IMPERFECTIONS IN SOLIDS

Week 3

1

2

• 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

Imperfections in Solids

• Crystals grow until they meet each other

nuclei crystals growing grain structureliquid

3

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

4

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

5

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.

Crystalline defect -> a lattice irregularity having one or more of its dimensions on the order of an atomic diameter

6

• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects

Types of Imperfections

• Dislocations Line defects

• Grain Boundaries Area defects

7

• 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

8

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

9

• 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

EXAMPLE PROBLEM 4.1

Calculate the equilibrium number of vacancies per cubic meter for copper at 1000C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000C) for copper are 63.5g/mol and 8.4g/cm3, respectively

10

11

Find the equil. # of vacancies in 1m3 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 sites8.62 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

=N.Acu/V.NA

12

• Low energy electron microscope view of a (110) surface of NiAl.• Increasing T causes surface island of atoms to grow.• Why? The equil. vacancy conc. increases via atom motion from the crystal to the surface, where they join the island.

Observing Equilibrium Vacancy Concentration.

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

IMPURITIES IN SOLIDS• Impurity or foreign atoms will always be

present, and some will exist as crystalline point defects

• Alloys -> impurity atoms have been added intentionally to impart specific characteristics to the material

• Alloying with copper significantly enhances the mechanical strength without depreciating the corrosion resistance appreciably

• The addition of impurity atoms to a metal will result in the formation of a solid solution

13

14

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

Point Defects in Alloys

15

Imperfections in Solids

Conditions for substitutional solid solution (S.S.)• W. Hume – Rothery rule

– 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

Substitutional Solid Solution – Cu-Ni

• The atomic radii for copper and nickel are 0.128 and 0.125nm, respectively

• Both have the FCC crystal structure

• Their electronegativities are 1.9 and 1.8

• Valencies for Cu and Ni are +2

16

17

Imperfections in SolidsApplication of Hume–Rothery rules – Solid

Solutions

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

2. More Zn or Al

in Cu?

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

Conditions for Interstitial Impurity

• The atomic diameter of an interstitial impurity must be substantially smaller than that of the host atoms

• The maximum allowable concentration of interstitial impurity atoms is low

• Even very small impurity atoms are ordinarily larger than the interstitial sites, and as a consequence they introduce some lattice strains on the adjacent host atoms

• Different crystal structures can fill interstitials

18

19

Specification of Composition

– weight percent100x

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

20

• 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

Dislocations - Line Defects

21

Imperfections in Solids

Linear Defects (Dislocations)– Are one-dimensional defects around which atoms are misalignedBurgers vector (b) represents the magnitude and direction of the

distortion of dislocation in a crystal lattice

Dislocation Line -> A curve running along the center of a dislocation.

• 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

22

Imperfections in Solids

Edge Dislocation

23

• Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here).• Bonds across the slipping planes are broken and remade in succession.

Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.

Motion of Edge Dislocation

24

Imperfections in Solids

Screw Dislocation

Burgers vector b

Dislocationline

b

(a)(b)

Screw Dislocation

25

Edge, Screw, and Mixed Dislocations

Edge

Screw

Mixed

26

Imperfections in Solids

Dislocations are visible in electron micrographs

51,450 magnified

27

Planar Defects in Solids• One case is a twin boundary (plane)

– Essentially a reflection of atom positions across the twin plane.

• A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry

• Annealing twins are typically found in metals that have the FCC crystal structure, while mechanical twins are observed in BCC and HCP metals

Planar Defects in Solids

• Stack Fault are found in FCC metals when there is an interruption in the ABCABCABC . . . stacking sequence of close-packed planes

• Phase boundaries exist in multiphase materials across which there is a sudden change in physical and/or chemical characteristics

28

Bulk or Volume Defects

• Other defects exist in all solid materials that are much larger than those discussed

• These include pores, cracks, foreign inclusions, and other phases

• They are normally introduced during processing and fabrication steps.

29

Numerical Problems

• Problems 4.1 to 4.5 and 4.7 to 4.25

30