Zero Dimensional systems

PG – Elective

Dr. S De

The ultimate zero dimensional (0D) structure is the atom

We are actually interested in quasi 0D structures

These are materials whose size is very small in all three dimensions

(x,y,z)

As a piece of a given material gets smaller and smaller, eventually

its properties begin to deviate from the bulk

How small is small?

It depends on what property we are considering. For example, the

melting temperature might begin to change from that of the bulk a given

particle size. However the ionization potential may begin to change at a

completely different size.

However, this is just a rule of thumb. A particle

of size 90nm, made up of atoms of a given element,

may have some properties that are identical to those

of the bulk.

We will look at some examples

o Nano-particles

– Metallic and semiconducting

o Molecular nanostructures

1 nm

As a general rule of thumb, we can consider

particles that have size <100nm in all directions to

be quasi 0D.

There are many different types of quasi 0D

structures

Au Nanoparticle

CdSe nanoparticle

C60

Nanoparticles

Nanoparticles are just very small particles of known materials such as aluminium, gold or CdSe

They have been studied intensely for the last 3 decades or so

However they have been used by mankind for thousands of years, without people having any idea what they were.

example is the Lycurgus Cup (4thC AD)

The Lycurgus Cup is unusual in that the reflected light colour (green) is different to the colour of transmitted light (red).

How do we make these things??

Nanoparticles have been studied for ~25 years. By now, there are many ways of making them: Some common examples

Mechanical

•Ball Milling

•Attritional milling

Wet Chemistry

•Sol gel

• Liquid phase chemistry

• Colloid chemistry

Thermal routes

•Thermolysis

Gas phase synthesis

•Laser ablation

•Chemical / physical vapour

synthesis

You all know about these Methods

Silver Nano particles

TEM Images of few Nanoparticles

N

HW1. For a sodium nanoparticle of size 60 nm a) Find out number of atoms in the nanoparticle b) fraction of atoms on the surface, Fs. Dws for sodium is 0.4 nm

Geometric structure

A nanocluster is a nanometer sized particle made up of equal subunits. These subunits can be atoms of a single element, molecules or even combinations of atoms of several elements in subunits with equal stoichiometries (alloys, etc.) E.g.: Nan, (SF6)n, (H2O)n, (Cu3Au)n, (TiO2) etc The properties of nanoclusters are solely guided by the number of subunits they contain.

Usually the crystal structure of a large nanocluster is the same as the bulk structure of the material with somewhat different lattice parameters E.g. Cu clusters tend to have an FCC structure (Wulff polyhedra).

Some exceptions do, however, occur. Smaller clusters of Cu (e.g. Cu55, Cu147, . . . ) have perfect icosahedral structures.

- structural magic numbers: occur when an exact amount of atoms is needed for a specific structure

We can think as a nanoparticle as a cluster of atoms all of which are attracted to each other. This is the liquid drop model.

As I Said in last class

The Liquid drop model is a crude approximation that works for relatively big particles. However it says nothing about the crystal structure of the nanoparticles. We need to consider this to more fully understand Nanoparticles We will focus on nanoparticles made from elements that form metals in the bulk.

Metal nanoparticles Most metals form close packed lattices in the bulk eg Face Centred Cubic (FCC) Ag, Al, Au, Co, Cu, Pb, Pt, Rh Hexagonal Close Packed (HCP) Mg, Nd, Os, Re, Ru, Y, Zn

We will focus on FCC

The FCC unit cell has ___ atoms

This means The nano-particle likes to have atomic planes on its surface

• These planes have different surface energies

• The total energy associated with the surface is given by where i represents each type of atomic plane

A general tendency of the clusters is to form structures where the total surface energy is minimized for a given volume the exact structure then depends on the surface energies related to the specific crystal facets of the material. This means we would expect atomic planes with high surface energy to account for a small fraction of the surface and vice versa

Thus the shape of a nano-particle depends on the crystal structure and the surface energies of the atomic planes (and hence the element)

This means the shape is independent of the nano-particle size

However this is not true for very small nano-particles The shape can only be size independent if we model the nanoparticles as made from a continuum

However for small nano-particles, the facet size will be of the same order as the atomic size

This means the discrete nature of the atoms will effect the shape

pc

Sticky Note

CUBOCTAHEDRON

Crystal Structure 29

3 - Face Centered Cubıc

Atoms are all same.

• Most, in fact form the 12 vertex polyhedron, the icosahedron. A smaller number form the decahedron.

There is one big difference between this and the 1D square well

In the 1D case each level takes only 2 electrons

Here we can have a level described by the quantum numbers: nx=1 ny=2 and nz=3

There is also a level with the quantum numbers: nx=3 ny=2 and nz=1

These levels have the same energy!!!!

Thus we can have energy levels with more than 2 electrons

The levels are degenerate!!!!!

The jellium model has successfully been used in the theoretical modelling of nanoclusters. The jellium model envisions a cluster of atoms as a single large atom, where the distribution of ionic cores is replaced by a constant positive background, the so called “jellium density”, and only valence electrons are treated explicitly.

Use the Brus equation to find how much bigger is a 1nm nanoparticles bandgap compared to the bulk.(take εr=10). Assume me*~3me and mh*~2me

HW