C6-Defects in Solid.pptx

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TM 6

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ISSUES TO ADDRESS...

• What types of defects arise in solids?

• Can the number and type of defects be varied and controlled?

• How do defects afect material properties?

• Are defects undesirable?

Defects in Solids

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Why Study Imperfection in Solids?

1. Properties of Materials are profoundly

influenced by the presence of imperfection

2. Mechanical properties of metals

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• _{Solidifcation}

- 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

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Polycrystalline Materials

Grain Boundaries

• _{regions between crystals}

• _{transition from lattice of}

one region to that of the

other

• _{slightly disordered}

• _{low density in grain}

boundaries

– _{high mobility} – high difusivity

– high chemical reactivity

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Solidifcation

Columnar in

area with less

undercooling

Shell of

equiaxed

grains due to

rapid cooling

(greater



T

)

near wall

heat

flow

Grains can be

- equiaxed (roughly same size in all

directions)

- columnar (elongated grains)

Adapted from Fig. 4.12, Callister 7e.

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Imperfections in Solids

There is no such thing as a perfect

crystal.

• _{What are these imperfections?}

• _{Why are they important?}

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• Vacancy atoms

• Interstitial atoms

• Substitutional atoms

Point defects

Types of Imperfections

• Dislocations

Line defects

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• Vacancies:

-vacant atomic sites in a structure.

• Self-Interstitials:

-"extra" atoms positioned between atomic sites.

Point Defects

Vacancy

distortion

of planes

self-interstitial

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Boltzmann's constant

No. of defects

No. of potential defect sites.

Activation energy

Temperature

Each lattice site is a potential

vacancy site

• Equilibrium concentration varies with temperature!

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• We can get Q_v from

Measuring Activation Energy

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• Find the equil. # of vacancies in 1 m3_{of Cu at 1000}_C.

• Given:

A _{Cu = 63.5 g/mol}

r = 8.4 g / cm 3

Q v = 0.9 eV/atom N _{A = 6.02 x 10}23 atoms/mol

Estimating Vacancy Concentration

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• Low energy electron

Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in

Solids and the Stability of Surface Morphology", Nature, Vol. 412, pp. 622-625 (2001). Image is 5.75 mm by 5.75 mm.) Copyright (2001) Macmillan Publishers, Ltd.

Observing Equilibrium Vacancy Conc.

I

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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

--diferent

composition

--often diferent structure.

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Imperfections in Solids

Conditions for substitutional solid

solution (S.S.)

• _{W. Hume – Rothery rule}

–

_1.



r

(atomic radius) < 15%

–

_{2. Proximity in periodic table}

• i.e., similar electronegativities

–

_{3. Same crystal structure for pure metals}

–

_{4. Valency}

• _{All else being equal, a metal will have a greater}

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Imperfections in Solids

Application of Hume–Rothery rules – Solid

Solutions

1. Would you predict

more Al or Ag

to dissolve in Zn?

2. More Zn or Al

in Cu?

Table on p. 106, Callister 7e.

Element Atomic Crystal Electro- Valence Radius Structure

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Imperfections in Solids

• _{Specifcation of composition}

–

weight percent

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• are line defects,

• slip between crystal planes result when dislocations

move,

• produce permanent (plastic) deformation.

Dislocations

:

Schematic of Zinc (HCP):

• before deformation

• after tensile elongation

slip steps

Line Defects

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Imperfections in Solids

Linear Defects (

Dislocations

)

–

_{Are one-dimensional defects around which atoms are}

misaligned

• Edge dislocation:

–

_{extra half-plane of atoms inserted in a crystal}

structure

–

b



to dislocation line

• Screw dislocation:

–

_{spiral planar ramp resulting from shear deformation}

–

b



to dislocation line

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Imperfections in Solids

Fig. 4.3, Callister 7e.

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• Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). • Bonds across the slipping planes are broken and remade in succession.

Atomic view of edge dislocation motion from left to right as a crystal is sheared.

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Imperfections in Solids

Screw Dislocation

Adapted from Fig. 4.4, Callister 7e.

Burgers vector

b

Dislocation line

b

(a)

(b)

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Edge, Screw, and Mixed Dislocations

Edge

Screw

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Imperfections in Solids

Dislocations are visible in electron

micrographs

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Dislocations & Crystal Structures

• Structure: close-packed

planes & directions are preferred.

view onto two close-packed planes.

close-packed plane (bottom)

close-packed plane (top)

close-packed directions

• Comparison among crystal structures:

FCC: many close-packed planes/directions;

HCP: only one plane, 3 directions;

BCC: none

• Specimens that were tensile

tested.

Mg (HCP)

Al (FCC)

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Planar Defects in Solids

•One case is a twin boundary (plane)

–Essentially a reflection of atom positions across the twin plane.

•Stacking faults

–For FCC metals an error in ABCABC packing sequence

–Ex: ABCABABC

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Dislocations & Materials Classes

• Covalent Ceramics

(Si, diamond): Motion hard.

-directional (angular) bonding

• Ionic Ceramics (NaCl):

Motion hard.

• Metals: Disl. motion easier.

-non-directional bonding

-close-packed directions

for slip.

electron cloud

ion cores

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Dislocation Motion

Dislocations & plastic deformation

• _{Cubic & hexagonal metals - plastic}

deformation by

plastic shear or slip

where one

plane of atoms slides over adjacent plane by

defect motion (dislocations).

• _{If dislocations don't move,}

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Dislocation Motion

• _{Dislocation moves along}

_{slip plane}

_in

_slip

direction

perpendicular to dislocation line

• _{Slip direction same direction as}

_{Burgers vector}

Edge dislocation

Screw dislocation

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Slip System

–

_{Slip plane}

_{- plane allowing easiest slippage}

• Wide interplanar spacings - highest planar densities

–

_{Slip direction}

_{- direction of movement -}

Highest

linear densities

–

_{FCC Slip occurs on {111} planes (close-packed) in}

<110> directions (close-packed)

=> total of 12 slip systems in FCC

Deformation Mechanisms

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 Stress has units:

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Elastic means reversible!

Elastic Deformation

1. Initial 2. Small load 3. Unload

F

d

bonds

stretch

return to

initial

F

d

Linear-

elastic

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Plastic means permanent!

Plastic Deformation (Metals)

F

d

linear

elastic linear elastic

1. Initial 2. Small load 3. Unload

p lanes still

sheared

F

d _{elastic + plastic}

bonds stretch

& planes shear

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(at lower temperatures, i.e.

T

<

T

melt

/3)

Plastic (Permanent) Deformation

• Simple tension test:

engineering stress,

s

engineering strain,

e

Elastic+Plastic

at larger stress

permanent (plastic)

after load is removed

e

_p

plastic strain

Elastic

initially

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Stress and Dislocation Motion

• Crystals slip due to a resolved shear stress, t_R. • Applied tension can produce such a stress.

slip plane normal, ns

Resolved shear

stress:

t

_R

=

_Fs

/

_As

Relation between

s

and

t

_R

Applied tensile

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Microscopic Examination

• _{Crystallites (grains) and grain}

boundaries. Vary considerably in size.

Can be quite large

–

_{ex: Large single crystal of quartz or}

diamond or Si

–

_{ex: Aluminum light post or garbage can -}

see the individual grains

• _{Crystallites (grains) can be quite small}

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• Useful up to 2000X magnifcation.

• Polishing removes surface features (e.g., scratches) • Etching changes reflectance, depending on crystal orientation.

Micrograph of

brass (a Cu-Zn alloy)

Optical Microscopy

Adapted from Fig. 4.13(b) and (c),

Callister 7e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co.

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Grain boundaries...

• are imperfections,

• are more susceptible

to etching,

and (b), Callister 7e.

(Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology,

Gaithersburg, MD].)

Optical Microscopy

ASTM grain size number

N = 2n -1

number of grains/in2

at 100x

Fe-Cr alloy

(b)

grain boundary

surface groove

polished surface

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Optical Microscopy

• _{Polarized light}

–

_{metallographic scopes often use}

polarized light to increase contrast

–

_{Also used for transparent samples}

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Microscopy

Optical resolution ca. 10

-7

m = 0.1

_

m = 100

nm

For higher resolution need higher frequency

–

_{X-Rays? Difcult to focus.}

–

_Electrons

• _{wavelengths ca. 3 pm (0.003 nm)}

–

_{(Magnifcation - 1,000,000X)}

• _{Atomic resolution possible}

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• Atoms can be arranged and imaged!

Carbon monoxide

molecules

arranged on a

platinum (111)

surface.

Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler.

Reprinted with permission from International

Business Machines Corporation,

Iron atoms

arranged on a

copper (111)

surface. These

Kanji characters

represent the word

“atom”.

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• Point, Line, and Area defects exist in solids.

• The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.)

• Defects afect material properties (e.g., grain boundaries control crystal slip).

• Defects may be desirable or undesirable

(e.g., dislocations may be good or bad, depending

on whether plastic deformation is desirable or not.)

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R

e

fe

re

n

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ISSUES TO ADDRESS...

•

What types of defects arise in solids? Calculate equilibrium

number of Vacancy and interstitial crystalline defects

• Name two types of dsolid solution, and provide a brief written defition and /or schemamtic