1. Eric Kort Undergraduate eak02000@pomona.edu
X-Ray Micro-densitometry of Amorphous MoRuB for LIGO Flex-Joint Mirror Suspensions
Eric Kort
Undergraduate
PONCY front page
LIGO-G R

2. Laser Interferometer Gravitational-Wave Observatory
Overview
• Gravity waves, LIGO, and Suspensions
- quick overview
• X-Ray Micro-densitometry
- why it is necessary
• The Process
- how x-ray micro-densitometry is done
• Results
- what we were and will be able to certify with this technique
slightly philosophical question for the first point?
Laser Interferometer Gravitational-Wave Observatory

3. Gravity waves, LIGO, and Suspensions
Einstein: Gravity is described by warping in space-time.
Gravity Wave: Ripple created in fabric of space-time that propogates at the speed of light.
(caused by things such as super nova explosions and the big bang)
explain spin casting
industrial process
large quantity of material
we need a small amount at this experimental stage and also want to test many different compositions
Laser Interferometer Gravitational-Wave Observatory

4. Gravity waves, LIGO, and Suspensions
LIGO will (hopefully) detect these gravity waves, directly confirming GR and opening a new realm of astronomy
Detection is done through a Michelson Morley laser interferometer
Gravity waves cause mirror displacement, resulting in length changes in different directions in each arm, producing signals for us to interpret
dropped in our jargon because will inevitably use it
unlike spin casting, splat quenching doesn’t produce homogeneous samples
imperfect meeting of the pistons – wedges (Sto’ working on this)
slower-cooled parts of the sample => xtalline parts
point out dendritic fingers of xtalline material – very delicate
splats are between the size of a nickel and a dime (3 to 6 pence or 5 to 10 Euro cents)
Laser Interferometer Gravitational-Wave Observatory

5. Gravity waves, LIGO, and Suspensions
However
Gravity Wave displacement very small (~10-18m!!!) (proton’s diameter ~10-15m)
Need to hang the mirrors very carefully
Currently- piano wire
Predicted upgrade- fused silica wires
Better upgrade?- amorphous metal flex joints
inhomogeneity in the samples results in non-uniform distribution of tensile stress (for example)
areas of high stress => breaks more easily
periodic stressing of a xtalline sample => heat dissipation through motion of dislocations
mention: cause of motion of dislocations is same mechanism as causes the dissipation (hence have the FDT here)
glasses have no dislocations => no such dissipation (though this effect is less serious than the local weaknesses)
because xtallite inclusions/intrusions are undesirable, we want to determine how much of them we have. Determine suitability.
need a method to determine which regions of splat are any good (we only need ~10% of the total area)
Laser Interferometer Gravitational-Wave Observatory

6. Gravity waves, LIGO, and Suspensions
Amorphous MoRuB currently being manufactured and tested here at Caltech
Looks Promising!!!
Current Plan of flex-joint shape
300 microns long, 3mm wide, and 10 microns thick
Plan to hang tens of kilogram, fraction of a million dollar mirrors off these joints
talk would be much shorter if we weren’t using XRD (crazy!)
despite flippant insertion in brackets, there are other possibilities:
bend testing – thin xtalline areas break easily when bend, glassy areas do not
BUT some areas that are e.g. ½ & ½ may not show up as being xtalline under this test as they may withstand sufficient stress
transmission electron microscopy – use this to observe crystallite intrusions
differential thermal analysis/differential thermal calorimetry – measure heat absorbed/released in phase transitions: can relate to composition
Last two are very good at quantitative analysis. Trouble is that they are DESTRUCTIVE, either by physically destroying the sample or by altering its phase composition (you can’t just heat up and cool these GMs as you please). Ultimately, we need a non-destructive method so that we can verify samples as glassy before performing other tests on them… XRD provides this.
Laser Interferometer Gravitational-Wave Observatory

7. X-Ray Micro-densitometry
Must be sure joint is correctly constructed
How?
• Series of tests verifying material properties (stress/strain etc..)
• X-Ray Diffraction
(determines glassiness)
• X-Ray Micro-densitometry
Bragg Jr.
Equation used by Braggs (William Henry and William Laurence). Nobel prize, Point out who is who. Apostrophe – did only one of them use it at a time?
Won’t dwell on the equation/derivation because most of audience familiar with it…
Laser Interferometer Gravitational-Wave Observatory

8. X-Ray Micro-densitometry
4 Incentives for X-Ray Micro-densitometry
 to determine the uniformity of the thickness, compactness, and density of the splat-quenched sample (splat-quenching- technique used to make glassy metals)
 to certify the absence of cracks or holes (larger than the critical defect size) in the splat-quenched sample
 to select a region of the splat-quenched sample suitable to flex-joint creation (glassy and flat)
 to certify the final flex joint is uniform, has the desired shape, and is defect free
use ~6kV x-rays produced by exciting Co atoms
section through curved detector – x-rays detected by their ionisation of the gas between the casing and the knife-blade, which are at a p.d of 10kV
conventional 2θ angle is the total deflection of the incident x-ray beam
different regions of a splat are irradiated
ideally, motion between scanning regions to scan would be done using precision motion stages, but this has not been possible
devoted a fair bit of time to getting this together… 
Laser Interferometer Gravitational-Wave Observatory

9. Incentives Incentives
Splat-Quenched Sample
Each splatted sample is unique
Need to know information
on each sample to pick a
region good for testing
and, eventually, good
for a flex joint
use ~6kV x-rays produced by exciting Co atoms
section through curved detector – x-rays detected by their ionisation of the gas between the casing and the knife-blade, which are at a p.d of 10kV
conventional 2θ angle is the total deflection of the incident x-ray beam
different regions of a splat are irradiated
ideally, motion between scanning regions to scan would be done using precision motion stages, but this has not been possible
devoted a fair bit of time to getting this together… 
(Thanks to Brian Emmerson for the photo)
Laser Interferometer Gravitational-Wave Observatory

10. How does it work? The Process
3 Main Stages:
 X-Ray imaging the sample (thanks to the animal care facility for their help and the use of their machines)
   digitizing the image (thanks to the digital media center for their assistance and the use of their machines)
 analyzing the image in Matlab
for a xtalline sample, there is a range of angles centred about a given peak over which the interference of diffracted rays is constructive enough to produce a decent signal
the same thing applies for glasses to a greater extent, even though they don’t have a periodic structure…
gives the results (read green and red)
Laser Interferometer Gravitational-Wave Observatory

11. The Process: X-Ray Imaging
We used a standard diagnostic
X-ray unit (just like what the doctor
uses on someone when they break a
finger, or what a vet would use to
see the babies in a pregnant lemur)
and standard mammography film
by adjusting power settings we
could image our sample so we
could see thickness fluctuations,
cracks etc..
(thanks to Dr. Russel Rose and
Dr. Virginio Sannibale for help with
this x-ray session)
xtals are v. regular arrays of atoms
=> extent of the scattering charge density chiefly determines the range of angles over which interference of diffracted beams is notable
peaks are not broadened a lot (FWHM ~½°)
xtalline peaks stick out of glassy data
refer to the diagram for silicon powder:
point out the inverted commas
all of this type of plot are “flux” plotted against total deflection of the incident beam (“2 theta”)
we really measure “intensity”, which is the number of counts at a detector channel
however, this depends on how long data is collected for, as well as how much of the beam is allowed through the aperture
need suitable way to ‘normalise’ the intensity at each channel to include these parameters
divide count value by the exposure time and area aperture used --> a “flux” of sorts… (a number per area per time)
get several peaks because there are different plane spacings: the spacing an incident x-ray “sees” depends on the orientation of the xtal it “sees”.
Color enhanced x-ray
Laser Interferometer Gravitational-Wave Observatory

12. The Process: Scanning and Analyzing
Digitizing
used Kodak Slide Scanner (4000ppi, translates to pixel dimensions of ~6x6 microns)
Analysis
done in Matlab
production of color maps, thickness-intensity number corrolation, pixel neighbor corrolation test, 2-d profiles
the main mechanism by which glasses produce diffraction peaks is different from the way xtals do.
it’s to do with short-range correlation between the separations of molecules in the glass
glasses have some short range order, but no long range order (they’re “frozen liquids”);
even simple mathematical treatment somewhat involved and so have not delved into it here
basic result is contained in 3rd bullet point
glasses here have FWHM ~10°
compare xtals: FWHM ~½°
Metglas produced by spin-casting. Homogeneous. No xtalline inclusions. Produces nice smooth curve.
Notice inclusion of boron here – it is used to frustrate the formation of a xtal lattice and that’s why we use it too.
Laser Interferometer Gravitational-Wave Observatory

13. Laser Interferometer Gravitational-Wave Observatory
Results
Whole splats
Cut strips OK
Can select suitable region to cut
Can re-asses cut region
Bad
see here the type of patterns we’re looking for (or not looking for) in the glasses we’re using – those made from molybdenum, ruthenium and boron
first plot is from a slowly cast sample of the alloy with the formula shown (we refer to as “MoRuB-17”)
other two plots are data taken from splats. First of these shows how splats produce semi- or pseudoxtalline samples (wouldn’t show up in a break test).
second of them is from a very glassy sample – first time I saw glass from a sample I had helped produce from start to finish. <feign enthusiasm here: we made GM. Whoopee, etc…>
when produced these, was not sure exactly where they came from on a sample because beam not easy to locate without precision movement
came up with a crude scale to locate approx position of beam… <next slide>
Bad
Want Uniform Strips
Laser Interferometer Gravitational-Wave Observatory

14. Laser Interferometer Gravitational-Wave Observatory
Results
Post Electro-chemically polished sample
(thanks to Stefano Tirelli for poloshing the sample) 5 45
Crystals are eaten preferentially, leaving holes which are evident is x-rays, indicating impure sample
explain (basically) what the rainbow colours are on the splat image
Eric’s talk will explain how this is produced – need to fly back in October to see it
lines 1-5 are the regions successively irradiated with x-rays
plots show data from regions 1,3 & 5
mainly xtalline one (1) is due to the xtalline fibres at the end of the splat – these show up thin because it’s not a sheet of metal there
personally surprised to see the thinnest part of the main body (3) of the splat is NOT the most glassy
would maybe expect “thinnest = cool fastest”
possible explanation: trade-off between thickness of sample and its radial position in the splat - both contribute to the cooling rate?
the two samples tested since this one was have shown v. amorphous in the central region but were far more amorphous in general anyway, so it remains to be shown whether this pattern is a trend or a “one-off” occurrence.
Laser Interferometer Gravitational-Wave Observatory

15. Laser Interferometer Gravitational-Wave Observatory
Quantitatively
• Can Detect Defect down to 6x6 microns
(critical defect size ~100 microns)
• Locally can resolve surface variations ~4 microns (large scale ~27 microns)
want to milk more out of the data…
Laser Interferometer Gravitational-Wave Observatory

16. Laser Interferometer Gravitational-Wave Observatory
Conclusions
Success
Have technique which fulfills 3 of 4 designated tasks
• Determine Uniformity
• Locate Cracks/Holes
• Identify Amorphous Regions
4th Task, characterize finished flex joint, is expected to be a straight-forward development
“Various types” = stuff like fitting curves with Gaussians ( errors big, fits not brilliant)
or = stuff like
RDF is the FT of the diffraction pattern
If I get a reliable technique, it will need calibrating against something other than ‘sight’, otherwise it’s pointless. Could use TEM or DTA to get better idea of % composition and how that relates to RDF curves.
Then would have a quant. way of determining composition, without destroying the sample.
Then could find what % composition has what Q-factor properties and choose regions of samples accordingly
This is quite a long way off at the moment (~a couple of months or so), but wouldn’t it be NICE?
Laser Interferometer Gravitational-Wave Observatory

17. Laser Interferometer Gravitational-Wave Observatory
Acknowledgments
Thanks to:
Dr. Riccardo DeSalvo, Hareem Tariq, Animal Care facility, Digital Media Center, Dr. Russel Rose, Professor Johnson, Dr. Jan Schroer, Stoyan Nikolov, Professor Francesco Fidecaro, Virginio Sannibale, Mike Hall, Yoichi Aso, Kelin Wang, Brian Emmerson, Stefano Tirelli, and the rest of Riccardo’s group. Caltech, LIGO, the LIGO REU program, and the SURF office. And, of course, the patient animals that waited in line for their X-rays.
glassy metal group – mentioned in Mike’s talk
Laser Interferometer Gravitational-Wave Observatory