Table of Contents
triclinic system
are given in Table 2. A total of 11 Ga-Nd compounds, comprising NdGa$_3$, NdGa$_5$, Nd$_2$Ga$_3$, Nd$_3$Ga$_7$, Nd$_9$Ga$_4$, Nd$_2$Ga$_7$, Nd$_2$Ga$_9$, Nd$_3$Ga$_5$, Nd$_3$Ga$_11$, Nd$_3$Ga$_{17}$, and Nd$_3$Ga$_{19}$, have been reported so far. The crystal structures of these compounds can be classified into three groups: the cubic $Pm\bar{3}m$ structure (NdGa$_3$), the tetragonal $P4/mmm$ structure (NdGa$_5$ and Nd$_2$Ga$_3$), and the trigonal $R\bar{3}m$ structure (Nd$_3$Ga$_7$, Nd$_9$Ga$_4$, and Nd$_3$Ga$_5$).
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\caption{Crystal structure of N
What is the Triclinic System?
The Triclinic System is a crystal system where the crystal is asymmetrical. This means that there is no threefold axis of rotation or fourfold axis of inversion. The Triclinic System is the least symmetrical of all the crystal systems.
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Classes in the Triclinic Crystal System
(A) The Triclinic Crystal System
In the triclinic crystal system, the crystallographic axes are inclined to each other and are not mutually perpendicular. These axes are represented by the following set of basis vectors:
a1 = a x1 + b y1 + c z1
a2 = a x2 + b y2 + c z2
a3 = a x3 + b y3 + c z3
The unit cell is a parallelepiped spanned by the basis vectors.
There are 7 crystal classes in the triclinic crystal system. They are listed in the following table.
Crystal Class Space Group Triclinic P 1 Monoclinic C 2 Orthorhombic C 222 Rhombohedral R 3 Hexagonal P 63 Tetrahedral I 4 Cubic I 23
(B) The Monoclinic Crystal System
In the monoclinic crystal system, the crystallographic axes are inclined to each other and are not mutually perpendicular. These axes are represented by the following set of basis vectors:
a1 = a x1 + b y1 + c z1
a2 = a x2 + b y2 + c z2
a3 = a x3 + b y3 + c z3
The unit cell is a parallelepiped spanned by the basis vectors.
There
Triclinic Crystal Structure
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Properties of Triclinic Crystals
Triclinic crystals are characterized by three unequal axes that are not perpendicular to each other. They have a plane of symmetry that contains one axis, and two twofold axes of rotation. The angle between the axes can be any value, and the crystal class is 1. Triclinic crystals lack any center of symmetry, making them the most asymmetrical type of crystal.
Some examples of triclinic minerals are plagioclase feldspar, orthoclase feldspar, tourmaline, and turquoise. Triclinic crystals can be transparent, translucent, or opaque.
The Triclinic Prism
atic Crystal Class
The triclinic prismatic crystal class is characterized by a threefold axis that is perpendicular to a twofold axis. The threefold axis intersects the twofold axis at a 60° angle, and the other two axes are perpendicular to each other.
The triclinic prismatic crystal class includes the following space groups:
P1, P-1, P2, P21, P22, and P23.
P1 is the only triclinic crystal class that does not have a center of symmetry. The other space groups in this class have either one or two centers of symmetry.
P1 is also the only space group in this class that does not have any mirror planes or glide planes. The other space groups have either one or two mirror planes or glide planes.
P1 is the only space group in this class that does not have any inversion centers. The other space groups have either one or two inversion centers.
P1 is the only space group in this class that does not have any screw axes. The other space groups have either one or two screw axes.
P1 is the only space group in this class that does not have any rotational axes. The other space groups have either one or two rotational axes.
