Crystallographydrgregsmaterialsweb.com/Crystal Structures KU 2018 given 2.pdf · –coordination number •number of contacting neighboursany one atom has •This is a function of

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Crystallography

Dr Greg’s Crystallography

Crystallography

What is crystallography?

the branch of science concerned with the structure and properties of crystals


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Crystallography

What are crystals?

a piece of a homogeneous solid substance having a natural geometrically regular form with symmetrically arranged plane faces.


Grains


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Crystal Growth


Making Solid Stuff

For materials we are ofteninterested in “grains”

What are these grains?


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Grains


For structures

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So what is it all about?Crystals

• Look pretty

• Lots of different shapes

Grains –Size & Structure

• Control properties of metals

Crystals Grains

• Particular arrangement of atoms

– 14 possibilities – Bravais lattice

Fe- High Resolution Transmission Electron Microscope picture of an iron crystaL

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This structure?• The arrangement of the atoms

• Their “order”


So the atoms bond together!

How do they arrange themselves?Depends on:1. Bonding


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Primary Bonds Summary

• What are they?


Order in materials

Long range order

Solids Metals, ceramics & polymers

Short range order

Liquids Inorganic and organic glasses

No long range order to atoms

Gases little or no interaction between components


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Packing atoms together

• atoms pack in periodic, 3D arrays• typical of:

Crystalline materials...

-metals-many ceramics-some polymers

• atoms have no periodic packing• occurs for:

Noncrystalline materials...

-complex structures-rapid cooling

Si Oxygen

crystalline SiO2

noncrystalline SiO2

"Amorphous" = NoncrystallineAdapted from Fig. 3.18(b),Callister 6e.

Adapted from Fig. 3.18(a),Callister 6e.

From Callister 6e resource CD.

Long Range Atomic Order

Short Range Atomic Order


Stacking Oranges

Stacking atoms together

Crystal Structure


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Hard Sphere Model • Atoms in a crystal represented by hard

sphere

• each atom is surrounded by as many other atoms as possible

– i.e minimum energy state

• Gives rise to

– coordination number

•number of contacting neighbours any one atom has

• This is a function of directionality of Dr Greg’s Crystallography

What controls the nearest number of

atoms?Dr Greg’s Crystallography

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Hard Sphere Model

# of atoms around

each atom

Relative atom size

Directionality of bond


Simple case - Nondirectionallybonded atoms of equal size

• Metals & noble elements– expect to solidify in closest packed arrangement as

possible

– WHY?

– # of bonds per unit vol maximised

– hence bonding energy per unit volume minimised


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How can these oranges pack?


• What is the maximum number of spheres that can pack around one sphere?

• Such a structure is said to be CLOSE PACKED


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Two such close packed arrangements

face centred cubicFCC

Hexagonal close packedHCP

These names come from the geometrythat results

Accounts forabout 2/3 of all metals

All the noble metals at low TDr Greg’s Crystallography

HCP Tetrahedral site Octahedral site

Close packing of atoms


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Figure 1.4 The hexagonal close-packed (hcp) crystal structure: (a) unit cell; and (b) single crystal with many unit cells. Source: W. G. Moffatt, et al., The Structure and Properties of Materials, Vol. 1, John Wiley & Sons, 1976.

Hexagonal Closed-Packed Crystal Structure - HCP


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HCP structures

• The hexagonal-closed packed (HCP) and FCC structures both have the ideal packing fraction of 0.74 (Kepler figured this out hundreds of years ago)

• The ideal ratio of c/a for this packing is (8/3)1/2 = 1.633

Crystal c/a

He 1.633

Be 1.581

Mg 1.623

Ti 1.586

Zn 1.861

Cd 1.886

Co 1.622

Y 1.570

Zr 1.594

Gd 1.592

Lu 1.586


Close packing of atoms

FCC


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fcc

Face-Centered Cubic (FCC)


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Not close packing of atoms

BCC


Body-Centered Cubic (BCC)

From Callister 6e resource CD.


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BCC metals have some covalency to their bond


HCP

FCC

BCC


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Simple Cubic

• Coordination Number = ?

Number of atoms per unit cell?Dr Greg’s Crystallography

Point and Space Groups

• 7 crystal systems

• 14 Bravaislattices


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So What?• Different crystal structures give different

properties

• e.g. ductility

– FCC > BCC > HCP

• A couple of examples


Napoleon Caught With His Pants Down


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Scott of the Antarctic

Disintegration of tin dishes and cutlery in cold weather expeditions, kerosene containers (Captain Robert Scott's Antarctic expedition)


Tin Plague

A (gradual) phase change occurs from white tin (tetragonal) to gray tin (cubic)

Tetragonal Cubic


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• Face Centred Cubic

• Body Centred Cubic

STRUCTURALLY DIFFERENT

850CAustenite

Pearlite

Martensite

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But nothing is perfect!

Imperfections


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What can go wrong?


Summary

impurities


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The surface of an alloy of platinum and rhenium (PtRh).

• Light spots are Rh atoms, • Grey spots are Pt. • Black spots are C impurities.

Magnification on the screen is over 300 million.

Impurities – aluminium oxide

+ Cr + Fe

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Impurities

•Remember, these imperfections are not always detrimental

•Give rise to:

– substitutional solid solutions

– interstitial solid solutions

• Provide unique properties unobtainable with the parent metals


Cu – Sn –bronze rods?


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Let’s have a look!

Line Defects

• “dislocations”

• aid plastic deformation

• three types

– edge

– screw

– mixed

•Dislocations are formed-solidification- plastic deformation- thermal stresses from cooling

TEM of titaniumdark lines are dislocations. 51450 X


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Edge Dislocation• Half plane of atoms inserted into lattice• distortion of lattice


Do they really exist?

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We can hear them too!!!

In tin the dislocations travel at the speed of sound

THE CRY OF TIN!!!!!

Brass/bronze• Cu 0.19 nm

• Sn 0.225 nm

• Zn 0.21nm

• Substitutional Solid Solution

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More than 1 type of atom?Dr Greg’s Crystallography

Ionic Ceramics

• Ions pack together as densely as possible to lower overall energy

– electrostatic attraction in all directions

– cations want to maximize # of neighboring anions and vice versa.


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Ionic Ceramics• Limitations to dense packing:

– relative sizes of ions

– and necessity to maintain charge neutrality

– Charge neutrality• e.g. Ca Ca2+

– F F-CaF2


Linear

triangular

tetrahedral

octahedral

cubic

And, of course, a co-ordination # of 12 gives HCP or FCCDr Greg’s Crystallography

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Example

CsCl NaClrCs = 0.167 nm rNa = 0.097 nm

rCl = 0.181 nm rCl = 0.181 nm

radius ratio = 0.92 radius ratio = 0.536

structure: SC structure: FCC


Examples: Ionic Ceramics

MgOMnSLiFFeO


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• Coordination # increases withIssue: How many anions can you arrange around a cation?

rcationranion

Coord #

< .155 .155-.225 .225-.414 .414-.732 .732-1.0

ZnS (zincblende)

NaCl (sodium chloride)

CsCl (cesium

chloride)

2 3 4 6 8

Coordination # And Ionic Radii


Directionally bonded atoms of equal size

• Materials with directional bonds have geometry controlled by bond angles,

– e.g. diamond


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Example: Covalent Ceramics

SiC


Covalent Ceramics

• Position and number of neighbours rigidly fixed by directional nature of bonds

• Energy is minimised, not by dense packing, but by forming chains, sheets or 3D networks

– often these are non-crystalline

• The results are quite different structures to ionic ceramics and also different properties


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Examples: Covalent Ceramics


Ceramic Structures

Generally more

complex than metals

Will be predominately ionic or covalent

•CaF2 89% ionic•MgO 73•NaCl 67•Al2O3 63•SiO2 51•Si3N4 30•ZnS 18•SiC 12


Documents

Crystallographydrgregsmaterialsweb.com/Crystal Structures KU 2018 given 2.pdf · –coordination number •number of contacting neighboursany one atom has •This is a function of