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POLYMORPHISM & ALLOTROPY

Some materials may exist in more than one crystal structure, this is called polymorphism. If the material is an elemental solid, it is called allotropy. An example of allotropy is carbon, which can exist as diamond, graphite, and amorphous carbon.

Graphite Diamond Nanotubes

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X-Ray Diffraction

Diffraction gratings must have spacings comparable to the wavelength of diffracted radiation. Can’t resolve spacings < λSpacing is the distance between parallel planes of atoms.

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X-Rays to Determine Crystal Structure

X-ray intensity (from detector)

θ

θc

d =nλ

2 sinθc

Measurement of critical angle, θc, allows computation of planar spacing, d.

• Incoming X-rays diffract from crystal planes.

Adapted from Fig. 3.20, Callister & Rethwisch 8e.

reflections must be in phase for a detectable signal

spacing between planes

d

incoming

X-rays

outgo

ing X

-rays

detector

θλ

θextra distance travelled by wave “2”

“1”

“2”

“1”

“2”

222 lkhadhkl

++=

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X-Ray Diffraction Pattern

Adapted from Fig. 3.22, Callister 8e.

(110)

(200)

(211)

z

x

ya b

c

Diffraction angle 2θ

Diffraction pattern for polycrystalline α-iron (BCC)

Inte

nsity

(rel

ativ

e)

z

x

ya b

cz

x

ya b

c

a=0.2866nmXray wavelength=0.1542

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Imperfections in SolidsDefects in Crystals

alter the properties….

LECTURE 10 4/12/2009

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Perfection…In terms of:1. Chemical composition – pure2. Atomic arrangement – defect free

Both are critical in determining the performance of material. But, real engineering materials are not perfect.Properties can be altered through defect engineering.

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Classification of Defects

The defects are classified on the basis of dimensionality:

0-dimensional: point defects1-dimensional: line defects2-dimensional: interfacial defects3-dimensional: bulk defects

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Point Defects – 0 dim.- localized disruption in regularity of the lattice- on and between lattice sites3 Types:1. Substitutional Impurity- occupies normal lattice site- dopant ☺, e.g., P in Si- contaminant Li+ in NaCl2. Interstitial Impurity- occupies position between lattice sites- alloying element ☺, e.g., C in Fe- contaminant, H in Fe3. Vacancy- unoccupied lattice site- formed at time of crystallization

Interstitial

SubstitutionalVacancy

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Population of vacancies in a crystalIn a crystal containing N atomic sites, the number nd of vacant sites:

nd = the number of defects (in equilibrium at T) N = the total number of atomic sites per mole ∆Hd = the energy necessary to form the defect T = the absolute temperature (K) k = the Boltzmann constant A = proportionality constant

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Point Defects in Ionic CrystalsMaintain global charge neutrality

1. Schottky Imperfectionformation of equivalent (notnecessarily equal) numbers ofcationic and anionic vacancies

2. Frenkel Imperfectionformation of an ion vacancy andan ion interstitial

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Line Defects - Dislocations

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Surface- Planar Defects

SEM (Scanning electron microscope) image (showing grains and grain boundaries)

Grain Boundaries

Photomicrographs of typical microstructures of annealed brass

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Solidification- result of casting of molten material2 steps

Nuclei form Nuclei grow to form crystals – grain structure

Start with a molten material – all liquid

Imperfections in Solids

• Crystals grow until they meet each otherAdapted from Fig. 4.14(b), Callister & Rethwisch 8e.

grain structurecrystals growingnucleiliquid

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Polycrystalline Material

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Bulk – Volume Defects – 3dimVoids – coalesced vacanciesCracksPitsGroovesInclusionsPrecipitates

SEM of CVD GaN 16

a) Interstitial impurity atom, b) Edge dislocation, c) Self interstitial atom, d) Vacancy,

e) Precipitate of impurity atoms, f) Vacancy type dislocation loop, g) Interstitial type dislocation loop, h) Substitutional impurity atom

Defects - Summary

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Effects of Defects on Properties

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Atomic Arrangement

SOLID: Smth. which is dimensionally stable, i.e., has a volume of its own

classifications of solids by atomic arrangement

ordered disorderedatomic arrangement regular random*order long-range short-rangename crystalline amorphous

“crystal” “glass”

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Single Crystal Polycrystalline

Grains

Grain boundaries

Amorphous

Disorder