Ferroelasticity

Ferroelastic materials have two stable phases and a transition can be induced by applying stress. Quite a lot of materials do this, but in most, when the stress is removed, the structure changes back. Ferroelastic materials however, do not change back and both phases must be stable under normal conditions.

These materials are actually quite rare, and more often than not a ferroelastic transition is coupled with a ferroelectric one. Gadolinium molybdate is one example which has a combined ferroelectric-ferroelastic transition and more rare, lead phosphate has a pure ferroelastic transition.

Links: Gadolinium Molybdate & Piezoelectric Switches

Optical Properties

There are three possible ways that light can interact with materials: Reflection, Transmission and Absorption.

A material is optically characterised by it's refractive index, n, which is the ratio between the speed of light in a vacuum and the speed of light through the material. Reflection occurs at a surface between to materials which have different refractive indices.

n = c/v
where n is the refractive index, c is the speed of light in a vacuum and v is the speed of light in the material.

Transmission also depends on the refractive index. Materials are often broadly characterised by their appearance however:

Transparent | Light is mostly transmitted
Translucent | Light is transmitted diffusely
Opaque | Light is not transmitted
Shiny | Light is mostly reflected

However, many materials look opaque because of the presence of grain boundaries. For example, a single crystal of rock salt is clear and and colourless, but table salt appears to be white. This is because each of the surfaces reflect light, and in a powder, there are a lot more surfaces than in a single crystal.

When light is reflected, the angle of reflection is always the same as the angle of incidence. When the refractive index of the first material (here shown in yellow) is less than that of the second material (here shown in pale blue), the angle of transmission is greater than the angle of incidence. That is why a spoon looks strange when it is placed into a glass of water. When the refractive index of the first material is greater than that of the second material, the angle of transmission is less than the angle of incidence. In this situation, as decreasing the angle of incidence, there is a point called the critical angle where each ray of light tries to travel through both materials at the same time. Since this is not possible, all the light is reflected, known as total internal reflection. And that is how fibre optic cables work.

Electrons have energy, which they can get from many places, including heat and electricity. Here however, we are concerned with light.

Energy is quantised which means that it comes in "packets". This means it is a bit like lottery tickets, which cost a pound each and if you only have 50p, you can't buy half of one. Light comes in "quanta" which electrons can absorb making them change energy level. When they relax back to the "ground state", they give out light again.

Electrons absorb energy from light equivalent to the change in level. When they relax back to the "ground state", they give out light.

Lasers are a very important application of electron absorption."Laser" is an acronym for light amplification by stimulated emission of radiation, which describes fundamentally how a laser works. Basically, the electrons are "pumped" up to an excited state and then stimulated so that they relax all at once creating a very intense beam of light. They are particularly important because they have a beam of a single wavelength, they are highly directional i.e. they form a tight, narrow beam and they are highly coherent, which means the waves are all in phase like well drilled soldiers marching.

Absorption is can also be described using "Band Theory". Using this description, the gap between the valence band and conduction band dictates the appearance a material.

If the band gap in the material is less than 1.8eV (left) complete absorption occurs and the material is opaque. When the band gap is between 1.8eV and 3.1eV, the light given out is within the visible spectrum which we see as colours.

Links: Reflection and Refraction, Luminescence, Vocabulary of Luminescence & How Lasers Work...

Non-Linear Optics (NLO)

The polarisation is defined a sum:

Pi = P(1) + P(2) + P(3) + ... where Pi is the total polarisation, P(1) is the linear polarisation P(2) is the second order polarisation etc...

For a material to be NLO active, the second order polarisation must not be zero and for this to be true the material must be non-centrosymmetric. In fact, NLO activity is encouraged by the presence of a permanent dipole moment. For this reason ferroelectricity and Non-Linear Optical behaviour often go hand in hand.

For this reason two of the best known NLO materials, barium titanate and potassium dihydrogenphosphate (KDP) are also ferroelectric.

In a centrosymmetric material (left), it you go the same distance in completely opposite directions, you get to an identical place (shown with the pale blue arrow). In a non-centrosymmetric material (right) this is not true.

There are two main applications of NLO materials: The Electro-optic Effect and Second Harmonic Generation (SHG).

The Electro-optic Effect is the conversion of linearly polarised light to circularly polarised light.

Light travels in waves. Normal light consists of two components - a horizontal component and a vertical component. It is possible to separate these, using a special type of filter to remove one component. This is done routinely, in fact that's what polarised lenses are in sunglasses - the glare is reduced by removing one component of the light to give polarised light. In fact, if you take the lenses out of a pair of these sunglasses and turn them at 90° to each other, both components should be removed i.e. no light should be allowed through. Circularly polarised light is light that travels in a helix.

Second Harmonic Generators are materials that convert two beams of light of one wavelength into one beam which has half the wavelength. This is also known as frequency doubling.

Schematics of Second Harmonic Generation and the Electro-optic Effect.

Examples of NLO materials include lithium niobate (LiNbO3), barium titanate (BaTiO3) and potassium dihydrogenphosphate (KDP)

Links: Nonlinear Optics Lecture Course & Introduction to Nonlinear Optics

Liquid Crystals

Liquid crystals are materials that have some mobility (like a liquid), but also some order (like a crystal). There are three types - Nematics, Smectics and Cholesterics. The difference between the first two is the amount of order. The third is different - named after cholesteric acid, cholesterics have a helical order.

| Description | Schematic
Nematics | One dimensional order - all the molecules have a general direction |
Smectics | Two to three dimensional Order - all the molecules line up and they also form layers. There are several types of smectics, all with different levels of ordering. |
Cholesterics | Chiral order - the molecules align to form a helix. |

Liquid Crystals have a wide range of industrial and domestic uses, the best known of which is in electronic displays.

Liquid crystals are also well known for making pretty pictures, here are three pictures of different hybrid nematics, courtesy of Prof. Lavrentovich from Kent State University - Pretty aren't they!

Links: Liquid Crystal Institute (Kent State University) & Introduction to Liquid Crystals

Negative Thermal Expansion (NTE)

Nearly all materials expand when heated and contract when cooled. There are however a small number of materials that actually contract when heated. There aren't many of these materials, but comprehensive understanding of these materials could lead to a number of technological applications. For example, a composite of two materials, one negatively thermally expanding and one positively thermally expanding could be used to make cookware that could be transferred from the freezer straight to a hot oven with out breaking. The cause of negative thermal expansion is thought to be the movement of rigid units, which vibrate in a special way.

Links: Introduction to Negative Thermal Expansion

Last updated 29 October, 2002