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Materials Moments:

Rich W.—Cooking Surfaces
Vanessa P. & Shelby R.—Flat Irons

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Dear Prof,
You said that this clicker trial is not going to count against our grades in the class, but it seems like it is counting against my grade.

A: Once students have had the chance to confirm that they are using their clickers correctly, I will remove the trial scores. (By the end of this week.)

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A: Whenever you are delayed with your clicker, during my countdown, just raise your hand or shout (nicely) “Wait!” and I will gladly wait a few moments for you.

Today clickers count toward your grade

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Family of Directions: <1 1 0>

Unit cube

1= [1 1 0]

4

3

1

2

5

5 = [1 1 0]

4 = [1 1 0]

2 = 3= [1 1 0]

y

x

z

p_pg44

  • Structurally equivalent

  • Atomic packing is equivalent

Family of Directions: <1 1 0>

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p_pg44.jpg

f07_03_pg54

[a1 a2 a3 z]

Vector:

[1 0 0 1]

Hexagonal

Crystallographic directions

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f07_03_pg54.jpg

Other Directions

[ 1 1 0]

[ 1 0 2]

[ 1 1 1]

[ 2 1 1]

[ 2 1 1]

[ 0 0 1]

[ 1 0 1]

Section 3.10
Crystallographic Planes:

Miller Indices

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Crystallographic Planes

Steps to finding Miller indices:

1) Translate plane away from origin or axis

2) Find length of planar intercept:
(x = a; y = b; z = c)

3) Take reciprocal of a, b, c

4) Find smallest equivalent integer set

5) Notation: (h k l)

Examples

1

2

3

z

x

y

Families of Planes:
All parallel planes are equivalent

Families of Planes

(100)

(010)

(001)

{100}

{010}

{001}

Family of Planes MI: (X Y Z)

Structurally equivalent planes: {X Y Z}

Hexagonal Crystallographic planes:
The basal plane

Other Planes:

( 1 2 3)

(0 0 1)

(0 1 1)

(1 1 2)

(2 0 1)

(1 0 1)

Notation Summary

Solved Examples posted on Canvas:

Files>Assignments, Homework, Extra Credit

Packing and Close-packed Planes

Close-packed Xl Structures

  • FCC & HCP—APF = .74
  • Most efficient packing

for equal-sized spheres.

  • BCC—APF = .68
  • Not as efficient

BCC: Which is the closest-packed plane?

z

z

A)

B)

C)

D)

z

x

y

y

x

z

y

x

y

x

Figs. 3.11, 3.12

f10_03_pg58

(110) plane packing

  • FCC

  • BCC

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f10_03_pg58.jpg

Different Packing…
So What?

Packing along planes:

  • Strongly affects deformation
  • Atoms can slip past each other on tightly packed planes (plastic deformation).

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f11_03_pg59.jpg

Figs. 3.11, 3.12

f10_03_pg58

(110) plane packing

  • FCC

  • BCC

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f10_03_pg58.jpg

SEM {100} planes

SEM single cadmium crystal deforming by dislocation slip on {100} planes.

SEM study of slip in deformed cadmium single crystal

Sections 3.13-3.15

Single Crystals
Polycrystalline Materials
Anisotropy

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Terms

  • Crystalline
  • Crystal structure
  • Crystal lattice
  • Single crystal
  • Polycrystalline

Crystal lattice:

http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Lattices-and-Unit-Cells-837.html

Unit Cell

Crystal Lattice

Long-range 3-D representation of a crystal

Specific location for each atom

Single Crystals

Crystal structure repeats perfectly over large atomic distance

Galena (Lead ore)

Polycrystalline materials

Many small crystals grow together

Polycrystalline materials

Extremely small crystals grow together.

Fig. 3.18

f17_03_pg65

Polycrystalline grain growth

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f17_03_pg65.jpg

Polycrystalline CaC03 (Calcite)
Thin Section

Anisotropy
Properties dependent on
crystallographic direction

Isotropy

Properties independent of crystallographic direction.

Polycrystalline copper (SEM)

SiO2 Thin section

Isotropy

Properties independent of crystallographic direction.

Thin section of schist

Anisotropy

  • Properties differ according to direction.

  • Atomic structure influential.

Random orientations of anisotropic material
yield isotropic behavior

Polycrystalline Calcite

Metal Thread Anisotropy

Section 3.17

Non-Crystalline Solids

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Non-Crystalline Solids

  • Amorphous—without ordered form.

  • Formed by rapid cooling from a melt

Non-crystalline solids

www.msm.cam.ac.uk

Hand sample of fractured glass

SEM of fractured glass

Glass: SiO2

(Glassy texture)

Fig. 3.23

f22_03_pg71

Crystalline SiO2

Non-Crystalline SiO2

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f22_03_pg71.jpg

Ancillary Materials

Notation Summary

  • Crystallographic directions:
  • Vectors: [x y z]
  • Families: <x y z>

  • Crystallographic planes:
  • Planes: (h k l)
  • Family of planes: {h k l}

Terms

  • Crystalline—regular repeating order over a long atomic distance

  • Crystal structure–shape of atomic arrangement

  • Crystal lattice–more specific–specified location expected for each atom or molecule.

  • Single crystal–Crystal structure repeats perfectly over large atomic distance.

  • Polycrystalline–Crystalline material having more than one crystal or grain.

Crystal lattice

The organization of atoms—allows for a specific place for every molecule or atom in the solid.

  • Crystal Structure–more general—how atoms

(or ions, or molecules)

are spatially arranged.

  • Crystal structures are unique to each material.

Crystallographic Planes

  • All parallel planes are equivalent.

  • Steps to finding Miller indices:

1) Translate plane away from origin or axis

2) Find length of planar intercept:

(x = a; y = b; z = c)

3) Take reciprocal of a, b, c

4) Find smallest equivalent integer set

5) Notation: (h k l)

Metallic xl Structures

Face-Centered Cubic (FCC)

Cu, Al, Ag, Au, Pb, Ni, Pt

Body-Centered Cubic (BCC)

Na, Fe, Cr, Mo, W

Hexagonal Close-Packed (HCP)

Ti, Zn, Cd, Co, Mg