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Nanotechnology SUWARNA DATAR| AP 608

Main Aspects of Nanotechnology

Synthesis and processing of nanostructures

Understanding the properties

Design and fabrication of devices

Characterization

Synthesis and processing of

nanostructures Nanoparticles

Nanowires, nanorods, nanotubes

Thin films

Top down and bottom up

approaches

Attrition or milling: top down

Colloidal dispersion: Bottom up

Lithography: Hybrid

Disadvantages of top down

approach

More defects are introduced in the crystal

Impacts physical and chemical properties of nanostructures

Tools we possess are too big for such tiny objects

Bottom up approach

Build atom by atom

production of salt

Growth of single crystal

Thin film deposition

It is driven by reduction of Gibbs free energy therefore at thermodynamic

equilibrium

Effect of large surface to volume

ratio Large fraction of surface atoms

Ratio of surface atoms to atoms at the interiors changes drastically as the size is reduced

For 1 cm cube:

Surface area: 6 cm2

Volume:1 cm3

S/V ratio: 6

6 parts surface area is exposed /unit volume

Nanostrctured materials possess huge surface

energy, therefore thermodynamically unstable

What is surface energy?

Crystal structures

Single Crystal Polycrystalline Amorphous

Crystal Lattice

What is crystal (space) lattice?

In crystallography, only the geometrical properties of the

crystal are of interest, therefore one replaces each atom by

a geometrical point located at the equilibrium position of

that atom.

Platinum Platinum surface Crystal lattice and

structure of Platinum (scanning tunneling microscope)

Crystal Lattice An infinite array of points

in space,

Each point has identical surroundings to all others.

Arrays are arranged exactly in a periodic manner.

α

a

b C B E D

O A

y

x

Unit Cell: Crystal

structure can be

understood in terms of

unit cell which, when

translated in any

direction can complete

space

Crystal Structures

Crystal Structure

When a group of atoms are attached to

each lattice points it forms a crystal

All metals, many ceramics, some

polymers exhibit Closely Packed

Structure

Crystal Structure

Crystal structure can be obtained by attaching atoms, groups of atoms or molecules which are called basis (motif) to the lattice sides of the lattice point.

Crystal Structure = Crystal Lattice + Basis +

1. By choosing different vectors, it is possible to choose variety of unit cells

2. There are only 5 types known as “Bravais Lattices” which are required to describe the

observed 2-D structure

Crystal Lattice

Bravais Lattice (BL) Non-Bravais Lattice (non-BL)

§ All atoms are of the same kind

§ All lattice points are equivalent

§ Atoms can be of different kind

§ Some lattice points are not

equivalent

§A combination of two or more BL

Types Of Crystal Lattices

Bravais lattice is an infinite array of discrete points with an arrangement

and orientation that appears exactly the same, from whichever of the

points the array is viewed. Lattice is invariant under a translation.

Nb film

14 Bravais Lattice in 3D

Unit Cell in 2D

The smallest component of the crystal (group of atoms, ions or molecules), which when stacked together with pure translational repetition reproduces the whole crystal.

S

S

The choice of

unit cell

is not unique.

a

S b

S

Three common Unit Cell in 3D

What is the basis for

classification of lattices into

7 crystal systems

and

14 Bravais lattices?

Lattices are

classified on the

basis of their

symmetry

If an object is brought into self-

coincidence after some operation

it said to possess symmetry with

respect to that operation.

Symmetry

Rotational symmetry

A rectangle comes into self-coincidence by 180

degrees rotation

If an object come into self-coincidence through smallest non-

zero rotation angle of then it is said to have an n-fold rotation

axis where

0360n

=180

=90

Rotation Axis

n=2 2-fold rotation axis

n=4 4-fold rotation axis

Reflection (or mirror symmetry)

Lattices also have

translational symmetry

Translational symmetry

Symmetry of lattices

Lattices have

Rotational symmetry

Reflection symmetry

Translational symmetry

Symmetry classification of lattices

Based on rotational and reflection symmetry alone 7 types of lattices

7 crystal systems

Based on complete symmetry, i.e., rotational, reflection and translational symmetry

14 types of lattices

14 Bravais lattices

7 crystal Systems System Required symmetry

• Cubic Three 4-fold axis

• Tetragonal one 4-fold axis

• Orthorhombic three 2-fold axis

• Hexagonal one 6-fold axis

• Rhombohedral one 3-fold axis

• Monoclinic one 2-fold axis

• Triclinic none

Crystal Structure 29

A primitive unit cell is made of primitive translation vectors a1 ,a2, and a3 such that there is no cell of smaller volume that can be used as a building block for crystal structures.

A primitive unit cell will fill space by repetition of suitable crystal translation vectors. This defined by the parallelpiped a1, a2 and a3. The volume of a primitive unit cell can be found by

V = a1.(a2 x a3) (vector products)

Cubic cell volume = a3

Primitive Unit Cell and vectors

Crystal Structure

The primitive unit cell must have only one lattice point.

There can be different choices for lattice vectors , but the volumes of these

primitive cells are all the same.

P = Primitive Unit Cell

NP = Non-Primitive Unit Cell

Primitive Unit Cell

1a

• Rare (only Po – Polonium -- has this structure)

• Close-packed directions are cube edges.

• Coordination No. = 6

(# nearest neighbors) for

each atom as seen

Simple Cubic Structure (SC)

• Coordination # = 8

• Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded

differently only for ease of viewing.

Body Centered Cubic Structure (BCC)

ex: Cr, W, Fe (), Tantalum, Molybdenum


• Atoms touch each other along face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded

differently only for ease of viewing.

Face Centered Cubic Structure (FCC)

ex: Al, Cu, Au, Pb, Ni, Pt, Ag

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites

• ABCABC... Stacking Sequence

• 2D Projection

• FCC Unit Cell

FCC Stacking Sequence

B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C


• ABAB... Stacking Sequence

• APF = 0.74

• 3D Projection • 2D Projection

Adapted from Fig. 3.3(a),

Callister 7e.

Hexagonal Close-Packed Structure (HCP)

6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

• c/a = 1.633 (ideal)

c

a

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

Bonding in Solids When two atoms come close to each other, they start interacting

The type and amount of interaction depends upon the distance between two atoms and the type of the atom (electronic configuration)

There are four classes of solids:

metallic, ionic, covalent, and molecular

General Considerations

Consider two atoms

At large distance compared to

their size the electrons do not have

any interaction

As soon as they come close to

each other they start interacting

This results into attractive force and repulsive force between them due to

mutual electrostatic interaction

General Considerations

There must be an attractive force

An apparent candidate is the Coulomb Force

Here r is a distance between atoms (ions) forming a solid

What stops atoms (ions) from getting closer than they do?

When ions are very close to each other, other forces arise. These are the so-called short-range repulsive forces, due to rearrangement of electrons as nuclei approach

Equilibrium distance, r0, is point at which energy is at a minimum, forces are balanced

221

04

1

r

qqF

Ionic Solids

Ionic crystals consist of the negative and positive ions, attracted to each other

Electron from one of the atoms removed and transferred to another: NaCl, AgBr, KCl

When the crystal is formed excess heat is generated

Formation of Ions from Metals

Ionic compounds result when metals react with nonmetals

Metals lose electrons to match the number of valence

electrons of their nearest noble gas

Positive ions form when the number of electrons are less than

the number of protons

Group 1 metals ion 1+



Ionic bonding Ionic bonding involves 3 steps (3 energies)

1) loss of an electron(s) by one element,

2) gain of electron(s) by a second element,

3) attraction between positive and negative

+ Na e– Na+ Ionization energy

Cl e– + Cl– Electron affinity

Lattice energy + Cl– Na+ Cl– Na+

+ 496

– 349

– 766

Crystalline Structure of NaCl

Covalent Solids

The covalent bond is usually formed from two electrons, one from each atom participating in the bonding: These electrons are shared by the atoms

Quantum Mechanics is required to calculate binding energies

The probability of finding electrons forming the bond between the two atoms is high

Covalent bonds are very strong and directional

Covalent Solids

In general, since there are no free electrons, these crystals are insulators or semiconductors

The Covalent Bond

• Shared electrons are attracted to the nuclei of both atoms.

• They move back and forth between the outer energy levels of each atom in the covalent bond.

• So, each atom has a stable outer energy level some of the time.

Covalent bonds- Two atoms share one or more pairs of outer-shell electrons.

Oxygen Atom Oxygen Atom

Oxygen Molecule (O2)

Crystalline Structure of Diamond

Metallic Bond

Metals may be seen as collections of stationary ions surrounded by a sea of electrons

Can be viewed as limit of covalent bonding, when electrons are shared by all the ions in the crystal

The metallic bond is not directional

Metallic Bond

Formed between atoms of metallic elements

Electron cloud around atoms

Good conductors at all states, lustrous, very high melting points

Examples; Na, Fe, Al, Au, Co

Surface Atoms

At surface, atoms or molecules possess fewer nearest neighbours:

They have more dangling bonds

Therefore they are under inwardly directed force

Therefore bond distance between surface atoms and subsurface atoms

becomes smaller

When the particles are smaller such decrease in bond length becomes

significant

Therefore the lattice constant of the entire particle shows a significant

change

The extra energy possessed by the surface atoms is

called surface energy/free energy/surface tension

Definition of surface energy

It is called as the energy required to create a unit area of a new

surface

On a newly created surface, each atom on

the surface will move towards interior

Extra force is required to pull back the atoms

to their original position

For each atom on the surface, the energy

required to get it back to the original

position:

1. proportional to the number of broken

bonds Nb 2. Bond strength ɛ

ν = ½ Nb ɛ ρA

ρA: no. Of atoms/unit area on the new surface

Surface energy

Concepts of thermodynamics are used to calculate the surface

energy of a material.

Thank you

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