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Chapter 4Solid Solutions and CrystallineImperfections

(Metals and Ceramics)

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Alloys

Most engineering metals are combined with other metals or

nonmetals to obtain improved properties. E.g. increased strength, higher corrosion resistance.

Alloy: a mixture of 2 or more metals, or a metal (metals) and a

nonmetal (nonmetals).

Simple

Cartrige

brassBinary alloy of70wt%

Cu & 30wt% Zn

Complex

Inconel Ni-base superalloy of10 elements

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Solid Solutions

The simplest type of alloy that contains 2 or more elements

dispersed in a single-phase structure.

Solvent atoms

Solute atoms

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2 Types of Metallic Solid Solutions

Iron host atoms

Solute atom (usually

larger than the host

atoms).

Iron host atoms

Solute atoms(usually small atoms

such as carbon).

Solute atoms displacing

atoms of the host (solvent).

Solute atoms located

between atoms of the host

(solvent).

Metalinterstitial solid solution

Metalsubstitutional solid solution

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Substitutional Solid Solution

Solute atoms substitute for parent

solvent atoms in a crystal lattice.

Crystal structure of parent (solvent)

element remains unchanged, but .

Lattice may get distorted by the

presence of solute atoms, especially if

their atomic diameters differ

significantly.

Solute percentage in solvent can

vary from fraction of a percentage

to 100%.

Solvent atoms Solute atoms

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Substitutional Solid Solutions (cont.)

Conditions that favor extensive solid solubility of 1

element in another:

1. Diameters of atoms must not differby more than 15%.

2. Crystal structures of both elements must be the same.

3. Similar e (else compounds will form).

4. Both elements have same valence.

Examples

SystemAtomic radius

difference (%)EN difference

Solid

Solubility (%)

Cu-Zn +3.9 0.1 38.3

Cu-Pb +36.7 0.2 0.17

Cu-Ni 2.3 0 100

H u m e -R o t h e ry solid solubility rules

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Application Hume-Rothery Rules

Is solid-solution favorable, or not?

Rule 1: %R 15%

2.3%( 100%)

nm0.128

nm0.128nm0.125( 100%)

R

RRR%

solvent

solventsolute

favorable

Rule 2: Both Cu and Ni have FCC crystal structure. favorable

Rule 3: ENCu = 1.90; ENNi= 1.80. Thus, EN = 0.10 favorable

Rule 4: Same valence, both Cu and Ni are +2. favorable

Cu-Ni system: Very high solid solubility - 100% solubility of Ni in Cu.

Cu-Ni Alloy

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Application Hume-Rothery Rules

Is solid-solution favorable, or not?

Rule 1: %R 15%

3.9%( 100%)

nm0.128

nm0.128nm0.133( 100%)

R

RRR%

solvent

solventsolute

favorable

Rule 2: Different crystal structure. Cu (FCC) ; Zn (HCP). NOT favorable X

Rule 3: ENCu = 1.90; ENZn= 1.70. Thus, EN = 0.20 favorable

Rule 4: Same valence, both Cu and Zn are +2. favorable

Cu-Zn system: limited solid solubility maximum solubility of 38.3%

Zn can be achieved at high temperature.

Cu-Zn Alloy

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Interstitial Solid Solution

Solute (foreign, impurity) atoms fit into spaces or holes (interstices)

between solvent (parent, matrix, host) atoms.

Solute atoms are much smallerthan solvent atoms.

E.g. ofsolute atoms: H, C, N & O.

E.g. of interstitial solid solution: carbon in FCC -iron. (RC atom = 0.075 nm;

RFe atom = 0.129 nm, Rlargest interstitial hole = 0.053 nm).

A maximum of 2.08% of carbon can dissolve interstitially in -iron.

Fe atoms

Distortion of Fe atoms

atoms around a C atom

Interstitial C atom

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Substitutional & Interstitial Solid Solutions

Thus, 2 possibilities when metals are alloyed:

Substitutional Solid Solution

foreign atom replaces host

atoms either in an orderly or

random arrangement.

Interstitial Solid Solution

foreign atom goes into holes

either in an orderly or random

arrangement.

Random: Cu in Ni

Ordered: Ni3Al super-alloy

Random: doped Si, C in Fe (steel)

Ordered: clays, ionic crystals,

ceramics

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Crystalline Imperfections

No crystal is perfect.

Real crystals contain defects or irregularities in the idealstructures described earlier.

Defects critically determine many of the electrical and

mechanical properties of real materials.

Crystal lattice imperfections are classified according to their

geometry & shape:

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Crystalline Defects

0-D orpoint defects (e.g. vacancy) 1-D or line defects (dislocations)

2-D orarea defects (interfacial defects) 3-D orvolume defects (cracks and pore)

Dislocation line

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Types of Defects in Crystalline Solids

Point, line, planar, and volumetric defects

Dimensional ranges of different classes of defects

Grain and twin

boundaries

Voids, precipitates

INTERFACIAL DEFECTS

Dislocations

LINE DEFECTS

Pores, cracks

Inclusions

VOLUME DEFECTS

DIMENSIONAL SCALE (m)

1014 1010 106 102 102

ELECTRONIC POINT

DEFECTS

Vacancies

impurities

ATOMIC POINT

DEFECTS

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Types of Point Defects in Metals

Point defect

Effect is localized to

a few atomic sites.

Atom of the same kind asthe host atoms occupy the

interstitial site.

Also called interstitialcy.

Cause distortion of planes

Selfinterstitial

Vacancy

Impurity atoms of substitutional or interstitial

type are defects present in metallic or

covalently bonded crystals. Substitutional can be smaller or larger than

host atoms; cause distortion of planes.

Interstitial impurity - smaller than host atoms

Leads to formation of substitutional or

interstitial solution.

Interstitial

Substitutional

Atom missing

from its atomic site

Cause distortion

of planes

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Point DefectsVacancy

Vacancy is formed due to a missing atom.

Vacancy is formed (one in 10,000 atoms) during crystallization or

mobility of atoms.

Energy of formation is 1 eV.

Vacancies can move by exchanging position with their neighbors.

Mobility of vacancy results in cluster of vacancies.

Also caused due to plastic deformation, rapid cooling or particlebombardment.

Vacancy

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Atom in a crystal, sometimes,

occupies interstitial site.

This does not occur naturally.

Can be induced by irradiation.

This defects caused structural

distortion.

Point Defects-Interstitialcy

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Complex, as electric neutrality has to be maintained,q = 0

Frenkel defect is created when a cation moves to interstitial site (cation

vacancy-interstitialcy).

If two oppositely charged ions are missing, a cation-anion divacancy is

created. This is Schottky defect.

Impurity ions are also considered as point defects in ionic crystals.

Cation interstitialcy

Cation vacancy

Cation vacancy

Anion vacancy

No te :

Both Fr e n ke l and

S c h o t t k y defects are

called S t o i c h i o m e t r i c

d e fe cts.Frenkel defects

Schottky defects

Point defects: How are they different from those in metals?

Point Defects in Ionic Crystals

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Other Point Defects in Ceramics

Frenkel and Schottky defects maintain 1:1 cation-anion ratio these

defects are stoichiometric.

Non-stoichiometry (cation-anion ratio 1:1) occurs when one ion

exists in multiple valence states: Fe2+ and Fe3+, Cu+ and Cu2+.

In FeO, the charge for Fe ion is +2. If we have Fe3+ ions, then Fe2+

vacancy is required to maintain charge neutrality. This unbalanced

number of ions is called non-stoichiometric defect.

Fe3+

O2-

Fe2+

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Point Defects: Impurity Ions

Impurity ions must also satisfy

charge balance = Electroneutrality.

Impurity ions: How are they

accommodated in the crystal

lattice?

Impurity ions are non-stoichiometric defects

cause unbalanced number of

ions.

Substitutional

anion impurity

Substitutional

cation impurity

Impurity can be:

atoms

anions**

cations**

**Will cause non-stoichiometric

defects.

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Cation Impurity

What point defect occur when a Ca2+ substitutes for Na+?

Replacing a Na+ by a Ca2+ ion introduces excess (+1) charge. Charge will be balanced if another (+1) charge is eliminated, i.e. create

one Na+ cation vacancy (FAVORABLE)

Charge can also be balanced if we add one Cl ion to the lattice (anion

interstitialcy) - UNLIKELY.

Non-stoichiometry occurs - unbalanced number of ions.

Initial geometry Resulting geometry

One Na+ cation

vacancy

ClNa+

Ca2+

Na+

Na+

Substitutional cation impurity

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Anion Impurity

What point defect occur when a O2 substitutes for Cl?

Replacing a Cl by a O2 ion introduces excess (-1) charge. For neutrality, one (-1) charge must be eliminated, i.e. create one Cl

anion vacancy (FAVORABLE).

Charge is also balanced if we add one Na+ ion into the crystal lattice

(i.e. cation interstitialcy)

Non-stoichiometric due to unbalanced number of ions.

Substitutional anion impurity

Initial geometry Resulting geometry

Anion vacancy

ClNa+

ClCl

O2

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Video

(this file opens in a new window and contains audio commentary

Link: http://www.youtube.com/watch?v=wz4LdX6UJcE

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Lattice Defects

Many of the important properties of materials are due to the

presence of defects.

Practically all mechanical and electrical properties are

sensitive to changes in structure.

S tr u ct u re-i n sen s it iv e (al m o s t) St ru c tu r e-s en s it iv e

Elastic constants Electrical conductivity

Melting points Semiconducting properties

Density Yield stress

Specific heat Fracture strength

Coefficient of thermal expansion Creep strength

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Significance of Point Defects

Example:

70% Cu-30% Zn

MetalsTensile

strength (Mpa)

Cartridge brass* 500

Unalloyed copper 330

* 70% Cu-30% Zn so lid solu t ion

Addition of 1 or more metals

increases the strength of pure

metals,

i.e. solid solutions are

stronger than pure metals.

Ductility usually reduces.

Effect of point defects onmechanical properties:

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Significance of Point Defects (cont.)

Electrical conductivity changes.

Addition of Ni atoms

(impurity) to pure Cu atoms

reduces electrical conductivityof the copper.

Addition of very small amount of

Ge impurity atoms to pure Si

greatly increases its electrical

conductivity for use in electronicdevices.

Effect of point defects on electrical properties: