Key Characteristics of the Tetragonal Crystal System
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: Structure, Properties, and Importance
1. What is the tetragonal crystal system in Chemistry?
The tetragonal crystal system is one of the seven fundamental crystal systems used to classify crystalline solids. It is defined by a unit cell with three axes at right angles to each other, where two axes are of equal length and the third is either shorter or longer. This structure is essentially a rectangular prism with a square base.
2. What are the defining axial lengths and angles for the tetragonal system?
The defining parameters for a tetragonal unit cell are based on its axial lengths (a, b, c) and the angles between them (α, β, γ). The specific conditions are:
- Axial lengths: a = b ≠ c (two axes are equal, the third is different).
- Axial angles: α = β = γ = 90° (all three axes intersect at right angles).
3. What are some common examples of substances with a tetragonal crystal structure?
Several common compounds and minerals crystallise in the tetragonal system. Notable examples include:
- Rutile (a form of Titanium dioxide, TiO₂)
- Cassiterite (Stannic Oxide, SnO₂)
- Zircon (ZrSiO₄)
- White tin (the metallic allotrope of tin)
- Wulfenite (PbMoO₄)
4. What types of Bravais lattices exist within the tetragonal system?
The tetragonal crystal system can be described by two types of Bravais lattices, which specify the arrangement of lattice points within the unit cell. These are:
- Simple (or Primitive) Tetragonal: Lattice points are located only at the corners of the unit cell.
- Body-Centred Tetragonal (BCT): Lattice points are at the corners plus one additional point in the exact centre of the unit cell.
5. How does the tetragonal system primarily differ from the cubic and orthorhombic systems?
The primary difference lies in the axial lengths.
- Compared to a Cubic system: In a cubic system, all three axes are equal (a = b = c). In a tetragonal system, only two are equal (a = b ≠ c). Both have all angles at 90°.
- Compared to an Orthorhombic system: In an orthorhombic system, all three axes are of different lengths (a ≠ b ≠ c). In a tetragonal system, two axes are identical. Both systems have all angles at 90°.
6. Why isn't there a face-centred tetragonal Bravais lattice?
While one could draw a face-centred tetragonal (FCT) lattice, it is not considered a fundamental Bravais lattice. This is because an FCT unit cell can always be represented by a smaller, more conventional body-centred tetragonal (BCT) unit cell. By reorienting the axes, the FCT arrangement is shown to be equivalent to a BCT lattice, and by convention, the simplest and smallest unit cell is always chosen.
7. How do the unique dimensions of the tetragonal system influence a material's physical properties?
The fact that one axis (c) is different from the other two (a and b) leads to a property called anisotropy. This means the material's physical properties are direction-dependent. For example, properties like electrical conductivity, thermal expansion, and refractive index will have different values when measured along the unique 'c' axis compared to when measured along the 'a' or 'b' axes in the basal plane.
8. What are the common crystal shapes or habits associated with the tetragonal system?
The internal arrangement of atoms in a tetragonal system results in distinct macroscopic crystal shapes. Common forms, also known as crystal habits, for the tetragonal system include four-sided prisms, four-sided or eight-sided pyramids (often as double pyramids), and trapezohedrons. These shapes reflect the underlying square symmetry of the unit cell's base.
