Chapter 4 - 1

ISSUES TO ADDRESS...

• What types of defects exist in solids?

• Can the number and type of defects be varied

and controlled?

• How do defects affect material properties?

Chapter 4:

Imperfections (Defects) in Solids

Chapter 4 -

2

• Vacancy

• Interstitial atoms

• Substitutional atoms

Point (0D) defects

Types of Imperfections (or Defects) in

Crystals

• DislocationsLinear/line (1D) defects

• Grain boundaries,

• Surfaces

• Interfaces

Area/planar (2D) defects

NO perfect crystals in reality: defects or imperfection always exist

Many of materials properties are determined or influenced by defects

• Foreign inclusions

• VoidsVolume (3D) defects

Chapter 4 -3

• Vacancies:-vacant atomic sites in a structure.

-very common (10-4 near melting point)

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

• Self interstitial – rare, i.e., extremely low concentration

• Impurity atom interstitial – common: e.g., C or H in Fe

Point Defect: Vacancy & Interstitials

Vacancy

distortion

of planes

Impurity atom

interstitials

(common)distortion of planes

Self-interstitials

(very rare)

Chapter 4 -

4

Boltzmann's constant

(1.38 x 10-23

J/K)

(8.62 x 10-5

eV/K)

Nv

N= exp

Qv

kT

# density of vacany

(v for vacancy here)

Lattice site density

Activation energy

(heat of formation

of vacancy, in unit

of kJ/mol or J per

vacancy)

Temperature

Each lattice site is a potential vacancy site

• Vacancies need extra energy to form (to break bonds between

neighboring atoms)

• Equilibrium concentration for vacancy varies with temperature:

Equilibrium Concentration of Vacancies

Chapter 4 - 5

• Vacancy concentration increases “exponentially” with T

Nv

N= exp

Qv

kT

Change of Vacancy Concentration

with Temperature

Nv

N

T

exponential dependence!

vacancy concentration

• If known Nv vs T, activation

energy QV could be measured

1/T

N

Nvln

-Qv /k

slope

Chapter 4 - 6

Estimate the total number of vacancies within 1 cubic meter

(1m3) of Cu at 1000C under equilibrium condition if knowing

ACu = 63.5 g/molr = 8.4 g/cm3

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

Example:

Estimating Vacancy Number/Concentration

For 1 m3 , N =N

A

ACu

r • • 1 m3= 8.0 x 1028 atoms (sites)

8.62 x 10-5 eV/atom-K

0.9 eV/atom

1273 K

= 2.7 x 10-4Nv

N= exp

Qv

kT

• Answer: total number of vacancies in 1m3 Cu at 1000C

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

Chapter 4 - 7

• Low energy electron

microscope view of a (110)

surface of NiAl

• Increasing temperature

causes surface island to

grow (expand).

• Why?

The equilibrium vacancy

concentration increases via

atom motion from the

crystal inside to the surface,

where they join the island.

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 Vacancy Movement

Island grows/shrinks to maintain equil. vancancy conc. in the bulk.

Click once on image to start animation

Chapter 4 -

Applications

• Example when vacancies are

desirable:

– Oxygen sensor at high temperature:

vacancies help ion conduction and sensing

• Example when vacancies are

undesirable:

– Voiding of materials at high temperatures

8

Chapter 4 - 9

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

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

• Solid solution of B in A plus particles of a new compound (in some

systems with with higher concentration of B in A)

OR

Substitutional solid solution.

Solute atom has similar size

(e.g., Cu in Ni)

Interstitial solid solution

Solute atom usually much smaller

(e.g., C or N in Fe)

Second phase particle

-- different composition

-- often different structure.

Point Defect: Impurity Atoms in Solids

Solute (atom)

Solvent

(matrix)

Chapter 4 - 10

Impurity Atoms in Solids (2)

Conditions for forming substitutional solid solution (S.S.)

with high solubility:

W. Hume – Rothery Rule (empirical)

– 1. r (atomic radius) < 15%

– 2. Proximity in periodic table, i.e., similar electronegativities

– 3. Same crystal structure

– 4. Same or similar valence

Chapter 4 - 11

Impurity Atoms in Solids (3)

Application of Hume–Rothery rules for Solid Solutions

When forming solid

solutions of

• Zn in Cu

• Ni in Cu

Which metal (Zn or Ni)

has higher solubility

in Cu and why?Ni has higher solubility

in Cu due to Ni has i) same

crystal structure, ii) very close radius, iii) very close electronegativity,

and iv) same valence as Cu.

Table on p. 118, Callister & Rethwisch 8e.

Element Atomic Crystal Electro- Valence

Radius Structure nega-

(nm) tivity

Cu 0.1278 FCC 1.9 +2

C 0.071

H 0.046

O 0.060

Ag 0.1445 FCC 1.9 +1

Al 0.1431 FCC 1.5 +3

Co 0.1253 HCP 1.8 +2

Cr 0.1249 BCC 1.6 +3

Fe 0.1241 BCC 1.8 +2

Ni 0.1246 FCC 1.8 +2

Pd 0.1376 FCC 2.2 +2

Zn 0.1332 HCP 1.6 +2

Chapter 4 -

Applications

• Examples when impurity atoms are

desirable

– Controlled doping of Si with P or B for

semiconductor

– Alloying Zn with Cu to improve mechanical

properties

• Examples when impurity atoms are

undesirable

– Fe or Ni contaminants in Si wafer

12

Chapter 4 - 13

Line (1D)/Linear Defects

Dislocations– One-dimensional defects around which atoms are

misaligned

– Two basic types

• Edge dislocation

• Screw dislocation

Chapter 4 - 14

1D Defect - Edge Dislocation

Fig. 4.3, Callister & Rethwisch 8e.

• Edge dislocation:– extra half-plane of atoms inserted in a crystal structure

– b perpendicular () to dislocation line

Chapter 4 - 15

1D Defect - Screw Dislocation

Screw Dislocation

Adapted from Fig. 4.4, Callister & Rethwisch 8e.

Burgers vector b

Dislocation

line

b

(a)

(b)

Screw Dislocationspiral planar ramp resulting from shear deformationb parallel () to dislocation line

Chapter 4 -

VMSE: Screw Dislocation

• In VMSE: – a region of crystal containing a dislocation can be rotated in 3D

– dislocation motion may be animated

16

Front View Top ViewVMSE Screen Shots

Chapter 4 - 17

Edge, Screw, and Mixed Dislocations

Adapted from Fig. 4.5, Callister & Rethwisch 8e.

Edge

Screw

Mixed

Chapter 4 - 18

Observation of DislocationsDislocations are visible in transmission electron

microscope (TEM)

Fig. 4.6, Callister & Rethwisch 8e.

Chapter 4 -

Application

• Examples when linear defects

(dislocations) are desirable

– Strain hardening of materials: dislocations

help improve mechanical strength of

metals

• Examples when linear defects are

undesirable

– Dislocation in polycrystalline Si for solar

cell wafers: dislocations cause degradation

of carrier lifetime and decrease solar cell

efficiency19

Chapter 4 - 20

Planar (2D) Defects in Solids (1)

Grain Boundaries

• Regions between

individual crystals

or grains

• Transition from lattice of

one ordered region to

that of another

• Slightly disordered

• Lower packing density in

grain boundaries

– Higher mobility

– Higher chemical reactivity

Adapted from Fig. 4.7,

Callister & Rethwisch 8e.

Chapter 4 -

Planar (2D) Defects in Solids (2)

21

Chapter 4 - 22

Additional Planar (2D) Defects in

Solids (3)• Twin boundary (plane)

– A special grain boundary with 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. 4.9,

Callister & Rethwisch 8e.

Chapter 4 -

Application

• Examples when we want planar defects

(e.g., grain boundary)

– Grain size reduction for improved

mechanical properties

• Examples when planar defects are

unwanted

– Grain boundary in polycrystalline Si for

solar cell wafers decrease carrier lifetime

and resulting solar cell efficiency

23

Chapter 4 - 24

Microscopic Examination

Techniques

• Crystallites (grains) and defects (e.g., grain

boundaries). Vary considerably in size.

– Can be quite large (~mm or larger).

• ex: Large single crystal of quartz, diamond, or Si

• ex: Metal light post or garbage can - see the individual

grains

– Can be quite small (~μm or smaller)

• necessary to observe with a microscope.

Chapter 4 - 25

• Based on visible light (wavelength of 0.4-0.7 μm)

• Up to 2000x magnification.

• Polishing removes surface features (e.g., scratches)

• Etching changes reflectance, depending on crystal

orientation.

Micrograph of brass (a

Cu-Zn alloy) after etching

0.75mm

Optical Microscopy

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

& Rethwisch 8e. (Fig. 4.13(c) is courtesy

of J.E. Burke, General Electric Co.)

crystallographic planes

Chapter 4 - 26

Grain boundaries...

• are imperfections,

• are more susceptible

to etching,

• may be revealed as

dark lines,

• change in crystal

orientation across

boundary.Adapted from Fig. 4.14(a)

and (b), Callister &

Rethwisch 8e.

(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 (2)

Fe-Cr alloy(b)

grain boundary

surface groove

polished surface

(a)

Chapter 4 - 27

Electron Microscopy– Electrons

• Wavelengths can be as short as ~3 pm (0.003 nm)

• Atomic resolution (~0.1 nm) possible (106 times!)

• Electron beam focused by magnetic lenses.

• On surface - Scanning electron microscope (SEM)

• Through bulk – Transmission electron microscope (TEM)

TEMSEM

Chapter 4 - 28

• Even 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 Probe Microscopy

(SPM)

Chapter 4 - 29

• Point, Line, and Planar 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

• Defects may be desirable or undesirable depending on

materials and specific application

Summary

Chapter 4 -

Homework

• Statement confirming reading of chapter 4

• Callister 8ed 4.1, 4.4 (c only), 4.29(a)

30

Chapter 4 -

• Calister 8ed, 4.1

Calculate the fraction of atom sites that are

vacant for lead at its melting temperature

of 327°C (600 K). Assume an energy for

vacancy formation of 0.55 eV/atom

Chapter 4 -

Element

Atomic

Radius

(nm)

Crystal

Structure

Electronegativi

ty Valence

Cu 0.1278 FCC 1.9 +2

C 0.071

H 0.046

O 0.060

Ag 0.1445 FCC 1.9 +1

Al 0.1431 FCC 1.5 +3

Co 0.1253 HCP 1.8 +2

Cr 0.1249 BCC 1.6 +3

Fe 0.1241 BCC 1.8 +2

Ni 0.1246 FCC 1.8 +2

Pd 0.1376 FCC 2.2 +2

Pt 0.1387 FCC 2.2 +2

Zn 0.1332 HCP 1.6 +2

Callister 8ed, 4.4(c)

Below, atomic radius, crystal structure, electronegativity, and the most

common valence are tabulated, for several elements; for those that are

nonmetals, only atomic radii are indicated. Which of these elements would

you expect to form the following with copper: (a) substitutional solid solution

with complete solubility; (b) substitutional solid solution with incomplete

solubility; (c) An interstitial solid solution

Chapter 4 -

• Calister 8ed, 4.29(a)

4.29 (a) For a given material, would you

expect the surface energy to be greater

than, the same as, or less than the grain

boundary energy? Why?