Intro to Crystalline Defects

8/3/2019 Intro to Crystalline Defects

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Defects, Dislocations, and

Other Imperfections

Learning Unit 2

ME 2340

Tuesday, October 19, 2010


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Lesson Objectives

Point defects: vacancy, interstitial atoms,substitutional atoms

Calculating the number of vacancies in a substance Calculate the number of solute atoms in an alloy

Calculate weight % and atomic %, and to convertfrom one to the other Name the different types of dislocations and define

Burgers vectors

Define Schottky and Frankel defects Describe stacking faults, twin boundaries, and grainboundaries

Describe in your own words what a slip system is



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Overview

Crystals can be imperfect in the following ways:1. Point Defects (no dimension)

2. Line Defects (1-D)

3. Planar Defects (2-D)4. Bulk Defects (3-D)

How we study and quantify defects

Why we care



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1. Point Defects: Six Types

a. Vacancies

b. Interstitial atoms

c. Substitutional atoms

d. Interstitialcy (not shown)

e. Frenkel Defects

f. Schottky Defects

(c)



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1 a) Vacancies: Missing Atoms

Vacant sites in lattice thatnormally contain atoms

Number of vacant sites (nv)

increases exponentially with

temperature (T) where n is given by:

n is the total number of latticepositions; Qv is the activation

energy



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We can get Qv froman experiment.

Measure this... Replot it...

Measuring Activation Energy



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Find the equil. # of vacancies in 1m3

of Cu at 1000 C. Given:

Answer:

Estimating Vacancy Concentration



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Practice Problem

Calculate the energy for vacancyformation in aluminum, given that theequilibrium number of vacancies at

500C (773 K) is 7.57 x 1023 m-3. Theatomic weight and density foraluminum are, respectively, 26.98 g/

mol and 2.62 g/cm3.



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Low energy electronmicroscope view of a (110)surface of NiAl. Increasing T causes surfaceisland of atoms to grow. Why? The equil. vacancyconc. increases via atom motionfrom the crystal to the surface,where they join the island.

Reprinted with permission from Nature (K.F.McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies inSolids and the Stability of Surface Morphology",Nature, Vol. 412, pp. 622-625 (2001). Image is 5.75m by 5.75 m.) Copyright (2001) Macmillan

Publishers, Ltd.

Observing Vacancy Concentration

http://www.nature.com/http://www.nature.com/


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Two possible 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)

OR

Substitutional alloy(e.g., Cu in Ni)

Interstitial alloy(e.g., C in Fe)

Second phase particle-- differentcomposition-- often different structure.

Point Defects in Alloys



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Interstitial Defects

Solute atomsin regularvoids

Possible sizedetermined bygeometry

Distorts latticesomewhat



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Substitutional Defects

Solute atom substitutes for a solvent atom Size and valence matters

Easiest when size and valence similar

Hume Rothery Rules Size Difference < +/- 15%

Same crystal structure in pure form

Similar electronegativity

Solute has same or higher valence than solvent

Satisfy all four complete substitutional solid solution

Satisfy some of four incomplete substitutional solid

solutionTuesday, October 19, 2010


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Other Point Defects

1d) Interstitialcy a.k.a self interstitial

Occurs when low packing factor

1e) Frenkel defect

Vacancy-interstitial pair

Much like self-interstitial with ions

1f) Schottky defect

Unique to ionic materials Both cation and anion missing



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Definition: Amount of impurity (B) andhost (A) in the system.

Weight %

Two descriptions: Atom %

Conversion between wt % and at% in an A-B alloy:

Basis for conversion:

Specifying Composition



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Line Defects - Dislocations

Whole lines of atomsthat are not where they

should be In metals, deformation

depends on dislocations

Edge dislocations

Screw dislocations

Mixed dislocations

Animations



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What is Slip?

Process of dislocation movement Occurs in direction of Burgers Vector, b

Occurs on the slip plane

Slip plane + Slip direction = Slip System

BCC up to 48 systems

FCC 12 systems

HCP 3 systems

More slip systems = more chance for cross slip Peierls-Nabarro stress required to move a dislocation

given by:

http://images.google.com/imgres?imgurl=http://www.fotosearch.com/comp/BDX/BDX273/bxp46994.jpg&imgrefurl=http://www.fotosearch.com/BDX273/bxp46994/&h=300&w=196&sz=17&tbnid=Vce3NOcIIHsJ:&tbnh=110&tbnw=72&prev=/images%253Fq%253Dbanana%252Bpeel%2526hl%253Den%2526lr%253D&oi=imagesr&start=2http://images.google.com/imgres?imgurl=http://www.fotosearch.com/comp/BDX/BDX273/bxp46994.jpg&imgrefurl=http://www.fotosearch.com/BDX273/bxp46994/&h=300&w=196&sz=17&tbnid=Vce3NOcIIHsJ:&tbnh=110&tbnw=72&prev=/images%253Fq%253Dbanana%252Bpeel%2526hl%253Den%2526lr%253D&oi=imagesr&start=2


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Dislocation motion requires the successive bumpingof a half plane of atoms (from left to right here).

Bonds across the slipping planes are broken andremade in succession.

Atomic view of edge

dislocation motion fromleft to right as a crystalis sheared.

(Courtesy P.M. Anderson)

Bond Breaking and Remaking



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Where will slip occur?

Slip happens on close packed directions inthe close packed plane

As dhkl decreases, lower required stress Covalent materials show little or no slip

Ionic materials also crack before slipping

Dislocations explain metal strength

Based on the bonds, metals should be 1000 timesstronger!



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Structure: close packedplanes & directions arepreferred.

Mg (HCP)

Al (FCC)tensile directionResults of tensile testing

view onto twoclose-packed planes.

Dislocations & Crystal Structure

Comparison among crystal structures:FCC: many close-packed planes/directions;HCP: only one plane, 3 directions;BCC: no close packed planes



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Schmids Law Single Crystals

Resolved shear force:

Schmids Law:

Yield strength depends onstress required to get the

first plane moving:Tuesday, October 19, 2010


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Planar Defects

a) Surfaces

b) Grain Boundaries

c) Stacking Faultsd) Twin boundaries

e) Domain boundaries All of these defects separate a larger

crystal lattice into smaller regions



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Grain boundaries

Where one crystallite meetsanother

Dislocations cant move

across easily

Nanomaterials can have upto 50 vol%

Hall-Petch equation relatesyield strength to grain size(d):

At normal temps, as grainsize , strength



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Grain boundaries: are boundaries between crystals. are produced by the solidification process, for example.

have a change in crystal orientation across them.

impede dislocation motion.

Schematic

~ 8cm

Metal Ingot

More on Grain Boundaries


S k F l


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Stacking Faults Normal FCC sequence:

ABC ABC ABC FCC sequence with stacking

fault:ABC ABAB ABC

Normal HCP sequence:ABABABABAB

HCP sequence with stackingfault:ABABCABABA


O h Pl D f


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Other Planar Defects

Twin boundaries Produced during deformation or

phase change

Not as effective at

stopping dislocationsDomain boundaries

In ferroelectric materials

Magnetization or polarizationchanges across boundary


Strengthening of Materials


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Strengthening of Materials

Dislocation motion = deformation occurs

Stop dislocations = stop deformation

Means for preventing movement: Other dislocations (strain hardening)

Impurity atoms (solid-solution strengthening)

Grain boundaries (grain size strengthening) Other phases (precipitation strengthening)

Well be discussing these later.


4) B lk D f


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4) Bulk Defects

Porosity

Amount of void space in material

Units of measure

between 01 (fraction less than one)

between 0100% (percentage)

Inclusions

material (usually a particle of acompound) that is trapped inside ametal or ceramic during itssolidification


M G l D f


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More General Defects

Cracks - more on that later

Voids

Shear bands - amorphous materials

Macroscopic structural flaws


S


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Summary

Defects are often present in structures

Sometimes use to advantage to strengthen

Sometime critical to remove to improve properties

An understanding of various types of defects

will lead to insight on best practices forprocessing and materials selection


Documents

Intro to Crystalline Defects