This document discusses crystal structures and atomic bonding. It begins by describing atomic structure, including the arrangement of electrons and composition of the nucleus. It then discusses atomic number, mass, and Bohr's atomic model of electron shells and orbits. The document outlines ionic, covalent, and metallic bonding between atoms. It also describes primary and secondary bonding. Finally, it summarizes different types of crystal structures including cubic, diamond, and their unit cells and packing efficiency. It discusses imperfections like point and line defects.

1. Crystal Structures

2. Atomic Structure
* An atom is a complex arrangement of negatively charged
electrons arranged in defined shells about a positively
charged nucleus. This nucleus contains most of the
atom's mass and is composed of protons and neutrons
(except for common hydrogen which has only one proton).

3. Atomic Number
* The atomic number or proton number (symbol Z) of a
chemical element is the number of protons found in the
nucleus of every atom of that element. The atomic
number uniquely identifies a chemical element. It is
identical to the charge number of the nucleus.

4. Atomic Mass
* The atomic mass is a weighted average of all of the isotopes
of that element, in which the mass of each isotope is
multiplied by the abundance of that particular isotope.
(Atomic mass is also referred to as atomic weight, but the
term "mass" is more accurate.)

5. Bohr’s Atomic Model
• In an atom, electrons (negatively charged) revolve around the positively charged
nucleus in a definite circular path called orbits or shells.
• Each orbit or shell has a fixed energy and these circular orbits are known as orbital
shells.
• The energy levels are represented by an integer (n=1, 2, 3…) known as
the quantum number. This range of quantum number starts from nucleus side with n=1
having the lowest energy level. The orbits n=1, 2, 3, 4… are assigned as K, L, M,
N…. shells and when an electron attains the lowest energy level, it is said to be in
the ground state.
• The electrons in an atom move from a lower energy level to a higher energy level
by gaining the required energy and an electron moves from a higher energy level
to lower energy level by losing energy.

6. Bohr’s Atomic Model

7. Atomic Bonding
* At large distances, the interactions between atoms are
negligible but as atoms are brought closer, the interatomic
forces come into play.
* There are two types of forces
* Attractive Force
* Repulsive Force
* Metals having large bonding energies tend to have high
melting points.

8. Atomic Bonding

9. Primary Bonding
* These are the bonds that exist between atoms and are also
called as interatomic forces. These are generally found in
solids and binding involves valence electrons.

10. Ionic Bonding
* Atoms are filled with an outer shell of electrons. Electron shells
are filled by transferring electrons from one atom to the next.
Donor atoms will take on a positive charge, and the acceptors
will have a negative charge. They will attract each other by being
positive and negative, and bonding will then occur.

11. Covalent Bonding
* Atoms like to share their electrons and this causes their outer
shell to be complete. A covalent bond is produced by the sharing
of atoms and electrons. This produces a strong covalent bond.

12. Metallic Bonding
* Metallic bonds are a metal, and share outer bonds with atoms in
a solid. Each atom gives off a positive charge by shedding its
outer electrons, and the negatively charges electrons hold the
metal atoms together.

13. Secondary Bonding
* Secondary bonds are significantly weaker than primary bonds in
that they often produce weak links, and create deformations in
the bond. Secondary bonds include hydrogen and van der wals
bonds.
* Hydrogen Bond: Hydrogen bonds share between covalent and
oxygenated atoms. This leads to very small electrical charges
around the hydrogen bond, and negative charges around the
oxygenated bonds.

14. Crystalline Solid
* A crystalline solid is formed by regular repetition of its
building blocks (atoms or molecule)in a three dimensional
periodic array. The examples of crystals are table salt
(NaCl), diamond, snowflakes, metals, ice, ceramics etc.

15. Amorphous solid
* materials in which constituents (atoms or molecules) are not
arranged in a regular manner over a long range. There is
no periodicity in structure, if periodicity occurs, it must be
over a short distance . The examples of crystalline solid are
glass, plastic, rubber etc.

16. Quasicrystal
* Quasicrystal, also called quasi-periodic crystal, matter formed
atomically in a manner somewhere between the
amorphous solids of glasses (special forms of metals and
other minerals, as well as common glass) and the precise
pattern of crystals. Like crystals, quasicrystals contain an
ordered structure, but the patterns are subtle and do not
recur at precisely regular intervals.

17. Some Important Terms
* Lattice:
* Defined as a regular periodic array of point in space.
Each point in a lattice has identical surrounding
everywhere. Lattice is basically imaginary points on
space with a periodic manner.
* Basis:
* Atoms or molecules which are constituents of a crystal
material. For example in NaCl crystal, NaCl molecule,
group of one Na and one Cl atoms form basis.

18. Lattice points
* Lattice points in 2
Dimensions
* Lattice points in 3
Dimensions

19. Crystal structure = lattice + basis

20. Unit Cell
* It is convenient to divide the crystal into small entities such
small group of atoms or molecules is a well defined
arrangement. These small cells are called unit cells. The
unit cells are building blocks for construction of crystal
structure.

21. Cubic crystal system
* The simplest and easiest structure.
* Three types of possible crystal structure under this family
named as simple cubic, body centered cubic and face
centered cubic.

22. Simple cubic crystal
* Lattice points are arranged at each 8
corner of cube.
* At each corner of cube, an
atom is shared by 8 nearby unit
cells.
* One unit cell contains 1/8×8=1
atoms.
* Each atom is surrounded by 6
nearest neighbors atoms. The
number of nearest neighbors of a
lattice point (or atom) in a crystal
lattice is called coordinate number.

23. Packing efficiency in Simple Cubic Lattice
A unit cell of simple cubic lattice contains one atom.
Packing Efficiency= 52.4 %

24. Body centred Cubic Structure
* One constituent particle lies at the center of the body of a unit
cell in addition to the particles lying at the corners.
* 8 corners × 1/8 atoms per corner =8×1/8=1atom
* Body center atom =1×1=1 atom
* Hence, total number of atoms per unit cell in bcc Unit cell
=1+1=2 atom

25. Packing Efficiency

26. Face – Centred Cubic Structure
* There are eight atoms present at each corner. A cube has six
faces, therefore total six atoms are present at the center of
each of the face.
* Each atom present at corners is shared by adjacent eight
atoms and each atom present at the center of face is shared
between adjacent two atoms.

27. Face – Centred Cubic Structure
* 8 corners × 1/8 atoms per corner = 8 × 1/8 = 1 atom
* 6 face centered atoms × ½ atom per unit cell = 6× ½ =3
* Hence, total number of atoms per unit cell in a fcc unit cell =
1+3=4

28. Packing Efficiency

29. Diamond Cubic Structure
* Diamond is a
metastable allotrope of
carbon where the each
carbon atom is
bonded covalently
with other surrounding
four
carbon atoms and
are arranged in
a
variation of the face

30. Diamond Cubic Structure
* Number of atoms contributed by the corner atoms to
an unit cell is 1/8×8 =1
* Number of atoms contributed by the face centred
atoms to theunit cell is 1/2 × 6 = 3
* Atoms inside the structure =4 ,so total
number of atoms present in a diamond
cubic unit cell is 1 + 3 + 4
= 8
* Since each carbon atom is surrounded by four
more carbon atoms,the co-ordination number is 4

31. Packing Efficiency
* Packing fraction = 8 x 4/3 × π × r3/ V unit cell
* Substitute the value for the unit cell volume. Since the unit
cell is cubic, the volume is V unit cell = a3
* The formula for packing fraction then becomes:
* Packing fraction = 8 x 4/3 × π × r3/ a3
* The radius of an atom r is equal to √3 x a/8
* The equation is then simplified to : √3 x π/16 = 0.3401

32. Types of Crystal Systems

33. Miller’s Indices

34. Miller’s Indices

35. Miller’s Indices

36. Imperfections in Crystals

37. Point Imperfections

38. Point Imperfections

39. Line Imperfections