Crystallographydrgregsmaterialsweb.com/Crystal Structures KU 2018 given 2.pdf · –coordination...
Transcript of Crystallographydrgregsmaterialsweb.com/Crystal Structures KU 2018 given 2.pdf · –coordination...
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Crystallography
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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.
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Grains
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Crystal Growth
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Making Solid Stuff
For materials we are ofteninterested in “grains”
What are these grains?
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Grains
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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”
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So the atoms bond together!
How do they arrange themselves?Depends on:1. Bonding
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Primary Bonds Summary
• What are they?
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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
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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
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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?
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• 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
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Close packing of atoms
FCC
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fcc
Face-Centered Cubic (FCC)
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Not close packing of atoms
BCC
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Body-Centered Cubic (BCC)
From Callister 6e resource CD.
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BCC metals have some covalency to their bond
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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
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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)
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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?
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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
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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
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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
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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
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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
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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
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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
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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
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