# Azimuthal direction vector notation

## Main Question or Discussion Point

Hello everyone!

I am trying to do a literature search about ion scattering spectroscopy experiments. But I am not good at the vector notation which is used in these articles. I mean the notations with square brackets like [11-2] or [1-10] etc. (-2: the bar is on 2). For instance in a graph like
"[URL=http://img9.imageshack.us/my.php?image=azim.png[/URL]
How that [11-2] azimuthal direction means 90 degrees or [-12-1] shows 150 degrees or so the others? Or when they say "the particle is sent in the [B][1-10] azimuthal direction[/B]" what does this mean in terms of degrees? How can I learn about and understand this notation?

Thanks
Love&respect...

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The graphic I'd sent is an azimuthal ICISS (impact collision ion scattering spectroscopy) scan of a fcc (111) lattice.

These notations look like directions in the lattice -or maybe Miller indices - but usually Miller index notation is in round brackets, like (111) .
In any case they have nothing to do with azimuthal notation.
If they are directions, then [1,1,1] means the direction of a vector with components 1*a+1*b+1*c where a,b,c are the three unit vectors of the lattice.

I don't know what the angles on the x-axis mean, I am not familiar with this method.

Thanks nasu for your reply. The x-axis in the figure which I'd sent before is the azimuthal angle. I'm posting another figure related the first one I'd sent before:
http://img13.imageshack.us/img13/7756/azim2.png [Broken]
What should I understand from these figures? It's not the miller indices I think. They don't match with the azimuthal angles.
Thanks&regards...

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The introduction to the Miller index page on wikipedia is good for an explanation of the bracket notation if you ever can't remember. The square brackets are directions in the lattice - i can't remember exactly since i studied this stuff a few years ago, but i think the direction points to the lattice site responsible for the dip in each case.

the azimuthal angle is the angle between the incoming ions incident onto the crystal and the position of the detector. if you look at the wiki page azimuth then you may get an idea, or the diagram just under the heading alternative derivation on the bragg's law page, where it would be equal to 180 - 2*theta. if i remember correctly, its used because thats how the x-ray diffraction setups work, you spin the detector around the crystal and the crystal twists a bit too, but as i said, been a few years since i played around with one of them.

anyway, sorry if i'm being condescending in any way, don't know what level to talk at in this forum, but hey, you'll probably never hear from me again

First I'd like to thank you for the reply.
English is not my native language. So I cannot understand what is meaning 'condescending' or not:)
The definition I knew: the azimuth of a point is the angle between the positive x-axis and the projection of the vector onto the xy-plane (the component of the vector in the xy-plane). According to this definition: shouldn't that [11-2] direction mean 45 degrees? Or did they use the 'horizontal coordinat system' or anything else? Or am I wrong?
Anyway, thanks for sharing your knowledge with me...

If you look at your original graph you see that the angle zero corresponds to the direction [-110]. So they measure the angle from this direction - this is your x axis.
So the angle between [-110] and [11-2] for example is 90 degrees (the dot product of the two vectors is zero.