introduction to materials science, chapter 4, imperfections in solids university of virginia, dept....

Introduction To Materials Science, Chapter 4, Imperfections in solids

University of Virginia, Dept. of Materials Science and Engineering 1

“Crystals are like people, it is the defects in them which tend to make them interesting!” - Colin Humphreys.

• Defects in Solids

0D, Point defects vacancies interstitials impurities, weight and atomic composition

1D, Dislocations edge screw

2D, Grain boundaries tilt twist

3D, Bulk or Volume defects

Atomic vibrations

4.9 - 4.11 Microscopy & Grain size determination –

Not Covered / Not Tested

Chapter Outline



Real crystals are never perfect, there are always defects

Schematic drawing of a poly-crystal with many defects by Helmut Föll, University of Kiel, Germany.

Defects – Introduction (I)



Defects – Introduction (II)

Defects have a profound impact on the macroscopic properties of materials

Bonding

+

Structure

+

Defects

Properties



Composition

Bonding Crystal Structure

ThermomechanicalProcessing

Microstructure

Defects – Introduction (III)

Processing determines the defects

defect introduction and manipulation



Types of Defects

Four categories depending on their dimension

0D, Point defects: atoms missing or in irregular places in the lattice (vacancies, interstitials, impurities)

1D, Linear defects: groups of atoms in irregular positions (e.g. screw and edge dislocations)

2D, Planar defects: interfaces between homogeneous regions of the material (grain boundaries, external surfaces)

3D, Volume defects: extended defects (pores, cracks)



Point defects: vacancies &interstitials

Self-interstitials

Vacancy

Vacancy - lattice position that is vacant because atom is missing.

Interstitial - atom that occupies a place outside the normal lattice position. May be same type of atom (self interstitial) or an impurity interstitial.



Equilibrium number of vacancies is due to thermal vibrations

How many vacancies?

Ns = number of regular lattice sites

kB = Boltzmann constant

Qv = energy to form a vacant lattice site in a

perfect crystal T = temperature in Kelvin (note, not in oC or oF).

Room temperature in copper: one vacancy per 1015 atoms.Just below the melting point: one vacancy for every 10,000 atoms.Above lower bound to number of vacancies. Additional (non-equilibrium) vacancies introduced in growth process or treatment

(plastic deformation, quenching, etc.)

Tk

QexpNNB

vsv



Estimate number of vacancies in Cu at room T

kB = 1.38 10-23 J/atom-K = 8.62 10-5 eV/atom-K

T = 27o C + 273 = 300 K. kBT = 300 K 8.62 10-5 eV/K = 0.026 eV

Qv = 0.9 eV/atom

Ns = NA/Acu

NA = 6.023 1023 atoms/mol

= 8.4 g/cm3

Acu = 63.5 g/mol

Tk

QexpNNB

vsv

3

223

23

s cmatoms108

molg5.63

cmg4.8mol

atoms10023.6N

atomeV026.0

atomeV9.0expcm

atoms108N

322

v

37 cmvacancies104.7



Large distortions in surrounding lattice Energy of self-interstitial formation is ~ 3 x larger than for vacancies (Qi ~ 3Qv) equilibrium concentration of self-interstitials is very low(< 1/ cm3 at 300K)

Self-interstitials

1

2

3

4

5

Point defects: self-interstitials, impurities

(1) vacancies(2) self-interstitial(3)interstitial impurity(4,5)substitutional impurities

Arrows local stress introduced by defect



Impurities

Impurities atoms which differ from host

All real solids are impure. Very pure metals 99.9999%

- one impurity per 106 atoms May be intentional or unintentional

Carbon in small amounts in iron makes steel. It is stronger.

Boron in silicon change its electrical properties.

Alloys - deliberate mixtures of metalsSterling silver is 92.5% silver – 7.5% copper alloy.

Stronger than pure silver.



How Are Impurities Contained in Alloy?Solid solutions

Host (Solvent or Matrix) dissolves minor component (Solute). Ability to dissolve is called Solubility. Solvent: element in greater amount Solute: element present in lesser amount Solid Solution:

homogeneous maintain crystal structure randomly dispersed impurities

(substitutional or interstitial)

Second Phase As solute atoms added: new compounds or structures form or solute forms local precipitates

Whether addition of impurities results in a solid solution or second phase depends nature of impurities, concentration, temperature and pressure



Substitutional Solid Solutions

Factors for high solubility(Solubility limit maximum that can dissolve)

Atomic size: need to “fit” solute and solvent atomic radii should be within ~ 15%

Crystal structure: solute and solvent the same

Electronegativities: should be comparable (otherwise new inter-metallic phases favored)

Valency: If solute has higher valency than solvent, generally more goes into solution

Ni

Cu



Interstitial Solid Solutions

Factors for high solubility:

FCC, BCC, HCP: void space between host (matrix) atoms relatively small atomic radius of solute should be significantly less than solvent

Max. concentration 10%, (2% for C-Fe)

Carbon interstitial atom in BCC iron

Interstitial solid solution of C in BCC Fe ( phase). C small enough to fit (some strain in BCC lattice).



Composition / Concentration

atom percent (at %): useful in understanding material at atomic level

Number of moles (atoms) of one element relative to total number of moles (atoms) in alloy.

2 component: concentration of element 1 in at. %:

Weight Percent (wt %)

Weight of one element relative to total alloy weight

2 components: concentration of element 1 in wt. %

100mm

mC

21

11

100nn

nC

21

1

mm

m'1

nm1= number density = m’1/A1 (m’1 = weight in

grams of 1, A1 is atomic weight of element 1)



Composition Conversions

Weight % to Atomic %:

100ACAC

ACC

2'21

'1

1'1

1

Atomic % to Weight %:

100ACAC

ACC

2'21

'1

2'2

2

100ACAC

ACC

1221

21'1

100ACAC

ACC

1221

12'2

Textbook, pp. 71-74



Dislocations = Linear Defects

Interatomic bonds significantly distorted in immediate vicinity of dislocation line

(Creates small elastic deformations of lattice at large distances.)

Dislocations affect mechanical properties Discovery in 1934 by Taylor, Orowan and Polyani marked beginning of our understanding of mechanical properties of materials



Describe Dislocations Burgers Vector

Burgers vector, b, describes size + direction of lattice distortion by a dislocation. Make a circuit around dislocation: go from atom to atom counting the same number of atomic distances in both directions.

Vector needed to close loop is bb

Burgers vector above directed perpendicular to dislocation line. These are called edge dislocations.



Screw dislocations

Screw dislocation: parallel to the direction in which the crystal is being displaced Burgers vector parallel to dislocation line

Edge dislocation: Burgers vector perpendicular to dislocation line.

Find the Burgers vector of a screw dislocation. How did it get its name?



Interfacial DefectsExternal SurfacesSurface atoms unsatisfied bonds higher energies than bulk atoms Surface energy, (J/m2)

• Surface areas try to minimize (e.g. liquid drop)

• Solid surfaces can “reconstruct” to satisfy atomic bonds at surfaces.

Grain BoundariesPolycrystalline: many small crystals or grains. Grains have different crystallographic orientation. Mismatches where grains meet.

1. Surfaces and interfaces are reactive

2. Impurities tend to segregate there.

3. Extra energy associated with interfaces

larger grains tend to grow by diffusion of atoms at expense of smaller grains, minimizing energy.



High and Low Angle Grain Boundaries

Misalignments of atomic planes between grains Distinguish low and high angle grain boundaries



Tilt and Twist Grain Boundaries

Tilt boundary Low angle grain boundary: an array of aligned edge dislocations (like joining two wedges)

Twist boundary - boundary region consisting of arrays of screw dislocations (like joining two halves of a cube and twist an angle around the cross section normal)

Transmission electron microscope image of a small angle tilt boundary in Si. The red lines mark the edge dislocations, the blue lines indicate the tilt angle



Bulk or Volume Defects

Pores: affect optical, thermal, mechanical properties

Cracks: affect mechanical properties Foreign inclusions: affect electrical,

mechanical, optical properties

Cluster of microcracks in a melanin granule irradiated by a short laser pulse. Computer simulation by L. V. Zhigilei and B. J. Garrison.



Atomic Vibrations

Heat causes atoms to vibrate

Vibration amplitude increases with temperature

Melting occurs when vibrations are sufficient to rupture bonds

Vibrational frequency ~ 1013 Hz

Average atomic energy due to thermal excitation is of order kT



Summary

Alloy Atom percent Atomic vibration Boltzmann’s constant Burgers vector Composition Dislocation line Edge dislocation Grain size Imperfection Interstitial solid solution Microstructure Point defect Screw dislocation Self-Interstitial Solid solution Solubility limit Solute Solvent Substitutional solid solution Vacancy Weight percent

Understand language and concepts:

introduction to materials science, chapter 4, imperfections in solids university of virginia, dept....

Documents

materials science

defects defect introduction

planar defects

linear defects

types of defects

solids university of

extended defects pores

lattice vacancies