How to demonstrate that there are just 14 types of Bravais lattice?
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Bravais lattices are those that fill the whole space without any gaps or overlapping, by simply repeating the unit cell periodically. The whole lattice can be generated starting from one point by operating the translation vector
R⃗ = n1a1 + n2a2 + n3a3R→ = n1a1 + n2a2 + n3a3
where (n1,n2,n3)(n1,n2,n3) are integers and (a1,a2,a3)(a1,a2,a3) are the basis vectors which span the lattice.
In three dimensions, there are exactly 14 types of Bravais lattices. A primitive lattice is one such example. A primitive lattice is generated by repeating a primitive unit cell, which contains a single lattice point.
An example of a primitve unit cell in three dimension would be a cube with lattice points only at the vertices. Now, each of these lattice points is shared by 8 unit cells (4 above, 4 below). So, in each unit cell, one lattice point is counted as 1818. Thus, the total no. of lattice points in each unit cell is 18×8 = 1
R⃗ = n1a1 + n2a2 + n3a3R→ = n1a1 + n2a2 + n3a3
where (n1,n2,n3)(n1,n2,n3) are integers and (a1,a2,a3)(a1,a2,a3) are the basis vectors which span the lattice.
In three dimensions, there are exactly 14 types of Bravais lattices. A primitive lattice is one such example. A primitive lattice is generated by repeating a primitive unit cell, which contains a single lattice point.
An example of a primitve unit cell in three dimension would be a cube with lattice points only at the vertices. Now, each of these lattice points is shared by 8 unit cells (4 above, 4 below). So, in each unit cell, one lattice point is counted as 1818. Thus, the total no. of lattice points in each unit cell is 18×8 = 1
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Hey dear here is the answer
The Bravais lattices. In two dimensions there are five distinct Bravais lattices, while in three dimensions there are fourteen. These fourteen lattices are further classified as shown in the table below where a1, a2 and a3 are the magnitudes of the unit vectors and a, b and g are the angles between the unit vectors.
Hope its help you
The Bravais lattices. In two dimensions there are five distinct Bravais lattices, while in three dimensions there are fourteen. These fourteen lattices are further classified as shown in the table below where a1, a2 and a3 are the magnitudes of the unit vectors and a, b and g are the angles between the unit vectors.
Hope its help you
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