What Is the Tetragonal Crystal System Definition Structure and Examples
A crystal structure contains atoms, and a crystal lattice is made of points. A crystal system is a set of axes, meaning it is a structure with an ordered array of atoms, ions, or molecules. Crystal structures occur due to the intrinsic nature of the particles for producing symmetric patterns.
Here is a brief description of unit cells, Bravais lattice, and various crystal systems, including the tetragonal pyramidal system.
Unit Cell
Different atoms give various signals with varying strengths and dependence on electron density distribution in the closed shells. If the atom is lighter, the released signal is weaker, and vice versa. The mutual arrangement of these atoms is called the crystal structure, and they are derived from the chemical formulas and physical density of the solids.
A unit is the smallest part of the crystal component. A group of atoms, ions or molecules, arranged together purely builds up the crystal. Unit cells have a structure in 3D space, describing the bulk arrangement of the crystal's atoms.
Bravais Lattice
Bravais Lattice means 14 different 3D configurations into which the atoms of a crystal can be arranged. There are various ways for describing a lattice, and the most fundamental one is known as Bravais Lattice.
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It is also referred to as an array of discrete points with an orientation and arrangement looking precisely the same as any other discrete points; that is, lattice points are indistinguishable. 7 main ones in 3D space are listed here.
Triclinic System
In this system, all three axes incline towards each other and are of the same length. Depending on the three inclination angles, various forms of crystals are in paired faces. There is only a primitive cell in the triclinic Bravais Lattice. Some standard triclinic structures are Kyanite, Amazonite, Labradorite, Turquoise, Aventurine Feldspar, and Rhodonite. This structure is also found in Potassium Dichromate.
Monoclinic Structure
There are three axes with two at right angles in this structure, and the third one is inclined. The length of all three axes is different based on the monocyclic system's inner structure, and it includes prisms and Basal pinacoids with inclined end faces. There can be primitive or base-centred monoclinic cells. Some common examples of monoclinic structure are Vivianite, Petalite, Gypsum, Howlite, etc. It is found in Sodium Sulfate and Monoclinic Sulfur.
Orthorhombic System
It has three axes, all at right angles to each other. They are of different lengths and based on the rhombic structure, the orthorhombic system contains several crystal shapes, like pyramids, double pyramids, pinacoids, and rhombic pyramids. There are four types of Orthorhombic systems in Bravais Lattice: simple, base-centred, face-centred, and body-centred. Some common examples of it are Topaz, Zoisite, Tanzanite, Iolite, etc.
Trigonal System
In the trigonal system, angles and axes are similar to the hexagonal systems. There are six sides at the system's base, and in all, there are three sides in this system. In the trigonal system, the crystal shape includes 3-sided pyramids, Rhombohedra, and Scalenohedral. For this Bravais Lattice, only the primitive unit cell exists. Some common examples of trigonal system are Quartz, Ruby, Jasper, Agate, etc. This system can be found in Sodium Nitrate.
Hexagonal System
This system has four axes; 3 are of equal length and lies on the same plane. They intersect at 60 degrees, and the 4th axis intersects the other at right angles. The shapes for the system include double pyramids, double-sided pyramids and 4-sided pyramids. Hexagonal Bravias Lattice is only available as a simple hexagonal cell. Common examples of hexagonal system are Apatite, Sugilite, Beryl, etc. It is found in Zinc Oxide and Beryllium oxide.
Tetragonal Crystal Shape System
The tetragonal crystalline structure contains three axes, and the central axis has a different length (either shorter or longer than others). The other two axes are in the same plane and have the same lengths. The tetragonal crystal shape includes double and 8-sided pyramids, 4-sided prism, pyrite, and trapezohedrons. A tetragonal system has simple and body-centred tetragonal cells, and the Bravais lattice follows the given relation:
a, b are equal but not equal to c
α, β and γ equals to 90 degree
Tetragonal crystal system examples are for the simple cells and body-centred cells structures. The typical examples of tetragonal crystal system are Titanium dioxide and Stannic Oxide.
Note: Here, a, b, and c denotes the dimensions of unit cells and α, β, and γ denotes the angles corresponding in the unit cells.
Cubic System
In this system, all three axes intersect at right angles and have equal lengths. Cubic crystal systems include cube, octahedral, and hexaciscohedron. Common examples of this system include Garnet, Silver, Diamond, and Gold. The Cubic Bravais Lattices are of 3 types, including primitive cubic cell, Body-centered cubic cell, and face-centred cubic cell.
FAQs on Tetragonal System in Crystallography
1. What is the tetragonal crystal system?
The tetragonal crystal system is a crystal system in which the unit cell has three perpendicular axes where two axes are equal in length and the third is different (a = b ≠ c; α = β = γ = 90°). This means:
- All angles between axes are 90°.
- The base is square (a = b).
- The height (c) is different from the base edges.
2. What are the lattice parameters of the tetragonal system?
The lattice parameters of the tetragonal system are a = b ≠ c and α = β = γ = 90°. Specifically:
- a = b (equal base edges)
- c ≠ a (different vertical edge)
- α = β = γ = 90° (all angles are right angles)
3. What are the types of Bravais lattices in the tetragonal system?
The tetragonal system has two Bravais lattices: simple tetragonal and body-centered tetragonal. They are:
- Simple tetragonal (P): Lattice points only at the eight corners of the unit cell.
- Body-centered tetragonal (I): Lattice points at the eight corners and one at the center of the unit cell.
4. How is the tetragonal system different from the cubic system?
The main difference between the tetragonal and cubic crystal systems is that in cubic a = b = c, while in tetragonal a = b ≠ c. Key differences include:
- Cubic: a = b = c and α = β = γ = 90°.
- Tetragonal: a = b ≠ c and α = β = γ = 90°.
- Cubic unit cells are perfectly symmetrical in all three dimensions.
- Tetragonal unit cells are elongated or compressed along one axis.
5. What is the formula for the volume of a tetragonal unit cell?
The volume of a tetragonal unit cell is given by V = a2c. Since a = b and all angles are 90°:
- Base area = a × a = a2
- Height = c
- So, Volume = a2 × c
6. What is an example of a tetragonal crystal in chemistry?
A common example of a tetragonal crystal is titanium dioxide (TiO2) in its rutile form. In the rutile structure:
- TiO2 crystallizes in a tetragonal lattice.
- Each Ti4+ ion is surrounded by six O2− ions.
- The structure influences its optical and catalytic properties.
7. How many lattice points are present in a body-centered tetragonal unit cell?
A body-centered tetragonal (BCT) unit cell contains 2 lattice points per unit cell. This is calculated as:
- 8 corner atoms × 1/8 contribution each = 1 atom
- 1 atom at the body center = 1 atom
- Total = 2 lattice points per unit cell
8. What is the coordination number in a simple tetragonal lattice?
The coordination number in a simple tetragonal lattice is typically 6. This means:
- Each atom is surrounded by 4 nearest neighbors in the same plane.
- There are 2 additional nearest neighbors along the vertical (c) axis.
9. Why is the tetragonal system important in solid-state chemistry?
The tetragonal system is important in solid-state chemistry because many technologically important materials crystallize in this structure. Its importance includes:
- Occurrence in compounds like TiO2 (rutile).
- Influence on electrical, optical, and catalytic properties.
- Role in phase transitions from cubic to tetragonal structures.
10. How do you identify a tetragonal crystal system from unit cell data?
A crystal belongs to the tetragonal system if unit cell data shows a = b ≠ c and α = β = γ = 90°. To identify it:
- Check if two lattice constants are equal (a = b).
- Confirm the third lattice constant is different (c ≠ a).
- Ensure all interaxial angles are 90°.
