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8 votes
2 answers
2k views

Why are there only 14 types of Bravais lattices and not 28 when there are 7 types of unit cells and each can have four variations?

As the title suggests, I can't understand why certain kinds of variations (like Face-centred or Body-centred) are restricted to certain types of unit cells. An orthorhombic unit cell has Primitive, ...
Tatai's user avatar
  • 337
1 vote
0 answers
37 views

HCP and hexagonal primitive cell [duplicate]

There are 14 types of Bravais lattices one of them is hexagonal which is just present as primitive cell ie the basis are at its corners , now when I read about hexagonal closed packing I came to know ...
Navraj Singh's user avatar
2 votes
2 answers
2k views

Conventional unit cell for a hexagonal crystal system

The figure shows a unit cell of a hexagonal crystal system. Drawn in bold, is the unit cell. The lightly shaded one is a unit cell as well and has a six fold symmetry along an axis, hence is more ...
Kashmiri's user avatar
  • 313
1 vote
1 answer
2k views

How do I find miller indices for a plane whose intercepts are fractions of the lattice constant?

[I'm talking with respect to cubic lattices alone.] For instance, if a plane has $x,y,z$ intercepts $a/2,a/2,a/2$ (where $a$ is the lattice constant) the miller index would be $[2\space2\space2]$. The ...
Elon Tusk's user avatar
  • 113
4 votes
2 answers
929 views

Is there a standard scholarly reference for lattice constants of crystals of the elements?

I need to discuss the lattice constants of bulk crystals of several metal and semiconductor elements. I can find plenty of tables and numbers that are probably "close enough" but for a paper ...
uhoh's user avatar
  • 5,997
5 votes
1 answer
3k views

How do the three Miller indices (hkl) denote planes orthogonal to the reciprocal lattice vector?

The Wikipedia page for Miller indices defines Miller indices as follows: There are two equivalent ways to define the meaning of the Miller indices: via a point in the reciprocal lattice, or as the ...
The Pointer's user avatar
  • 1,103
3 votes
1 answer
185 views

Does a molecule need to be placed symmetrically in the unit cell?

I was watching an OCW by MIT (3.091X) on solid state. My previous notion of lattice point and unit cell got shattered after this example. Where are the unit cell and lattice points in this picture? ...
Aditya Shrivastava's user avatar