08 MTE 271 Point Defects

8/19/2019 08 MTE 271 Point Defects

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LECTURE #08

o n e ec so n e ec s n rys a sn rys a s

ChapterChapter 55

Learning objectives:

1. What are the different types of defects in materials?

.

properties of materials?

R l t R di f thi L t

• Pages 135-142.

Relevant Reading for this Lecture

1

Types of Imperfections:Types of Imperfections:

• Vacancy atoms

There is no such thing as a perfect crystal

• Interstitial atoms

• Substitutional atoms

Point defects [0-D]

• Dislocations Line defects [1-D]

• Grain Boundaries Planar defects [2-D]

• Cracks, voids Volume defects [3-D]

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– –

•

another type of atom ‘substitutes’ on a particular

lattice site.

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In chemistry, you are likely are familiar with mixing two liquids

‘ ’o ma e a qu so u on….you can o e same w

solids! But in this case the different atoms in the solid occupy

the equivalent crystal (lattice) sites making a ‘solid’ solution

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Solid SolutionSolid SolutionSolid solution of nickel in copper shown along a (100) plane. This is a

substitutional solid solution with nickel atoms substituting for copper

atoms on FCC atom lattice sites.

=u .

r = 0.125 nm

= = ,

• Ni and Cu are so close in size, they can form a solid solution

in all proportions5

MECHANICAL PROPERTIES:MECHANICAL PROPERTIES: CuCu--Ni SystemNi System• Effect of solid solution strengthening on:

--Tensile strength (TS) --Ductility (%EL,%AR)

% E L )60

%EL for pure Cu

( M P a )

400

g

a t i o n (

40

pure Ni

t

r e n g t

300

TS forpure Ni

E l o

Cu Ni0 20 40 60 80 100

20

30

e n s i l e

Cu Ni0 20 40 60 80 100

200

TS for pure Cu

--Peak as a function of Co --Min. as a function of Co

Adapted from Fig. 9.5(a), Callister 6e. Adapted from Fig. 9.5(b), Callister 6e.

Composition, wt%NiComposition, wt%Ni

r Cu = 0.128nm

r Ni = 0.125nmSmall atomic size difference causes the bonds to stretch

which makes the alloy stronger!6


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HumeHume--RotheryRothery RulesRules

1. < 15% difference in atomic radii

2. The same crystal structure

3. Similar electronegativity (i.e., ability of an

atom to attract an electron)

4. Same valence

If one or more of these rules are violated,

only partial solubility is possible.

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Ordering of the solid solutionOrdering of the solid solution-- IntermetallicsIntermetallicsin the AuCuin the AuCu33 alloy system.alloy system.

(a) > ~390°C, random (b) < ~390°C, Au atoms

distribution of Au and Cu

atoms among FCC sites.

preferentially occupy corners, while

Cu atoms occupy faces (the Au

.

When atoms occupy specific site – the bond strength can be directional and

can make the material stronger (but more brittle)8


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– –

An interstitial defect: the lacement of an atom in a

interstitial (in between regular lattice sites).

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Interstit ial Solid SolutionsInterstit ial Solid Solutions

.

They may occupy interstitial sites.HUME-ROTHERY RULES DO NOT APPLY TO INTERSTITIALS.

Figure 4.4 Interstitial solid solution of carbon in α-iron. The carbon atom is small

enough to fit with some strain in the interstice (or opening) among adjacent Fe atoms in

this structure of im ortance to the steel industr . This unit-cell structure can be

compared with that shown in Figure 3.4b.]

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– –

•

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Are vacancies an equilibrium defect? Are vacancies an equilibrium defect?• Yes, vacancies contribute to entropy to the

s stem and can hel to reduce the

crystal’s energy, up to a point.

Energy to breaking bonds+n w

Total energy r g y

GV

number of vacancies, nV

Do you think vacancy

E n e

n1ne

Energy gained by entropy (disorder)

concen ra on goes up w

temperature? – –TS

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• In ionic crystals (such as NaCl), single vacanciescan not occur. Wh ?

Because of the constraints of charge neutrality, either a

.

Frenkel defect: vacancy-interstitial combination.

Schottky defect: pair of oppositely charged ion vacancies.

Adapted from Fig.12.21, Callister

& Rethwisch 8e. (Fig. 12.21 is

from W.G. Moffatt, G.W. Pearsall,

Shottky

Defect:

. ,

Properties of Materials, Vol. 1,

Structure, John Wiley and Sons,Inc., p. 78.)

Frenkel

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Random, substitut ional solid solut ion ofRandom, substitut ional solid solution of NiONiO inin MgOMgO..

2− .

The substitution occurs only among Ni2+ and Mg2+ ions.

Ri = 0.069 nm

Ri = 0.072 nm

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What happens if the charges do not balance?

2 3 NiO in MgO. The overall compound must be charge neutral, this permits only two

Al3+ ions to fill every three Mg2+ vacant sites, leaving one Mg2+ vacancy.

Ri = 0.053 nm

Ri = 0.072 nm

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In class example:

Calculate the number of Mg2+

vacancies produced by the solubility of 1 mol of

Approach:

• Calculate amount of O

• a cu a e amoun o ca ons

• Difference btw. O & cations = amt. vacancies

99 mol O sites (from MgO) 99 mol cation sites (from MgO)+ 3 mol O sites (from Al2O3)

102 mol O sites in solid solution

+ 2 mol cation sites (from Al2O3)

101 mol cation sites in solid solution

102 mol – 101 mol = I mol Mg2+ vacancies or 6.02 x1023 vacancies

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Stoichiometric vs. NonStoichiometric vs. Non--Stoichiometric CompoundsStoichiometric Compounds

Stoichiometric

formula, Fe2

O3

, NiO2

, Fe3

04

, CuSO4

, etc.

•

Non-Stoichiometric

• The amounts (moles) of each element does vary, this

can be reflected by using variables in the formula, FexOyor Fe

1-xO (x ≈ 0.05)

• The ratio does vary!

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Fig. 4.7 Iron oxide, Fe1−xO (x ≈ 0.05), is an example of a nonstoichiometric

compound. Similar to Fig 4.6, both Fe + and Fe + ions occupy the cation sites.

One Fe2+ vacancy occurs for every two Fe3+ ions.

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• Example: Ferrous oxide, FeO (Fe2+ + O2-)

– an e e err c s a e s su s u e or an e , ca on vacanc es

are needed to offset charge

– Extra oxygen associated with the ferric iron is accommodated in the

norma oxygen su a ce eaves some ca on on s es unoccup e

– Thus the composition is Fe1-xO, where x is small and


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NaClNaCl (Na(Na(1(1--x)x)CaCaxx))ClCl

http://1.bp.blogspot.com/_EBqHz1Oipb4/TCtpx7Sk6jI/AAAAAAAAABQ/_2Os-

inoQ5Q/s1600/sodium-chloride.jpg

http://www.fromnaturewithlove.com/images/SaltBolivianCoarse.jpg

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•Three t es of 0-D defects Point Defects :

SummarySummary

•Vacancies

•Interstitial atoms

•

•Vacancies help control charge neutrality in ionic crystals; variations in charge

state change vac. Concentration and properties (like color)

•

A solid solution forms when, as the solute atoms are added to the host

material, the crystal structure is maintained and no new crystal structures are

formed.

•Hume-Rothery Rules:

1. < 15% difference in atomic radii

.

3. Similar electronegativity (i.e. ability of an atom to attract an electron)

4. Same valence

•

If one or more rules are violated, only partial solubility is possible.

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08 MTE 271 Point Defects