Chapter 4 - 1

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 4

IMPERFECTIONS IN SOLIDS

• What are the solidification mechanisms?

Chapter 4 -

IntroductionIdeally: Perfect OrderReally: various defects or imperfectionsAtomic Vibration: Every Atom is vibrating around its lattice position DefectsLevels of Defects• Point• Linear • Interfacial • Bulk: pores, cracks and foreign inclusions (bubble, sand ..etc).Require: Examination of Structure ? TechniquesApplication:Solid Solutions = Solvent (host atoms) and Solute AlloyWhy?

1) to improve mechanical properties2) Most metals are alloys (impurities always exist).

Chapter 4 - 3

Imperfections in Solids

There is no such thing as a perfect crystal !

• Thermodynamically “impossible”

• “defects” lower the energy of a crystal & make it more stable

• always have vacancies and impurities, to some extent

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

Defect does not necessarily imply a bad thing

• addition of C to Fe to make steel

• addition of Cu to Ni to make thermocouple wires

• addition of Cr to Fe for corrosion resistance

• introduction of grain boundaries to strengthen materials

• “Defect” can be either desirable or undesirable.

Chapter 4 - 4

• Solidification- result of casting of molten material• Mechanism - 2 steps

• Nuclei form • Nuclei grow to form crystals – grain structure

• Start with a molten material – all liquid

Solidification Mechanism

• Crystals grow until they meet each other

nuclei crystals growing grain structureliquid

Chapter 4 - 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

Chapter 4 - 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)~ 8 cm

Chapter 4 - 7

• Vacancy atoms• Substitutional atoms• Interstitial atoms

Point defects

Types of Imperfections

• Dislocations Line defects

• Grain Boundaries Area defects -Planar

Chapter 4 - 8

• Vacancies:

-vacant atomic sites in a structure.

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

Point Defects

Vacancydistortion of planes

self-interstitial

distortion of planes

Chapter 4 - 9

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 of vacancies varies with temperature!

Equilibrium Concentration:Point Defects - Vacancy

Chapter 4 - 10

• 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 4 - 11

• 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 =NAACu

x x 1 m3 = 8.0 x 1028 sites

8.62 x 10-5 eV/atom-K

0.9 eV/atom

1273K

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

Chapter 4 - 12

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

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

Partial Solubility: 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.

Point Defects in Alloys

When similar smaller

Chapter 4 -

Interstitial Solid Solution

• Impurity atoms fill voids among the host atoms• Always APF < 1 there are always voids• For metals: strong (metallic bonding) highly packed small voids Small portion can be dissolved

Condition: Atomic radius must be very small compared to host atom

Example: carbon in steel

Exercise Calculate the maximum size of an interstitial atom for dissolving in

BBC iron ?

Chapter 4 - 14

Conditions for Substitutional Solid Solution SSS

For Material A and B: they can form substitutional solid solution if they satisfy: W. Hume – Rothery rule i.e.

IF:1. r (atomic radius) < + or - 15% 2. Same crystal structure for pure metals3. Similar electronegativities - i.e., Proximity in periodic table

the difference in electronegativity must be ≤ ± 0.4 eV(i.e. large differences → compound formation (intermetallics))

4. ValencyAll else being equal,

a solute with a higher valency is more likely to be soluble than one of lower valency

If only part of the conditions are satisfied SSS with partial solubility

If any portion of A dissolves in any portion of B SSS with complete solubility

Chapter 4 - 15

Examples: Substitutional Solid Solution

Examples:1) Check Cu in NiAll O.K. SSS with complete solubility

2) Check Cu in AgAll O.K.SSS with complete solubility

3) Check Ni in CoCrystal structure is differentSSS with partial solubility

Element Atomic Crystal Electro-Valence

Radius 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

Application of Hume–Rothery rules – Solid Solutions

Chapter 4 - 16

Composition of Solutions

• 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

Chapter 4 - 17

Linear Defects

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 to dislocation line

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

Chapter 4 - 18

Dislocations

Edge Dislocation

Chapter 4 - 19

Dislocations

Screw Dislocation

Burgers vector b

Dislocationline

b

(a)(b)

Screw Dislocation

Chapter 4 - 20

Edge, Screw, and Mixed Dislocations

Edge

Screw

Mixed

Chapter 4 - 21

Planar Defects in Solids1. External Surfaces2. Grain Boundaries3. Twin boundary (plane): Essentially a reflection of atom positions across the twin plane.

4. Stacking faults- For FCC metals an error in ABCABC packing sequence- Ex: ABCABABC

Chapter 4 - 22

Microscopic ExaminationCrystallites (grains) - Have grain boundaries. - Vary considerably in size. - Crystallites 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. Preparation of specimen

- Cutting - grinding – polishing mirror like surface - etching (immersing in chemical solution)

reaction with atoms at grain boundaries: high chemical reactivity They dissolve into the solution forming grooves among the grain boundaries

Chapter 4 - 23

• 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

Optical Microscopy

crystallographic planes

Chapter 4 - 24

Grain boundaries...• are imperfections,• are more susceptible to etching,• may be revealed as dark lines,• change in crystal orientation across boundary.

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 4 - 25

• 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