Chapter 5Defects in solids

Defects in solids

Solidification process…

classification

zero

dim

en

sio

n

Defects… - imperfection in structures of solid materials crystal structure due to irregular/disordered atomic arrangement. amorphous structure due to molecular chains error. - classify in terms of geometry (dimension) & size.- normally, formed during solidification process.

on

e d

ime

nsi

on

two

dim

en

sio

n

thre

e d

ime

nsi

on

po

int

de

fect

s

Lin

ea

r/d

islo

catio

n d

efe

cts

are

a/p

lan

ar/

surf

ace

d

efe

cts

volu

me

de

fect

s (i.

e:

cra

ck)

- result of primary materials forming/working. i.e: for metals, casting process.- 2 steps: 1. Nuclei form – formation of stable nuclei. 2. Nuclei grow to form crystals – formation of grain structure.- start with a molten (all liquid) material & grains

(crystals) grow until they meet each other.

nucleiliquid

grain structure

All solid materials… - contain large # of defects.

Solidification process…

crystal growing

- Grains structure can be: 1. equiaxed grains (roughly same size in all directions). 2. columnar grains (elongated grains).

Columnar grains in area with less undercooling

Equiaxed grains due to rapid cooling (greater -T) near wall

above Tm

room temp.

Mold

crystals growing

Casting process

Defects in solids

classification

zero dimension

point defects

me

tals

self-

inte

rstit

ial &

va

can

cy (

me

tals

)

cera

mic

s

inte

rstit

ial &

su

bst

itutio

na

l (m

eta

l allo

ys)

inte

rstit

ial,

vaca

ncy

, F

ren

kel &

Sch

ott

ky,

sub

stitu

tion

al a

nio

n &

ca

tion

imp

urit

y

po

lym

ers

Ch

ain

pa

ckin

g e

rro

r

Cation Interstitial

Cation Vacancy

Anion Vacancy

Point defects in ceramics

1. Vacancies - vacancies exist in ceramics for both cations and anions.

2. Interstitials - exist for cations only. - interstitials are not normally observed for anions because anions are large relative to the interstitial sites.

3. Frenkel defect - a cation vacancy-cation interstitial pair.

4. Schottky defect - a paired set of cation and anion vacancies.

Schottky defect

Frenkel defect

Point defects in metals

1. Self-Interstitials- "extra" atoms positioned between atomic sites.- cause structural distortion.

self-interstitial

distortion of planes

2. Vacancies- vacant atomic sites exist in a

structure.- form due to a missing atom.- form (one in 10,000 atoms) during crystallization, mobility of atoms or rapid cooling.

Vacancy

distortion of planes

Point defects in polymers

10 nm

Adapted from Fig. 4.12, Callister & Rethwisch 3e.

- Defects due in part to chain packing errors and

impurities such as chain ends and side chains. i.e: thin platelets

Defects in solids

classification

zero dimension

point defects

me

tals

self-

inte

rstit

ial &

va

can

cy (

pu

re m

eta

ls)

cera

mic

s

inte

rstit

ial &

su

bst

itutio

na

l (m

eta

ls a

lloy)

po

lym

ers

Ch

ain

pa

ckin

g e

rro

r

inte

rstit

ial,

vaca

ncy

, F

ren

kel &

Sch

ott

ky,

sub

stitu

tion

al a

nio

n &

ca

tion

imp

urit

y

Equilibrium concentration: Point defects

k = Boltzmann's constant

(1.38 x 10-23 J/atom-K)(8.62 x 10-5 eV/atom-K)

Nv = # of defects (vacancies site)

Qv = activation energyT = temperature

- each lattice/atom site is potential vacancy site.

- equilibrium # of point defects (vacancies) for solids depends on & increase with temperature. - apply the formula:

çN v

N= exp

- Q v

k T

æ

è ç

ö

ø

N = total # of atomic sites

• We can get Qv from an experiment.• Measure this...

N v

N

T

exponential dependence!

Defect (@ vacancy) concentration

• Replot it...

1/ T

N

N vln

-Q v /k

slope

Measuring Activation Energy…

Example:

In 1 m3 of Cu at 1000-C, calculate:(a) vacancy concentration, Nv/N.(b) equilibrium # of vacancies, Nv.Given that,

ACu = 63.5 g/mol

r = 8.4 g/cm3

Qv = 0.9 eV/atom

NA = 6.02 x 1023atoms/mol

8.62 x 10-5 eV/atom-K

0.9 eV/atom

1273 K

ç ÷ NvN

= exp- QvkT

æ

è ç

ö

ø÷ = 2.7 x 10-4

Answer:

(a)

(b) - = N ACu

VCu NA

For 1 m3 , N =N

A

ACu

r x x 1 m3 = 8.0 x 1028 atom sites

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

Vacancy concentration

# of vacancy sites, Nv

total # of atomic sites, N=

Defects in solids

classification

zero dimension

point defects

me

tals

self-

inte

rstit

ial &

va

can

cy (

me

tals

)

cera

mic

s

inte

rstit

ial &

su

bst

itutio

na

l (m

eta

l allo

ys)

inte

rstit

ial,

vaca

ncy

, F

ren

kel &

Sch

ott

ky,

sub

stitu

tion

al a

nio

n &

ca

tion

imp

urit

y

po

lym

ers

Ch

ain

pa

ckin

g e

rro

r

Impurities in ceramics- Electroneutrality (charge balance) must be maintained when impurities are present.

i.e: NaCl Na+ Cl -

1. Substitutional cation impurity

without impurity Ca2+ impurity with impurity

Ca2+

Na+

Na+Ca2+

cation vacancy

2. Substitutional anion impurity

without impurity O2- impurity

O2-

Cl-

anion vacancy

Cl-

with impurity

Impurities in metals

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

1. Small amount of B added to A

Substitutional solid soln.(e.g., Cu in Ni)

Interstitial solid soln.(e.g., C in Fe)

2. Large amount of B added to A plus particles of a new phase Second phase particle

- different composition.- often different structure.

- Metal alloys are used in most

engineering applications.

- Metal alloy is a mixture of two or

more metals and nonmetals.

- Solid solution is a simple type of

metal alloy in which elements are

dispersed in a single phase.

General concept…

Defects in solids

classification

zero dimension

point defects

me

tals

self-

inte

rstit

ial &

va

can

cy (

me

tals

)

cera

mic

s

inte

rstit

ial &

su

bst

itutio

na

l (m

eta

l allo

ys)

inte

rstit

ial,

vaca

ncy

, F

ren

kel &

Sch

ott

ky,

sub

stitu

tion

al a

nio

n &

ca

tion

imp

urit

y

po

lym

ers

Ch

ain

pa

ckin

g e

rro

r

SystemAtomic radius

difference

Electro-negativity difference

Solidsolubility

Cu-Zn 3.9% 0.3 38.3%

Cu-Pb 36.7% 0.2 0.17%

Cu-Ni 2.3% 0.1 100%

Example 2:

Element Atomic Crystal Electro-Valence Radius (nm) Structure negativity

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

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

2. More Zn or Al in Cu?

Example 1:

Example 3:

A hypothetical alloy consist of 120 g element A & 80 g element B. Determine the composition (in wt%) for each element?

Impurities in metals

The solubility of solids is greater if:1. -r (atomic radius difference) < 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 another metal of higher valency than one of lower valency.

Conditions for solid solubility- apply W. Hume – Rothery rule.- have 4 conditions which is applied

for substitutional solid solution.

Specification of composition- determine the composition for a 2 element in alloy system.- specify in weight percent, wt % @ atom percent, at %.

weight percent, wt%

atom percent, at%

C2 = 100 – C1

C’2 = 100 – C’1

C1 = m1 x 100 m1+ m2

C’1 = nm1 x 100 nm1+ nm2

m1 & m2 = mass of component 1 & 2C1 & C2 = composition (in wt%) of component 1 & 2

nm1 = m1/A1 nm2 = m2/A2

nm1 & nm2 = number of moles of component 1 & 2A1 & A2 = at. weight of component 1 & 2C’1 & C’2 = composition (in at%) of component 1 & 2

Higher solid solubility (subs. S.S)

Lower solid solubility (interstitial S.S)

Defects in solids

classification

one dimension

linear defects

All materials

ed

ge

dis

loca

tion

Linear defects in materials- also known as dislocations.- defects around which atoms are

misaligned in a line @ lattice distortions are centered around a line. - slip between crystal planes result when

disl. moves.- formed during solidification @ permanent deformation.

scre

w d

islo

catio

n

mix

ed

dis

loca

tion

1. Edge dislocation: - extra half-plane of atoms inserted in a crystal structure. - b perpendicular to dislocation line.

2. Screw dislocation:- spiral planar ramp resulting from shear

deformation.- b parallel to dislocation line.

Screw Dislocation

Burgers vector b

Dislocationline

(a)

b(b)

Edge

Screw

Mixed

3. Mixed dislocation: - most crystal have components of both edge and screw dislocation.

SEM micrograph shows dislocation as a dark lines

Screw dislocation

Edge dislocation

Mixed dislocation

Type of dislocations… SEM micrograph

slip steps

after tensile elongation

initial

Dislocations in Zinc (HCP)

Dislocations & Crystal Structures• Structure: close-packed planes & directions are preferred.

view onto twoclose-packedplanes.

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)tensile direction

Higher solid solubility (subs. S.S)

Defects in solids

classification

two dimension

planar/surface defects

All materials

gra

in b

ou

nd

arie

s

Planar defects in materials- Defects due to formation of grains structure.

sta

ckin

g f

au

lts

twin

bo

un

da

ries

1. Grain boundaries - region between grains (crystallites). - formed due to simultaneously growing crystals meeting each other. - slightly disordered. - restrict plastic flow and prevent dislocation movement (control crystal slip). - low density in grain boundaries

-- high mobility. -- high diffusivity. -- high chemical reactivity.

Grain boundariesin 1018 steel

2. Twin boundaries - essentially a reflection of atom positions across the twin plane. - a region in which mirror image of structure exists across a boundary. - formed during plastic deformation and recrystallization. - strengthens the metal.

Twin

Twin plane

3. Stacking faults - piling up faults during recrystallization due to collapsing. - for FCC metals an error in ABCABC packing sequence, i.e: ABCABABC.

Catalysts and Surface Defects• Catalyst is a substance in

solid form.• A catalyst increases the rate

of a chemical reaction without being consumed.– Reactant molecules in a gas @

liquid phase (CO, NOx & O2) are absorbed onto catalyst surface.

– Reduce the emission of exhaust gas pollutants.

• Adsorption/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

Defects in solids

microscopic examination

Grain boundaries observation- used metallographic techniques.- the metal sample must be first mounted for easy handling.- then the sample should be ground and polished -- with different grades of abrasive paper and abrasive solution. -- removes surface features (e.g., scratches).- the surface is then etched chemically. -- tiny groves are produced at grain boundaries. -- groves do not intensely reflect light. -- may be revealed as dark lines.- hence observed by optical microscope.

0.75mm

Fe-Cr alloy

grain boundary

surface groove

polished surface

Unetched Steel200 X

Etched Steel200 X

Unetched Brass200 X

Etched Brass200 X

Effect of etching…

Microscopic examination- such microscope used to observe &

analyze structures @ defects of materials. i.e: OM, IM, SEM, TEM, STM, AFM etc.

Opt

ical

Mic

rosc

ope

(OM

)

Sca

nnin

g E

lect

ron

Mic

rosc

ope

(SE

M)

Inve

rted

Mic

rosc

ope

(IM

)

Sca

nnin

g T

unne

ling

Mic

rosc

ope

(ST

M)

Ato

mic

For

ce M

icro

scop

e (A

FM

)

Tra

nsm

issi

on E

lect

ron

Mic

rosc

ope

(TE

M)

ob

serv

e g

rain

str

uct

ure

&

bo

un

da

ries

an

aly

ze g

rain

siz

e

Process flow…

1. mount

2. grind

3. polish

4. clean

5. etch

6. observe

7. analyze

exa

min

e t

op

og

rap

hic

al

ma

p (

surf

ace

fe

atu

res)

metallographic techniques

SEM micrograph

STM topographic

Measuring average grain diameter

Size of grains…- affects the mechanical properties of the material.- the smaller the grain size, more are the grain boundaries. - more grain boundaries means higher resistance to slip (plastic deformation occurs due to slip).- more grains means more uniform the mechanical properties are.

Defects in solids

microscopic examination

Opt

ical

Mic

rosc

ope

(OM

)

Sca

nnin

g E

lect

ron

Mic

rosc

ope

(SE

M)

Inve

rted

Mic

rosc

ope

(IM

)

Sca

nnin

g T

unne

ling

Mic

rosc

ope

(ST

M)

Ato

mic

For

ce M

icro

scop

e (A

FM

)

Tra

nsm

issi

on E

lect

ron

Mic

rosc

ope

(TE

M)

ob

serv

e g

rain

str

uct

ure

&

bo

un

da

ries

an

aly

ze g

rain

siz

e

exa

min

e t

op

og

rap

hic

al

ma

p (

surf

ace

fe

atu

res)

metallographic techniques

n < 3 – Coarse grained4 < n < 6 – Medium grained7 < n < 9 – Fine grainedn > 10 – ultrafine grained

N = number of grains per square inch of a polished & etched specimen at 100x magnification.

n = ASTM grain size number.

1018 cold rolled steel, n=10

1045 cold rolled steel, n=8

How to measure grain size?

- ASTM grain size number ‘n’ is a

measure of grain size.

- use the formula:

N = 2n -1

- If ASTM grain size #, n increase,

-- size of grains decrease.

-- # of grains/in2, N increase.

- Average grain diameter, d more directly represents grain size.- Random line of known length is drawn on photomicrograph.- Number of grains intersected is counted.- Ratio of number of grains intersected to length

of line, nL is determined.

d = C/nL(M) C = 1.5 & M = magnification

3 inches 5 grains

Example:Determine the ASTM grain size number of a metal specimen if 45 grains per square inch are measured at a magnification of 100x.

log N = (n-1) log 2n = log N

log 2+ 1

n = log 45 log 2

+ 1

n = 6.5

• 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