Find the lattice type and base in 2D crystal

In summary, the question is asking for the position of atoms in neighboring planes of a GaAs crystal perpendicular to [010], as well as the type of lattice and basis for a 2D crystal made from those planes. The top view of the lattice is similar to ZnS and the 2D lattice is oblique with primitive vectors given by \vec{a}_1=\frac{a}{4\sqrt{2}}(\hat{x}+\hat{y}) and \vec{a}_2=a\hat{x}, where a is the length of the side of the crystal. The basis for the 2D crystal is made up of two atoms at positions (0,0) and (a/4, a/
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Homework Statement



Draw the position of the atoms in the two neighboring planes of the GaAs crystal perpendicular to vector [010].

Find the type of the lattice and the basis of 2D crystal which is made by singling out those two neighboring layers from 3D lattice.

Homework Equations



GaAs is the same structure as ZnS. And I've drawn the 'top view' of the lattice, the one that can be found in Kittel, Solid State, on the page 17. The plane perpendiculat to [010] is (010) - one that goes on the side parallel with the x-axis and through point 1 on the y-axis, if the corner atoms are on the positions 0 and 1.

The top view of the lattice looks like this:

6TiwR.png


And if I got it right the 2D lattice looks like this:

LYdJf.png


But what are the primitive vectors? And what kind of a latice is this?

IS the 2D Bravais lattice oblique? With primitive vectors:

[itex]\vec{a}_1=\frac{a}{4\sqrt{2}}(\hat{x}+\hat{y})[/itex]
[itex]\vec{a}_2=a\hat{x}[/itex]

Where a is the length of the side of a crystal?
 
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  • #2
The Attempt at a SolutionThe 2D Bravais lattice is indeed oblique, with the primitive vectors given by:\vec{a}_1=\frac{a}{4\sqrt{2}}(\hat{x}+\hat{y})\vec{a}_2=a\hat{x}where a is the length of the side of a crystal. The basis of the 2D crystal is made up of two atoms at positions (0,0) and (a/4, a/4).
 

Related to Find the lattice type and base in 2D crystal

1. What is a lattice type in a 2D crystal?

A lattice type in a 2D crystal refers to the arrangement of atoms or molecules in a regular, repeating pattern. It determines the overall shape and symmetry of the crystal.

2. How is the lattice type determined in a 2D crystal?

The lattice type in a 2D crystal is determined by analyzing the angles and distances between neighboring atoms or molecules. This information can be obtained through techniques such as X-ray diffraction or microscopy.

3. What are the different types of lattice structures in a 2D crystal?

The most common lattice types in 2D crystals are square, hexagonal, triangular, and rectangular. These structures can be further classified as primitive, centered, or non-primitive, depending on the arrangement of atoms within the unit cell.

4. What is a base in a 2D crystal?

A base in a 2D crystal refers to the smallest repeating unit of the lattice structure. It is typically a parallelogram or rectangle that can be stacked together to form the crystal lattice.

5. How is the base determined in a 2D crystal?

The base in a 2D crystal is determined by identifying the smallest repeating unit within the crystal lattice. This can be done by examining the symmetry and repeating pattern of the lattice and finding the smallest set of atoms or molecules that make up the whole structure.

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