1. Solid state
The solids are the substances which have definite volume and definite shape.
The following are the characteristic properties of the solid state:
(i) They have definite mass, volume and shape.
(ii) Intermolecular distances are short.
(iii) Intermolecular forces are strong.
(iv) Their constituent particles (atoms, molecules or ions) have fixed positions and can only oscillate about their mean positions.
(v) They are incompressible and rigid.

2. Crystalline solids (True solids)
Classification of solids based on arrangement of particles
Crystalline solids (True solids)
Amorphous solids (Pseudo solids)
They have long range order.
They have short range order.
They have definite melting point
Not have definite melting point
They have a definite heat of fusion
Not have definite heat of fusion
They are rigid and incompressible
Not be compressed to any appreciable extent
They are given cleavage i.e. they break into two pieces with plane surfaces
They are given irregular cleavage i.e. they break into two pieces with irregular surface
They are anisotropic because of these substances show different property in different direction
They are isotropic because of these substances show same property in all directions
There is a sudden change in volume when it melts.
There is no sudden change in volume on melting.
These possess symmetry and interfacial angles
Not possess any symmetry and interfacial angles.
examples, naphthalene, benzoic acid, potassium nitrate, copper. etc
Examples Polyurethane, cellophane, polyvinyl chloride, fibre glass, , teflon , Glass, rubber ,plastics etc

5. Polymorphism is the ability of a specific chemical composition to crystallize in more than one form. This generally occurs as a response to changes in temperature or pressure or both. The different structures of such a chemical substance are called polymorphic forms, or polymorphs. For example, the element carbon (C) occurs in nature in two different polymorphic forms, depending on the external (pressure and temperature) conditions. These forms are graphite, with a hexagonal structure, and diamond

6. Crystalline and amorphous silica
Silica occurs in crystalline as well as amorphous states. Quartz is a typical example of crystalline silica. Quartz and the amorphous silica differ considerably in their properties.
Quartz
Amorphous silica
It is crystalline in nature
It is light (fluffy) white powder
All four corners of tetrahedron are shared by others to give a network solid
The tetrahedra are randomly joined, giving rise to polymeric chains, sheets or three- dimensional units
It has high and sharp melting point (1710°C)
It does not have sharp melting point

7. Diamond and graphite
Diamond and graphite are tow allotropes of carbon. Diamond and graphite both are covalent crystals. But, they differ considerably in their properties.
Diamond
Graphite
It occurs naturally in free state
It occurs naturally, as well as manufactured artificially
It is the hardest natural substance known.
It is soft and greasy to touch
It has high relative density (about 3.5)
Its relative density is 2.3
It is transparent and has high refractive index (2.45)
It has black in colour and opaque
It is non-conductor of heat and electricity.
Graphite is a good conductor of heat and electricity
It burns in air at 900°C to give CO2
It burns in air at 700°C to give CO2
It occurs as octahedral crystals
It occurs as hexagonal crystals

8. Electrical Conductivity
Classification of crystalline solids according to forces of attraction and type of particles
Types of Solid
Constituents
Bonding
Examples
Physical Nature
M.P.
B.P.
Electrical Conductivity
Ionic
Positive and negative ions network systematically arranged
Coulombic
NaCl, KCl, CaO, MgO, LiF, ZnS, BaSO4 and K2SO4 etc.
Hard but brittle
High (≃1000K)
High (≃2000K)
Conductor
(in molten state and in aqueous solution)
Covalent
Atoms connected in covalent bonds
Electron sharing
SiO2 (Quartz),
SiC, C (diamond),
C(graphite) etc.
Hard
Very high (≃4000K)
Very high
(≃5000K)
Insulator except graphite
Molecular
Polar or non-polar molecules
(i) Molecular interactions (intermolecu-lar forces)
(ii) Hydrogen bonding
I2,S8, P4, CO2, CH4, CCl4 ,.
Urea,benzene
etc
Starch,sucrose, water, ammonia etc.
Soft
Low
(≃300K to 600K)
(≃400K)
(≃ 450 to 800 K)
(≃373K to 500K)
Insulator
Metallic
Cations in a sea of electrons
Sodium , Au, Cu, magnesium, metals and alloys
Ductile malleable
High
(≃800K to 1000 K)
(≃1500K to 2000K)
Atomic
Atoms
London dispersion force
Noble gases
Very low
Poor thermal and electrical conductors

9. Crystalline Solids Examples Quartz SiO2 Cholesterol CuSO4• 5H2O Ag
MnB(OH)3 Cu

10. Crystal?
Crystal is a homogeneous portion of a crystalline substance, composed of a regular pattern of structural units (ions, atoms or molecules) which is bound by plane surfaces making definite angles with each other and have sharp edges giving a regular geometric form.
Lattice?
a regular three dimensional arrangement of points in space is called a crystal lattice

11. What is the relation between the two?
Crystal = Lattice + Motif
Motif or basis: an atom or a group of atoms associated with each lattice point

12. CRYSTAL STRUCTURE
Crystal structure is the periodic arrangement of atoms in the crystal. Association of each lattice point with a group of atoms(Basis or Motif).
Lattice: Infinite array of points in space, in which each point has identical surroundings to all others.
Space Lattice  Arrangements of atoms
= Lattice of points onto which the atoms are hung.
Space Lattice + Basis = Crystal Structure =
• • • +
Elemental solids (Argon): Basis = single atom.
Polyatomic Elements: Basis = two or four atoms.
Complex organic compounds: Basis = thousands of atoms.

13. Love Pattern =
Love Lattice
+ Heart +

14. The unit cell of a crystal lattice
Two dimentional lattice have 5 types of unit cells which are possible
Square Lattice: x = y, 90° angles
Parallelogram lattice x ≠ y, angles < 90°
Rectangular lattice x ≠ y, angles = 90°
Rhombic or centered-rectangle lattice: x = y, angles neither 60° or 90°;
Hexagonal lattice (but unit cell is a rhombus with x = y and angles 60°)

15. The crystal lattice and the unit cell in 3D
The unit cell is the minimum repeating unit necessary to describe the crystal.

16. Crystals are made of infinite number of unit cells
The smallest repeating unit in a three dimensional structure (lattice) is unit cell
A crystal’s unit cell dimensions are defined by two lattice parameters
1.Edge lengths of the 3 axes, a, b, and c
2.Interaxial angles, ,  and  .

17. Crystal system
Crystals are grouped into seven crystal systems, according to characteristic symmetry of their unit cell.
The characteristic symmetry of a crystal is a combination of one or more rotations and inversions.

18. THREE DIMENTIONAL UNIT CELLS / UNIT CELL SHAPES1 7 2 3 4 5 6

19. Unit cells can be broadly divided into two categories,primitive and centred unit cells.
Primitive Unit Cells When constituent particles are present only on the corner positions of a unit cell, it is called as primitive unit cell.
(b) Centred Unit Cells When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell.
Centred unit cells are of three types:
(i) Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners.
(ii) Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.
(iii) End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.
Primitive (p)
Body Centered (i)
Face Centered (f)
End Centered (c)

20. Lattices
Auguste Bravais
( )
In 1848, Auguste Bravais demonstrated that in a 3-dimensional system there are fourteen possible lattices
A Bravais lattice is an infinite array of discrete points with identical environment
seven crystal systems + four lattice centering types = 14 Bravais lattices
Lattices are characterized by translation symmetry

21. BRAVAIS LATTICES
7 UNIT CELL TYPES + 4 LATTICE TYPES = 14 BRAVAIS LATTICES

22. Location of lattice point
Analysis of cubic system
1. Number of atoms in per unit cell
The total number of atoms contained in the unit cell for a simple cubic called the unit cell content and is defined represented by Z . Following relation can be used to know the contribution of atom from each lattice point
Location of lattice point
Contribution of atom to the unit cell per lattice point
Corner
1/8
Edge centre
1/4
Face centre
1/2
Body centre 1
diagonal
corners 8
Faces 6
Face diagonals 12
Face centres
Edges
Edge centre
Body diagonals 4
Body centre 1

24. Total atom in per unit cell(Z)
The simplest relation can determine for it is,
Number of atoms at the corners of the cube
Number of atoms at six faces of the cube
Number of atoms inside the cube
Number of atoms at edges
Cubic unit cell nc nf ni
Total atom in per unit cell(Z)
Simple cubic (sc) 8 1
body centered cubic (bcc) 2
Face centered cubic (fcc) 6 4

25. Coordination number Primitive cubic Body centered cubic
2. Co-ordination number (C.N.) : It is defined as the number of atoms or particles which are in direct contact or touching any given atom or particle in a crystal. It depends upon structure of the crystal. 8 12
Coordination number 6
Primitive cubic
Body centered cubic
Face centered cubic
(SCC) C.N. = 6.
(BCC) C.N. = 8
(FCC) C.N. = 12.

26. ATOMIC PACKING FRACTION
Fill a box with hard spheres
Packing Fraction = total volume of spheres in box / volume of box
In crystalline materials:
Atomic packing fraction = total volume of atoms in unit cell / volume of unit cell
(as unit cell repeats in space)
Packing fraction (P.F.) : It is defined as ratio of the volume of the unit cell that is occupied by atoms inside the unit cell to the total volume of the unit cell.
Let radius of the atom in the packing = r
Edge length of the cube = a
Volume of the cube V = a x a x a
Volume of the atom (spherical) =
Packing fraction

27. Relation between radius and edge length (r & a)
Structure
Relation between radius and edge length (r & a)
Volume of the atom ()
Packing fraction
Packing efficiency
Simple cubic
52 %
Face-centred cubic
74 %
Body-centred cubic
68 %

28. SIMPLE CUBIC STRUCTURE (SC)
• Cubic unit cell is 3D repeat unit
Rare (only Po has this structure)
• Close-packed directions (directions along which atoms touch each other)
are cube edges.
• Coordination # = 6
(# nearest neighbors)
(Courtesy P.M. Anderson)

29. ATOMIC PACKING FRACTION
Adapted from Fig. 3.19,
Callister 6e.
Lattice constant
close-packed directions a
R=0.5a
contains 8 x 1/8 = 1
atom/unit cell
• APF for a simple cubic structure = 0.52

30. BODY CENTERED CUBIC STRUCTURE (BCC)
• Coordination # = 8
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.

31. ATOMIC PACKING FACTOR: BCC
Adapted from
Fig. 3.2,
Callister 6e.
• APF for a body-centered cubic structure = p3/8 = 0.68

32. FACE CENTERED CUBIC STRUCTURE (FCC)
• Coordination # = 12
Adapted from Fig. 3.1(a),
Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.

33. ATOMIC PACKING FACTOR: FCC
Adapted from
Fig. 3.1(a),
Callister 6e.
• APF for a body-centered cubic structure = p/(32) = 0.74
(best possible packing of identical spheres)

35. CALCULATION OF DENSITY OF CUBIC CRYSTAL SYSTEM (d)
Density of any crystal can be defined as mass of crystal per unit volume
Density(gm/ml) = mass of crystal (gm)
volume of crystal(ml)
Since crystal is formed by repeating unit cell we can also calculate density by
Determining ratio of mass of unit cell and volume of unit cell
Density(gm/ml) = mass of unit cell (gm)
volume of unit cell(ml)
Mass of one unit cell depends on number of atoms in unit cell (z) and is given by
Mass of one atom in grams = Molar mass
Avogadro number
Mass of one unit cell in grams = z x molar mass = Z x M
Avogadro number N
Volume of one unit cell in cm3 = a3 , where a is edge length in cm
Density of cubic crystal = Z x M
N x a3

36. Calculation of number of unit cell
Number of unit cell can be calculated from different data
From weight of crystalline solid - if weight is given we can use following formula to calculate number of atoms and number of unit cell
number of atoms = weight of crystal (gm) x Avogadro number = W x N
molar mass of metal M
Number of unit cells = number of atoms = W x N
number of atoms per unit cell M x Z
2. From volume of crystal – if volume of crystal (V) and edge length (a) of unit cell is given
Number of unit cells = volume of crystal =
volume of one unit cell

37. CLOSE PACKING OF SPHERES

38. Close-packing-HEXAGONAL coordination of each sphere
SINGLE LAYER PACKING
SQUARE PACKING
CLOSE PACKING
Close-packing-HEXAGONAL coordination of each sphere

39. Arrangement in two dimension :
In two dimensions also there are two ways of packing the the spheres(in moving from one dimension to two dimensions it can be imagined that the two dimensional array will be made up of 1-D closed pack arrays / lines which are stacked one on top of each other.
1.Square packing :
If the one dimensional arrays are placed on top of one another, we get the square packing in twio dimensions. ś
One sphere will be in constant contact with 4 other spheres.
area of square = a2 = 4r2
area of atoms in the square =
fraction of area occupied by spheres = = 78%

40. 2. hexagonal close packing :
(in 2-D) If in a two dimensional arrangement,every one dimensional array is placed in the cavity of the just preceding array, we get the hexagonal packing in two dimensions.
area of hexagon = 6 × a2 = 6 × × 4r2
area of atoms = r × r2 = r2
fraction of area occupied = = 98%
As is evident from the above calculations, the spheres are in closer contact in the hexagonal arrangement, hence the hexagonal arrangement is considered to be a better way of packing as compared to the square packing.

41. TWO LAYERS PACKING

42. THREE LAYERS PACKING

44. Hexagonal close packing
Cubic close packing

45. NON-CLOSE-PACKED STRUCTURES
a) Body centered cubic ( BCC )
b) Primitive cubic ( P)
68% of space is occupied
Coordination number = 8
52% of space is occupied
Coordination number = 6

46. Hexagonal close packed
ABCABC… 12
Cubic close packed
ABABAB…
Hexagonal close packed 8
Body-centered Cubic
AAAAA…
Primitive Cubic
Stacking pattern
Coordination number
Structure
Non-close packing
Close packing 6

48. FCC STACKING SEQUENCE • FCC Unit Cell • ABCABC... Stacking Sequence
• 2D Projection

49. B A C

50. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

51. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
• ABAB... Stacking Sequence
• 3D Projection
• 2D Projection
Adapted from Fig. 3.3,
Callister 6e.
• Coordination # = 12
• APF = 0.74,