Creating a heterostructure in VESTA

Question

I have two different crystal structure and I want to create a heterostructure but the problem is that the shape of their unit cell is different. I know how to combine them if their unit cell are same. Is there anyone who can tell me how to do that? I am a complete beginner in this field. Thank you very much!

Answer 1

• Since the constituent monolayers have generally differing lattice constants, special care is needed in the construction of the atomic models in such a way that the strain is minimized.

• Let us denote the primitive cell basis vectors of a hexagonal 2D material $i$ as {$a_i$,$b_i$}. The supercell basis vector may be constructed as $n_ia_i$+$m_ib_i$, where $n_i$ and $m_i$ are integers. The second basis vector is always oriented at a $120^\circ$ angle (Keep $\alpha=\beta=90^\circ$ and $\gamma=120^\circ$).

• We then search for a set of integers such that the magnitude of the supercell basis vectors in materials $i$ and $j$ approximately match:

$$\boxed{|n_ia_i + m_ib_i| \approx |n_j a_j + m_j b_j |}$$

• In practice, we choose the smallest supercell for which the strain is less than $2\%$.

• Example: MoS$_2$/MoSe$_2$ heterostructure.

• Ref: Phys.Rev.B 88, 085318

• In particular, if you want to stack a monolayer with cubic lattice ($a_i,b_i, \alpha=\beta=\gamma=90^\circ$) on a hexagonal lattice ($a_i,b_i, \alpha=\beta=90^\circ, \gamma=120^\circ$), you can first transform the hexagonal lattice ($a_j,b_j$) into a rectangular lattice ($a_k,b_k, \alpha=\beta=\gamma=90^\circ$) with rotation matrix $P$ in VESTA:

$$\begin{bmatrix} 1 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$

and then use the following equations to find matched lattice constants:

$$\boxed{|n_i a_i| \approx |n_k a_k| \quad |m_i b_i| \approx |m_k b_k| }$$

Answer 2

Make a supercell of both the unit cells, so that they fit on top of each other.