What is meant by crystal structure?

The fundamental assumption in the domain of continuum mechanics and physics is that matter is assumed to be continuous. This means, the matter is free of voids and spaces, the distribution is uniform throughout the system under consideration. Matters are composed of atoms that are grouped to form molecules, this grouping leads to molecular bonds which stack them together. This stacking may be completely compact or with minor spaces. The continuity approach assumes the stacking to be uniform without these spaces. An orderly and uniform arrangement of atoms, molecules, or ions in a crystalline material forms a crystal lattice or crystal structure. In the crystal structure, this is a systematic arrangement of molecules in a three-dimensional space. The study of analysis of crystal structure is essential to get information about the cleavage, electronic band structure, and optical transparency of matter. In crystallography, cleavage is the tendency of a crystalline material to undergo splitting along multiple crystallographic structural planes.

The molecular structure/arrangement that forms the crystal structure is organized in a highly ordered fashion microscopically. They are held together by strong and weak interatomic forces such as covalent bonds, Van der Waals forces, ionic bonds, and so on. The specialized domain of study that determines these arrangements of molecules in a crystalline material is called crystallography. The science of crystallography and its approach towards efficient crystal structural analysis adopts experimental methodologies. In earlier days, before the development of technologies, crystallography was limited to only simpler physical measurements of so-called lattice parameters. These parameters involve the lengths and angles of a specific unit cell of a crystal structure.

In this article, a brief overview has been provided about various techniques used in the analysis of crystal structures.

Analysis of crystal structure

The main idea in the crystal structure analysis is based on the theories of symmetry and interaction of radiation with solids, which is also known as diffraction. Diffraction techniques are coupled with powerful computers which aid in the analysis of internal structures. Depending on the nature and problem being analyzed X-rays, electrons, and neutrons are used. They usually provide the electron density, electrostatic potential density, and nuclear density in a crystal.

Scattering experiments form the basis of crystal structure analysis. These experiments make use of rays or beams targeted towards a fraction of the crystal under test. Upon impacting the particles inside the crystal, these rays and beams get scattered in various directions. A receiver captures them and they are computer-processed to give a full picture of the molecular arrangements.

The analysis of crystal structure is done by three experimental methods, they are:

• X-ray crystallography or X-ray diffraction
• Electron diffraction
• Neutron scattering

These techniques are discussed in detail in the subsequent sections.

Crystal structure analysis by X-ray crystallography

X-ray crystallography is an experimental technique to determine the internal arrangement of molecules of matter. This method uses X-rays in the process. A crystalline material diffracts the X-ray beam incident on it after impact, hence, this technique is also known as x-ray diffraction. The method in X-ray diffraction measures the intensity and angles of the diffracted X-rays to produce a three-dimensional image of the electron density. This density of electrons forms the base for the determination of mean positions of molecules of the molecular structure.

An X-ray beam or simply X-rays are part of electromagnetic radiation possessing specific wavelengths. The atoms that constitute the crystal, scatter these X-rays. Electrons are the primary subatomic particles that are responsible for X-ray scattering. X-rays striking an electron produces secondary spherical waves from an electron. The multiple existence of electrons produce multiple arrays of spherical waves. Some of these waves cancel out one another and this is known as destructive interference, and some add up which is called constructive interference. These added waves appear as dark spots in the X-ray diffraction experiment. The size of wavelengths of X-rays is the same as the distance between the planes of a crystal hence, X-rays diffraction techniques prove to be an effective way in the determination of crystal structure. This technique of X-ray crystallography can be also used to estimate other crystal parameters such as analysis of crystalline phases, molecular analysis to perform co-crystallization, internal elastic strains, and so on.

Crystal structure analysis using electron diffraction

Electron diffraction is mostly used in solid-state physics which relies on the phenomenon of the dual nature of electrons, which describes electrons as both particles and waves. This experimental technique fires a stream of electrons onto an active site of the crystal, due to electron scattering, the resulting interference is analyzed. The experiments in electron diffraction use majorly a scanning electron microscope and transmission electron microscope. The mechanism of these instruments is such that, it accelerates the electrons to a certain speed by the electrostatic potential to the desired threshold energy, and the wavelength associated with the electrons at this energy state are analyzed before they make an impact on the crystal. A method called Fourier synthesis allows the analyzers to obtain the electron density mathematically. This method takes the sum of many reflections in the crystal structure analysis by adding phases into the amplitudes of the diffraction spots obtained.

Apart from physics, these instruments are also used in the biotechnology domain for the analysis of amino acid parameters such as carboxyl-terminus (C-terminus) and Amine-terminus (N-terminus), which form the end of an amino acid chain that is determined by a carboxyl group.

Crystal structure analysis using neutron scattering

Neutron scattering is also known as elastic neutron scattering, this process is extensively used to estimate the atomic and magnetic structure of a crystal. The crystal to be examined is placed under a beam of cold or thermal neutrons that forms an intensity pattern around the material. Analyzing the intensity pattern gives the crystal structure pattern. Unlike X-rays, which interact with the electrons of an atom to form a distinct diffraction pattern, neutrons primarily interact with the nucleus of an atom. The intensity of the scattered ray is different for different isotopes of the element. The neutron scattering causes a change in the spacing between the lattice planes inducing a shift from their stress-free condition. One of the major advantages achieved with neutron scattering over X-ray scattering is the higher depth of penetration.

Context and Applications

This topic is widely taught in many undergraduate and postgraduate degree courses of:

• Bachelors in Science (Physics)
• Bachelors in Science (Chemistry)
• Masters in Science (Crystallography)

Practice Problems

1. What is the other name of X-ray crystallography?

1. X-ray diffraction
2. Single-crystal X-ray diffraction
3. Electron beam scattering
4. High-energy beam diffraction

Answer: Option a

Explanation: The other name of X-ray crystallography is X-ray diffraction.

2. What is the science of crystallography?

1. To analyze the internal crystal structure of a material
2. To analyze reciprocal lattices
3. To analyze both reciprocal lattice and crystal structure
4. Analysis of both reciprocal lattice and unit cell

Answer: Option a

Explanation: The science of crystallography is used to analyze the internal crystal structure of crystalline materials.

3. Which mathematical method is used by the analyzers to determine the electron density mathematically?

1. Least-squares method
2. Fourier synthesis method
3. Discrete Fourier-transform method
4. Both b and c

Answer: Option b

Explanation: The Fourier synthesis method is used by the analyzers to determine the electron density mathematically.

4. Which of the following is true for a crystal structure?

1. They are analyzed by a laser beam.
2. They are three-dimensional structures in space.
3. They are two-dimensional structures in space.
4. They consist of particles that form a charged couple.

Answer: Option b

Explanation: A crystal structure is primarily a three-dimensional structure in space.

5. X-rays are diffracted by which of the following subatomic particles?

1. Neutrons
2. Quarks
3. Bosons
4. Electrons

Answer: Option d

Explanation: The X-rays are diffracted by electrons forming a secondary spherical wave pattern.