1. crystal imperfections

7/29/2019 1. Crystal Imperfections

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SCES2338: SOLID STATE CHEMISTRY

A. Outline of the Overall Topic

Course Content1 Crystal and close-packed structures

2 Bonding in solids specifically ionic and partial covalent bonding

3 Bonding in metals and band theory

4 Crystal imperfections

5 Cases of non-stoichiometry in compounds and solid solutions

6 Phase diagrams

7 Electrical, magnetic and optical properties

References

1 West, A. R. (1996). Basic Solid State Chemistry. John Wiley & Sons.

2 Rodgers, G. E. (1994). Introduction to Coordination Solid State and Descriptive

Chemistry.

3 Christman, J. R. Fundamentals of Solid State Physics.

4 Ladd, M. F. F. (1979). Structure and Bonding in Solid State Chemistry. Halsted Press.


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A. Outline of the Overall Topic

Timetable

Tuesday: 9.00-9.50 AM D112; Dr. Rusnah Syahila; L6-29

Thursday: 9.00-9.50 AM D112; Dr. Nor Asrina ; L7-33

Examination Schedule

4-January-2013

11.30 AM

B. Assessment Method

Evaluation

1 Final examination: 70%

2 Continuous assessment: 30%

Soft Skills

1 CRITICAL THINKING AND PROBLEM SOLVING SKILLS

CT2 (The ability to develop and improve thinking skills such as to explain, analyse and evaluate discussions)

2

COMMUNICATION SKILLS

CS1 (The ability to present ideas clearly, effectively and confidently, in both oral and written forms)


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1.0 Introduction to Solid State Chemistry

Historical PerspectiveMaterials are so important in the development of civilization

Stone Age natural materials (stone, clay, skins, and wood).

Bronze Age (3000 BC) people found copper and how to make it harder by alloying

1200 BC use of iron and steel, a stronger material that gave advantage in wars

1850 discovery of a cheap process to make steel, which enabled the railroads and

the building of the modern infrastructure of the industrial world.

http://www.llbchamber.ca

monaghan.ie

http://www.exploringsurreyspast.org.uk

https://mywebspace.wisc.edu http://www.ehow.com


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Material Science and EngineeringUnderstanding of how materials behave and why they differ in properties

Materials Science: the combination of physics, chemistry, and the focus on the

relationship between the properties of a material and its microstructure.

Materials Engineering: the development of material science allowed designing

materials and provided a knowledge base for the engineering applications.

Structure: At the atomic level: arrangement of atoms in different ways. (Gives different

properties for graphite than diamond both forms of carbon.)

Properties are the way the material responds to the environment. For instance, the

mechanical, electrical and magnetic properties are the responses to mechanical,

electrical and magnetic forces, respectively. Other important properties are thermal(transmission of heat, heat capacity), optical(absorption, transmission and scattering of

light), and the chemical stabilityin contact with the environment (like corrosion

resistance).

Processing of materials is the application of heat (heat treatment), mechanical forces,

etc. to affect their microstructure and, therefore, their properties.


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Why Study Material Science and Engineering

To be able to select a material for a given use based on considerations of cost and

performance.

To understand the limits of materials and the change of their properties with use.

To be able to create a new material that will have some desirable properties.

All engineering disciplines need to know about materials. Even the most "immaterial",

like software or system engineering depend on the development of new materials,

which in turn alter the economics, like software-hardware trade-offs. Increasing

applications of system engineering are in materials manufacturing (industrial

engineering) and complex environmental systems.


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Classification of Materials

According to the way the atoms are bound together

Metals: valence electrons are detached from atoms, and spread in an 'electron

sea' that "glues" the ions together. Strong, conduct electricity and heat and are

opaque to light. Examples: aluminum, steel, brass, gold.Semiconductors: covalent bonding. Electrical properties depend on proportions

of contaminants. They are opaque to visible light but transparent to the

infrared. Examples: Si, Ge, GaAs.

Ceramics: atoms behave mostly like either positive or negative ions, and are

bound by Coulomb forces between them. Usually combinations of metals or

semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides).

Examples: glass, porcelain, many minerals.

Polymers: bound by covalent forces and weak van der Waals forces, and usually

based on H, C and other non-metallic elements. They decompose at moderate

temperatures (100 400 C), and are lightweight. Other properties vary greatly.

Examples: plastics (nylon, Teflon, polyester) and rubber.


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Solid materials are classified according to the regularity withwhich atoms or ions are arranged with respect to one another.

Crystalline Solids vs. Amorphous Solids

In crystalline materials atoms are

situated in a repeating array over

large atomic distances.

In amorphous materials long range

order do not exist


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1.0 Crystal Imperfections

Imperfections in solidsThe properties of some materials are greatly influenced by the presence

ofimperfections.

It is important to have knowledge about the types of imperfections that

exist and the roles they play in affecting the behavior of materials.

Atom Purity and Crystal PerfectionIf we assume a perfect crystal structure containing pure elements, then

anything that deviated from this concept or intruded in this uniform

homogeneity would be an imperfection.

1. Real crystalline solids are almost never perfect.

2. Many materials are technologically of value because they are disordered.

3. Many material properties are improved by the presence of imperfections

and deliberately modified (alloying and doping).


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1.0 Solidification

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

grain structurecrystals growingnuclei liquid


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1.0 Grain Boundaries

Regions between crystals

Transition from lattice of

one to that of the other

Slightly disordered

Low density in grainboundaries

- high mobility

- high diffusivity

-high chemical reactivity

grain can be

- roughly same size in all

directions

- columnar

Adapted from Fig. 5.12,

Callister & Rethwisch 3e.


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1.0 Structural Imperfections (Defects) in Crystalline Solids

Perfect crystal vs. Imperfect crystal

all atoms on their correct lattice positions

(actual positions affected by extent of

thermal vibrations which can be

anisotropic)

1. Point defects (0-Dimension)

2. Line defects (1-D)

3. Interfacial defects (2-D)

4. Volume defects (3-D)

Imperfections can be classified according to their dimensionality

Intrinsic defects - do not change overall composition- stoichiometric defects

- two common types: Schottky and Frenkel defects

Extrinsic defects - created when foreign atom(s) introduced or there isvalence change

Real crystals contain both intrinsic and extrinsic defects


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1.0 Types of Imperfections (Defects)

Crystal defects

Point defects Line defects Volume defects

Self interstitial

Interfacial defects

Inclusions

VoidsScrew dislocations

Edge dislocations

Schottky

Vacancy

Frenkel

Substitutional

Colour centres

Grain boundaries

Tilt boundaries

Twin boundaries

Stacking faults


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1.0 Point Defects in Crystals

0D(Point defects)

Vacancy

Impurity

Frenkel defect

Schottky defect

Non-ionic

crystals

Ioniccrystals

Interstitial

Substitutional

Other

Zero Dimensional or Point Defects

Vacancy equals an empty lattice site.

Interstitialcy equals an atom occupying a site between atoms inthe crystal lattice.

Schottky defect - cation - anion vacancy pair in an ionic crystal.

Frenkel defect - vacancy interstitial pair in an ionic lattice.

Point defects provide opportunity for atomic mixing.


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1.0 Point Defects in Crystals: Vacancy

Missing atom from an atomic siteAtoms around the vacancy displaced

Stress field produced in the vicinity of the vacancy

Based on their origin vacancies can be

Random/Statistical (thermal vacancies, which are required by

thermodynamic equilibrium) or Structural (due to off-stoichiometry in a compound)

Based on their position vacancies can be random or ordered

Vacancies play an important role in diffusion of substitutional atoms

Non-equilibrium concentration of vacancies can be generated by:

quenching from a higher temperature or

by bombardment with high energy particles

Vacancy

distortion

of planes


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1.0 Point Defects in Crystals: Impurity

Impurity

Interstitial

Substitutional

Tensile Stress

Fields

Or alloying element

Foreign atom replacing

the parent atom in the

crystal

Compressive

stress fields

-Interstitials exist for

cations.

-interstitials are not

normally observed for

anions because

anions are large

relative to the

interstitial sites

Cation

interstitial


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1.0 Impurities in Metals

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.

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

Solid solution ofB in A plus particles of a new

phase (usually for a larger amount of B)


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1.0 Impurities in Ceramics

Electroneutrality (charge balance) must be maintainedwhen impurities are present

Eg: NaCl Na+ Cl-

Substitutional cation impurity

without impurity Ca2+ impurity with impurity

Ca2+

Na+

Na+Ca2+

cation

vacancy

Substitutional anion impurity

without impurity O2-impurity

O2-

Cl-

an ion vacancy

Cl-

with impurity


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1.0 Impurities in Polymers

Defects due in part to chain packing errors and impurities such as

chain ends and side chains



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1.0 How Do Impurities Affect the Structure and Properties of A Solid?

To obtain a perfectly pure substance is almost impossible.Purification is a costly process.

In general, analytical reagent-grade chemicals are of high purity, and yet

few of them are better than 99.9% pure.

This means that a foreign atom or molecule is present for every 1000

host atoms or molecules in the crystal. The most demanding of purity is

in the electronic industry.

Silicon crystals of 99.999 (called 5 nines) or better are required for IC

chips productions. These crystal are doped with nitrogen group elements

of P and As or boron group elements B, Al etc to form n- and p-typesemiconductors.

In these crystals, the impurity atom substitute atoms of the host crystals.


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Presence of foreign atoms with one electron more or less than the

valence four silicon and germanium host atoms is the key of making n- a

and p-type semiconductors.

Having many semiconductors connected in a single chip makes the

integrated circuit a very efficient information processor.

The electronic properties change dramatically due to these impurities.

In other bulk materials, the presence of impurity usually leads to a

lowering of melting point.


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For example, Hall and Heroult tried to electorlyze natural aluminum

compounds.

They discovered that using a 5% mixture of Al2O3 (melting point 273 K) in

cryolite Na3AlF6 (melting point 1273 K) reduced the melting point to 1223

K, and that enabled the production of aluminum in bulk.

Recent modifications lowered melting temperatures below 933 K.

Some types of glass are made by mixing silica (SiO2), alumina (Al2O3),

calcium oxide (CaO), and sodium oxide (Na2O).

They are softer, but due to lower melting points, they are cheaper to

produce.


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1.0 Point Defects in Crystals: Frenkel defects

In ionic crystal, during the formation of the defect the overall electrical neutrality hasto be maintained (or to be more precise the cost of not maintaining electrical

neutrality is high)

Frenkel defects

A cation vacancyCation being smaller get displaced to interstitial voids

A Frenkel defect usually occurs only on one sublattice of a crystal, and consists of

an atom or ion moving into an interstitial position thereby creating a vacancy.

For an alkali-halide-type structure, such as NaCl, where one cation moves out of

the lattice and into an interstitial site.

This type of behaviour is seen, for instance, in AgCl, where we observe such acation Frenkel defectwhen Ag+ ions move from their octahedral coordination

sites into tetrahedral coordination.

This kind of self interstitial costs high energy in simple metals and is not usually

found [Hf(vacancy) ~1eV; Hf(interstitial) ~3eV]


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1.0 Point Defects in Crystals: Schottky defects

Schottky defectsPair of anion and cation vacanciesFor a 1:1 solid MX, a Schottky defect consists ofa pairof vacant sites, a cation

vacancy, and an anion vacancy.

The number of cation vacancies and anion vacancies have to be equal to

preserve electrical neutrality.

A Schottky defect for an MX2 type structure will consist of the vacancy caused by

the M2+ ion together with two X anion vacancies, thereby balancing the

electrical charges.

Schottky defects are more common in 1:1 stoichiometry and examples of

crystals that contain them include rock salt (NaCl), wurtzite (ZnS), and CsCl.


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1.0 Point Defects in Crystals: Other defects

Other defects due to charge balanceIf Cd2+ replaces Na+ one cation vacancy is created


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1.0 Point Defects in Crystals: Methods of Producing Point Defects

Growth and synthesis- Impurities may be added to the material during synthesis

Thermal & thermochemical treatments and other stimuli- Heating to high temperature and quench

- Heating in reactive atmosphere- Heating in vacuum e.g. in oxides it may lead to loss of oxygen

Plastic Deformation

Ion implantation and irradiation- Electron irradiation (typically >1MeV)

Direct momentum transfer or during relaxation of electronic excitations)

- Ion beam implantation (As, B etc.)

- Neutron irradiation


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1.0 Thermodynamics of Point Defects

All macroscopic samples of materials contain some defects as defectformation is entropically favored ( the presence of vacancies increases the

entropy (randomness))

when defect formation is enthalpically very unfavorable there may be very

small numbers of defects

Free energy,

G = H - TS

Ener

gy

[defect]

Entropy, -TS

Enthalpy, H

at this point a breakdown in structure

will occur to form a new phase

requires energy to create defects !

H inc but S also inc

G = H - TS

Temperature

-TS incs with inc T moredefects at higher T

SC S2338 SO S C S


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1.0 How often Do Vacancies Jump

The equilibrium number of vacancies for a given quantity of material dependson and increases with temperature (an Arrhenius model).

Distance

Energy

Atom Vacancy

EV

Rj= Ro exp(-Ev/kBT)E

v= activation energy (energy needed by the atom to jump)

Rj= frequency of jumps (depend on temperature)

Ro= attempt frequency

kB=Boltzmann constant (1.381 x 10-23 J/K

T=temperature

SCES2338 SOLID STATE CHEMISTRY


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1.0 Thermodynamics of Point Defects

To follow dotted arrow - Na+ would have to push two Cl- apart to pass through to vacancy

Less energy needed to follow solid arrow

This is a close-packed

lattice, so the Cl-

ions are incontactNa+

Cl-

V-Na

migrating Na+

EV

length of jump



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1.0 How Many Vacancies are There?

NvN

=exp -EvkBT

Each lattice

site is a

potential

vacancy site

Equilibrium concentration varies with temperature!

Nv= number of defects

N= number of potential defect sitesEv= activation energy

kB=Boltzmann constant (1.381 x 10-23 J/K or 8.62 x 10-5 eV/K)

T=temperature

Ev obtained from an experiment.

Nv

N

T

exponentialdependence!

1/T

N

Nvln

-Ev/k

slope



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1.0 Line (Dislocation) Defects

Are one-dimensional defects around which atoms are misaligned Edge dislocation:

- extra half-plane of atoms inserted in a crystal structure

- b perpendicular () to dislocation line Screw dislocation:

- spiral planar ramp resulting from shear deformation

- b parallel () to dislocation line

Burgers vector, b: is a measure of lattice distortion and is measured as a distance

along the close packed directions in the lattice

EDGE

DISLOCATIONS

MIXED SCREW



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1.0 Line (Dislocation) Defects

Mixed dislocation. This dislocation

has both edge and screw character

with a single Burgers vector

consistent with the pure edge and

pure screw regions.

Screw dislocation. The spiral

stacking of crystal planes leads to

the Burgers vector being parallel to

the dislocation line.

Definition of the Burgers vector, b, relative to an edge dislocation. (a) In the

perfect crystal, an m n atomic step loop closes at the starting point. (b) In

the region of a dislocation, the same loop does not close, and the closure

vector (b) represents the magnitude of the structural defect. For the edge

dislocation, the Burgers vector is perpendicular to the dislocation line.



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1.0 Line (Dislocations) Defects

Dislocation is a boundary between the slipped and the unslipped partsof the crystal lying over a slip plane

slip between crystal planes result when dislocations move,

produce permanent (plastic) deformation.

Slipped

part

of the

crystal

Unslipped

part

of the

crystal

Deformation of Zinc:

before after tensile elongation

slip steps



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1.0 Imperfections in Solids

Edge Dislocation

Adapted from Fig. 5.9, Callister & Rethwisch 3e.

Screw Dislocation

Edge

Screw

MixedFig. 5.8, Callister & Rethwisch 3e.



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Plane/planar/surface/interfacial defects twin boundary (plane)

Essentially a reflection of atom positions across the twinplane.

Stacking faults

For FCC metals an error in ABCABC packing sequence

Ex: ABCABABC34


1.0 Interfacial Defects Twin & Stacking Faults Defects

Adapted from Fig. 5.14,


change in crystalorientation during

growth



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1.0 Interfacial Defects Grain Defects

Solids generally consist of a number ofcrystallites or grains.

Grains can range in size from nanometers

to millimeters across and their orientations

are usually rotated with respect to

neighboring grains

Grain boundaries limit the lengths andmotions of dislocations

Therefore, having smaller grains (more

grain boundary surface area) strengthens a

material

The size of the grains can be controlled by

the cooling rate when the material cast orheat treated

Generally, rapid cooling produces smaller

grains whereas slow cooling result in larger

grains



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1.0 Volume (Bulk) Defects

Volume/bulk/area defectsBulk defects occur on a much bigger scale than the rest of the crystal defects

VoidsVoids are regions where there are a large number of atoms missing from the lattice.

When voids occur due to air bubbles becoming trapped when material solidifies, it is

commonly called porosity. When a void occurs due to the shrinkage of a material as itsolidifies, it is called cavitation.

InclusionsImpurity atoms cluster together to form small regions of a different phase. The term

phase refers to that region of space occupied by a physically homogeneous material.

These regions are often called precipitates or inclusions.



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1.0 Visualization of Defects

Crystallites (grains) and grain boundaries. Vary considerably in size. Canbe quite large.

Crystallites (grains) can be quite small (mm or less) necessary to

observe with a microscope (OPM, SEM, STM).

Scanning Tunneling Microscopy (STM)Optical Polarizing Microscopy (OPM)

Carbon

monoxide

molecules

arranged on a

platinum (111)

surface.

Iron atoms

arranged on a

copper (111)

surface.

Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M.

Eigler.

0.75mm

Micrograph of

brass (a Cu-Zn alloy)

Adapted from Fig. 5.18(b) and (c), Callister & Rethwisch 3e. (Fig. 5.18(c) is

courtesy of J.E. Burke, General Electric Co.)



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1.0 Importance of Imperfections

Most of the properties of materials are affected by imperfections:

Small amount of impurity atoms may increase the electrical conductivity

of semi conductors.

Dislocations are responsible for ductility.

Strength of materials can be increased to a large extent by the

mechanism strain-hardening which produces line defects that act as a

barrier to control the growth of other imperfections.

Presence of bulk defects such as cracks, notches, holes causes brittle

materials, which break at very low stresses without showing large

deformations.

1. crystal imperfections

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