Hexagonal crystal system is based on four crystallographic axes. The system of crystallographic axes of the hexagonal crystal system consists of three equivalent horizontal (equatorial) axes of which the positive ends make an angle of 120°. These axes are sometimes denoted as a, b and d axes. The fourth axis is (c) is perpendicular to and shorter or longer than the other three.
Crystal system is a method of classifying crystalline substances on the basis of their unit cell. There are seven unique crystal systems. The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube. The other six systems, in order of decreasing symmetry, are hexagonal, tetragonal, rhombohedral (also known as trigonal), orthorhombic, monoclinic and triclinic.
Crystal system
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Unit-cell
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Conditions on unit-cell edges and angles |
cubic |
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a=b=c α=β=γ=90° |
hexagonal |
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a≠c α=γ=90° β=120° |
tetragonal |
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a=b≠c α=β=γ=90° |
rhombohedral |
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a=b=c α=β=γ≠90° |
orthorhombic |
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a≠b≠c α=β=γ=90° |
monoclinic |
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a≠b≠c α=γ=90°≠β |
triclinic |
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a≠b≠c α≠β≠γ≠90° |
Cubic crystal system is also known as the isometric system. The Isometric crystal system characterizes itself by its three equivalent crystallographic axes perpendicular to each other.
a = b = c
α = β = γ = 90°
Minerals of the monoclinic crystal system are referred to three unequal axes. Two of these axes (a and c) are inclined toward each other at an oblique angle; these are usually depicted vertically. The third axis (b) is perpendicular to the other two and is called the ortho axis. The two vertical axes therefore do not intersect one another at right angles, although both are perpendicular to the horizontal axis.
a ≠ b ≠ c
α = γ = 90° ≠ β
Orthorhombic crystal system is also known as the rhombic system. Minerals of the orthorhombic crystal system are referred to three mutually perpendicular axes, each of which is of a different length than the others.
a ≠ b ≠ c
α = β = γ = 90°
Rhombohedral crystal system is also known as the trigonal system. The crystallographic axes used in this system are of equal length. None of the axes are perpendicular to any other axis.
a = b = c
α= β = γ ≠ 90°
Minerals of the tetragonal crystal system are referred to three mutually perpendicular axes. The two horizontal axes are of equal length, while the vertical axis is of different length and may be either shorter or longer than the other two.
a = b ≠ c
α = β = γ = 90°
Minerals of the triclinic crystal system are referred to three unequal axes, all of which intersect at oblique angles. None of the axes are perpendicular to any other axis.
a ≠ b ≠ c
α ≠ β ≠ γ ≠ 90°
Allotropes are the elements which exist in two or more different forms in the same physical state. Allotropes generally differ in physical properties and may also differ in chemical activity.
Diamond, graphite and fullerenes are three allotropes of the element carbon. Graphite is a soft, black, slippery substance; by contrast, diamond is one of the hardest substances known. The different properties of the allotropes arise from their chemical structures. Diamonds typically crystallize in the cubic crystal system and consist of tetrahedrally bonded carbon atoms. Graphite crystallizes in the hexagonal system. In the fullerenes, the carbon atoms taking the form of a hollow sphere, ellipsoid, or tube.
In some cases, the allotropes are stable over a temperature range, with a definite transition point at which one changes into the other. For instance, tin has two allotropes: white (metallic) tin stable above 13.2 °C and grey (nonmetallic) tin stable below 13.2 °C.
The term allotropes may also be used to refer to the molecular forms of an element. Ozone is a chemically active triatomic allotrope of the element oxygen.
Bravais lattice is a set of points constructed by translating a single point in discrete steps by a set of basis vectors. The French crystallographer Auguste Bravais (1811-1863) established that in three-dimensional space only fourteen different lattices may be constructed. All crystalline materials recognised till now fit in one of these arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown to the bottom.
Crystal system
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Bravais lattices
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cubic a=b=c α=β=γ=90° |
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simple cubic
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body-centered cubic
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face-centered cubic
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tetragonal a=b≠c α=β=γ=90° |
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simple tetragonal
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body-centered tetragonal
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orthorhombic a≠b≠c α=β=γ=90° |
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simple orthorhombic
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base-centered orthorhombic
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body-centered orthorhombic
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face-centered orthorhombic
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monoclinic a≠b≠c α=γ=90°≠β |
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simple monoclinic
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base-centered monoclinic
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hexagonal a=b≠c α=β=90° γ=120° |
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hexagonal
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rhombohedral a=b=c α=β=γ≠90° |
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rhombohedral
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triclinic a≠b≠c α≠β≠γ≠90° |
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triclinic
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Generalic, Eni. "Hexagonal_crystal_system." Croatian-English Chemistry Dictionary & Glossary. 29 June 2022. KTF-Split. {Date of access}. <https://glossary.periodni.com>.
Glossary
Periodic Table