# Why is a single layer of atoms referred to as 2d ?

1. Apr 30, 2013

### sym_

Why is a single layer of atoms referred to as "2d"?

I commonly hear a single layer of atoms referred to as being a "2-dimensional structure", when it so clearly is not 2-dimensional. Why do people make that obvious mistake?

The same exact folks will also tell you that spacetime is a continuum, but by that logic, we should be able to split that "2-dimensional structure" up into infinitely smaller 3d volumes, correct?

How is this reconciled?

2. May 1, 2013

### Staff: Mentor

The size of that layer is large in two dimensions only, and it has no (relevant) structure in the third dimension.

I think you mean the opposite direction?

3. May 1, 2013

### sym_

What if you were to consider the orbital of an electron around the nucleus? Still irrelevant? Are you saying the orbital is only relevant in 2 dimensions, as if the electron somehow does not move in 3 dimensions?

What I mean is: imagine you put an atom in a box. Now, shrink the box until it's smaller than the atom (just suppose that the atom doesn't care that the box is getting smaller than what it contains).

If you imagine now a cube, made up of 8 of these individual boxes and align the boxes as such:

Black lines are the outlines of the boxes, the red is the atom.

You've split the atom into 8 different pieces, with each of the boxes representing a different volume of space.

Considering this, how is an atom at all 2-dimensional?

Last edited: May 1, 2013
4. May 1, 2013

### ehild

The atom is a three - dimensional object but the array of atoms is two-dimensional. You can describe the position of atoms by a two-dimensional matrix.

ehild

5. May 1, 2013

### sym_

Okay, that makes sense. Thanks

An array would still actually be 3d though, correct?

6. May 1, 2013

### Trollegionaire

A 2-dimensional structure cannot physically exist. If you're talking about a manipulation of light against a flat screen, that still isn't 2-D.

7. May 1, 2013

### sym_

This was my concern about the whole thing. 1d and 2d structures appear to me as purely logical, not physical.

8. May 1, 2013

### ehild

It is like the map, a two-dimensional representation of a very 3D thing. Only the atoms are supposed identical, so their 2D map does not contain detailed information about their height.
There are physical things connected to the dimension and symmetry. There can be waves travelling in the plane of the 2D atomic array but that wave does not exist in the third dimension.
A two dimensional crystal, for example, has translational symmetry in its plane, and has not in the third dimension.

ehild

9. May 1, 2013

### Staff: Mentor

"2-dimensional" is an approximation.

In the same way, you can consider the surface of earth as 2-dimensional, even if it is not (or if you do not mean) a mathematical surface.