Find the lattice type and base in 2D crystal

[dingo_d]

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:

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

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

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

\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?

 

[member 553083]

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).