CHAPTER 4

IMPERFECTIONS 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

undesirab

le?

• What are the

solidification

mechanisms?

Chapter 4 1

Introduction

Ideally : Perfect Order Really : various defects or imperfections Atomic Vibration : Every Atom is vibrating around its lattice position



Defects

• • • •

Levels of Defects Point Linear Interfacial Bulk: pores, cracks and foreign inclusions (bubble, sand ..etc).

Require : Examination of Structure ? Techniques Application : Solid Solutions = Solvent (host atoms) and Solute



Alloy Why?

1) to improve mechanical properties 2) Most metals are alloys ( impurities always exist).

Chapter 4 -

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

“ De fect ” can be either desirable or undesirable.

Chapter 4 3

Solidification

Mechanism

• 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 nuclei crystals growing grain structure liquid • Crystals grow until they meet each other Chapter 4 4

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 5

Grains can be

Solidification

- equiaxed (roughly same size in all directions) - columnar (elongated grains) ~ 8 cm heat flow 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.

Chapter 4 6

Types of Imperfections • Vacancy atoms • Substitutional atoms • Interstitial atoms • Dislocations • Grain Boundaries Point defects Line defects Area defects -Planar

Chapter 4 7

Point Defects

• Vacancies : -vacant atomic sites in a structure.

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

Vacancy self interstitial distortion of planes Chapter 4 8

Equilibrium Concentration: Point Defects -

Vacancy • Equilibrium concentration of

vacancies

varies with temperature!

No. of defects No. of potential defect sites.

N N v

Activation energy = exp     -

Q v k T

Temperature Boltzmann's constant (1.38 x 10 -23 J/atom-K) (8.62 x 10-5 eV/atom-K) Each lattice site is a potential vacancy site Chapter 4 9

Measuring Activation Energy

• We can get

Q v

an experiment.

from • Measure this...

N N v

= exp     -

Q v k T

• Replot it...

Nv N

exponential dependence!

defect concentration

T

ln

Nv N

slope -

Qv

/

k

1/

T

Chapter 4 10

Estimating Vacancy Concentration

• Find the equil. # of vacancies in 1 m 3 • Given: r = 8.4 g /cm 3

A

of Cu at 1000 Cu = 63.5 g/mol  C.

Qv

= 0.9 eV/atom

N

A = 6.02 x 10 23 atoms/mol • Answer:

N N v

= exp     -

Q v k T

 = 2.7 x 10 1273K -4 8.62 x 10 -5 eV/atom-K For 1 m 3 ,

N

= r x

N

A

A

Cu x 1 m 3 = 8.0 x 10 28 sites

Nv

= (2.7 x 10 -4 )(8.0 x 10 28 ) sites = 2.2 x 10 25 vacancies Chapter 4 11

Point Defects in Alloys

Two outcomes if impurity (B) added to host (A): • Solid solution of B in A (i.e., random dist. of point defects)

OR Substitutional (e.g., Cu solid soln.

in Ni )

When similar

Interstitial solid soln.

(e.g., C in Fe )

smaller

Partial Solubility: Solid solution of B (usually for a larger amount of B) in A plus particles of a new phase Second phase particle - different composition - often different structure.

Chapter 4 12

Interstitial Solid Solution

• Impurity atoms fill voids • Always APF < 1  among the host atoms there are always voids • • For metals : strong (metallic bonding)   small voids  highly packed 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 -

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 metals 3. Similar electronegativities

the difference

- i.e., Proximity in periodic table

in electronegativity must be ≤ ± 0.4 eV (i.e. large differences → compound formation (intermetallics)) 4.

Valency All 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 14

Examples: Substitutional Solid Solution

Application of Hume –Rothery rules – Solid Solutions Examples: 1) Check Cu in Ni All O.K.  SSS with complete solubility 2) Check Cu in Ag All O.K.

SSS with complete solubility 3) Check Ni in Co Crystal structure is different SSS with partial solubility Cu C H O Ag Al Co Cr Fe Ni Pd Zn

Element Atomic Crystal Radius Structure (nm)

FCC 0.1278

0.071

0.046

0.060

0.1445

0.1431

0.1253

0.1249

0.1241

0.1246

0.1376

0.1332

FCC FCC

HCP

BCC BCC

FCC

FCC HCP

Electro nega tivity

1.9

1.9

1.5

1.8

1.6

1.8

1.8

2.2

1.6

Valence

+2 +1 +3 +2 +3 +2 +2 +2 +2 Chapter 4 15

Composition of Solutions

• Specification of composition – weight percent

C

1 =

m

1

m

1 

m

2 x 100

m 1

= mass of component 1 – atom percent

C

1 ' =

n m

1

n m

1 

n m

2 x 100

n m1

= number of moles of component 1 Chapter 4 16

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 17

Dislocations

Edge Dislocation Chapter 4 18

Screw Dislocation

Screw Dislocation

Dislocations

Dislocation line Burgers vector b (a) b (b) Chapter 4 19

Edge, Screw, and Mixed Dislocations

Mixed Edge Screw Chapter 4 20

1.

2.

3.

Planar Defects in Solids

External Surfaces Grain Boundaries 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 21

Microscopic Examination

Crystallites (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 22

Optical Microscopy

• Useful up to 2000X magnification.

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

crystallographic planes 0.75mm

Micrograph of brass (a Cu-Zn alloy) Chapter 4 23

Optical Microscopy

Grain boundaries...

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

polished surface (a) surface groove grain boundary ASTM grain size number

N

= 2

n

-1 number of grains/in 2 at 100x magnification Fe-Cr alloy (b) Chapter 4 24

Summary

• 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.) Chapter 4 25