass -sodaConcrete

Si nitrideDiamondAl oxide

Zirconia

HDPE, PSPP, LDPEPC

PTFE

PETPVCSilicone

Wood

AFRE*CFRE*GFRE*Glass fibers

Carbon fibersAramid fibers

Metals have...• close-packing

(metallic bonding)• often large atomic masses

Ceramics have...• less dense packing• often lighter elements

Polymers have...• low packing density

(often amorphous)• lighter elements (C,H,O)

Composites have...• intermediate values

In general

Book Section 3.5

Page 8: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Crystallographic planes are typically identified with which of the following:

A. Direction indicesB. Planar DirectionsC. Miller Indices

8

Page 9: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

The direction of the red arrow is:

A. [1 0 0]B. <1 0 1>C. <1 1 1>D. [1 1 0]E. [1 1 1]

9

Page 10: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Which of the following has the highest atomic packing factor (APF)?(Give me your best answer)

A. Simple CubicB. FCCC. BCCD. HCP

10

Page 11: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Select the correct set of indices for this plane

A. (211)B. (213)C. (332)D. (201)E. (110)

11

Page 12: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Crystal Coordinates, Directions, Planes

• How can we identify crystal coordinates, directions, and planes?– Or how we talk a common language about

crystals

12

Page 13: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

POINTS

13

Page 14: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 14

Point CoordinatesPoint coordinates for unit cell

center area/2, b/2, c/2 ½ ½ ½

Point coordinates for unit cell corner are 111

z

x

ya

b

c

000

111

Book Section 3.8

Page 15: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

DIRECTIONS

15

Page 16: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 16

Crystallographic Directions

1. Vector repositioned (if necessary) to pass through origin.

2. Read off projections in terms of unit cell dimensions a, b, and c

3. Adjust to smallest integer values4. Enclose in square brackets, no commas

[uvw]

families of directions <uvw>

ex: 1, 0, ½ 2, 0, 1 [201 ]

-1, 1, 1

z

x

Algorithm

where overbar represents a negative index

[111 ]

y

Book Section 3.9

× 2

Page 17: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

PLANES(MILLER INDICES)

17

Page 18: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 18

Crystallographic Planes• Miller Indices: Reciprocals of the (three) axial

intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices.

• Algorithm1. Read off intercepts of plane with axes in

terms of a, b, c2. Take reciprocals of intercepts3. Reduce to smallest integer values4. Enclose in parentheses, no commas i.e., (hkl)

Book Section 3.10

(100) (110) (111)Why?(FCC)

z

x

ya b

c

Page 19: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 19

Crystallographic Planesz

x

ya b

c

4. Miller Indices (110)

example a b cz

x

ya b

c

4. Miller Indices (100)

1. Intercepts 1 1 ∞2. Reciprocals 1/1 1/1 1/∞

1 1 03. Reduction 1 1 0

1. Intercepts 1/2 ∞ ∞2. Reciprocals 1/½ 1/∞ 1/∞

3. Reduction 1 0 0

example a b c

Book Section 3.10

2 0 0

Page 20: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 20

Crystallographic Planesz

x

ya b

c

4. Miller Indices (634)

example1. Intercepts 1/2 1 3/4

a b c

2. Reciprocals 1÷½ 1÷1 1÷¾

3. Reduction 6 3 4

(001)(010),

Family of Planes {hkl}

(100), (010),(001),Ex: {100} = (100),

Book Section 3.10

2 1 4/3

Page 21: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 21

Crystallographic Planes

Adapted from Fig. 3.10, Callister & Rethwisch 8e.

Book Section 3.10

Page 22: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Summary

• Points– 111

• Directions– [111]– Families <111>

• Will be used in Ch 7

• Planes– (111)– Families {111}

• Will be used in Ch 722

z

x

ya b

c

z

x

ya b

c

Page 23: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 - 23

Crystallographic Planes (HCP)• In hexagonal unit cells the same idea is used

example a1 a2 a3 c

4. Miller-Bravais Indices (1011)

1. Intercepts 1 ∞ -1 12. Reciprocals 1 1/∞

1 0 -1-1

11

3. Reduction 1 0 -1 1a2

a3

a1

z

Adapted from Fig. 3.8(b), Callister & Rethwisch 8e.

Book Section 3.10

Page 24: Chapter 3 - 1mjm82/che378/Fall2019/LectureNotes/... · 2019-09-17 · Chapter 3 - 4 Theoretical Density, ρ where n = number of atoms/unit cell. A = atomic weight (g/mol) . V C =

Chapter 3 -

Bigger Picture

• Classifying crystals– Metrics ✔– Planes/directions ✔– Densities

• Real Materials– Single/Polycrystal– Anisotropy– Characterization

24

(100)(111)