Fundamental types of lattice or Bravais lattice

In this particular article Fundamental types of lattice or Bravais lattice, we are going to discuss different types of lattices in detail. If we keep the crystal structure having the same type of crystallographic axes and their orientation in one group, then all the crystals can be classified into the following seven types of crystals. These crystal systems are as-

  1.  Cubic
  2.  Tetragonal
  3.  Orthorhombic
  4.  Rhombohedral
  5.  Hexagonal
  6.  Monoclinic
  7.  Triclinic

These crystals systems are identified by axis and intra axis angle. Generally for crystalline axis for a, b, c and for intra axis angle are denoted by α, β γ. The angles between b and c, c and a and a and b are denoted by α, β, and γ respectively as shown in fig.

Fundamental Types of Lattice or Bravais Lattice
In 1848, Bravais studied different space lattices crystal and shaved that there are only 14 ways of arranging point in space lattices such that all the points have exactly the same environment. There 14 lattice types are conventionally grouped into 7 crystal groups. Their space lattices are called Bravais lattice. Now let us discuss types of different lattices in detail-

1. Cubic 

 In the cubic crystal, all the three crystal axes are perpendicular to one another ( α=β=γ=90⁰) and the repetitive interval is same along the three axes  (a = b = c). The cubic lattice may be simple primitive (p), body-centered (I) and face-centered (F). The example is NaCl, Cu etc.

∴ a = b = c and  α=β=γ=90⁰

2. Tetragonal

In this crystal, all the three crystal axes are perpendicular to one another ( α=β=γ=90⁰) and the repetitive intervals are the same but the repetitive interval is the same along the third axis is different (a = b ≠ c). Tetragonal lattices may be primitive (P) and body-centered (I). The example is TiO2, SnO2 etc.

∴ a = b ≠ c and  ( α=β=γ=90⁰)

3. Orthorhombic

In this crystal, all the three crystal axes are perpendicular to one another  ( α=β=γ=90⁰) but the repetitive interval is different along all the three axes (a ≠ b ≠ c). Orthorhombic may be primitive (P), base centered I and face-centered (F). The example is KNO3, BaSO4 etc.

∴ a ≠ b ≠ c and  ( α = β = γ = 90⁰)

4. Rhombohedral

In this crystal, all the three axes are equal in length  (a = b = c). And are equally in claimed to each other at an angle other than 90° (α=β=γ ≠ 90⁰). The Rhombohedral crystal is only primitive (P). The examples of this crystal are As, Sb etc.

∴ a = b = c and (α=β=γ ≠ 90⁰) but < 120°

5. Hexagonale

Two axes of this crystal are 60° apart and the third axis is perpendicular to both of them. ( α=β=γ=90⁰ and γ = 120°). The repetitive intervals are the same along those axes that are 60° apart and the repetitive interval along the third axis is different ( a = b ≠ c ). This crystal is only primitive (P). The example of this lattice and Zn, Mg etc.

∴ a = b ≠ c and α= β = γ =90⁰ and γ ≠ 120°

6. Monoclinic

Two of the crystal axes are perpendicular to each other but the third is not perpendicular of them ( α=γ=90⁰,β ≠ 90⁰ ). The repetitive intervals are different along all the three axes (α ≠  b ≠ c ). Monoclinic crystal may be primitive (P) or base centered (C).

The example is FeSo4, NaSO4 etc.

∴ a ≠ b ≠ c and α = γ = 90⁰ ≠ β

7. Triclinic

In this crystal, none of the crystal axes is perpendicular to any of the others (α ≠ β ≠ γ) and the repetitive intervals are different along all the three axes (a ≠ b ≠ c). This crystal is only primitive. The example is K2Cr2O7, CuSo4.5H2O.

∴ a ≠ b ≠ c and α ≠ β ≠ γ

Conclusion

In this particular article Fundamental Types of Lattice or Bravais Lattice, we have discussed different types of lattices in detail and in the easiest way possible.

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