Crystalline Materials

Crystalline materials are materials with long range order. This means that there is a repeat unit that continues in three dimensions - a building block. This building block can be almost any size, but the shape is limited to those that fit together to make a three dimensional array. Such shapes are said to tessellate. For example, pentagons don't tessellate.

The study of crystalline materials is called crystallography. The building block crystallographers use is called the unit cell and it is described using three lengths (a, b and c) and three angles (a, b and g).

When all three unit cell edges are the same and the angles are 90°, the unit cell resembles a cube and the structure is therefore known as cubic. Changing the combination of the angles and lengths of the edges gives a total of seven types of structure, known as "crystal systems".

One example of a crystalline material is salt. If you look at the tiny salt granules, you should be able to see that they are tiny crystals. Salt is an array of sodium and chlorine atoms that alternate in all three directions.

Salt is cubic. Here it is shown with the chloride ions in red and the sodium ions in blue. |

Salt is an example of a continuous solid - that is a material that just carries on continuously in all directions with lots of short contact distances. However, it is also possible to get molecules to crystallize. For example, ice is a crystalline material and if water is cooled under the right conditions, it will form single crystals. In fact, there are many possible different structures for ice. When this happens, it can be said that the material is polymorphic.

Links: Crystallography & International Union of Crystallographers

Amorphous Materials

So a single crystal is a piece of material that contains ordered atoms. They are usually small (less than 1mm in each direction), but their size depends on how long they have taken to grow and the conditions they were grown under. Materials that contain many tiny crystals grown together is called a crystalline powder.

An eample of good quality single crystals single crystals and poor quality intergrown crystals .

Not all materials are crystaline however, and some have a crystalline phase and an amorphous phase. Quartz (also known as silica or SiO2) is one such material.

Crystalline quartz is shown here on the left with amorphous quartz on the right. You can clearly see the well defined edges of the crystals. (Courtesy of Prof. Shanaka de Silva, Indiana State University). |

Amorphous materials have no long range order, but often have short range order. For example, amorphous quartz (SiO2) has a regular tetrahedral arrangement of oxygen atoms around each silicon atom, but their is no regular repetition of the SiO4 units.

|  | The picture on the left is crystalline quartz, and the picture on the right is amorphous quartz. If you choose any silicon atom (yellow), you should see that they are surrounded by a regular arrangement of oxygen atoms (red ). These pictures are from a simulation of crystalline quartz under pressure carried out at Bath University, (courtesy of Prof. Steven Parker).

Links: Minerals and Pressure Induced Amorphisation of Quartz

Diffraction

Light is a wave and as such it has a wavelength, a frequency and an energy. The the wavelength (l), frequency (f) and energy (E) are related by equations involving the speed of light (c) and Planck's Constant (h):

f = l/c

E = hf

Light is also a source of energy and the higher the frequency, the higher the energy. We can see some light, but there are many wavelengths that are outside the range of our eyes.

Waves can also be seen in nature - in the sea, or simple ripples on a pond. When a stone is dropped into a pond ripples radiate from the center in concentric circles. When two stones are dropped at the same time the ripples radiate out and where they cross interference happens. This is where the waves combine. Where there are two peaks, they add up and make a peak twice as high, where there are two troughs, they add together to make a trough twice as deep and when a peak and a trough of equal size add together they cancel out.

| The two, blue waves on the left are the same. The peaks are adding together to make a peak twice as high and the troughs are adding together to make a trough twice as deep. This is called "Constructive Interference".
The two, blue waves on the left are now offset so that the peaks almost coincide with the troughs and vice versa. The peaks and the troughs are adding together and almost cancel out. They don't quite cancel out because here, the offset is not exact. This is called "Destructive Interference". |

Light can behave in the same way. One of the key properties of light is that it can be diffracted. That is to say that when you shine light at a grating, if the light has a similar wavelength to the size of the grating, it is scattered and the waves add up in exactly the same way. This remarkable phenomenon is used repeatedly in science, but particularly in structure determination. By a happy chance, the wavelength of X-rays is is very similar to the distance between atoms, approximately 1-5 Å (or 10-50 nm). Since crystalline materials have long range order, they behave like a diffraction grating in three dimensions. The result is an interference pattern that can be deciphered using a computer to give the structure of the crystalline material.

A single crystal will give rise to three dimensional a diffraction pattern, however many materials do not form single crystals. Many of these will form a "crystalline powder". This is either a powder that is made up of microcrystals (or crystallites) or a material that forms a solid with crystalline areas (or domains). Since the orientation is now random, or effectively all orientations, instead of diffraction "spots", powders give diffraction "cones".

Schematic of single crystal diffraction and powder diffraction, showing the spots and cones of the diffracted beam in green, the sample in yellow and the incident beam in red. Below is a simulated powder pattern.

It is not only possible to use X-rays for diffraction, it is also possible to use small particles like neutrons, a product of radioactive decay. According to de Broglie, matter can also behave like a wave and has a "de Broglie Wavelength" - l = h/mv, where l is the wavelength, h is Planck's constant 6.626 x 10E–34 Js, m is the mass and v is the speed that the particle is traveling at.

Whereas X-rays are scattered by electrons and are therefore scattered more by larger elements with more electrons. Neutrons however, are scattered by the nucleus, so the scattering is dependent on other factors. For this reason it is often difficult for example, to reliably locate small elements like hydrogen using X-ray diffraction. So in this case neutron diffraction is very important as hydrogen diffracts neutrons relatively strongly, although other elements may not. In fact, a comparison using neutrons and X-rays is often necessary to see the full picture. The disadvantage of neutrons is that since you need a nuclear reactor (or similar) to generate them, there are very few so called "central facilities" around and this means that experiment time is both in demand and expensive.

There are other "central facilities" available for diffraction, such as synchrotron sources. These generate high powered X-rays, which are particularly useful when trying to study very small crystals, or crystals that decay over time and where data must be collected quickly.

It is important to note that crystallography is the only lab technique that allows the measurement of distances and angles between atoms. However, amorphous materials do not have long range order, so they do not behave like a diffraction grating and crystallography cannot be carried out on them. This is the main disadvantage of this technique.

Links: Würzburg University Diffraction Tutorial, Institut Laue-Langevin, ISIS and Daresbury Laboratory Synchrotron Radiation Source

NMR (Nuclear Magnetic Resonance)

Nuclear Magnetic Resonance (NMR) is a very common technique in science; more usually used on solutions, it can also be applied to solids.

Materials are made up of atoms and atoms contain a nucleus and a number of electrons. These electrons have a spin and it is this property that results in magnetism. A less well known fact is that some nuclei also have a spin and although this spin is much smaller in magnitude, it is still useful when not dwarfed by the presence of unpaired electrons. This nuclear spin is isotope dependent, so cannot be used on all materials, especially as the cost of isotope enrichment may be prohibitive. However, hydrogen has a spin and as it is very common (it has a high "natural abundance") in organic materials this is very useful.

Although the natural abundance is important, the sensitivity is also critical. The sensitivity is dependent on the gyromagnetic ratio, g0. This ratio is a constant dependant on the nucleus. For this reason fluorine, carbon, phosphorus, sodium, aluminium, tin, vanadium and silicon can all be used fairly routinely, though hydrogen is by far the most frequently used.

| Hydrogen | Carbon | Phosphorus
Gyromagnetic Ratio /108 sT | 2.675 | 0.673 | 1.081
Natural Abundance /% | 99.985 | 1.108 | 100
Relative Sensitivity | 1.00 | 0.016 | 0.066

This spin causes the atoms to behave like miniature bar magnets. The idea is that if these bar magnets are put into a field, there are then two state - one with high energy and one with low energy. The low energy state has both fields in the same direction and the high energy state has the fields opposing each other.

Absorption of a photon with the same energy as the difference between the two states, can cause a change in state a "spin flip". The frequency of a photon is in the radio frequency (RF) region of the electromagnetic spectrum. This frequency is dependent on the environment of the atom, so from an NMR spectrum, the "connectivity" can be deduced.

While NMR can give information on bonding in amorphous systems and liquids, it is only possible to get very limitted geometric information.

Links: Isotopes, NMR Periodic Table, MRI Imaging and Joseph Hornak - The Basics of NMR

XAS (X-ray Absorption Spectroscopy)

X-ray Absorption Spectroscopy (XAS) is another technique that can be used to study short range order.

The absorption of light by metals is dependent on the energy (E) of the incoming light:

E = hf/2p (f = frequency, p = 3.1416... and h = Planck's constant, 6.626 x 10-34 Js).

A schematic for the absorption of X-rays above and below the absorption edge for a copper molecule, the green is the EXAFS region and the blue is the XANES region.

Every element has an "Absorption Edge", which is the energy at which the absorption in the solid increases suddenly. Above this energy, the absorption fluctuates until it becomes a straight line again. Information can be got from both the region just below the absorption edge and the region above it. The analysis of the first is known as X-ray Absorption Near Edge Spectroscopy (XANES) and above the absorption edge it is known as Extended X-ray Absorption Fine Structure (EXAFS).

The EXAFS region is caused by the close environment of the atom, so EXAFS can be used to refine the local environment of a metal. For example, in a copper complex where the formula and connectivity (what is bonded to what) is known, the bond lengths and angles can be refined. The main advantage of this method over diffraction is that since it does not rely on long range order, it can be used for amorphous materials, liquids and in theory, even gases. However, there is a major disadvantage. Since the fluctuations in absorption are very small and the X-ray source needs to be easily tunable, this is not generally a lab based technique and can only be carried out at "central facilities" (Synchrotron Radiation source), which means it is very expensive, though measurement times are very short.

Links: EXAFS Lab. University of Lavia, European Synchrotron Radiation Facility and National Synchrotron Light Source

Phase Transitions

Changes in structure can be induced by changes in temperature, pressure or other aspects of the environment. Changes in the structure are often accompanied by changes in the physical properties of the material. For example, some perovskite based materials become superconducting below a certain temperature. For this reason there is considerable interest in this area of research.

Here are some of the phase transitions in LiKSO4, shown in polyhedral representation. The darker blue the background, the colder the temperature. The high temperature structures are disordered so the polyhedra are constantly moving, caused by the energy the structure gets from the heat.

Links: Phase Transitions in the Eerly Universe, Shape Memory Alloys and Memory Metal

Last updated 31 October, 2002