Chapter 5Imperfections in Solids

Thanks to Jeff DePue, Greg Dykes, Alex EatonThanks to Jeff DePue, Greg Dykes, Alex Eaton

Chapter 5 - 2

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?

CHAPTER 5:IMPERFECTIONS IN SOLIDS

• What are the solidification mechanisms?

5.1 Introduction

• Every single solid has defects and imperfections.

• Sometimes the imperfections are purposely created and used for a specific purpose.

• Types of defects:– Point Defects (One or two atomic positions)– Linear Defects (One Dimensional)– Interfacial Defects (Boundaries)

Chapter 5 - 4

• 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

5.1 Imperfections in Solids

• Crystals grow until they meet each otherAdapted from Fig. 5.19 (b), Callister & Rethwisch 3e.

grain structurecrystals growingnucleiliquid

Chapter 5 - 5

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 diffusivity– high chemical reactivity

Adapted from Fig. 5.12, Callister & Rethwisch 3e.

Chapter 5 - 6

Solidification

Columnar in area with less undercooling

Shell of equiaxed grains due to rapid cooling (greater T) near wall

Grain Refiner - added to make smaller, more uniform, equiaxed grains.

heat

flow

Grains can be - equiaxed (roughly same size in all directions)

- columnar (elongated grains)

Adapted from Fig. 5.17, Callister & Rethwisch 3e.

~ 8 cm

Chapter 5 - 7

Imperfections in Solids

There is no such thing as a perfect crystal.

• What are these imperfections?

• Why are they important?

Many of the important properties of materials are due to the presence of imperfections.

Chapter 5 - 8

• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects

Types of Imperfections

• Dislocations Line defects

• Grain Boundaries Area defects

Chapter 5 - 9

I. Point defects

Chapter 5 - 10

• Vacancies:-vacant atomic sites in a structure.

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

5.2 Point Defects in Metals

Vacancydistortion of planes

self-interstitial

distortion of planes

Chapter 5 - 11

Boltzmann's constant

(1.38 x 10-23 J/atom-K)

(8.62 x 10-5 eV/atom-K)

Nv

Nexp Qv

kT

No. of defects

No. of potential defect sites

Activation energy

Temperature

Each lattice site is a potential vacancy site

• Equilibrium concentration varies with temperature!

Equilibrium Concentration:Point Defects

Chapter 5 - 12

• We can get Qv from an experiment.

Nv

N= exp

Qv

kT

Measuring Activation Energy

• Measure this...

Nv

N

T

exponential dependence!

defect concentration

• Replot it...

1/T

N

Nvln

-Qv /k

slope

Chapter 5 - 13

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

ACu = 63.5 g/mol = 8.4 g/cm3

Qv = 0.9 eV/atom NA = 6.02 x 1023 atoms/mol

Estimating Vacancy Concentration

For 1 m3 , N =N

A

ACu

x x 1 m3 = 8.0 x 1028 sites8.62 x 10-5 eV/atom-K

0.9 eV/atom

1273 K

Nv

Nexp

Qv

kT

= 2.7 x 10-4

• Answer:

Nv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies

5.2 Point Defects in Metals• Vacancies:

– Impossible to create a material without vacancies due to the laws of Thermodynamics.

– The number of vacancies (Nv) calculated from

Nv = N exp(-Q/kT)

N = number of atomic sites; Q = energy for vac. formation; k = boltzmann’s constant = 1.38×10-23 J/atom-K = 8.62×10-5 eV/atom-KT = absolute temperature (K)

http://www.matter.org.uk/matscicdrom/manual/po.html

Self Interstitial:– When an atom is

pushed into an interstitial site which is normally unoccupied.

– Very small amount in metals because when it occurs, it highly distorts the metal.

– Much lower concentrations than vacancies.

http://www.substech.com/dokuwiki/doku.php?id=imperfections_of_crystal_structure

5.2 Point Defects in Metals

Chapter 5 - 16

• Vacancies -- vacancies exist in ceramics for both cations and anions • Interstitials -- interstitials exist for cations

-- interstitials are not normally observed for anions because anions are large relative to the interstitial sites

Adapted from Fig. 5.2, Callister & Rethwisch 3e. (Fig. 5.2 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)

5.3 Point Defects in Ceramics (i)

Cation Interstitial

Cation Vacancy

Anion Vacancy

Chapter 5 - 17

• Frenkel Defect -- a cation vacancy-cation interstitial pair.

• Shottky Defect -- a paired set of cation and anion vacancies.

• Equilibrium concentration of defects

Adapted from Fig. 5.3, Callister & Rethwisch 3e. (Fig. 5.3 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)

Point Defects in Ceramics (ii)

Shottky Defect:

Frenkel Defect

/kTQDe

5.3 Point Defects in Ceramics• More types of defects than metals because

there are more types of ions.• In order to keep electroneutrality, ions must be

lost in equal amounts of charge. For example: One cation and one anion.

• Two main types: Frenkel Defect, Shottky Defect• Most ceramics stay in a stoichiometric state,

that is, they generally keep the same ratios as predicted by their empirical formula.– Exceptions occur in atoms like iron: Fe2+ and Fe3+

Frenkel Defect

• Neighboring cation vacancy and cation interstitial.

• Nfr = N exp(-Qfr/2kT)

Shottky Defect

• Neighboring cation vacancy and anion vacancy.

• Ns=N*exp(-Qs/2kT)

http://mrsec.wisc.edu/Edetc/SlideShow/slides/defects/Schottky_Frenkel.html

Chapter 5 - 21

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.

5.4 Impurities in Metals

Chapter 5 - 22

Impurities in Metals

Conditions for substitutional solid solution (S.S.)

– 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 tendency to dissolve a metal of higher valency than one of lower valency

Chapter 5 - 23

Imperfections in Metals (iii)

1. Would you predictmore Al or Ag to dissolve in Zn?

2. More Zn or Al

in Cu?

Table on p. 159, Callister & Rethwisch 3e.

Element Atomic Crystal Electro- ValenceRadius Structure nega-

(nm) tivity

Cu 0.1278 FCC 1.9 +2C 0.071H 0.046O 0.060Ag 0.1445 FCC 1.9 +1Al 0.1431 FCC 1.5 +3Co 0.1253 HCP 1.8 +2Cr 0.1249 BCC 1.6 +3Fe 0.1241 BCC 1.8 +2Ni 0.1246 FCC 1.8 +2Pd 0.1376 FCC 2.2 +2Zn 0.1332 HCP 1.6 +2

Chapter 5 - 24

• Electroneutrality (charge balance) must be maintained when impurities are present

• Ex: NaCl

Imperfections in Ceramics

Na+ Cl-

• Substitutional cation impurity

without impurity Ca2+ impurity with impurity

Ca2+

Na+

Na+Ca2+

cation vacancy

• Substitutional anion impurity

without impurity O2- impurity

O2-

Cl-

anion vacancy

Cl-

with impurity

5.4 Impurities in Solids

Solid Solutions:– Substitutional– replacement of ions– Interstitial filling of voids– Dependent on:• Atomic size factor• Crystal Structure• Electronegativity• Valences

Impurities in Ceramics•Both types as well Can occur for the cations or for the anions•Usually both occur at same time (one cation + one anion).

http://www.chem.ufl.edu/%7Eitl/2045/lectures/lec_i.html

5.4 Impurities in Solids

Chapter 5 - 27

5.5 Point Defects in Polymers• Defects due in part to chain packing errors and impurities such as chain ends and

side chains

Adapted from Fig. 5.7, Callister & Rethwisch 3e.

Adapted from Fig. 5.7, Callister & Rethwisch 3e.

5.5 Point Defects in Polymers

• Different from ceramics and metalsDifferent from ceramics and metals• Chains can bond together forming loops.Chains can bond together forming loops.• Chains can tie two molecules together.Chains can tie two molecules together.• Impurities may include interstitials, side Impurities may include interstitials, side

branches, or incorrect bending.branches, or incorrect bending.• Vacancies can occur and alter the chain Vacancies can occur and alter the chain

sequence.sequence.• Every chain end is considered a defect.Every chain end is considered a defect.

Chapter 5 -29

5.6 Specification of Composition (or concentration)

• Specification of composition

– weight percent 100x 21

11 mm

mC

m1 = mass of component 1

100x 21

1'1

mm

m

nn

nC

nm1 = number of moles of component 1

– atom percent

m = mass; n = moles (Compositions are easily converted from one type to the other by manipulating m to n, or vice versa, using the atomic weight, A)

Chapter 5 - 30

II. Miscellaneous Imperfections

Chapter 5 - 31

• 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

5.7 Line Defects

Chapter 5 - 32

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 perpendicular () to dislocation line

• Screw dislocation:– spiral planar ramp resulting from shear deformation– b parallel () to dislocation line

Burger’s vector, b: measures the magnitude and direction of the lattice distortion

Chapter 5 - 33

Imperfections in Solids

Fig. 5.8, Callister & Rethwisch 3e.

Edge Dislocation

extra half-plane of atoms inserted in a crystal structure

Chapter 5 - 34

Imperfections in Solids

Screw Dislocation

Adapted from Fig. 5.9, Callister & Rethwisch 3e.

Burgers vector b

Dislocationline

b

(a)(b)

Screw Dislocation: b || dislocation line

Chapter 5 - 35

Edge, Screw, and Mixed Dislocations

Adapted from Fig. 5.10, Callister & Rethwisch 3e.

Edge

Screw

Mixed

Chapter 5 - 36

Imperfections in SolidsDislocations are visible in electron micrographs; TEM Titanium alloy, dark lines are

dislocations 51,450x

Fig. 5.11, Callister & Rethwisch 3e.

5.7 Dislocations – Linear Defects

• A dislocation is a linear (one dimensional) defect around which other atoms are misaligned

• Edge Dislocation – where an extra plane or half plane of atoms stops

• Screw Dislocation – where a shear stress causes a region of a crystal to shift

• Mixed Dislocation – a combination of edge and screw dislocations

• Burges Vector – the magnitude and direction of lattice distortion associated with a dislocation

Chapter 5 -

5.8 Interfacial defects2D Boundaries Separate xtal structures & xtalographic orientations

Examples:

-external surfaces -Lower nearest neighbors-Atoms in higher energy states-Tend to minimize the total surface area

- grain boundaries-Low angle example: tilt boundary-High angle

- twin boundaries- stacking faults- phase boundaries (in multiphased materials)

Chapter 5 - 39

Chapter 5 - 40

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

Adapted from Fig. 5.14, Callister & Rethwisch 3e.

Chapter 5 - 41

Catalysts and Surface Defects• A catalyst increases the

rate of a chemical reaction without being “consumed”

• Active sites on catalysts are normally surface defects

Fig. 5.15, Callister & Rethwisch 3e.

Fig. 5.16, Callister & Rethwisch 3e.

Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converter

5.8 Interfacial Defects• Interfacial defects are two dimensional boundaries with

different crystal structures and/or orientations• External Surfaces – where the crystal terminates• Grain Boundaries – crystals often form groups of atoms known

as grains, which when combined with other grains in a large crystal, often have misalignments that form boundaries

• Phase Boundaries – where a crystal forms more than one phase (i.e. solid and liquid)

• Twin Boundaries – A special grain boundary where one grain forms a mirror lattice symmetry with another

• Other miscellaneous interfacial defects include stacking faults and ferromagnetic domain walls.

Grain Boundary

http://www.corrosionlab.com/Failure-Analysis-Studies/Failure-Analysis-Images/20030.SCC.304H-pipeline/20030.microstructure-ditched-grain-boundaries.jpg

5.8 Interfacial Defects

Chapter 5 - 44

5.9 Bulk or Volume defects(Introduced during processing and fabrication steps)

Pores Cracks“Foreign” inclusionsOther phases

5.9 Bulk or Volume Defects• Much larger defects than the previous

ones, usually introduced during processing and fabrication

• Examples include:– Pores– Cracks– Foreign Inclusions– Other Phases

http://www.fossil.energy.gov/images/education/rockpore.jpg

Chapter 5 - 46

5.10 Atomic Vibrations(Introduce during the creation of the universe)

Every atom vibrates even at zero Kelvin (OK?)Frequencies in the order of 10 THz

Chapter 5 - 47

III.Microscopic Examination

Chapter 5 - 48

5.10 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 (mm or less) – necessary to observe with a microscope.

5.10 Atomic Vibrations

• At any given time, each atom in a crystal is vibrating about its lattice position within the crystal

• The amplitudes and frequencies of the vibrations vary between atoms and can be considered imperfections or defects

• The vibrations change with temperature and influence many properties of the crystal such as melting point

5.11 Microscopic Examination – General

• The grains of many crystals have diameters in the order of microns (10-6 meters)

• Microstructure – Structural features subject to observation under a microscope

• Microscopy – Use of a microscope in studying crystal structure

• Photomicrograph – A picture taken by a microscope

Optical Microscope

http://science.kukuchew.com/wp-content/uploads/2008/06/

modernmicroscope.jpg

http://rsic.puchd.ac.in/images/image002.jpg

Electron Microscope

Scanning Probe Microscope

http://img.directindustry.com/

images_di/photo-g/scanning-probe-microscope-spm-

47975.jpg

5.11 Microscopic Examination – General

Chapter 5 - 52

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

Micrograph ofbrass (a Cu-Zn alloy)

0.75mm

5.12 Optical Microscopy

Adapted from Fig. 5.18(b) and (c), Callister & Rethwisch 3e. (Fig. 5.18(c) is courtesyof J.E. Burke, General Electric Co.)

crystallographic planes

Chapter 5 - 53

Grain boundaries...• are imperfections,• are more susceptible to etching,• may be revealed as dark lines,• change in crystal orientation across boundary. Adapted from Fig. 5.19(a)

and (b), Callister & Rethwisch 3e.(Fig. 5.19(b) is courtesyof L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

5.12 Optical Microscopy

ASTM grain size number

N = 2n-1

number of grains/in2 at 100x magnification

Fe-Cr alloy(b)

grain boundary

surface groove

polished surface

(a)

Chapter 5 - 54

Optical Microscopy

• Polarized light – metallographic scopes often use polarized

light to increase contrast– Also used for transparent samples such as

polymers

Chapter 5 - 55

MicroscopyOptical resolution ca. 10-7 m = 0.1 m = 100 nm

For higher resolution need higher frequency– X-Rays? Difficult to focus.– Electrons

• wavelengths ca. 3 pm (0.003 nm) – (Magnification - 1,000,000X)

• Atomic resolution possible• Electron beam focused by magnetic lenses.

Chapter 5 - 56

• 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, copyright 1995.

Iron atoms arranged on a copper (111)

surface. These Kanji characters represent

the word “atom”.

Scanning Tunneling Microscopy (STM)

Section 5.12

Microscopic Techniques

http://www.lakewoodconferences.com/direct/dbimage/50242774/Microscope.jpg

Microscopic Techniques:Optical Microscopy

• “light” microscope• Uses a series of lenses to magnify images• Three basic lenses (4x, 10x, and a third

ranging from 20x - 100x)• Magnification limit of 2000x

Microscopic Techniques:Electron Microscopy

• Uses focused beam of electrons to magnify target

• Magnification up to 2,000,000x

• 4 main types– TEM, SEM, REM, STEM

http://www.engr.uky.edu/~bjhinds/facil/images/2010.jpg

Microscopic TechniquesTransmission Electron Microscopy (TEM)

• Original form of electron microscope

• Utilizes an electron gun with a tungsten filament

• Image projected unto a phosphor viewing screen

Microscopic TechniquesScanning Electron Microscopy (SEM)

• Scans rectangular area by using a focused beam of electrons

• Electrons give off differing energies based on structure of target

• Microscope reads these energies and produces a visual representation

Microscopic TechniquesReflection Electron Microscopy (REM)

• Like TEM, uses a beam of electrons to develop a picture of the target

• Reads the reflected beam of electrons to form visual representation

http://www.zaiko.kyushu-u.ac.jp/z9/Letter/PL1.JPG

Microscopic TechniquesScanning Transmission Electron Microscope

(STEM)• A type of Transmission Electron

Microscope

• Electrons focus on a small area of specimen

• Electrons pass through the sample, and a visual is formed

Chapter 5 - 64

5.13 Grain size determination

American Society for Testing and Materials

N = ASTM grain size number

N = 2n-1

n = number of grains/in2 at 100× magnification

Section 5.13

Grain Size Determination

http://www.scielo.br/img/revistas/mr/v11n1/11f1a.gif

Grain Size Determination• Photomicrographic techniques used for

determination

http://www.eos.ubc.ca/courses/eosc221/images/sed/sili/pic/sedsize.gif

Two techniques used:

Intercept comparison

Standard comparison

Grain Size DeterminationIntercept Method

• Draw straight lines through photograph of grain structure

• Count number of grains that pass through each line

• Line length divided by number of intersected grains

Grain Size MethodStandard Method

• Developed by American Society for Testing and Materials (ASTM)

• Photograph specimen at 100x• Compare grain size to a set of charts

with grain size scale 1-10• Grain size (n) is determined by number

of grains per square inch (N) at 100x• N = 2n-1

Chapter 5 - 69

• 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 affect 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.)

Summary