1. CRYSTALLINE STATE

2. INTRODUCTION Electronic structure Bonding State of aggregation
Primary:
Ionic
Covalent
Metallic
Van der Waals
Gas
Liquid
Solid
Octet stability
Secondary:
Dipole-dipole
London dispersion
Hydrogen

3. STATE OF MATTER GAS LIQUID SOLID
The particles are arranged in tight and regular pattern
The particles move very little
Retains its shape and volume
The particles move past one another
The particles close together
Retains its volume
The particles move rapidly
Large space between particles

4. CRYSTAL SYSTEM CLASSIFICATION OF SOLID BY ATOMIC ARRANGEMENT Ordered
regular
long-range
crystalline
“crystal”
transparent
Disordered
random*
short-range*
amorphous
“glass”
opaque
Atomic arrangement
Order
Name

5. 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?

6. 7 crystal systems 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

7. 3 AXES
4 AXES
yz = 
xz = 
xy = 
yz = 90
xy = yu = ux = 60
CRYSTALLOGRAPHIC AXES

8. The Seven Crystal Systems

10. (rombhohedral)

12. SPACE FILLING
TILING

18. 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

19. The Fourteen Bravais Lattices

20. 1 2 3
Face-centered
cubic
Simple cubic
Body-centered
cubic

21. 4 5
Simple tetragonal
Body-centered tetragonal

22. 6 7
Simple orthorhombic
Body-centered orthorhombic

23. 8 9

24. 10 11 12

25. 13 14
Hexagonal

26. Repeat unit
A point lattice

27. a, b, c z
Lattice parameters
, ,  b c   O y  a x
A unit cell

28. Crystal structure Bravais lattice Basis
(Atomic arrangement in 3 space)
Bravais lattice
(Point environment)
Basis
(Atomic grouping at each lattice point)

29. EXAMPLE: properties of cubic system*)
BRAVAIS LATTICE
BASIS
CRYSTAL STRUCTURE
EXAMPLE
FCC
atom
Au, Al, Cu, Pt
molecule
CH4
ion pair
(Na+ and Cl-)
Rock salt
NaCl
Atom pair
DC (diamond crystal)
Diamond, Si, Ge C
109
*) cubic system is the most simple
most of elements in periodic table have cubic crystal structure

30. CRYSTAL STRUCTURE OF NaCl

31. CHARACTERISTIC OF CUBIC LATTICESSC
BCC
FCC
Unit cell volume a3
Lattice point per cell 1 2 4
Nearest neighbor distance a
a3 / 2
a/2
Number of nearest neighbors (coordination no.) 6 8 12
Second nearest neighbor distance
a2
Number of second neighbor
a = f(r) 2r
4/3 r
22 r
or 4r =
a4
a3
Packing density
0.52
0.68
0.74

32. EXAMPLE: FCC
74% matter (hard sphere model)
FCC
26% void

33. 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.

35. CRYSTALLOGRAPHIC NOTATION
POSITION: x, y, z, coordinate, separated by commas, no enclosure
O: 0,0,0
A: 0,1,1
B: 1,0,½ z
Unit cell A B O y a x

36. 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 z
OB ½ [2 0 1] 
Unit cell AO  A O B y x

37. Denote entire family of directions by carats < >
e.g.
all body diagonals: <1 1 1>

38. all face diagonals: <0 1 1>
all cube edges: <0 0 1>

39. 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 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}
etc.

40. (h k l)  [h k l] c Miller indices: (h k l) (2 1 0) (2 1 0) b a
Intercept at  c
Miller indices: (h k l)
(2 1 0)
(2 1 0) b
Intercept at b a
Parallel to z axes
[2 1 0]
Intercept at a/2
MILLER INDICES

41. Miller indices of planes in the cubic system
(0 1 0)
(0 2 0)
Miller indices of planes in the cubic system

42. CRYSTAL SYMMETRY
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)

43.  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 

44. Symmetry about a LINE
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.

45. AXIS OF SYMMETRY DIAD AXIS TRIAD AXIS TETRAD AXIS HEXAD AXIS
Rotated 180
Twofold rotation axis
DIAD AXIS
TRIAD AXIS
Rotated 120
Threefold rotation axis
AXIS OF SYMMETRY
TETRAD AXIS
Rotated 90
Fourfold rotation axis
Rotated 60
Sixfold rotation axis
HEXAD AXIS

46. The 13 axes of symmetry in a cube

47. Symmetry about a plane
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:
The 9 planes of symmetry in a cube

48. 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.

49. ELEMENTS OF SYMMETRY

50. Combination forms of cube and octahedron

51. SOLID STATE BONDING IONIC COVALENT SOLID STATE BONDING MOLECULAR
Composed of ions
Held by electrostatic force
Eg.: NaCl
IONIC
COVALENT
Composed of neutral atoms
Held by covalent bonding
Eg.: diamond
SOLID STATE BONDING
MOLECULAR
Composed of molecules
Held by weak attractive force
Eg.: organic compounds
Comprise ordered arrays of identical cations
Held by metallic bond
Eg.: Cu, Fe
METALLIC

52. 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.

53. CHROME ALUM CRYSTAL

54. POLYMORPH
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:

55. ARAGONITE

56. CRISTOBALITE

57. Polymorphic Forma of Some Common Substances

59. Polymorphic transition
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.
Poly-
morph 1
Polymorph 1
Polymorphic transition

60. 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)

61. POLYMORPH MONOTROPIC ENANTIOTROPIC
Different polymorphs are stable at different temperature
One of the polymorphs is the stable form at all temperature
The most stable is the one having lowest solubility

62. 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 =  L3

64. External shape of hexagonal crystal displaying the same faces? =
Internal structure
External habit
Tabular
Prismatic
Acicular
External shape of hexagonal crystal displaying the same faces

65. Crystal habit is controlled by: Internal structure
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

66. (a) (b) Sodium chloride grown from: (a) pure solution;
(b) Solution containing 10% urea