Euclidean Geometry of Diffraction

Experiment is now going and getting results. However, frustratingly we are spending most of our time not acquiring the good data but getting the settings correct to collect good data. This is just the way of things, and the reason why it takes 7 days (24hrs) So as I hinted to before we need to find ourselves, the truncation rods (high angle diffraction) and specular ridges (reflectivity) in a 3D reciprocal space.

After trawling around a bit I have found a good paper for example of geometries and I'll show the main examples here.

If you imagine a 3D sample suspended in a vacuum with no external forces then the simple motions of that sample are clear forward-back, left-right and up-down. The complication comes when you consider the freedom to rotate about any axis (figure) and the fact that you must keep the scattering vector S normal to the sample surface in order to conduct the tests we are looking at.

Examples of possible rotations of the sample, while retaining the scattering vector S normal to the sample

 However you may have noticed that there is one other possible rotation possible which amounts to what we call asymmetric case (figure) and the scattering vector no longer normal to the sample surface.

Examples of the required case and off specular due to a rotation

In order to get scattering theoretically your sample is flat the 2omega = 2theta as shown but in reality there will be some offset in omega due to the relative rotation around our forward-backwards axis.

If you have done all this, understanding and accounting for the "flatness" of your sample through a series of complex compound rotations the you are ready to scan through omega-2theta (linked) so that S the scattering vector is always perpendicular to the sample resulting in the intensity readings on the detector that give you information about the sample. "What information you ask?" well I'll get to that next time. For now I'm off to look at L edge absorption.

Measuring your photons

X-rays are incident on a sample and then they bounce off, because of their coherent incidence it means that some scattered X-rays add together and others cancel out and we call this diffraction. But the key thing it means is that there are not X-rays everywhere only at allowed angles relative to the surface and in the case of single crystals as we have here at Diamond only in particular directions as well.

A simple 1D version of X-ray Diffration

So imagine a sphere around your sample (which is illuminated by your X-rays) and if you were to look around on the surface of that sphere only at distinct spots would you observe any X-rays scattered from the sample. This makes measuring the X-rays an initial mental calculation as to where to look in 3D space where you have control over the x, y, z, rotation around x, rotation around y and rotation around z of the sample and then motion of the detector in polar co-ordinates with a fixed r value centred around your sample.
So far too many compound motions translated into reciprocal space with very distinct peak intensity locations, our very own version of a needle in a haystack.
I'm sure this sounds all nice and complicated I unfortunately could not find a clear diagram, so I will have to make one. Watch this space (after lunch) as a photo of the actual kit is somewhat confusing without being able to look round it.

Photo of the set up

Controlling your photons; Flux and Shape

First things first is to select our prefered beam shape and flux using the X-ray optics on the beamline to utilise the X-rays produced by the synchrotron.

The beamline we are using is I07 which specialises in surface and interface diffraction and I'll talk about the detector and sample set up for conducting the experiments later.
So we have three main methods of controlling the beam shape and flux; slits, lenses and attenuators. First things first is to put a camera in the sample position to image the X-ray beam shape and alter the lensing to give a uniform symmetrical gaussian beam profile in both horizontal and vertical directions.  I won't go into too much detail here on the X-ray optics as others have done a far better job elsewhere, such as this presentation from the European Synchrotron Radiation Facility.Then for our uses we then draw in the slits to box off the centre of the beam to give a nice neat square beam footprint. Note there is still some gradient due to the divergence of the beam in the distance between the slits and the samples. That's the shape then we move on to the flux.

Image of the flux detector in the middle of the beam

Replacing the camera with a silicon photodiode detector allows direct and quantitative measurement of the photon flux of the X-rays. This however can only be used for calibration, rather than ion chamber detectors which can be used during the experiment showing relative flux. If you are really interested have a look here for more information on the detectors. This allows us to measure the flux while we change the attenuation using filters, which when it comes to X-rays means big lumps of material. In this case predominantly different thicknesses of aluminium and molybdenum.

So put all these pieces of information together and it means we know what beam profile and what flux of photons are hitting our sample, which is key for our calculations at the end converting observed intensity on the detector into information about the illuminated volume.

What am I doing here? Lab vs Synchrotron

With X-rays you can do a lot of cool physics in terms of investigating crystal structures, elemental analysis, electronic structures and surface topology but why Diamond light source? The simple answer is flux and energy; a far greater flux of photons and greater control over the energy of the incident X-rays.
So in a standard lab X-ray experimental set up you generate soft X-rays by accelerating electrons into an anode of chosen material producing two types of X-ray; Bremsstrahlung (German for breaking-radiation) due to the quick deceleration of electrons hitting the anode (the low energy bump) and characteristic X-rays which are at distinct energies associated with the electron energies in the anode material (the spikes labeled Kbeta and Kalpha). Thus most science is done with the characteristic X-rays, by filtering out the Bremsstrahlung X-rays, at the elemental distinct energy with copper tubes being the most used.

As shown in the figure the accelerating voltage of the electrons alters the intensity of X-rays out put of the tube. And the flux of a tube source is of the order 1x10^7 photons per second per mm^2.

Where as with a synchrotron you can select your energy through using magnets to decelerate your electrons emitting the X-rays and using such a large facility leads to fluxes of the order of 5x10^14 photons per second per mm^2.

I need to dash off and sort the sample order for the first experiment so,
I'll be back  . . .

New Science, for me anyway

So I put blogging to one side, like a lot of things, when I started to really focus on my thesis. That was now well over 12 months ago and I sit in front of my keyboard as a Doctor of Philosophy, not that it feels any different.

Anyway so I thought I would throw myself back into blogging with the inspiration of a new experience for me; A synchrotron experiment at Diamond Light Source.

So I'm going to attempt to keep a running commentary with here and twitter on how things go every high (peak) and every low (noise). Here's to high energy photons and successful experiments.

Wasp

Books, we know we should read them it seems like the done thing for those of intelligence. But do to this representation it some times feels like a chore to pick up a big book sit down and try and work your way through it.

However, I come to you with a suggestion, a small book. More specifically Wasp by Eric F. Russell a mere fourteen chapters and only 175 pages yet so engrossing most will not put it down until they are finished.

Wasp is a book with the plot based on the idea that a small wasp can irritate a driver of a car to the point of crashing and killing all the passengers. The idea a small almost insignificant, in size, being can cause the death of four giants and a huge machine. This then links with the timing of the piece set years into the future where a one James Mowry is sent to be a “Wasp” on an alien planet. Mowry’s work is used to help earth fight a war against an alien race far more numerous than humanity.

This compelling book to me is similar in many ways to George Orwell’s Classic 1984 with its way of gripping writing telling the tale of literally one man against the world.

For me whether you are interested in sci-fi or not this is still a must for anyone and everyone.

(Exepose 18/05/07)

Perception of Science

Cross posted from University of Bristol Science Faculty Blog:

I often wonder what the world thinks of science and scientists as through out my life I am surround by those within the bubble, as it were. To try and unravel what maybe thought of us by the outside world you have to look at what hits the main stream news and popular culture.

Looking the popular view you get tv shows and definitely Prof Brian Cox with his previously life as a pop star with D:Ream. I see things such as the big bang theory being created showing and increase the scientists stereotype, that is they are socially awkward brainy people that are funny to laugh at as they fail to fit in with the world around us. Brain Cox on the other hand has come to previalance because he is the exact opposite, like Richard Feynman he is easy to talk to and has the ability to explain complex ideas with ease for everyone to understand. Now I am not saying we are all like Brian but think of it this way. We wouldn't have science if scientists where unable to communicate.

This then leads me to labels. Prof Cox labels himself a geek, and you could say that those comic book loving social outcasts in big bang are nerds. But really what is the difference. Can you be a nerd, without being geek or vice versa. Interestingly a team that put together a 'Geek Calender' this year, containing snaps of people like Simon Singh and Ben Goldacre, have at the head of their website 'nerds on the march'. This would suggest that a 'nerd' driven movement has created a calender about geeks.

Admittedly these points lead me further from finding the difference between nerd and geek, but more importantly I see the use of the words changing. No longer are people negatively labelled using these words but more using it as an empowerment.