System Trigonal
The trigonal system is also called the rhombohedral crystal system. It is one of the finest structural categories that can be assigned to a crystalline solid.
The trigonal system is considered the subdivision of the hexagonal system. We commonly call the rhombohedral crystal system the synonym of the trigonal system, however, they both vary.
This page will clear all your doubts regarding the difference between the trigonal crystal system and the rhombohedral crystal system. We will also discuss the trigonal system definition with the trigonal system examples in detail.
Crystal System Definition
Do you know what the crystal system is?
Well! A crystal system is a system with a set of point groups in which each point group itself and its corresponding space groups is assigned the lattice system.
Here,
A lattice system is defined as the class of lattices with an equal set of lattice point groups, which are subgroups of the arithmetic crystal classes.
The 14 Bravais lattices are grouped into seven lattice systems are as follows:
Triclinic
Monoclinic
Orthorhombic
Tetragonal
Rhombohedral crystal system
Hexagonal
Cubic
Point to Note:
The hexagonal crystal family comprises two crystal systems that are trigonal and hexagonal.
The trigonal crystal system consists of the 5 point groups that have one three-fold rotation axis, which incorporates space groups 143 to 167.
Crystal Family
A crystal family is determined by lattices and point groups and it's formed by combining crystal systems that have space groups allocated to a standard lattice system.
In 3-d, the crystal families and systems are identical, except the crystal systems, hexagonal and trigonal are combined into one hexagonal crystal family.
The six crystal families are:
Triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, and cubic.
Do You Know?
The aforementioned 5 point groups (of the trigonal crystal system) have seven analogous space groups, denoted by R, which is assigned to the rhombohedral lattice system, whereas 18 comparable space groups, denoted by P, are assigned to the hexagonal lattice system.
Hence, the trigonal crystal system is that the only crystal system whose point groups have quite one lattice system related to their space groups.
The hexagonal crystal system comprises the seven-point groups that have one six-fold rotational axis.
These seven-point groups have 27 space groups from 168 to 194, and the hexagonal lattice system is allocated to all of these.
Now, let’s understand the Hexagonal Crystal System in detail:
Hexagonal Crystal System
Since the trigonal system is a part of the hexagonal crystal system, let’s start our page with an understanding of this system.
Regarding crystallography, the hexagonal crystal family is one of the six crystal families that involve two crystal systems, called hexagonal and trigonal, and two lattice systems, hexagonal and rhombohedral).
The hexagonal crystal family comprises 12 point groups, in which a minimum of their space groups has the hexagonal lattice as cardinal lattice and that is the unison of the hexagonal crystalline system, and henceforth, the trigonal crystal system.
Hexagonal Crystal Family
In a hexagonal crystal family, 52 space groups are related to it, whose space lattice is either hexagonal or rhombohedral.
The below diagram shows the hexagonal family arrangement of crystals with their Bravais lattice, Pearson symbol, and the unit cell diagrams of both hexagonal and trigonal system:
Trigonal Structure
A Trigonal Crystal System looks like the following:
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Trigonal System Definition
The unique geometry of the trigonal system says that the system is absolute with a 3-fold axis of rotational symmetry or a 3-fold axis of rotatory inversion as its optic axis.
A 6 - fold inversion axis within the hexagonal system is mistaken for the trigonal 3-fold axis. So too, an isometric 3-fold axis, when only the corner of a cube is visible, is often misinterpreted as trigonal when it's a part of isometric symmetry.
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Trigonal Crystal System
Now, let us understand the meaning of the trigonal crystal system:
The 5 point groups (discussed above, i.e., from 143 - 167) during this crystal system are listed below, with their international number and notation, their space groups in name only, and example crystals.
Trigonal Crystal System Example
Components of crystals within the trigonal crystal system are like the hexagonal system. They are located by regard to four axes - three of equal length with 120° intersections and one perpendicular to the plane of the opposite three.
The trigonal unit is distinguished by the presence of one line called an axis of three-fold symmetry about which the cell is often rotated by 120° to supply a face indistinguishable from the face presented within the starting position.
For instance, Selenium and quark may crystallize in trigonal form.
FAQs on Trigonal System
Q1: Describe the Overview of Trigonal Crystal System?
Ans: In a crystal system, a group of point groups and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to just one lattice system, during which case both the crystal and lattice systems have an equivalent name.
However, five point groups are allocated the two lattice systems: rhombohedral and hexagonal, because both possess a threefold rotational symmetry. These point groups are allocated to the trigonal crystal system. Among these, there are seven crystal systems, namely triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.
Q2: What is the Unit of the Trigonal Cell?
Ans: While classifying 6 crystal families, the trigonal crystal system is combined with the hexagonal crystal system and grouped into a huge hexagonal crystal family. There are two (illustrations) settings of the rhombohedral lattice system.
The unit maybe expressed as;
a = b ≠ c
α = β = 90°, and
γ = 120°
Q3: Explain Rhombohedron.
Ans: The rhombohedron may be a six-sided solid with all sides being a rhomb (or parallelogram). The body diagonal through two opposite points is either longer or shorter than the opposite three. This longer or shorter diagonal is that the c axis.
There are three faces on the upper half and three on the lower half, like the scalenohedron (a trigonal system with 12 faces), i.e., a zigzag beltline.
Also, there are positive and negative forms. With the axes in their standard positions, the positive one has an upper rhomb facing the observer, and for the negative, it is a lower rhomb.
However, both positive and negative ones are geometrically identical.
