# Given cell edge lengths and dihedral angles, calculate lattice vectors?

I am given a list of edges: [a, b, c] and dihedral angles: [alpha, beta, gamma]. Can we determine the lattice vector directions of this unit cell?

e.g Edge lengths: [5.25953209086, 6.08183093896, 6.17370692269] angles: [119.50892382300002, 107.841528116, 89.9999968787].

I used cell = Cell.fromcellpar([5.25953209086, 6.08183093896, 6.17370692269, 119.50892382300002, 107.841528116, 89.9999968787]). Such that it gave me the bravaise lattice as

print(cell.get_bravais_lattice())

> TRI(a=6.08183, b=5.25953, c=6.17371, alpha=107.842, beta=119.509,
> gamma=90)


How to find the directions of this unit cell? For example, if this unit cell has an atom positioned at pos_atom = [0.3, 2.3, 1.8] then I may find the translated atom in the adjacent unit cell by travelling unit_cell length in some unit vector direction.

• +1 and thanks for contributing this question! You had 'angels' instead of 'angles' in your title and some awkward spacing, which I fixed in my edit, but I would appreciate it if you could proofread your question since we would like our site to have good overall presentation. Feb 11 at 15:48
• @NikeDattani Thanks for the fixes, I'll note this for my future questions. Feb 11 at 15:49

The data you presented ARE the cell parameters: a, b, c and $$\alpha$$, $$\beta$$ and $$\gamma$$ . They are not called "edge lengths" neither "dihedral angles".
Also, you don't need to change your lattice to the Bravais one. If you want the position of an atom in (any of) the adjacent cell, the translation vector will be: $$\vec{T}=u_1\vec{a}+u_2\vec{b}+u_3\vec{c}\tag{1}$$ where $$u_1$$, $$u_2$$ and $$u_3$$ are integers. The final position of the atoms ($$\vec{r}'$$) will be: $$\tag{2}\vec{r}'=\vec{r}+\vec{T}$$ with $$\vec{r}$$ being the initial coordinate.
Also, the directions are set using the Miller indices $$h$$, $$k$$, and $$l$$.
• Are the integers, $u_1$, $u_2$ and $u_3$ connected with miller indices? Feb 13 at 9:56
• No. The integers $u_1$, $u_2$, and $u_3$ are just how may times would you like to repeat the cell in the $x$, $y$, and $z$ directions to create supercells.