CHAPTER 5:IMPERFECTIONS IN SOLIDSIMPERFECTIONS IN SOLIDS

ISSUES TO ADDRESS...

• What types of defects arise in solids?• What types of defects arise in solids?

• Can the number and type of defects be variedd t ll d?and controlled?

• Are defects undesirable?

• How do defects affect material properties?

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TYPES OF IMPERFECTIONS

• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects

• Dislocations Line defects

• Grain Boundaries Area defects

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POINT DEFECTS• Vacancies:

-vacant atomic sites in a structure.

Vacancydistortion of planesof planes

• Self-Interstitials:-"extra" atoms positioned between atomic sites.

self-interstitialdistortion

of planes

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EQUIL. CONCENTRATION:POINT DEFECTS

• Equilibrium concentration varies with temperature!

POINT DEFECTS

⎛ ⎞ No. of defects Activation energy

⎜ ⎟ NDN

= exp−QDkT

⎛

⎝ ⎜ ⎞

⎠ ⎟ No. of potential Temperature

Boltzmann's constant

(1.38 x 10-23 J/atom K)

No. of potential defect sites.

Temperature

(8.62 x 10-5 eV/atom K)Each lattice site

is a potential

Chapter 4-Department of Materials Engineering at Isfahan University of Technology

is a potential vacancy site

4

MEASURING ACTIVATION ENERGY

• We can get Q from ⎜ ⎟ ND = exp−QD

⎛

⎝⎜ ⎞

⎠⎟ an experiment.⎜ ⎟

Nexp

kT⎝ ⎜ ⎠ ⎟

• Measure this... • Replot it...

N

NDln 1

slopeND

N N-QD/k

N

exponential dependence!

1/TT

dependence!

defect concentration

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defect concentration

ESTIMATING VACANCY CONC.

Example: Find the equil. # of vacancies in 1m3 of Cu at 1000C.

• Given:• Given:ACu = 63.5g/molρ = 8.4 g/cm3

QV = 0 9eV/atom NA = 6 02 x 1023 atoms/moleQV = 0.9eV/atom NA = 6.02 x 10 atoms/mole

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POINT DEFECTS IN ALLOYS

Two outcomes if impurity (B) added to host (A):1. Solid solution of B in A (i.e., random dist. of point defects)

OR

Substitutional alloy(e g Cu in Ni)

Interstitial alloy(e g C in Fe)

2. Solid solution of B in A plus particles of a newphase (usually for a larger amount of B)

(e.g., Cu in Ni) (e.g., C in Fe)

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

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ALLOYING A SURFACE

• Low energy electronmicroscope view ofa (111) surface of Cu.

• Sn islands move alongthe surface and "alloy"the surface and alloythe Cu with Sn atoms,to make "bronze".

Th i l d ti ll• The islands continuallymove into "unalloyed"regions and leave tiny

R i t d ith i i f A K S h id bronze particles •

Eventually, the islandsdisappear.

Reprinted with permission from: A.K. Schmid, N.C. Bartelt, and R.Q. Hwang, "Alloying at Surfaces by the Migration of Reactive Two-Dimensional Islands", Science, Vol. 290, No. 5496, pp. 1561-64 (2000). Field of view is 1.5 μm and the temperature is 290K

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disappear. μm and the temperature is 290K.

LINE DEFECTS

• are line defects,• cause slip between crystal plane when they move,

Dislocations:

cause slip between crystal plane when they move,• produce permanent (plastic) deformation.

S h ti f Zi (HCP)Schematic of a Zinc (HCP):• before deformation• after tensile elongation

slip steps

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Edge Dislocation

• Due to extra plane or half plane of atoms

Burgers vector is perpendicular to the dislocation line • The dislocation line (the moving red dot)...

...separates slipped material on the leftfrom unslipped material on the right.

Simulation of dislocationmotion from left to right

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as a crystal is sheared.

BOND BREAKING AND REMAKING

• Dislocation motion requires the successive bumpingof a half plane of atoms (from left to right here).

• Bonds across the slipping planes are broken and• Bonds across the slipping planes are broken andremade in succession.

Atomic view of edgedislocation motion fromleft to right as a crystalleft to right as a crystalis sheared.

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(Courtesy P.M. Anderson)

Screw Dislocation

The upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion

Burgers vector is parallel to the dislocation line

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Burgers vector is parallel to the dislocation line

Screw Dislocation

The upper front region of the crystal is shifted one atomic distance to the right relative to thedistance to the right relative to the bottom portion

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Dislocations

All crystal materials contain some dislocations

Dislocations introduce during:S lidifi ti• Solidification

• Plastic deformation• Thermal stresses from rapid cooling

A Transmission Electron Micrograph of a Ti alloy

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x 51,450

AREA DEFECTS: GRAIN BOUNDARIES

Grain boundaries:• are boundaries between crystals.• are produced by the solidification process, for example. are produced by the solidification process, for example.• have a change in crystal orientation across them.• impede dislocation motion.

Schematic ~ 8cmMetal Ingot

Schematic 8cm

heat flow

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flowAdapted from Fig. 4.7, Callister 6e.

Adapted from Fig. 4.10, Callister 6e. (Fig. 4.10 is from Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985.)

OPTICAL MICROSCOPY (1)

• Useful up to 2000X magnification.• Polishing removes surface features (e.g., scratches)• Etching changes reflectance depending on crystal• Etching changes reflectance, depending on crystal

orientation.microscope

close-packed planesAdapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesyof J.E. Burke, General Electric Co.

micrograph ofBrass (Cu and Zn)

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Grain boundaries

OPTICAL MICROSCOPY (2)

microscope

Grain boundaries...

• are imperfections,• are more susceptible

surface groove

polished surface

pto etching,

• may be revealed asdark lines,

grain boundarydark lines,

• change direction in apolycrystal.

Adapted from Fig. 4.12(a) Adapted from Fig. 4.12(a) and (b), Callister 6e.(Fig. 4.12(b) is courtesyof L.C. Smith and C. Brady, the National Bureau of Standards,

ASTM grain size number

N = 2 n-1

Fe-Cr alloyWashington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

N = 2 n 1

no. grains/in 2 at 100x

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magnification

SUMMARY

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

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

• Defects affect material properties (e.g., grainboundaries control crystal slip).

• Defects may be desirable or undesirable(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)p )

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