Materials Engineering – Day 5• Crystallinity in Metals• Types of Metallic Crystals

1. Face-centered cubic (FCC)2. Body-centered cubic (BCC)3. Hexagonal close-packed (HCP)

• Crystalline Imperfections• Dislocations

1. Edge2. Screw3. Mixed

• Relationship of Dislocations and Plasticity

You need to know/be able to

• Describe the difference between amorphous and crystalline and state how that structure affects properties.

• Name the three most common types of unit cells for metals and explain how the unit cell affects properties

• State the relationship of dislocation motion and planar slip on the behavior of metals, and explain how it affects strength and ductility.

Amorphous

• No repeating structure (amorphous is pile of bricks compared to a brick wall (crystalline))

• Must cool very rapidly from the liquid to prevent diffusion or combine a number of incompatible (size,crystal structure, electronegativity) atoms.

• Currently marketed by Liquidmetal http://www.liquidmetal.com/index/ in bulk and Metglas http://www.metglas.com/products in ribbon, but still a niche market.

Crystallinity in Metals• First discovered, using x-ray diffraction, in the

early years of the 1900’s.• The crystallinity of metals is simple. Why?

Strong, non-directional, metallic bonding. (We are not dealing with positive and negative ions of different size.) We are dealing with spheres of about the same size.

• It involves several concepts. Here are two of them.1. The close-packed plane.2. The unit cell.

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Section 3.4 – Metallic Crystal Structures • How can we stack metal atoms to minimize

empty space?2-dimensions

vs.

Now stack these 2-D layers to make 3-D structures

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• Tend to be densely packed.

• Reasons for dense packing:

- Typically, only one element is present, so all atomic radii are the same.- Metallic bonding is not directional.- Nearest neighbor distances tend to be small in order to lower bond energy.- Electron cloud shields cores from each other

• Have the simplest crystal structures.

We will examine three such structures...

Metallic Crystal Structures

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• Coordination # = 8

Adapted from Fig. 3.2, Callister 7e.

(Courtesy P.M. Anderson)

• Atoms touch each other along cube diagonals.

--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.

Body Centered Cubic Structure (BCC)

ex: Cr, W, Fe (), Tantalum, Molybdenum

2 atoms/unit cell: 1 center + 8 corners x 1/8

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Atomic Packing Factor: BCC

a

APF =

4

3 ( 3 a/4 ) 32

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =

Close-packed directions:

3 a

• APF for a body-centered cubic structure = 0.68

aR

Adapted from Fig. 3.2(a), Callister 7e.

a 2

a 3

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• Coordination # = 12

Adapted from Fig. 3.1, Callister 7e.

(Courtesy P.M. Anderson)

• Atoms touch each other along face diagonals.

--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.

Face Centered Cubic Structure (FCC)

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

4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

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• APF for a face-centered cubic structure = 0.74Atomic Packing Factor: FCC

maximum achievable APF

APF =

4

3 ( 2 a/4 ) 34

atoms

unit cell atom

volume

a 3

unit cell

volume

Close-packed directions:

length = 4R = 2 a

Unit cell contains:

6 x 1/2 + 8 x 1/8

= 4 atoms/unit cella

2 a

Adapted fromFig. 3.1(a),Callister 7e.

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A sites

B B

B

BB

B B

C sites

C C

CA

B

B sites

• ABCABC... Stacking Sequence• 2D Projection

• FCC Unit Cell

FCC Stacking Sequence

B B

B

BB

B B

B sites

C C

CA

C C

CA

AB

C

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• Coordination # = 12

• ABAB... Stacking Sequence

• APF = 0.74

• 3D Projection • 2D Projection

Adapted from Fig. 3.3(a), Callister 7e.

Hexagonal Close-Packed Structure (HCP)

6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

• c/a = 1.633

c

a

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

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Theoretical Density,

where n = number of atoms/unit cell A = atomic weight VC = Volume of unit cell = a3 for cubic NA = Avogadro’s number = 6.023 x 1023 atoms/mol

Density = =

VC NA

n A =

Cell Unit of VolumeTotalCell Unit in Atomsof Mass

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• Ex: Cr (BCC) A = 52.00 g/mol R = 0.125 nm n = 2

theoretical

a = 4R/ 3 = 0.2887 nm

actual

aR

= a 3

52.002

atoms

unit cellmol

g

unit cell

volume atoms

mol

6.023 x 1023

Theoretical Density,

= 7.18 g/cm3

= 7.19 g/cm3

Type Name Properties Example

FCC Face-Centered-cubic

Ductile at all temps

Aluminum, copper, Nickel

BCC Body-centered-cubic

ductile-brittle transition with temp or strain rate

Iron (steel) tungsten

HCP Hexagonal-close-packed

less ductile Magnesium, zinc

Overview

Grand Truth - Strengthening in metals

•Yield strength is the onset of plastic flow•Plastic flow results from planar slip•Planar slip results from dislocation motion

Therefore

To increase Strength - Prevent/Impede Dislocation Motion

Ductility Corollary•Impeding dislocation motion makes slip harder•Lower slip means lower ductility

Therefore:

Increasing Strength generally Lowers Ductility

Concept of Slip• Slip in metal crystals is the primary mechanism of

plastic deformation.• Adjacent planes of atoms slip, or move past one

another. This deformation is not recoverable. Atoms have new neighbors. It is plastic deformation.

• A slip system consists of the most close-packed planes in the crystal and the most close-packed directions in that plane.

• Crystallographers have studied the geometry of the crystals and here is the ranking.

Slip Systems and DuctilityMetal Crystalline structure

Rank in terms of slip systems

Typical Metal Typical Ductility

FCC 1 CopperPure and annealed

60%

BCC 2 Iron (very Low carbon steel – hot rolled)

30%

HCP 3 Magnesium (cast) 6%

The basic ductility is going to be tied to the type of crystallinity. But, ductility rises and falls within a material type due to the way the material is processesed. This is a very important lesson!

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• Solidification- result of casting of molten material– 2 steps

• Nuclei form • Nuclei grow to form crystals – grain structure

• Start with a molten material – all liquid

Imperfections in Solids

Adapted from Fig.4.14 (b), Callister 7e.• Crystals grow until they meet each other

nuclei crystals growing grain structureliquid

Imperfections in Crystals• Point imperfections1. Vacancy. Lattice point not occupied by an atom.

Position of nearby atoms slightly affected.2. Impurity atom – substitutional. An atom of

approximately the same size can, and will, be found filling a lattice point. Position of nearby atoms is affected. Eg. Chromium in Iron as in stainless steel.

3. Impurity atom – interstitial. A much smaller atom is dissolved in the unoccupied space in the lattice. Eg. Carbon in iron as in steel.

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• Vacancies:

-vacant atomic sites in a structure.

• Self-Interstitials:

-"extra" atoms positioned between atomic sites.

Point Defects

Vacancydistortion of planes

self-interstitial

distortion of planes

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Two outcomes if impurity (B) added to host (A):

• Solid solution of B in A (i.e., random dist. of point defects)

• Solid solution of B in A plus particles of a new phase (usually for a larger amount of B)

OR

Substitutional solid soln.(e.g., Cu in Ni)

Interstitial solid soln.(e.g., C in Fe)

Second phase particle--different composition--often different structure.

Point Defects in Alloys

Area Imperfections

• The most common area imperfections are grain boundaries. (The grains adhere tightly.)

photomicrograph

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Imperfections in Solids

Fig. 4.3, Callister 7e.

Edge Dislocation

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Imperfections in Solids

Screw Dislocation

Adapted from Fig. 4.4, Callister 7e.

Burgers vector b

Dislocationline

b

(a)(b)

Screw Dislocation

Slip and Dislocation Motion

• It is possible to predict yield strength in perfect crystals. The value is G/5. This would imply yield in iron over 1,000,000 psi. Way too high! The idea that all slip system atoms simultaneously move in plastic deformation is not correct.

• Instead, if you look at a dislocation moving through and producing one unit of slip by it’s motion, the value is about G/180. This agrees with experiment.

• Slip occurs locally by dislocation movement.

Dislocation Motion

• Schematic, and picture of slip in a crystal.

Dislocations

Bubble raft movie

Slip paralled to direction dislocation moves.

More on Dislocations – The screw dislocation.

• Various concepts

Slip produced by a screw dislocatonNotice that slip is perpendicular to

the direction the dislocation moves.

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Imperfections in SolidsDislocations are visible in electron micrographs

Adapted from Fig. 4.6, Callister 7e.