Part 1. Crystals and Crystal structures

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Part 1. Crystals and Crystal structures (From
Chapter 1 of Textbook 1)
?The Nature of crystalline state A lot of
materials created in Nature have certain
patterns or shapes
Snowflake hexagonal pattern www.its.caltech.edu/
atomic/book/snowflake1.jpg
from SnowCrystals.com
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Bright Fracture surfaces
Hematite Fe2O3
Pyrite FeS2
Calcite CaCO3
Diamond C
From www.calstatela.edu/faculty/acolvil/minerals.h
tml
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the pattern and fracture surfaces ? materials
have internal order! ? How to links the
internal order to the external shape? In
1784, Haüy showed how to pack together little
rhombs to from different habits of calcite.
? Development of X-ray and electron
diffraction techniques ? most materials
including biological materials are
crystalline or partly so. Assume the
smallest unit for arranging the internal order
is a hard sphere (Hooks spheres). (This sphere
can represent a very complex entity!)
Arrangement of these spheres is space ?
structure. In 2-D, the sphere could be packed
in close-packed
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Hexagonal or simple square.
larger void or gap
?Constructing crystals from closed packed
hexagonal layers of atoms
Define the first layer to be site A!
A
A
A
A
A
A
There two equal sets of sites ( and ) for
the second layer. We could choose either one as
site B and the other set is site C.
A
A
A
A
A
A
A
A
A
A
A
A
B
C
When the second layer of atoms is placed, There
are two possible sites for the atoms on the third
layer to place (A and C sites)
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? If the atoms were stacked in ABA..
sequence ? Hexagonal close-packed
structure. (See Fig. 1.5) Open channels ?
layers running through connecting sites (C).
HCP
? If the atoms were stacked in ABC..
sequence ? Cubic close-packed structure.
(See Fig. 1.6)
? The stacking sequences can be mixed - e.g.
ABACABAC. ? 4-layer repeat ? If a
materials make mistakes in stacking
sequence ? stacking fault e.g. ABCBABC
CCP
CCP
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?Unit Cells of the HCP and CCP Structures
Unit cell a model can be repeated to represent a
structure ? Simple Hexagonal and HCP
Structure (Fig. 1.5)
Stacking Sequence AAAA
Stacking Sequence ABAB
? CCP Structure (Fig. 1.6 and 1.7)
Rhombohedral cell
Cubic cell
C
B
A
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?Constructing crystals from square layers of
atoms
Define the first layer to be site A! There are
only another kind of site available! (site X)
X
X
X
X
X
X
The next layer can only be put in site A or site
X.
One has the stacking sequence of ABAB and
another AAAA
Body Center Cubic (BCC)
Simple Cubic (SC)
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? If the atoms were stacked in ABAB.. sequence
? BCC ? If the atoms were stacked in AAAA..
sequence ? SC ? These two structure can not be
obtained from hexagonal close-packed layer!
The close packed plane of BCC is
B interstices Saddle configuration The atoms on
top might slip a small distance.
B
B
B
? Comparing the hexagonal close-packed plane
and BCC close packed plane
distortion
HCP Or CCP
BCC
Some important transformations in materials
science occur via this kinetic path (e.g.
Fe quenched from above 910 oC, ccp low temp
? bcc)
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?Interstitial Structure The different
stacking sequences previously discussed can
describe variety of crystal structures of a wide
range of materials with one and more
elements. Elements with large size
differences, the smaller atoms can occupy the
interstices of the hcp, ccp, SC, and BCC to
form new structures. ? Interstices in ccp
structure (Fig. 1.10)
x
x
x
x
x
x
x
x
Tetraherdal interstices
Octahedral interstices
x
x
x
x
x
x
x
x
x
x
x
x
x
2ra
ra rx
Tetraherdal interstices
? rx 0.225ra
x
rx
x
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Atoms interstitial sites
8?(1/8)6?(1/2) 8 48 12
2ra
Octahedral interstices
? rx 0.414ra
x
2ra 2rx
Atoms interstitial sites 4 12?(1/4)1
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? Interstices in SC structure (Fig. 1.12)
2ra
? rx 0.732ra
2ra 2rx
x
Cubic interstitial site
CsCl structure
Atoms interstitial sites 8?(1/8)1 11
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? Interstices in BCC structure (Fig. 1.13)
Octahedral interstices and Tetrahedral
interstitices
a/2
x
ra rx a/2
x
Octahedral interstices
x
x
x
? rx 0.154ra
a
Atoms interstitial sites
8?(1/8)112?(1/4)6?(1/2) 26 13
a/4
a/2
x
ra rx
Tetraherdal interstices
x
x
a
x
? rx 0.291ra
x
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Atoms interstitial sites 224?(1/2)
212 16
? You should work out interstices in HCP
structure!
? The radius of an atom depends on its
ionization state! Li atom 258 pm, Li 60
pm ccp Fe 258 pm, BCC Fe 248 pm. ?
Metal hydride, nitride, boride, carbides, etc.
belongs to these kind of interstitial
compounds. But, oversize of the
non-metallic atoms are frequently observed ?
larger atoms are not in contact with each
other (push apart!)
? See Fig. 1.14 for TiN, TiH2, and TiH.
TiN oversize ? Ti atoms are separated ?
ccp ? Face centered cubic TiH2 and
TiH H atoms occupy all or half of the eight
interstices)!
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? See Fig. 1.15 for AlB2 and WC structures!
Hexagonal plane stacked in AAA All or half
of the interstices are occupied ? AlB2 and
WC structure!
? BCC interstitial compound Not known to
exist! BCC interstitial solid solution!
Yes, e.g. Fe(C) ferrite
?Some simple ionic and covalent structures ?
Atom size is only one of the factors that
influence the crystal structures. Some
arrangements of the atoms are
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similar. E.g. TiN is isomorphous to ()
NaCl (ionic structure), TiH2 Li2O TiH
ZnS (zinc blende structure).
?Representing Crystals in projection (crystal
plans) ? The more complicate the crystal, the
larger the unit cell ? difficult to
visualize with diagram. Some structures
even have alternative unit cell. E.g. Perovskite
ABO3 structure.
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One form to represent the structure is
using crystal plan or crystal projection.
? See Fig. 1.16 for example.
?Stacking faults (SF) and twins ? Nature
makes mistakes in the stacking sequence of the
structure. It may occur during (1)
crystallization from the melt or solid
state, (2) solid state processes or
recrystallization, phase transition, and crystal
growth, and (3) deformations. ? consider
ccp structure ABCABC. or CBACBA
Shockley notation upright and inverted
triangle
ABCBCABC ABCBABC
missing a layer
extra layer
Intrinsic extrinsic
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? consider HCP structure ABABAB. or CBCBCB
HCP Alternate Upright and inverted
stacking sequence! CCP (FCC) all upright
or all inverted stacking sequence.
? Twins ABCABCBACBA HCP not possible for
twin
Twin plane
? Hard sphere model the stacking of next
layer in different sites is equally likely.
If one consider second nearest neighbor,
the minimization of the energy determined the
stacking sequence (CCP or HCP). EHCP ECCP ?
many stacking faults. ? Interface ?
interfacial energy stacking fault has
stacking fault energy (ESF). Small ESF, much
easier to form SF. The energy for twin
boundary 0.5 ESF for intrinsic SF 0.25
ESF for extrinsic SF.
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? If deformation is accomplished by the
gliding of close- packed layers over each
other. See Fig. 1.19. The full gliding
direction is B to B. The zig-zag path (B-C-B)
can accomplish the the same overall result. The
partial slip B-C or C-B is name Shockley
partial. Extrinsic SF, twins, and ccp-hcp
transformation may be accomplished by
mechanism involving the partial slip of the
close-packed layer. ? See fig. 1.20 for the
generation of twin crystal through the
mechanism. ? Twin crystal two parts related
to each other by a rotation about some
particular axis (twin axis). See fig. 1.21.
Twins can occur in different plans. Twining is
very common in minerals (result of phase
transition during cooling).
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?Introduction to some more complex crystal
structures ? The atoms described previously
can be replaced by a group of atoms which
is usually the cases for more complex
inorganics or organics. Take SiC, Al2O3, SiO2,
, and C as examples to see the complexity that
can be extended from basic structures. ?
Tetrahedral and Octahedral structures Silicon
carbide and alumina Consider
tetrahedral as an atom Variation in
stacking sequence ? different structures ?
cases of SiC (Fig. 1.22)
Each C will link to 4 Si
Si
C
Look at 1/3 of the cell Two positions (B, C)
to choose!
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B4 (Wurtzite) stacking sequence is ABABAB
or tetrahedral
stacking in the pattern of HCP B3 (Zinc
Blnde) stacking sequence is ABCABC. or
tetrahedral stacking in the
pattern of CCP B5 (Carborundum III)
Sequence is ABACABAC or
two upright two inverted B6
(Carborundum II) Sequence is ABCACBABCACB
or three upright three
inverted B7 (Carborundum I) Sequence is
ABACBCACBCABA
Polytypism One compound with different
structures Fig. 1.23 eight
polytypes of SiC. Representation letter
representing type of unit cell C for
cubic, H for hexagonal, R for rhombohedral
number represents the repeat distance of a
unit cell
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In Fig. 1.23 (a) 3C B3 in fig.
1.22 (b) 2H B4 (c) 4H
B5 (ABCBABCBA. ).
Change B ?A, C?B, A?C, BCBA ?ABAC Or use Shockley
notation both structures are two Uprights
followed by two inverteds!
(d) 6H B6, microtwinned form of 3C
(f) 15R B7 Alumina structure
find the structure from the web
? Silicate structures SiO4 tetrahedron

Si
Each O will link to 2 Si Si (1), O (4/2)
SiO2
O
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? Silicate structures SiO4 tetrahedron

Si
Each O will link to 2 Si Si (1), O (4/2)
SiO2
O
Linking of tetrahedron to form chains,
sheets, or complete frameworks. In term of
charge balance, the silicates may be
achieved in seven different ways (See Fig.
1.25 (SiO4)4- nesosilicates (Si2O7)6-
Sorosilicates (Si6O18)12-
Cyclosilicates (Si2O6)4- and (Si4O11)6-
Inosilicates (single and double chain)
(Si2O5)2-Phyllosilicates (SiO2)0
Tectosilicates. ? The replacing of the Si
with a trivalent metal ? e.g. (SiO4)4-
? (AlO4)5- ? create new paths for linking
the structure, especially for chains or sheets
The basic type of silicate pattern can be
extended to different arrangements, see
Fig. 1.26 for possible arrangements of
inosilicates.
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? The structures of Carbon All the
elements in the periodic table, only C and S are
capable of forming elemental rings or chains
whose stability is independent of length.
The carbon is the only elements that can
form thermally stable complex rings and
long-chains compounds (prerequisite of life).
Important structures of carbon diamond,
graphite, and fullerenes (bulky balls).
? Diamond (sp3 hybride bonding, i.e covalent
bond) Tetrahedral of carbon ? ccp
stacking ? diamond structure (see Fig.
1.27(a)) hcp stacking ? hexagonal
structure (see Fig. 1.27(b)) rare! ?
Graphite (sp2 hybride bonding) C atoms
are linked together to form plane hexagonal
nets. See top views in the next page and Fig.
1.28.
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A and B layer ? two sites available One is
and the other is
If one choose ? ABAB
If one choose ? ABCABC Rhombohedral form
of graphite.
Uncommon!
?Fullerenes (bulky balls) If a
hexagon is replaced by pentagon, a dome shape is
formed. See fig. 1.29. Distribution of
hexagons and pentagons ? determine the
shape and stability of the
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structure. To complete a closed sphere,
12 pentagons is required, Fig. 1.30
pentagonal dodecahedron (one of the five
Plantonic solids tetrahedron, Cubic,
Octahedron, isocahedron (Fig. 1.30), ).
Simplest and smallest bulky balls 20 carbon
atoms to form dodecahedron.
With increasing number of hexagons are
included in the structure ? a family of
fullerenes is formed, see Fig. 1.31
(sizes ? thermal stability ?) C20,
C28, C32, C50, C60, C70, . Magic numbers