Simple or primitive monoclinic lattice (monoclinic-P) has one lattice point at the each corner of the unit cell. It has unit cell vectors a≠b≠c and interaxial angles α=γ=90°≠β.
Base-centered or side-centered or end-centered monoclinic lattice (monoclinic-C), like all lattices, has lattice points at the eight corners of the unit cell plus additional points at the centers of two parallel sides of the unit cell. It has unit cell vectors a≠b≠c, and interaxial angles α=γ=90°≠β.
Simple or primitive cubic lattice (sc or cubic-P) has one lattice point at the each corner of the unit cell. It has unit cell vectors a = b = c and interaxial angels α=β=γ=90°.
The simplest crystal structures are those in which there is only a single atom at each lattice point. In the sc structures the spheres fill 52 % of the volume. The number of atoms in a unit cell is one (8×1/8 = 1). This is only one metal (α-polonium) that have the sc lattice.
Simple or primitive orthorhombic lattice (orthorhombic-P) has one lattice point at the each corner of the unit cell. It has unit cell vectors a≠b≠c and interaxial angles α=β=γ=90°.
Simple or primitive tetragonal lattice (tetragonal-P) has one lattice point at the each corner of the unit cell. It has unit cell vectors a=b≠c and interaxial angles α=β=γ=90°.
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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Base-centered or side-centered or end-centered monoclinic lattice (orthorhombic-C), like all lattices, has lattice points at the eight corners of the unit cell plus additional points at the centers of two parallel sides of the unit cell. It has unit cell vectors a≠b≠c and interaxial angles α=β=γ=90°.
Body-centered cubic lattice (bcc or cubic-I), like all lattices, has lattice points at the eight corners of the unit cell plus an additional points at the center of the cell. It has unit cell vectors a = b = c and interaxial angles α=β=γ=90°.
The simplest crystal structures are those in which there is only a single atom at each lattice point. In the bcc structures the spheres fill 68 % of the volume. The number of atoms in a unit cell is two (8 × 1/8 + 1 = 2). There are 23 metals that have the bcc lattice.
Face-centered cubic lattice (fcc or cubic-F), like all lattices, has lattice points at the eight corners of the unit cell plus additional points at the centers of each face of the unit cell. It has unit cell vectors a =b =c and interaxial angles α=β=γ=90°.
The simplest crystal structures are those in which there is only a single atom at each lattice point. In the fcc structures the spheres fill 74 % of the volume. The number of atoms in a unit cell is four (8×1/8 + 6×1/2 = 4). There are 26 metals that have the fcc lattice.
Body-centered orthorhombic lattice (orthorhombic-I), like all lattices, has lattice points at the eight corners of the unit cell plus an additional points at the center of the cell. It has unit cell vectors a≠b≠c and interaxial angles α=β=γ=90°.
Generalic, Eni. "Simple monoclinic lattice." Croatian-English Chemistry Dictionary & Glossary. 29 June 2022. KTF-Split. {Date of access}. <https://glossary.periodni.com>.
Glossary
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