Electronic structure Bonding State of aggregation Octet stability Primary: 1.Ionic 2.Covalent...
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CRYSTALLINE STATE
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INTRODUCTIONElectro
nic structur
e
Bonding
State of aggrega
tion
Octet stability Primary:1. Ionic2. Covalent3. Metallic4. Van der Waals
Secondary:1. Dipole-dipole2. London dispersion3. Hydrogen
GasLiquidSolid
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STATE OF MATTER
GAS LIQUID SOLID
• The particles move rapidly
• Large space between particles
• The particles move past one another
• The particles close together
• Retains its volume
• The particles are arranged in tight and regular pattern
• The particles move very little
• Retains its shape and volume
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CLASSIFICATION OF SOLID BY ATOMIC ARRANGEMENT
Ordered
• regular• long-range• crystalline• “crystal”• transparent
Disordered
• random*• short-range*• amorphous• “glass”• opaque
Atomic arrangementOrderName
CRYSTAL SYSTEM
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EARLY CRYSTALLOGRAPHY
ROBERT HOOKE (1660) : canon ball
Crystal must owe its regular shape to the packing of spherical particles (balls) packed regularly, we get long-range order.
NEILS STEENSEN (1669) : quartz crystal
All crystals have the same angles between corresponding faces, regardless of their sizes he tried to make connection between macroscopic and atomic world.
If I have a regular cubic crystal, then if I divide it into smaller and smaller pieces down to an atomic dimension, will I get a cubic repeat unit?
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RENĖ-JUST HAŪY (1781): cleavage of calcite
• Common shape to all shards: rhombohedral
• Mathematically proved that there are only 7 distinct space-filling volume elements
7 CRYSTAL SYSTEMS
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CRYSTALLOGRAPHIC AXES
3 AXES 4 AXESyz = xz = xy =
yz = 90xy = yu = ux = 60
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THE SEVEN CRYSTAL SYSTEMS
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(rombhohedral)
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SPACE FILLING
TILING
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AUGUST BRAVAIS (1848): more math
How many different ways can we put atoms into these 7 crystal systems and get distinguishable point environment?
He mathematically proved that there are 14 distinct ways to arrange points in space
14 BRAVAIS LATTICES
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The Fourteen Bravais Lattices
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Simple cubic Body-centeredcubic
Face-centeredcubic
1 32
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4
Simple tetragonal Body-centered tetragonal
5
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Simple orthorhombic Body-centered orthorhombic
6 7
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8 9
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10 1211
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1413
Hexagonal
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A point lattice
Repeat unit
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z
x
y
A unit cell
O
b
a
c
a, b, c
, , Lattice parameters
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CRYSTAL STRUCTURE(Atomic arrangement in 3 space)
BRAVAIS LATTICE(Point environment)
BASIS(Atomic grouping at each lattice point)
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EXAMPLE: properties of cubic system*)
BRAVAIS LATTICE
BASIS CRYSTAL STRUCTURE
EXAMPLE
FCC atom FCC Au, Al, Cu, Pt
molecule FCC CH4
ion pair(Na+ and Cl -)
Rock salt NaCl
Atom pair DC (diamond crystal)
Diamond, Si, Ge
C
C109
*) cubic system is the most simplemost of elements in periodic table have cubic crystal structure
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CRYSTAL STRUCTURE OF NaCl
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CHARACTERISTIC OF CUBIC LATTICES
SC BCC FCCUnit cell volume a3 a3 a3
Lattice point per cell 1 2 4Nearest neighbor distance a a3 / 2 a/2Number of nearest neighbors (coordination no.)
6 8 12
Second nearest neighbor distance
a2 a a
Number of second neighbor 12 6 6a = f(r) 2r 4/3 r 22 r
or 4r = a4 a3 a2Packing density 0.52 0.68 0.74
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volumetotalatomsofvolume
densitypacking
3
3
344
a
r
EXAMPLE: FCC
3
3
223
44
r
r
74.02322
344
3
3
r
r
FCC74% matter (hard sphere model)
26% void
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• In crystal structure, atom touch in one certain direction and far apart along other direction.
• There is correlation between atomic contact and bonding.
• Bonding is related to the whole properties, e.g. mechanical strength, electrical property, and optical property.
• If I look down on atom direction: high density of atoms direction of strength; low density/population of atom direction of weakness.
• If I want to cleave a crystal, I have to understand crystallography.
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CRYSTALLOGRAPHIC NOTATION
POSITION: x, y, z, coordinate, separated by commas, no enclosure
O: 0,0,0
A: 0,1,1
B: 1,0,½
B
A
z
x
y
Unit cell
O
a
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DIRECTION: move coordinate axes so that the line passes through origin
Define vector from O to point on the line Choose the smallest set of integers No commas, enclose in brackets, clear fractions
OB 1 0 ½ [2 0 1]
AO 0 -1 -1 110
B
A
z
x
y
Unit cell
O
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Denote entire family of directions by carats < >
e.g.
all body diagonals: <1 1 1>
111 111 111 111
111 111 111 111
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all face diagonals: <0 1 1>
110 110 110
101
110
101 101 101
011 011 011 011
all cube edges: <0 0 1>
100 100 010 001 010 001
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MILLER INDICESFor describing planes.
Equation for plane: 1cz
by
ax
where a, b, and c are the intercepts of the plane with the x, y, and z axes, respectively.
Let:
so that
No commas, enclose in parenthesis (h k l) denote entirely family of planes by brace, e.g. all faces of unit
cell: {0 0 1}
ah
1
cl
1
bk
1
1 lzkyhx
100 100 001 etc.
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MILLER INDICES
a
b
cIntercept at
Intercept at a/2
Intercept at b
Miller indices: (h k l)
121
(2 1 0)
Parallel to z axes
(h k l) [h k l]
[2 1 0]
(2 1 0)
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Miller indices of planes in the cubic system
(0 1 0) (0 2 0)
011 111 210
011
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Many of the geometric shapes that appear in the crystalline state are some degree symmetrical.
This fact can be used as a means of crystal classification.
The three elements of symmetry:
Symmetry about a point (a center of symmetry)
Symmetry about a line (an axis of symmetry)
Symmetry about a plane (a plane of symmetry)
CRYSTAL SYMMETRY
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SYMMETRY ABOUT A POINT
A crystal possesses a center of symmetry when every point on the surface of the crystal has an identical point on the opposite side of the center, equidistant from it.
Example: cube
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If a crystal is rotated 360 about any given axis, it obviously returns to its original position.
If the crystal appears to have reached its original more than once during its complete rotation, the chosen axis is an axis of symmetry.
SYMMETRY ABOUT A LINE
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DIAD AXIS
TRIAD AXIS
TETRAD AXIS
HEXAD AXIS
AXIS OF SYMMETRY
• Rotated 180• Twofold rotation axis
• Rotated 120• Threefold rotation axis
• Rotated 90• Fourfold rotation axis
• Rotated 60• Sixfold rotation axis
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THE 13 AXES OF SYMMETRY IN A CUBE
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A plane of symmetry bisects a solid object in a such manner that one half becomes the mirror image of the other half in the given plane.
A cube has 9 planes of symmetry:
SYMMETRY ABOUT A PLANE
THE 9 PLANES OF SYMMETRY IN A CUBE
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Cube (hexahedron) is a highly symmetrical body as it has 23 elements of symmetry (a center, 9 planes, and 13 axis).
Octahedron also has the same 23 elements of symmetry.
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ELEMENTS OF SYMMETRY
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Combination forms of cube and octahedron
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IONIC
COVALENT
MOLECULAR
METALLIC
SOLID STATE
BONDING
• Composed of ions• Held by electrostatic force• Eg.: NaCl
• Composed of neutral atoms• Held by covalent bonding• Eg.: diamond
• Composed of molecules• Held by weak attractive force• Eg.: organic compounds
SOLID STATE BONDING
• Comprise ordered arrays of identical cations
• Held by metallic bond• Eg.: Cu, Fe
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ISOMORPH Two or more substances that crystallize in almost
identical forms are said to be isomorphous.
Isomorphs are often chemically similar.
Example: chrome alum K2SO4.Cr2(SO4)3.24H2O (purple) and potash alum K2SO4.Al2(SO4)3.24H2O (colorless) crystallize from their respective aqueous solutions as regular octahedral. When an aqueous solution containing both salts are crystallized, regular octahedral are again formed, but the color of the crystals (which are now homogeneous solid solutions) can vary from almost colorless to deep purple, depending on the proportions of the two alums in the solution.
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CHROME ALUM CRYSTAL
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A substance capable of crystallizing into different, but chemically identical, crystalline forms is said to exhibit polymorphism.
Different polymorphs of a given substance are chemically identical but will exhibit different physical properties, such as density, heat capacity, melting point, thermal conductivity, and optical activity.
Example:
POLYMORPH
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ARAGONITE
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CRISTOBALITE
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Polymorphic Forms of Some Common Substances
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Material that exhibit polymorphism present an interesting problem:
1. It is necessary to control conditions to obtain the desired polymorph.
2. Once the desired polymorph is obtained, it is necessary to prevent the transformation of the material to another polymorph.
Polymorph 1Poly-
morph 2
Polymorphic transition
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In many cases, a particular polymorph is metastable
Transform into more stable state
Relatively rapid infinitely slow
Carbon at room temperature
Diamond(metastable)
Graphite(stable)
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POLYMORPH
MONOTROPIC ENANTIOTROPIC
One of the polymorphs is the stable form at all
temperature
Different polymorphs are stable at different
temperature
The most stable is the one having lowest
solubility
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CRYSTAL HABIT
In nature perfect crystals are rare.
The faces that develop on a crystal depend on the space available for the crystals to grow.
If crystals grow into one another or in a restricted environment, it is possible that no well-formed crystal faces will be developed.
However, crystals sometimes develop certain forms more commonly than others, although the symmetry may not be readily apparent from these common forms.
The term used to describe general shape of a crystal is habit.
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Crystal habit refers to external appearance of the crystal.
A quantitative description of a crystal means knowing the crystal faces present, their relative areas, the length of the axes in the three directions, the angles between the faces, and the shape factor of the crystal.
Shape factors are a convenient mathematical way of describing the geometry of a crystal.
If a size of a crystal is defined in terms of a characteriza-tion dimension L, two shape factors can be defined:
Volume shape factor : V = L3
Area shape factor : A = L2
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Some common crystal habits are as follows.
Cubic - cube shapes
Octahedral - shaped like octahedrons, as described above.
Tabular - rectangular shapes.
Equant - a term used to describe minerals that have all of their boundaries of approximately equal length.
Fibrous - elongated clusters of fibers.
Acicular - long, slender crystals.
Prismatic - abundance of prism faces.
Bladed - like a wedge or knife blade
Dendritic - tree-like growths
Botryoidal - smooth bulbous shapes
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Internal structure External habit ?=
Tabular Prismatic Acicular
External shape of hexagonal crystal displaying the same faces
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Crystal habit is controlled by:
1. Internal structure
2. The conditions at which the crystal grows (the rate of growth, the solvent used, the impurities present)
Variation of sodium chlorate crystal shape grown: (a) rapidly; (b) slowly
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(a) (b)
Sodium chloride grown from: (a) pure solution; (b) Solution containing 10% urea