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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!

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  • 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.

enter image description here

  • 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:

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

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  • $\begingroup$ In your cases, these 2 material have same shape of unit cell. but in my cases Im trying to combine cubic lattice structure with a hexagonal lattice. The unit cell of these 2 structure is completely different. The basis vector of these 2 structures is pointed in different direction. Therefore your equation cannot be used. $\endgroup$ – JensenPang Sep 16 at 12:17
  • $\begingroup$ @ JensenPang The idea is the same. I have updated my answer to consider your situation. $\endgroup$ – Jack Sep 16 at 12:56
  • $\begingroup$ Hello, Jack. Your explanation is very clear. May I ask one more naive question. How can u explicit construct this transformation matrix to modify the unit cell. You are not doing the scaling, you modify the structure of the unit cell. Does it affect periodic structure of the crystal ? $\endgroup$ – JensenPang Sep 16 at 16:59
  • $\begingroup$ +1. For such a fast answer! Looks like this may become a Hot Network Question! $\endgroup$ – Nike Dattani Sep 16 at 18:00
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    $\begingroup$ @JensenPang We just choose a new group of lattice vectors to construct a supercell following fundamental principles. I think it doesn't affect the periodic structure of the crystal. You can search for papers like your situation. $\endgroup$ – Jack Sep 16 at 20:03
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Make a supercell of both the unit cells, so that they fit on top of each other.

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    $\begingroup$ Hi Str91, Welcome to the community. Can you elaborate your answer with details $\endgroup$ – Thomas Sep 16 at 12:09
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    $\begingroup$ Welcome to the site !!! We hope to see much more of you, and thank you for offering your knowledge to our community. We would appreciate if you could expand this answer a bit. Take a look at other questions to see what the "standard" for an answer is :) $\endgroup$ – Nike Dattani Sep 16 at 17:58

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