materials

1. BME 303 - Lesson 2
Structure of Solids
Part I
By
Prof Md Enamul Hoque

3. Matter exists in three states as solids, liquids and gas.
Many times, Liquid and gaseous states are also
collectively called fluid state.
Different types of matter have different characteristics.
They melt and boil at different temperatures.
They might be with different colors or have different
odors.
Some can stretch without breaking, while others shatter
easily.
These and many such properties help us to distinguish one
kind of matter from another.
They also help us choose which kind of material to use for a
specific purpose.
Solids - Overview

4. Solids are characterised by their definite shape
and also their considerable mechanical strength
and rigidity.
The particles that compose a solid material (with
few exceptions), whether ionic, molecular,
covalent or metallic, are held in place by strong
attractive forces between them.
Solids tend to resist the deformation of their shape
due to strong intra molecular forces and absence of
the translatory motion of the structural units called
atoms, ions, etc.
Solids - Overview

5. Characteristics of Solids
A solid is characterized by structural rigidity and
resistance to changes of shape or volume.
The atoms in a solid are tightly bound to each other,
either in a regular geometric lattice (crystalline solids,
which include metals and ordinary water ice) or
irregularly (an amorphous solid such as common
window glass).
Solid substances are rigid, possess a definite
shape and their volume varies very less with the
variance or change in temperature and pressure.
Or, solids have a fixed shape, size and volume.

6. The solids are characterized by incompressibility,
rigidity and mechanical strength.
The molecules, atoms or ions in solids are closely
packed.
They are held together by strong forces and cannot
move about at random.
Thus solids have definite volume, shape, slow
diffusion, low vapour pressure and possess the
unique property of being rigid.
Such solids are known as true solids. e.g. NaCl, KCL,
Sugar, Ag, Cu, etc.
Characteristics of Solids

7. On the other hand the solid which loses its shape on long
standing, flows under its own weight and is easily distorted
by even mild distortion force is called pseudo solid e.g.
glass, pith etc.
Some solids such as NaCl, sugar, sulphur etc. have
properties not only of rigidity and incompressibility but
also of having typical geometrical forms. These solids
are called crystalline solids.
While discussing about solids, we need to consider the
positions of atoms, molecules or ions, which are essentially
fixed in space, rather than their motions (which are
important for liquids and gases).
Characteristics of Solids

8. Classifications of Solids – Crystal Structure
Crystalline solids have regular ordered arrays of
components held together by uniform intermolecular
forces.
The components of amorphous solids are not arranged
in regular arrays.
o Crystalline solids= atoms show short and long range
order
o Amorphous (non-crystalline)= atoms show short range
order only
• Crystalline materials= atoms (ions or molecules) in
repeating 3D pattern (called a lattice)
• long-range order; ex.: NaCl,

11. Crystalline Solids
Crystalline solids, or crystals, have distinctive internal
structures that in turn lead to distinctive flat surfaces, or
faces.
The faces intersect at angles that are characteristic
of the substance.
When exposed to x-rays, each structure also produces a
distinctive pattern that can be used to identify the material.
The characteristic angles do not depend on the size of the
crystal; they reflect the regular repeating arrangement of the
component atoms, molecules, or ions in space.

12. Amorphous Solids
• Example: glasses
• Not stable state for most pure metals
• Can be formed by very rapid cooling (106 K/sec)
• Readily formed from many metal alloys,
semiconductors, oxides - especially at low
temperatures
• Generally less dense than crystalline materials
• No crystalline defects since no crystal structure
• No ordered structure to the particles of the solid
• No well defined faces, angles or shapes
• Often are mixtures of molecules which do not stack
together well, or large flexible molecules
• Examples would include glass and rubber

13. Amorphous Solids
Amorphous solids have two characteristic properties.
When cleaved or broken, they produce fragments with
irregular, often curved surfaces; and they have poorly
defined patterns when exposed to x-rays because their
components are not arranged in a regular array.
An amorphous, translucent solid is called a glass.
Almost any substance can solidify in amorphous form if the
liquid phase is cooled rapidly enough.

14. Amorphous Solids
Some solids, however, are intrinsically amorphous, because
either their components cannot fit together well enough to
form a stable crystalline lattice or they contain impurities that
disrupt the lattice.
For example, although the chemical composition and the
basic structural units of a quartz crystal and quartz glass
are the same—both are SiO2 and both consist of linked SiO4
tetrahedra—the arrangements of the atoms in space are
not.

15. Solids - Based on Bonding
Solids are classified according to what bondsor forces
are responsible for holding the material in the solid state.
Covalent bonding= Strong
Ionic bonding/Metallic bonding
Van der Waals bonding= Weak
The solid types include: ionic solids, covalent solids, metallic
solids, molecular solids (by hydrogen bonding, by dipole-
dipole attractions, by London forces)

16. Ionic solids
Ionic solids can be composed of simple ions as see in
NaCl (sodium chloride).
Ionic solids can also be composed of polyatomic ions as
seen in ammonium nitrate NH4NO3. Here we see them
individually: NH4+ and NO3-
Ionic solids have ions at the points of the lattice that
characterize the structure of the solids.
Examples include: NaCl, CaF2, Na2S (binary ionics),
NaNO3, K2SO4, Mg(ClO4)2 (ternary) plus others.

17. Covalent Solids
Covalent Solids are substances with covalent bonds that
extend throughout a crystalline solid, and sometimes the
entire crystal is held by very strong forces.
In a covalent solid the entire solid is held together with
covalent bond.
Diamond is a typical covalent solid.
All the carbon atoms are bonded together with covalent
solids.
An example of network covalent solids are two allotrops of
carbon: diamond, and graphite.
Diamonds have each carbon atom bonded to four other
atoms in a tetrahedral fashion/network. Many polymers are
also covalent solids. Example : polyethylene.

18. Metallic Solids:
The metals are those elements that are on the left of the
periodic chart.
This includes the lanthanides and actinides at the
usually shown at the bottom of the chart.
The metal bond explains metal properties:
1) metals conduct electricity easily - since the electrons
are very mobile.
2) metals are ductile, since the binding electrons move
easily to accommodate distortion.
Molecular Solids:
For the “molecular solids” the forces responsible for the
formation of the solid phase (and the liquid) are the weak
forces of hydrogen bonding/ dipole-dipole attractions.

19. Unit Cell
A crystal is a solid composed of atoms, ions, or molecules
arranged in a pattern that is repeated in three dimensions.
The smallest volume of a crystal that produces the entire
crystal, is called a unit cell.
Each atom or molecule in a unit cell is considered as a lattice
point. The distance between two adjacent atoms or ions of the
same type is considered to be the ‘length of a unit cell’.

20. Lattice:
• Lattice: periodic arrangement of atoms in a crystal.
• The locations of atoms are called aslattice points.
• Lattice points are the dots used to represent a particular atomic
array,in a crystal.
• The point can be an atom, a group of atoms, an ion or a molecule.
• When a unit cell is repeatedly translated to fill all of 2D or 3D
space, the vertices of all the unit cells in the filled space
constitute a lattice.

21. Lattice:

22. Unit Cell of NaCl
Sodium chloride structure consists of equal numbers of sodium and
chlorine ions placed at alternate points of a simple cubic lattice.

23. Lattice Parameters
In a unit cell the vectors a, b and c are called
translation vectors or primitive basis
vectors.
In two dimensions the area of the unit cell is
(a x b) while in three dimension the
volume of the unit cell is (a x b x c).
In Fig. the direction of the primitive basis
vectors defines the crystallographic axis.
The angles between these axes are called
interfacial angles, which are ,  and ,
between (b and c), (c and a), and (a and
b), respectively.
Primitive vectors and interfacial angles
together are called lattice parameters.

24. Kinds Of Unit Cells - Seven
There are seven fundamentally different kinds of unit cells,
which differ in the relative lengths of the edges and the
angles between them.
Each unit cell has six sides, and each side is a
parallelogram.
We focus primarily on the cubic unit cells, in which all sides
have the same length and all angles are 90°, but the
concepts that we introduce also apply to substances whose
unit cells are not cubic.

25. Unit Cell Types
There are seven fundamentally different
kinds of unit cells, which differ in the relative
lengths of the edges and the angles
between them.

26. No. Crystal class Intercepts
on Axes
Angles between
Axes
Bravais space lattice
1 Cubic a  b  c       900 Simple, body-centred,
face-centred
2 Tetragonal a  b  c       900 Simple, body-centred
3 Orthorhombic a  b  c       900 Simple, body-centred,
face-centred,
Base(side)-centred
4 Trigonal a  b  c       900 Simple
5 Hexagonal a  b  c     900, Simple
  1200
6 Monoclinic a  b  c     900   Simple, base-centred
7 Triclinic a  b  c      Simple
Characteristic features of these crystal
systems are as follows:

27. Crystal Systems And Bravais Lattices
Crystals of different substances have similar shapes and hence the
crystals are classified into crystal systems depending upon their axial
ratio and the interfacial angles ,  and .
In 3D, there are7 crystal systems. These are known as Bravais or space
lattices. These seven crystal systems with examples are:
• Cubic (CsCl, NaCl, Cu)
• Tetragonal (SnO2)
• Orthorhombic (PbSO4, MgSO4)
• Monoclinic (FeSO4, LiSO4.H2O)
• Triclinic (FeSO4.5H2O,K2Cr2O7)
• Trigonal (Rhombohedral) (Sb, As, CaCO3)
• Hexagonal (Zn, Cd, Ni, As, SiO2)

28. Cubic
The cubic crystal system is also known as the isometric
system.
It is characterized by its complete symmetry.
This system contains three crystallographic axes, which
are perpendicular to each other, as well as all equal in
length.
These axes are all at angles 90° to one another.
The cubic system contains one lattice point at each of its four
corners, and has

29. Tetragonal
A tetragonal crystal is a simple cubic shape that is extended
along its vertical axis to create a rectangular prism.
It consists of a square base and top, as well as three axes.
These axes have one perpendicular and two horizontal with
angels of 90°.
Like the cubic system it is composed of six faces.

30. Hexagonal
The hexagonal crystal system contains four
crystallographic axes.
These consist of three equal horizontal axes at120° of
each other.
It has one vertical axis which is perpendicular to the other
three, which maybe shorter or longer than the other three,
horizontal axes.
It is composed of eight faces.

31. Rhombohedral
The rhombohedral is a trigonal system, that has a three-
dimensional shape similar to a cube, but it has been inclined
to one side making it oblique.
It consists of three axes, one vertical and two horizontal all
laid perpendicular to one another. These axes are at angles
of 90° to one another.
The rhobohedral is composed of six faces, although since the
faces are not square they are more commonly known as
rhombi.

32. Orthorhombic
Orthorhombic crystal systems consist of three axes. These
axes are mutually perpendicular having all different lengths.
Yet, the axes angles are all equidistant laying at 90° to each
other. The orthorhombic has six faces.

33. Monoclinic
A monoclinic system has three unequal axes.
The vertical and forward facing axes are inclined toward
each other at an oblique angle, and the horizontal axis is
perpendicular to the other two axes, this is known as the
ortho axis.
These angles are all arranged 90° to each other. A
monoclinic system is made up of six faces.

34. Triclinic
A triclinic system is made up of three unequal crystallographic
axes.
The axes intersect at oblique angles.
These angles are 90° to one another.
The triclinic system has six faces.

35. Cubic Structures
Simple cubic structure
Body-centered cubic (bcc) structure
Face-centered cubic (fcc) structure

36. Simple Cubic
In the simple-cubic structure only the corners of the cube
are occupied with atoms. Each corner atom is shared by
eight neighbor unit cells.
So, each simple cubic unit cell contains 8x1/8 = 1 atom.

37. Face-centered Cubic
The face-centered cubic unit cell contains an atom at each
corner of the unit cell and an atom situated in the middle of
each face of the unit cell.

38. Body-Centered Cubic
In body-centered cubic unit cell there is an atom at each
corner of the unit cell and an atom in the middle of the cube.
Each atom at the corner of a unit cell is shared by eight
nearest neighbor unit cells, and 68% of the volume is
occupied by the atoms.

40. Any intensive property of the bulk material such as its
density, is therefore related to its unit cell.
As the density is the mass of substance per unit volume, we
can calculate the density of the bulk material from the density
of a single unit cell.
To do this, we need to know the size of the unit cell (to obtain
its volume), the molar mass of its components, and the
number of atoms per unit cell.
The density of a solid is the mass of all the atoms in the
unit cell divided by the volume of the unit cell.
Unit Cells

41. When we count atoms or ions in a unit cell, we need to consider
that the atoms or ions lying on a face, an edge, or a corner are
shared by more than one unit cells.
An atom at the corner of a unit cell is shared by eight adjacent unit
cells. So, it contributes 1/8 atoms to each cell.
In contrast, the atom that lies in the center of a unit cell
contributes 1 atom to each cell.
An atom that lies on a face of a unit cell is shared by two adjacent
unit cells. So, it contributes 1/2 atoms to each cell.
An atom at the edge of a unit cell is shared by four adjacent unit
cells. So, it contributes 1/4 atoms to each cell.
In summary, for all unit cells except hexagonal, atoms on the
corners contribute 1/8 atoms to each unit cell, atoms on the faces
contribute 1/2 atoms to each unit cell, atoms on the edges
contribute 1/4 atoms to each unit cell, and atoms in the center
contribute 1 atom to each unit cell.
Unit Cells - Summary

42. Thank you