# LEED - determining surface structures

How can one describe surface structures (before and after adsorption)? I understand the diffraction theory but I have never really tried to determine the structures of samples by myself.

LEED (low electron energy diffraction images of Pd(1,1,0) surface (clean and with adsorbed CO):

• All I can see is a rectangular diffraction pattern (which is regular so we are dealing here with a single crystal) and that the pattern has changed a bit after the adsorption. Is there any other information I can get from the images? I searched online for some tutorials but all I could find were scientific articles and I really could not grasp it fully. I need to work out some examples.

EDITED:

An incomplete list of suggestions:

• From the position of the spots, did you determine their mutual distances (e.g., to discern a square from a rectangle), and angles if you connect «the dots»? Beside symmetry, this eases to relate between direct and reciprocal space.

• What about the intensity of the spots (in either one of the frames) relative to each other, is there a regular (symmetry related) pattern? Depending on the space group (in 3D crystallography), there are systematic extinctions, so I think 2D and 2.5D crystallography may have an equivalent to this, too. For the clean substrate, match the spots the relative anticipated position (e.g., $$d$$-spacing) and intensity pattern?

• Do you recognize a second, weaker pattern if you extend the time of exposure for the sample (substrate + deposit)? (Again in analogy from 3D crystallography, where an additional set of diffraction spots may be observed in presence of a sample's superstructure). If the experiment anyway is recorded with a CCD detector, this may be easier to recognize visually if intensity $$I$$ is not scaled linearly, but follows e.g., $$\sqrt(I)$$ (this pushes a bit the weaker signals relative to the stronger ones) and good color map (e.g., viridis, cross-reference) for visualization. For this, a good correction vs. background and empty substrate is helpful.

Palladium is fcc so you are looking at the fcc(110) surface.

If the 3D lattice constant is $$a$$ then the (110) surface has a rectangular 2D lattice with lattice constants $$a$$ and $$a/\sqrt{2}$$.

click for larger

The longer direction in space is the shorter direction in reciprocal space as shown by LEED.

In the drawings below the added red spots could represent added features to the real and reciprocal lattices, perhaps CO adsorption on the Pd(110) surface. We don't know if they are on top of Pd atoms or in the bridge or hollow points and can't tell from normal LEED images.

A: fcc(111) surface

B: one explanation for the LEED image seen

C: another explanation for the LEED image seen

### But I don't have those extra spots

With only one image at one beam energy, it's impossible to tell if those spots are missing due to interference at 76 eV only, or if they never appear at any energy.

If a spot appears, you know you have some structure with the periodicity it suggests, but the mere absence of a spot in one image does not by itself guarantee that there is no corresponding periodicity present.

The electrons pass through several atomic layers before attenuating and so the returning reflections can interfere constructively and destructively in complicated ways.

If you have many images at many energies and you never see the spots appearing in C but not B, then you can *tentatively conclude your structure is most likely B and probably not C, but without more advanced studies like IV-LEED (plots of spot intensity versus beam energy for a long series of closely spaced energies, fit by a theoretical calculation or surface XRD or electron holography, it's sometimes hard to differentiate definitively between possible solutions.

From Matter Modeling SE: