Periodic Boundary Conditions on non sq lattice

In summary, boundary conditions can be imposed on other 2d lattices such as a rhombic lattice, a hexagonal lattice, and an oblique lattice. These lattices can be indexed in the same way as a square lattice, with basis vectors and periodic boundary conditions.
  • #1
cmphys1
1
0
Is it possible to impose boundary conditions on the other 2d lattices like
a rhombic lattice?
a hexagonal lattice?
an oblique lattice?

How does one typically index such lattices?
 
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  • #2
Yes, and in the same way as for a square lattice. In any lattice you still have basis vectors. For example, in the hexagonal lattice the basis vectors can be chosen to look like they point along two sides of a triangle. Call one of these \vec R_1 and the other \vec R_2. You can pick some N_1 tending to infinity and identify the lattice point N_1 \vec R_1 with 0. Also pick some N_2 tending to infinity and identify the lattice point N_2 \vec R_2 with 0. Then you have periodic boundary conditions.
 

1. What are periodic boundary conditions on non sq lattice?

Periodic boundary conditions on non sq lattice refer to a boundary condition in which the edges of a non-square lattice system are connected to each other, creating a periodic or repeating pattern. This allows for the simulation of an infinite lattice system, which is useful for studying the behavior of materials.

2. How are periodic boundary conditions implemented in simulations?

In simulations, periodic boundary conditions are typically implemented by wrapping the edges of the non-square lattice to create a continuous and repeating system. This can be done by applying a translation operation to the lattice coordinates, or by using specialized algorithms.

3. What are the advantages of using periodic boundary conditions on non sq lattice?

One advantage of using periodic boundary conditions on non-square lattices is that it allows for the simulation of larger systems without actually having to create a physically large lattice. This can save computational resources and time. Additionally, periodic boundary conditions can mimic the behavior of an infinite lattice, providing more accurate results.

4. Are there any limitations to using periodic boundary conditions on non sq lattice?

While periodic boundary conditions can be useful in simulating large systems, they do have limitations. These conditions assume that the behavior of the material at the edges of the lattice is the same as the behavior within the lattice. This may not always be accurate, especially for materials with highly anisotropic properties.

5. How do periodic boundary conditions affect the results of simulations on non sq lattice?

Periodic boundary conditions can affect the results of simulations on non-square lattices in various ways. They can influence the behavior of defects and interfaces, and may also affect the accuracy of certain physical properties, such as diffusion coefficients. Therefore, it is important to carefully consider the use of periodic boundary conditions and their potential impact on the results.

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