Chapter+4+ +Imperfections+in+Crystals

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IMPERFECTION S

(DEFECTS) IN SOLIDS



ISSUES TO ADDRESS...

• What types of defects arise in solids?

• Can the number and type of defects be varied

and controlled?

• How do defects affect material properties?

• Are defects undesirable?

IMPERFECTIONS (DEFECTS) IN SOLIDS



Defects in Crystals

• Introduction

• What is a defect?

• Types of defects in crystals

• Why are defects important?



Defects in Crystals

• Point Defects

• Linear Defects

• Planar Defects: Surfaces and Grain

Boundaries

• Volumetric Defects: Precipitates and

Inclusions



• Vacancy atoms• Interstitial atoms

• Substitutional atoms

• Dislocations

• Grain Boundaries

• Precipitates/inclusions

Point defectsLine defects

Area defectsVolume defects

TYPES OF IMPERFECTIONS



• Vacancies: -vacant atomic sites in a structure.

Vacancydistortionof planes

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

self-interstitialdistortionof planes

POINT DEFECTS



Crystal Defects

Schottky Defect

Frenkel Defect

-another possibility is for smallpositive ion to move into aninterstice or interstitial site

-leaves a vacancy plus aninterstitial ion Frenkel defect

-formation energy is lower thanthat for a Schottky defect

Recall:

-ionic crystals tend to form vacancies in pairs to preservecharge neutrality Schottky defect

- e.g., NaCl both positive ion and negative ion migrate tosurface

vacancy

Interstitial ion

Both ions are removed



Defects can be categorized as either

•Intrinsic: Defects required to be present because of physical

laws.

•

Extrinsic: Defects present because of the environment and/orprocessing conditions. Most defects are extrinsic.



Crystal Defects

Substitutional Defect

(1) Metals

(2) Ionic Solids

limit to solubility for both interstitial or

substitutional atoms solubility limit

other phases form

- large impurity atoms that replacehost atoms on their lattice sites may be either larger or smaller thanhost atom produces compressiveor tensile strain fields respectively

-e.g., Ag dissolved in Au-and dopant atoms in Si

- for ionic solids, must maintain chargebalance, which may lead to formation ofvacancy as well

- e.g., for Ca 2+ ions in NaCl, 2 Na+ ions

are removed, which leaves a vacancy

- in compounds, may also get anti-sitedefects

- ex; GaAs - Ga may be found on anAs site and vice versa (charge

balance must be maintained)

Ca2+

replacesNa+

Space previouslyoccupied by thesecond Na+ ion(vacancy)



Why are defects important?

• Defects, even in very small concentrations,can have a dramatic impact on the

properties of a material.• Without defects:

– solid-state electronic devices could not exist

– metals would be much stronger

– ceramics would be much tougher

– crystals would have no color



Boltzmann's constant

(1.38 x 10 -23 J/atom K)

(8.62 x 10-5 eV/atom K)

N

DN exp

QD

kT

No. of defects

No. of potentialdefect sites.

Activation energy

Temperature

Each lattice siteis a potentialvacancy site

• Equilibrium concentration varies with temperature!

EQUIL. CONCENTRATION:POINT DEFECTS

Depending on the units for Q, you

may use the Stephan Boltmann

constant k or R



• We can get Q froman experiment.

• Measure this... • Replot it...

1/ T

N

NDln

1

-QD /k

slope

MEASURING ACTIVATION ENERGY



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

• Given:

8.62 x 10 -5 eV/atom-K

0.9eV/atom

1273K

ND

N exp QD

kT

For 1m 3, N =N

AACu x x 1m3 = 8.0 x 1028 sites

= 2.7 · 10-4

• Answer:

ESTIMATING VACANCY CONC.



Crystal Defects

Example:

Assuming that 83.7 KJ/mole of energy is required to produce a vacancy in copper, what

heating temperature is required to increase the vacancy concentration of a wire to 1000times the room temperature value?

For FCC copper aCu = 0.36151 nm; 4 atoms/cell

# of Cu atoms per m3, N = 4 (atoms/cell)/(3.6151 x 10-10 m)3 = 8.47 x 1028 atoms/m3

At RT (T = 273 + 25 = 298 oK)

Recall, nv = N exp[-Q/RT]nv = (8.47 x 1028) exp[-83,700/(8.314)(298)] = 1.774 x 1014 vacancies per m3 (at RT)

Need to produce 1000 x nv or 1.774 x 1017 vacancies/m3

Therefore, nv = 1.774 x 1017 = (8.47 x 1028) exp[-83,700/(8.314)(T)]

T = 375oK ( or 102oC)

By heating copper wire to 102oC and rapidly cooling back to RT,these vacancies can be trapped in the metal!



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 newphase (usually for a larger amount of B)

OR

Substitutional alloy(e.g., Cu in Ni)

Interstitial alloy(e.g., C in Fe)

Second phase particle--different composition

--often different structure.

POINT DEFECTS IN ALLOYS



• are line defects,

• cause slip between crystal plane when they move,

• produce permanent (plastic) deformation.

Dislocations:

Schematic of a Zinc (HCP):

• before deformation • after tensile elongation

slip steps

LINE DEFECTS



• Structure: close-packed

planes & directionsare preferred.

• Comparison among crystal structures:FCC: many close-packed planes/directions;HCP: only one plane, 3 directions;BCC: none

Mg (HCP)

Al (FCC)

tensile direction

• Results of tensiletesting.

view onto twoclose-packed

planes.

DISLOCATIONS & CRYSTAL STRUCTURE

i l t li d f t t i li i



Crystal Defects

2) Line Defects (1-D) – Dislocations

Edge dislocation

- simplest line defect to visualize isedge dislocation

- resembles an extra half plane ofatoms inserted into crystal (not actuallyhow it forms)

- form during processing thermal ormechanical

Burgers vector is

equivalent to the

shortest distancebetween 2

equivalent atoms

Extra plane

Burgers vector

only need to move dislocation and break bonds around dislocation



Crystal Defects

1) Deformation

- only need to move dislocation and break bonds around dislocation

- do not need to break all bonds across slip plane at once

- strengthen metals and alloys by blocking dislocations (look at this later, timepermitting)

Recall analogies



Grain boundaries:• are boundaries between crystals.

• are produced by the solidification process, for example.

• have a change in crystal orientation across them.

• impede dislocation motion.

grainboundaries

heatflow

Schematic

Adapted 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.)

~ 8cm Metal Ingot

AREA DEFECTS: GRAIN BOUNDARIES



Crystal Defects

Surface Defects (cont’d)

• Free (or external) surface

•Internal surface – Grain boundaries

• Low angle

• High angle

• Grain size

• Phase boundaries

– Fully coherent

– Incoherent

– Partial or semi-coherent

Tend to increase energy of solid

Grain boundaries:

-most materials are not single crystal, but are composed of many small crystals or grains, 10-4 to 10-2 cm in diameter material is said to be polycrystalline

-boundary separating grains is an internal surface called a grain boundary energy is 1/2 of

that for an external surface

-simplest type to visualizeis low angle or tilt boundary two slightly misorientedgrains

-consists of parallel edgedislocations equispaced bya distance D

-angle of misorientation isgiven by:

sin(q /2) = b/(2D)

q< 10 low angleboundaries

q> 10 high angleboundaries structuremore complicated but

similar



• Useful up to 2000X magnification.

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

orientation.

close-packed planes

micrograph ofBrass (Cu and Zn)

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

0.75mm

OPTICAL MICROSCOPY (1)



Grain boundaries...

• are imperfections,• are more susceptible

to etching,• may be revealed as

dark lines,• change direction in a

polycrystal. Adapted from Fig. 4.12(a)and (b), Callister 6e. (Fig. 4.12(b) is courtesy ofL.C. Smith and C. Brady,the National Bureau ofStandards, Washington, DC[now the National Institute ofStandards and Technology,Gaithersburg, MD].)

OPTICAL MICROSCOPY (2)



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

• The number and type of defects can be varied

and controlled (e.g., T controls vacancy conc.)

• Defects affect material properties (e.g., grain

boundaries 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.)

SUMMARY



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