Calculation of GaN Unit Vectors for making a Wurtzite lattice

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1

Hello,
I am trying to define GaN wurtzite crystal in LAMMPS based on what was posted on the LAMMPS-users forum, which is:

> variable x equal 5.19294/3.18
>
> variable y universe 3.18
>
>
>
> lattice         custom $y a1 0.5 -0.866025 0.0 a2 0.5 0.866025 0.0 a3 0.0
> 0.0 $x  basis 0.33333333 0.66666667 0.1252 basis 0.66666667 0.33333333 0.625
> basis 0.33333333 0.66666667 0.5 basis 0.66666667 0.33333333 0.0

Q1: Considering the unit vectors, why we have 0.5 -0.866025 0.0 for a1 (i), 0.5 0.866025 0.0 for a2(j). And where do 0.5, -0.866025, and 0.866025 come from?
Q2: Shouldn’t the unit vectors be defined as follows and not by numbers like 0.5 or -0.866025:

1	0	0
0	1	0
0	0	1

I appreciate your input.
Farzad

2

two comments:

  1. you should be looking up the difference between a primitive and a conventional cell. for example in a crystal structure or solid state physics text book or on the web.
  2. a [1 0 0][0 1 0][0 0 1] cell would be the primitive cell for a simple cubic system. or it would be the conventional cell vectors for any cubic system.

axel.