## What is Crystallography?

Crystallography is the category of science that focuses on the atomic and molecular arrangements with their bonding constituting the crystal structure. It is derived experimentally and originated in the year 1912. It is a combination of two words; those are crystal, meaning a cold drop, and graph, meaning writing.

## What is the Objective of Crystallography?

The goal of crystallography is to display the concepts and theories related to the study of crystals so that a proper understanding of crystal structure is attained. Through crystallography, a sample could be characterized both qualitatively and quantitatively. Moreover, its properties and morphologies are obtained.

## Laws of Crystallography

Crystallography follows three laws, and they determine the relation between the crystal and its faces, axes, angles, symmetries, etc. The three fundamental laws are as follows:

### Law of Constancy of Interfacial Angle

Interfacial angle is the angle formed from the corresponding faces lying next to each other in a crystal. This law demonstrates that the interfacial angle is constant irrespective of the crystal’s development, size, or shape. Steno’s law is the other name of it.

### Law of Rational Indices

Each crystal possesses intercepts and axes on distinct faces, which are considered constant. Along the crystallographic axes, the intercepts of a crystal are depicted by rational numbers. Hauy’s law is the other name of it.

• OP, OR and OQ are the faces of the crystal.
• A, B and C are the unit cell axes.
• h, k and l are the Miller indices.

### Law of Constancy of Symmetry

This law demonstrates the symmetry of crystals. Symmetry elements are identical for all crystal substances. The plane of symmetry, the axis of symmetry, and the center of symmetry are the three types of imaginary symmetries in a crystal and are as follows:

• Plane of symmetry: The plane of symmetry splits the crystal into two parts by passing through the center of the crystal, and these two parts are mirror images of each other.
• Axis of symmetry: The axis of symmetry in which the crystal undergoes a complete circular rotation, and this symmetry passes through it, producing an identical structure multiple time.
• Centre of symmetry: Centre of symmetry is depicted by a point through which the crystal’s surface intersects with equal distance.

## The Crystal Systems in Crystallography

Seven crystal systems are existing in crystallography and each crystal has its specific unit cell geometry, axial length (a, b, c), and angles α, β, γ. The names of seven crystal systems are given below:

• Cubic system in which all angles are equal to ${90}^{0}$.
• Tetragonal system in which all angles are equal to ${90}^{0}$.
• Orthorhombic system in which all angles are equal to ${90}^{0}$.
• Rhombohedral system in which all angles are equal to 90o except gamma angle.
• Hexagonal system in which alpha and beta angles are equal to 90o and gamma angle is 120o.
• Monoclinic system in which alpha and beta angles are equal to 90o and gamma angle is not equal to 120o.
• Triclinic system in which all angles are not equal to 90o.

## X-Ray Crystallography

X-rays were discovered by Sir Wilhelm Roentgen, and they are electromagnetic radiations possessing high energy and penetrating power. X-ray crystallography is a type of crystallography method utilized to attain the structure of atoms and molecules in crystals. This information is gained when X-rays undergo diffraction in the crystal. It was discovered by Sir William Henry Bragg.

The crystal sample gets hit by incident X-rays, and then electrons in the atom undergo a diffraction process. This diffraction is emitted by a clear pattern formed on the screen/film, and the pattern is named the X-ray diffraction pattern. Further research paved the way for the determination of the helical structure of DNA. It operates on the principle of Bragg’s law, which is represented as follows:

nλ=2dsinθ

Where,

λ is the wavelength of the X-ray.

n is the order of reflection, which is an integer.

d is the path difference.

θ is the angle of incidence.

## Protein Crystallography

The association of amino acids bonded through peptide linkages gives rise to compounds called proteins, and they comprise carbon (C), oxygen (O), hydrogen (H), and nitrogen (N). Protein crystallography focuses on a given protein crystal and provides information regarding the future of protein, its molecular structure, and its utilization in various fields.

Here, the sample is a protein crystal through which an X-ray beam is passed, and the detector captures its diffraction producing a particular X-ray pattern. Their diffraction spots are being collected and undergo data processing with the help of computers and graphics. The software helps to interpret the three-dimensional structure of the sample protein and further save it as a Protein Data Bank (PDB). This information helps in drug designing, modification of structure and other research areas.

## Applications of Crystallography

• The structure of proteins, DNA, RNA, antibodies and various other biomolecules are researched by crystallography.
• The kind of bonds, such as covalent or ionic bonds, present in a crystal can be determined.
• The structure of molecules and the orientation of atoms are examined through crystallography.
• The composition and their process occurring biologically and chemically can be identified by crystallography.

### Common Mistakes

When crystallography is performed, a common mistake that exists is the “sample selection.”

• One must choose the sample and incident radiation based on its requirements because each sample and radiation give distinct patterns with different energy intensities.
• An amorphous sample provides low resolution, whereas a crystalline sample high resolution.
• X-ray, neutron and electron radiations are three radiations out of which anyone is used on a sample.

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses. Especially for

Bachelor of Technology in Chemical Engineering

Bachelors in Chemistry

Bachelors in Physics

Masters in Physics

Masters in Material Science

Bachelors in Pure and Applied Chemistry

Bachelors in Biochemistry

Masters in Biochemistry

Crystal Lattice

Atomic Structure

Analytical Chemistry

Solid-State Chemistry

## Practice Problem

Q1: Name the crystal system in which all angles are not equal to 90o.

(a) Monoclinic

(b) Tetragonal

(c) Cubic

(d) Triclinic

Correct option: (d)

Q2: How many imaginary symmetries does a crystal have?

(a) One

(b) Three

(c) Four

(d) Zero

Correct option: (b)

Q3: In the X-ray diffraction method, what is the relation between wavelength and path difference?

(a) Directly related

(b) Inversely related

(c) No relation

(d) None of the above

Correct option: (a)

Q4: Who discovered the X-rays?

(a) Sir William Henry Bragg

(b) Sir Isaac Newton

(c) Sir Wilhelm Roentgen

(d) Albert Einstein

Correct option: (c)

Q5: What is the full form of PDB?

(a) Path Data Bragg

(b) Protein Data Bank

(c) Protein Data Biology

(d) Protein Data Base

Correct option: (b)

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