Octet stability Primary Ionic Covalent Metallic Van der Waals Secondary Dipoledipole London dispersion Hydrogen Gas Liquid Solid STATE OF MATTER GAS LIQUID SOLID The particles move rapidly ID: 648182
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Slide1
CRYSTALLINE STATESlide2
INTRODUCTION
Octet stability
Primary:
Ionic
CovalentMetallicVan der Waals
Secondary:Dipole-dipoleLondon dispersionHydrogen
Gas
Liquid
SolidSlide3
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 volumeSlide4
CLASSIFICATION OF SOLID BY ATOMIC ARRANGEMENT
Atomic arrangementOrderName
CRYSTAL SYSTEMSlide5
Early crystallography
Robert Hooke (1660) : canon ballCrystal must owe its regular shape to the packing of spherical particles (balls) packed regularly, we get long-range order.Neils
Steensen
(1669) : quartz crystalAll 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?Slide6
Ren
ė-Just Haūy (1781): cleavage of calciteCommon shape to all shards: rhombohedralMathematically proved that there are only 7 distinct space-filling volume elements
7 crystal systemsSlide7
CRYSTALLOGRAPHIC AXES
3 AXES4 AXES
yz
=
xz = xy = yz =
90xy = yu = ux
= 60Slide8
The Seven Crystal SystemsSlide9Slide10
(
rombhohedral)Slide11Slide12
SPACE FILLING
TILINGSlide13Slide14Slide15Slide16Slide17Slide18
August
Bravais (1848): more mathHow 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
latticesSlide19
The Fourteen
Bravais LatticesSlide20
Simple cubic
Body-centeredcubicFace-centeredcubic
1
3
2Slide21
4
Simple tetragonal
Body-centered tetragonal
5Slide22
Simple orthorhombic
Body-centered orthorhombic
6
7Slide23
8
9Slide24
10
12
11Slide25
14
13
HexagonalSlide26
A point lattice
Repeat unitSlide27
z
x
y
A unit cell
O
b
a
c
a, b, c
, ,
Lattice parametersSlide28
Crystal structure
(Atomic arrangement in 3 space)Bravais lattice(Point environment)Basis
(Atomic grouping at each lattice point)Slide29
EXAMPLE: properties of cubic system
*)BRAVAIS LATTICEBASISCRYSTAL STRUCTURE
EXAMPLE
FCC
atomFCCAu, Al, Cu, Pt
moleculeFCCCH
4
ion pair
(Na
+
and
Cl
-
)
Rock salt
NaCl
Atom pair
DC (diamond crystal)
Diamond, Si,
Ge
C
C
109
*)
cubic system is the most simple
most of elements in periodic table have cubic crystal structureSlide30
CRYSTAL STRUCTURE OF
NaClSlide31
CHARACTERISTIC OF CUBIC LATTICES
SCBCCFCCUnit cell volumea
3a3
a3Lattice point per cell
124Nearest neighbor distanceaa3 / 2
a/2Number of nearest neighbors (coordination no.)68
12
Second nearest neighbor distance
a
2
a
a
Number of second neighbor
12
6
6
a = f(r)
2r
4/
3 r22 r
or 4r = a4a3a2
Packing density
0.52
0.68
0.74Slide32
EXAMPLE: FCC
FCC
74% matter (hard sphere model)
26% voidSlide33
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.Slide34Slide35
CRYSTALLOGRAPHIC NOTATION
POSITION: x, y, z, coordinate, separated by commas, no enclosureO: 0,0,0 A: 0,1,1 B: 1,0,½
B
A
z
x
y
Unit cell
O
aSlide36
DIRECTION:
move coordinate axes so that the line passes through originDefine vector from O to point on the lineChoose the smallest set of integersNo commas, enclose in brackets, clear fractions
OB 1 0 ½ [2 0 1]
AO 0 -1 -1
B
A
z
x
y
Unit cell
OSlide37
Denote entire family of directions by carats < >
e.g. all body diagonals: <1 1 1>Slide38
all face diagonals
: <0 1 1>
all cube edges
: <0 0 1>Slide39
MILLER INDICES
For describing planes.Equation for plane:
where a, b, and c are the intercepts of the plane with the x, y, and z axes, respectively.
Let:
so thatNo commas, enclose in parenthesis (h k l)
denote entirely family of planes by brace, e.g. all faces of unit cell: {0 0 1}
etc.Slide40
MILLER INDICES
a
b
c
Intercept at
Intercept at
a/2
Intercept at
b
Miller indices: (h k l)
(2 1 0)
Parallel to z axes
(h k l)
[h k l]
[2 1 0]
(2 1 0)Slide41
Miller indices of planes in the cubic system
(0 1 0)(0 2 0)Slide42
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 SYMMETRYSlide43
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
Slide44
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 LINESlide45
DIAD AXIS
TRIAD AXISTETRAD AXIS
HEXAD AXIS
AXIS OF SYMMETRY
Rotated 180
Twofold rotation axisRotated 120
Threefold rotation axis
Rotated 90
Fourfold rotation axis
Rotated 60
Sixfold
rotation axisSlide46
The 13 axes of symmetry in a cubeSlide47
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 cubeSlide48
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.Slide49
ELEMENTS OF SYMMETRYSlide50
Combination forms of cube and octahedronSlide51
IONIC
COVALENTMOLECULAR
METALLIC
SOLID STATE BONDING
Composed of ions
Held by electrostatic forceEg.: 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, FeSlide52
ISOMORPH
Two or more substances that crystallize in almost identical forms are said to be
isomorphous.
Isomorphs are often chemically similar. Example: chrome alum K
2SO4.Cr2(SO4)3.24H
2O (purple) and potash alum K2SO4.Al
2
(SO
4
)
3
.24H
2
O (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.Slide53
CHROME ALUM CRYSTAL Slide54
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:
POLYMORPHSlide55
ARAGONITESlide56
CRISTOBALITESlide57
Polymorphic Forma of Some Common SubstancesSlide58Slide59
Material that exhibit polymorphism present an interesting problem:
It is necessary to control conditions to obtain the desired polymorph.Once the desired polymorph is obtained, it is necessary to prevent the transformation of the material to another polymorph.Polymorph 1
Poly-
morph 1
Polymorphic transitionSlide60
In many cases, a particular polymorph is
metastableTransform into more stable state
Relatively rapid
infinitely slow
Carbon at room temperature
Diamond
(
metastable
)
Graphite
(stable)Slide61
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 solubilitySlide62
CRYSTAL HABIT
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
=
L
3Slide63Slide64
Internal structure
External habit?
=
Tabular
Prismatic
Acicular
External shape of hexagonal crystal displaying the same facesSlide65
Crystal habit is controlled by:
Internal structureThe 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) slowlySlide66
(a)
(b)
Sodium chloride grown from: (a) pure solution; (b) Solution containing 10% urea