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MSE 280: Introduction to Engineering Materials D.D. Johnson 2004, 2006-10

Chapter 3: Structures via Diffraction

Goals

Define basic ideas of diffraction (using x-ray, electrons, or neutrons,

which, although they are particles, they can behave as waves) and show

how to determine:

rystal !tructure

"iller #ndex $lanes and Determine the !tructure

#dentify cell symmetry%

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Chapter 3: Diffraction

Learning Objective

&now and utili'e the results of diffraction pattern to get:

lattice constant%

allow computation of densities for close-paced structures%

#dentify !ymmetry of ells%

!pecify directions and planes for crystals and be able to relate

to characteri'ation experiments%

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Someengineering applications require single crystals:

Crystal properties reveal features of atomic structure.

(Courtesy P.M. Anderson)

--E: Certain crystal planes in quart!

fracture more easily t"an ot"ers.

--diamond singlecrystals for a#rasives

--tur#ine #lades

$ig. %.&'(c) Callister 6e.($ig. %.&'(c) courtesyof Pratt and "itney).(Courtesy Martin *ea+ins

,E upera#rasives ort"ington/. 0sed 1it" permission.)

CRYSTALS AS BUILDING BLOCKS

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MSE 280: Introduction to Engineering Materials D.D. Johnson 2004, 2006-10

Mostengineering materials are polycrystals.

2#-/f- plate 1it" an electron #eam 1eld.

Eac" 3grain3 is a single crystal. 4f crystals are randomly oriented overall component properties are not directional. Crystal si!es range from 5 nm to 6 cm

(i.e. from a fe1 to millions of atomic layers).

Adapted from $ig. 7color inset pages ofCallister 6e.($ig. 7 is courtesy ofPaul E. *anielson8eledyne a" C"ang

Al#any)

5 mm

POLYCRYSTALS

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MSE 280: Introduction to Engineering Materials D.D. Johnson 2004, 2006-10

SIMPLE Diffraction in Crystals and Polycrystals

Diffraction $attern ransmission *lectron "icroscopy (*")

antalum with ordered structure containing +xygen%

Ta

diffraction

oxygen

diffraction

wo ordered patterns appear, one w a and the other w +%

kx

ky

Ta2O5

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MSE 280: Introduction to Engineering Materials D.D. Johnson 2004, 2006-10

Diffraction by Planes of Atoms

o have constructive interference (#%e%, waves DD)%

.ight gets scattered off atoms/0ut since d(atomic spacing) is on

the order of angstroms, you need x-ray diffraction(wavelength 1 d)%

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Diffraction Experiment and Signal

Diffraction *xperiment !can versus 2x ngle: Polycrystalline Cu

Measure 69

3ow can 24 scans help us determine crystal structure type and

distances between "iller #ndexed planes (#%e% structural parameters)5

Diffraction collects data in 6reciprocal space7 since it is the e8uivalent of

a Fourier transform of real space7, i%e%, eir

, as 1 9r%

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Crystal Structure and Planar Distances

or cubic crystals:

dhkl=

a

4

3(h

2 + hk+ k2 ) +l 2 a

c

2

or hexagonal crystals:

Distances between "iller #ndexed planes

h, k, lare the "iller#ndices of the planes of

atoms that scatter;

!o they determine the

important planes of

atoms, or symmetry%

0ravais.attice

onstructive#nterference

Destructive#nterference

+dd

(h,,l) ll +dd

or ll *ven

(h,,l) ?ot ll+dd or ll *ven

3$ ny other (h,,l) h=2>@n, l > +dd

n> integer

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(h l) h2=2=l2 h==l h,,l all evenor odd5

9AA 9 9 ?o110 2 2 ?o

999 @ @ Bes

200 C 2 Bes

29A @ ?o

211 E 4 ?o

220 F 4 Bes

229 G ?o

@AA G @ ?o

310 9A 4 ?o

@99 99 Bes

222 92 6 Bes

@2A 9@ ?o

321 9C 6 ?o

Allowed (hkl) in FCC and BCC for principal scattering (n=1)

h = = l was even and gave the labels on

graph above, so crystal is 0%

!elf-ssessment:

rom what crystal structure is this5

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Po1der diraction ;gures ta+en from 8". Proe and

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Po1der diraction ;gures ta+en from 8". Proe and

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Po1der diraction ;gures ta+en from 8". Proe and

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Po1der diraction ;gures ta+en from 8". Proe and

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Example from QuasiCrystals

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SUMMARY

"aterials come in rystallineand !on-crystalline!olids, as wellas Li"#ids$%&o'r(o#s% $olycrystals are important%

rystal !tructurecan be defined by space latticeandbasis atoms

(lattice decorations or motifs), which can be found by diffraction%

+nly 9C 0ravais .atticesare possible (e%g% , 3$, and 0)%

rystal types themselves can be described by their atomic positions,

planes and their atomic pacing (linear, planar, and volumetric)%

We now know how to determine structure mathematically andexperimentallyby diffraction%

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