Materials Discovery Camp
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Transcript of Materials Discovery Camp
1
Crystallography World ofWonders
Claudia J. [email protected]
University of Tennessee/Oak Ridge National Laboratory
2
Al vs Al2O3AlMelts at 660 oCFCC a = 4.0495 ÅDensity = 2.71 gm/cm3
Al2O3Melts at 2000 oCBased on HCP a = 4.7589 and c = 12.991 ÅDensity = 3.98 gm/cm3
3
• Bond length, r
• Bond energy, Eo
F F
r
• Melting Temperature, Tm
Tm is larger if Eo is larger.
PROPERTIES FROMBONDING: TM
From W.D. Callister: Materials Science and Engineering: An Introduction
4
!metals! !ceramics! !polymers
Why? Metals have... • close-packing (metallic bonding) • large atomic mass Ceramics have... • less dense packing (covalent bonding) • often lighter elements Polymers have... • poor packing (often amorphous) • lighter elements (C,H,O) Composites have... • intermediate values Data from Table B1, Callister 6e.
DENSITIES OF MATERIAL CLASSES
From W.D. Callister: Materials Science and Engineering: An Introduction
5
• Occurs between + and - ions.• Requires electron transfer.• Large difference in electronegativity required.• Example: NaCl
IONIC BONDING
From W.D. Callister: Materials Science and Engineering: An Introduction
6
• Predominant bonding in Ceramics
Give up electrons Acquire electrons
He-
Ne-
Ar-
Kr-
Xe-
Rn-
F4.0
Cl3.0
Br2.8
I2.5
At2.2
Li1.0
Na0.9
K0.8
Rb0.8
Cs0.7
Fr0.7
H2.1
Be1.5
Mg1.2
Ca1.0
Sr1.0
Ba0.9
Ra0.9
Ti1.5
Cr1.6
Fe1.8
Ni1.8
Zn1.8
As2.0
CsCl
MgO
CaF2
NaCl
O3.5
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of theChemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by CornellUniversity.
EXAMPLES: IONIC BONDING
From W.D. Callister: Materials Science and Engineering: An Introduction
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• Requires shared electrons• Example: CH4
C: has 4 valence e, needs 4 more
H: has 1 valence e, needs 1 more
Electronegativities are comparable.
Adapted from Fig. 2.10, Callister 6e.
COVALENT BONDING
H, atomic number 1, electronic configuration 1s1
C, atomic number 6, electronic configuration 1s22s22p2
From W.D. Callister: Materials Science and Engineering: An Introduction
8
• Molecules with nonmetals
• Molecules with metals and nonmetals• Elemental solids (RHS of Periodic Table)
• Compound solids (about column IVA)
He-
Ne-
Ar-
Kr-
Xe-
Rn-
F4.0
Cl3.0
Br2.8
I2.5
At2.2
Li1.0
Na0.9
K0.8
Rb0.8
Cs0.7
Fr0.7
H2.1
Be1.5
Mg1.2
Ca1.0
Sr1.0
Ba0.9
Ra0.9
Ti1.5
Cr1.6
Fe1.8
Ni1.8
Zn1.8
As2.0
SiC
C(diamond)
H2O
C2.5
H2
Cl2
F2
Si1.8
Ga1.6
GaAs
Ge1.8
O2.0
co
lum
n I
VA
Sn1.8
Pb1.8
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 isadapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
EXAMPLES: COVALENT BONDING
From W.D. Callister: Materials Science and Engineering: An Introduction
10
Ceramics(Ionic & covalent bonding):
Metals(Metallic bonding):
Polymers(Covalent & Secondary):
Large bond energylarge Tm
large Esmall α
Variable bond energymoderate Tm
moderate Emoderate α
Directional PropertiesSecondary bonding dominates
small Tsmall Elarge α
SUMMARY: PRIMARY BONDS
From W.D. Callister: Materials Science and Engineering: An Introduction
11
• Non dense, random packing
• Dense, regular packing
Dense, regular-packed structures tend to have lower energy.
ENERGY AND PACKING
From W.D. Callister: Materials Science and Engineering: An Introduction
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• Coordination # = 12
• APF = 0.74
• 3D Projection • 2D Projection
A sites
B sites
A sites
Adapted from Fig. 3.3, Callister 6e.
HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
From W.D. Callister: Materials Science and Engineering: An Introduction
14
FCC and HCP close-packed lattices
• Both lattices are formed by a sequentialstacking of planar layers of close packedatoms.
• Within each layer each atom has six nearestneighbors.
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FCC and HCP close-packed latticesThe “A” layerall positions that are directly abovethe centers of the A atoms arereferred to as “A” positions,whether they are occupied or not
16
FCC and HCP close-packed lattices• Both FCC and HCP lattices are formed by
stacking like layers on top of this first layer in aspecific order to make a three dimensional lattice.
• These become close-packed in three dimensionsas well as within each planar hexagonal layer.
• Close packing is achieved by positioning theatoms of the next layer in the troughs between theatoms in the “A” layer
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FCC and HCP close-packed lattices
• Each one of these low positions occursbetween a triangle of atoms. Some pointtowards the top of the page and some pointtowards the bottom of the page.
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FCC and HCP close-packed lattices
• Any two of these immediately adjacenttriangles are too close to be both occupiedby the next layer of atoms.
• Instead the next close-packed “B” layer willfill every other triangle, which will all pointin the same direction.
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FCC and HCP close-packed lattices
• The “B” layer is identical to the A-layerexcept for its slight off translation.
• Continued stacking of close-packed layerson top of the B-layers generates both theFCC and HCP lattices.
“A” layer
“B” layer
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The FCC close-packed lattice
• The FCC lattice is formed when the thirdlayer is stacked so that its atoms arepositioned in downward-pointing trianglesof oxygen atoms in the “B” layer.
• These positions do not lie directly over theatoms in either the A or B layers, so it isdenoted as the “C” layer
“A” layer
“B” layer
“C” layer
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The FCC close-packed lattice
• The stacking sequence finally repeats itself when afourth layer is added over the C atoms with itsatoms directly over the A layer (the occupiedtriangles in the C layer again point downward) soit is another A layer.
• The FCC stacking sequence (ABCA) is repeatedindefinitely to form the lattice:
• …ABCABCABCABC...
“A” layer
“B” layer
“C” layer
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The FCC close-packed latticeEven though this lattice is made by stacking hexagonal planarlayers, in three dimensions its unit cell is cubic. A perspectiveshowing the cubic FCC unit cell is shown below, where the body-diagonal planes of the atoms are the original A, B, C, and layersof oxygen atoms
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The HCP close-packed lattice
• The HCP lattice is formed when the third layer isstacked so that its atoms are positioned directlyabove the “A” layer (in the upward facingtriangles of the “B” layer).
• The HCP stacking sequence (ABAB) is repeatedindefinitely to form the lattice:
• …ABABABAB...
“A” layer
“B” layer
Repeat “A” layer
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• ABCABC... Stacking Sequence• 2D Projection
• FCC Unit Cell
FCC STACKING SEQUENCE
From W.D. Callister: Materials Science and Engineering: An Introduction
25
Perspective of FCC and HCP structuresviewed parallel to close-packed planes
FCC (...ABCABCABC…) HCP (...ABABABAB…)
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Ceramics• Characteristics
– Hard– Brittle– Heat- and corrosion-resistant
• Made by firing clay or other mineralstogether and consisting of one of moremetals in combination with one or morenonmetals (usually oxygen)
27
Nomenclature
• The letter a is added to the end of anelement name implies that the oxide of thatelement is being referred to:
• SiO2 - silica Si4+ + 2(O2-)• Al2O3 - alumina 2(Al3+) + 3(O2-)• MgO - magnesia Mg2+ + O2-
Positively charged ions cations example: Si4+, Al3+, Mg2+
Negatively charged ions - anions example: O2-
Charge balanced
28
Closed Packed LatticesThe Basis for Many Ceramic Crystal Structures
• Ionic crystal structures are primarily formedas derivatives of the two simple closepacked lattices: face center cubic (FCC)and hexagonal close packed (HCP).
• Most ionic crystals are easily derived fromthese by substituting atoms into theinterstitial sites in these structures.
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Closed Packed Lattices• The larger of the ions, generally the anion, forms the
closed-packed structure, and the cations occupy theinterstices.– We will often consider the anion to be oxygen (O2-) for
convenience since so many important ceramics are oxides.However, the anion could be a halogen or sulfur.
– In the case of particularly heavy cations, such as zirconium anduranium, the cations are larger than the oxygen and the structurecan be more easily represented as a closed packed arrangement ofcations with oxygen inserted in the interstices.
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Interstitial Sites
• The interstitial sites exist between the layersin the close-packed structures
• There are two types of interstitial sites– tetrahedral– octahedral
• These are the common locations for cationsin ceramic structures
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Interstitial Sites• Each site is defined by the local coordination shell formed
between any two adjoining close-packed layers– the configuration of the third layer does not matter– the nearest neighbor configuration of oxygen atoms around the
octahedral and tetrahedral cations is independent of whether thebasic structure is derived from FCC or HCP
• FCC and HCP have the same density of these sites
33
Interstitial sites
• Octahedral: 3-6-7-b-c-f– 3 from the A layer and 3 from the B layer– an octahedron has eight sides and six vertices– the octahedron centered between these six
atoms, equidistant from each - exactly half waybetween the two layers
31 2 4
5 6 78 9 10
a b c
d e f g
h i j
Numbers = A siteslower case letters = B sites
34
Interstitial sites
The octahedral site neither directly above nor directlybelow any of the atoms of the A and B layers thatsurround the site
– The octahedral site will be directly above or below a C-layered atom (if it is FCC)
– These octahedral sites form a hexagonal array, centeredexactly half-way between the close-packed layers
31 2 4
5 6 78 9 10
a b c
d e f g
h i j
Numbers = A siteslower case letters = B sites
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Interstitial sites
• Tetrahedral: 1-2-5-a and e-h-i-9– 1 negative tetrahedron– 1 positive tetrahedron– three of one layer and one of the second layer– 3A and 1B – one apex pointing out of the plane of the
board– 3B and 1 A – one apex pointing into the plane of the
board
31 2 4
5 6 78 9 10
a b c
d e f g
h i j
Numbers = A siteslower case letters = B sites
36
Interstitial sites
• Tetrahedral: 1-2-5-a and e-h-i-9– For both tetrahedral sites the center of the
tetrahedron is either directly above or below anatom in either the A or B layers
– The geometric centers are not halfway betweenthe adjacent oxygen planes but slightly closer tothe plane that forms the base of the tetrahedron
31 2 4
5 6 78 9 10
a b c
d e f g
h i j
Numbers = A siteslower case letters = B sites
37
Interstitial sites31 2 4
5 6 78 9 10
a b c
d e f g
h i j
Numbers = A siteslower case letters = B sites
38
Octahedral sites in the FCC Unit Cell
oo
oo
oo
o
o
o
o
oo
The FCC cell contains fouratoms
six faces that eachcontribute one half and atom
eight corners thateach contribute one-eighth anatomFCC cell contains fouroctahedral sites
12 edges each withone quarter of a site
one site in the center
o
One octahedral site halfwayalong each edge and one atthe cube center
The ratio of octahedral sites to atomsIs 1:1
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Tetrahedral sites in the FCC Unit CellOne tetrahedral site insideeach corner
Eight tetrahedral sites
The ratio of tetrahedral sites to atomsIs 2:1
ttt
tt
t
t
t
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General Structural formula forclose-packed structures
• T2nOnXn
T – Tetrahedral sitesO – Octahedral sitesX – Anions
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Example:
A2nBnXnA = tetrahedral sitesB = octahedral sitesX = anions
MgAl2O4If fully occupied A8B4X4
Mg in tetrahedral sites - 1/8 of the sites occupiedAl in octahedral sites - 1/2 of the sites occupied
43
Linus Pauling
• Nobel Prize in Chemistry 1954– “for his research into the nature of the chemical bond
and its application to the elucidation of the structure ofcomplex substances”
• Nobel Peace Prize 1962• Born in 1901 and died in 1994• We may use Pauling’s rules to predict the
tendency for a specific compound to form aspecific crystal structure
44
Pauling’s Rules
• Pauling’s rules are based on the geometricstability of packing for ions of differentsizes and simple electrostatic stabilityarguments.– These geometric arguments treat the ions as
hard spheres which is an over implication
45
Ionic crystal radii
• Ionic radii (as defined by interatomicspacings) do vary from compound tocompound– they tend to vary most strongly with the
valance state of the ion and the number ofnearest neighbor ions of the opposite charge
• We may consider an ionic radius to be constant for agiven valance state and nearest-neighborcoordination number
47
CN Disposition of ions rc/raabout
central atom
8 corners of ≥ 0.732 a cube
6 corners of ≥ 0.414 an octahedron
4 corners of ≥ 0.225 a tetrahedron
2 corners of ≥ 0.155 a triangle
1 linear ≥ 0
When the radiusratio is less than thisgeometricallydetermined criticalvalue the next lowercoordination ispreferred
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Cubic a = b = c α = β = γ = 90ο
Hexagonal a = b ≠ c α = β = 90ο, γ = 120ο
Tetragonal a = b ≠ c α = β = γ = 90ο
Rhombohedral a = b = c α = β = γ ≠ 90ο
Orthorhombic a ≠ b ≠ c α = β = γ = 90ο
Monoclinic a ≠ b ≠ c α = γ = 90ο, ≠ β
Triclinic a ≠ b ≠ c α ≠ β ≠ γ
49
Rocksalt
• NaCl, KCl, LiF, MgO, CaO, SrO, NiO,CoO, MnO, PbO– for all of these the anion is larger than cation
and forms the basic FCC lattice
The lattice parameterof the cubic unit cell is“ao” and each unitcontains 4 formulaunits
ao
50
Calculating density• NiO -rocksalt structurea = 4.1771 Å space group Fm3mAtom Ox Wy x y zNi +2 4a 0 0 0O -2 4b 0.5 0.5 0.5
ρ =n’(∑MNi +∑� MO)
Vunit cellNAV
4(58.69 + 15.999) g/mol((4.1771 x 10-8 cm)3)(6.022 X 1023 atom/mol) =
g/molcm3 x molecules/mol
= 6.81 g/cm3