I put up the stacks with a similar configuration as Gabriele built in Elog 851. To integrate them into the chamber, I added another square bread board to the bottom for mounting the posts for horizontal support. it’s now a rubber >> square board >> spring >> round board >> rubber >> round board >> optical setup (from bottom to top) layers of cake.
However unfortunately, the setup overshoots the chamber celling, but I think we can simply cut the post by 3’’ to solve the problem.
The central post has been trimmed by 3 inch. We rebuilt the crackle1 optical layout with the PZT mirror replacing one of the 45 degree mirrors out side of the chamber and got fringes.
I also finished soldering the ribbon cable with shadow sensors and photodiodes connectors on board for the improved re-cabling use.
We are going to put everything into the chamber this week.
We reorganized cables with the improved cabling configuration and put everything into the chamber.
Before taking further steps, I am going to mount an accelerometer onto the post with the chamber pumped, to characterize the seismic noise in this current setup.
During the holidays I built the optical layout referring to our former design, but soon we found that because of the shorter actual blade length, the input beam has to be sent through the clearance between the cage edge and the suspended block, which will lead possible clipping problem.
Gabriele redesigned the layout accordingly (Elog 874) . Last week we re-built the layout and suspended the blocks using our custom-built positioner, which consists of x, y, z tranlational stages and a rotating plate. We hope to align the magnets to the OSEMs with desired precision, but everytime the suspension wire is being clamped, the block will rotate away from the aligned angle. This might be a result of the screwed clamping surface.
[Gabriele, Xiaoyue] For the past week we finished soldering all the OSEM electronic components and cables, and now the 6 OSEMs for damping the two blades are all mounted.
Today we built the model X1KR2 for sensing and controlling,
and the interfacing medm screen kr2_damping,
We fitted the whitening TFs for all 12 circuit boards and uploaded the dewhitening filters. Finally we checked the OSEMs and they are all working properly now after some debugging Our next step is to do calibration, and start to design the damping loop.
We calibrated the shadow sensor /coil driver from counts to volt and then to micron / N according to Enrico’s calibration [Enrico's report] (actually mN would be a better scale but we didn’t realize it later), and uploaded the conversion to the sensing filter to OSEMX/Y/Z and COILX/Y/Z. Then we designed the damping loop, with DAMP being a differentiator to reduce the resonance Q, ELP100 being the low pass 100 Hz to suppress high frequency noise, and int being the integrator to enhance the control in low frequency range. We compared the damped spectrum with the free-running spectrum and the control works very well.
However we found that the amplitude y-direction low frequency oscillation is higher than x, and it’s corresponding to the 100mHz peak appearing in the spectrum. The problem was solved by stiffening the board using two posts to clamp down the board in y direction, but the trade-off is an increase of some high frequency noises. Unfortunately we didn’t save the comparison right away. We have to do more investigation on if the stiffening helps with this low frequency oscillation.
We also tried to measure the transfer function but the coherence was not good enough with a quick noise injection and then a quick try of sine sweep.
Then we realigned the interferometer and see the fringes on both photodiodes. The slow oscillating fringes indicates that the layout is now very robust with its arm difference confined in few wavelengths.
We made the servo model by creating the LOCK mask and added the lock input/filter to the blade block.
The next step is to lock the interferometer.
I have been using single crystalline copper nanopillar to study metal’s pre-yield behavior. I chose copper because it’s FCC (face-centered-cubic) crystal, that has well-defined slip systems so the dislocation dynamics is relatively simple to understand. Pillars with diameter D = 500 nm, aspect ratio D: L = 1:3 are FIB (focused ion beam) milled. We want small system to further simplify our first investigation as the “mechanical annealing” theory and experiment have shown that in small enough system there’s no dislocation multiplication but only slipping. I first did compression tests to measured the yield stress to be ~ 400 MPa and young’s modulus to be 143 GPa. They are very close to what’s been reported in literatures [1, 2].
Then I carried out nanoDMA tests in which, I prescribed an increasing “elastic” load in steps with a small sinusoidal oscillation on top. With the displacement data being taken, I first plotted the histogram of the displacement residual rate. Some outliers are observed as possible crackle events.
I also analyzed the storage and loss modulus, defined as the real and imaginary parts of the input-output transfer function. Interestingly there seems to be non-zero peaks as the static load is approaching the yielding!
To deal with the data more carefully, I thought over the calibration for machine noise. Since the resonance frequency of pillar is in MHz range and the machine resonance is ~ 130 Hz. We have the simple relationship that k_calibr = k_raw - k_air.
I took several more data and chose the “good” ones based on the criteria that their storage stiffness saturates to near E ~ 19uN/nm. After taking absolute values of the loss moduli and plotting modulus vs. stress we see features at ~ 180 and ~ 320 MPa load.
My interpolation of the “good” data shows promising consistency.
However for now I don’t quite understand why I see negative loss moduli in my analysis. I keep doubting my error analysis but so far I don’t see how it could be wrong: I fit the data with sinusoids and use the fitted paramaters and their associated standard errors to do monte-carlo simulation. The means also agree with my FFT analysis. I am attaching the sample matlab codes for both my monte-carlo and FFT.
%% load data
filename = 'B8P6_QS.txt';
data = importdata(filename);s
fs = 1000;
tag = 'B8P6';
% work for P4-7
time = data.data(:,1);
disp = data.data(:,2);
load = data.data(:,3);
function [kr0, ki0, ekr, eki, kr_raw, ki_raw] = monte_carlo(A0, B0, dA, dB, yr0, yi0, dyi, dyr)
A = A0 + randn(1e6, 1).*dA;
B = B0 + randn(1e6, 1).*dB;
yr = yr0 + randn(1e6, 1).*dyr;
yi = yi0 + randn(1e6, 1).*dyi;
H = (A+1i*B)./(yr+1i*yi);
kr_raw = real(H);
ki_raw = imag(H);
%% load data
filename = 'CuB3P8_QS.txt';
data = importdata(filename);
fs = 1000;
time = data.data(:,1);
disp = data.data(:,2);
load = data.data(:,3);
load0 = data.data(:,4);
dispV = data.data(:,5);
Today I realigned crackle2 optical layout, obtaining fringes with better contrast defect (AP ~98%, SP ~94%); however I have to check it the contrast defect is due to unbalanced BS reflectivity, as the reflectivity and transmission depends on the polarization, and can be as low as 40% according to Thorlabs specsheet for BSW17. Note also that our AOI is not 45 degree.
The damping loop is working ok without modification, but from time to time, the z2, y2 corrections are large. I doubted it's due to y2 magnet touching in z direction but I have to check if all filter banks are engaged. Neverthless the position readouts all have small variance.
I started soldering the breakout boards for suspending the optical setup. We are having problem with not enough spacing between the 2-pin connectors. I am going to live with it by soldering one another connectors to the back for now. Meanwhile we are going to redesign the PCB board.
I soldered the breakout PCBs according to Gabriele's design. In addition to cabling all the 2-pin connectors, I cut the translational stage cable and resolder it to the 4-pin connector.
I mounted the board to the back of the optical breadboard and connected it to another board on the table using the 26-pin ribbon cable. I tested that the translational stage is working properly. The damping loop are also working, except that Z1 is reading ~1700 (max) no matter how I change the position of OSEM. The LED's are all on so there must be something wrong with Z1 PD. I still need to cut and solder the power supply for the AP/SP PDs.
In Elog 929 when I was trying to relate the loss modulus G'' to the energy dissipation I naively took the absolute value, which turns out to be wrong. By directly integrate the stress over strain the energy dissipation is proportional to sin(loss angle), which should be 0 < loss angle < pi/2 for the system to be physical, otherwise my pillar is doing work to the machine.. which makes no sense. Thus the negative G'' indicates some hidden machine anomaly. Following Rana's suggestion we want to do similar test on "loss-less" materials.
At first I was thinking about using fused silica, but it turned out to be difficult to image and FIB fused silica pillars since the material is non-conductive. I will suffer from charing problem if I don't deposite Au or Cr. Before moving on to KNI I borrowed a sputtered metallic glass (MG) substrate, (composition around 50 at. % Zr, 30 at. % Ni, 20 at. % Al) from my labmate since it's also amorphous and known to have low internal damping. I FIBed 500 nm pillars out of the MG sample and did 1Hz DMA tests as I did on the Cu pillars:
Compared to those of the Cu pillars the values of MG G'' are very small, though not always zero. Also the two-peak trend and the presence of negative values should call further cautions to the machine reliability. We need to understand if we can use the MG data to "calibrate" Cu DMA measurements.
I fixed the Z1 PD circuit — it was simply due a poor connection. I also soldered the AP, SP connections. Now everything works out pretty well with the breakout cables.
I fixed the connections broken during the rearrangment, and tested the electronics. At first the PD's were all working properly but DAC channels were outputing 0 or 2V voltage no matter what commands were sent, but this problem was solved after rebooting CyMAC. Everything is now in place, working as normal. The boards are good to go for suspension!
In order to prevent the cable short circuiting seismic noise, we clamped the flat cable to the second isolation stage and then to the first stage. I glued threads to serve as bolt holes for clamping. Rubber is underneath to give necessary support. The cable was loosely rolled in U shape in each stage to reduce the stiffness.
Using KNI Kurt Lesker Ebeam evaporator, Ottman (grad student in Julia group) helped me deposit 40 nm thickness film of gold to the fused quartz sample [specsheet HERE, GO-FS100-1 family, gift from Matt]. I FIBed two batches of ~ 500 nm diameter nanopillars.
Since evaporated gold does not have great adhesion so it's not on top of the pillar after FIBing -- you can see it gradually go away, but there's enough on the whole sample for it to be still effectively conductive.
The next step is to do same DMA test on FQ pillars as the ones done on Cu pillars to calibrate for machine nonlinearity.
I did several 1Hz oscillation DMA tests on fused quartz using the same loading function used for Cu pillars. Notice there are four branches of storage moduli and the lower end correponds to a consistent, non-crazy loss modulus sweep. This calls a review on the MG data (Elog 934), where the storage modulus seem to exibit two-branch trend, and the higher-end corresponds to the loss modulus curves with larger fluctuation and presence of negative values. I have no clue where this branching in storage modulus comes from and how it's related to the loss modulus insanity, but undertanding it might be crucial to resolve the nagative phase lag issue.
If zoom in only those good ones, we see: 1. the loss modulus are all postive, although definitely not zero.. 2. there's no obvious two-peak feature showing up; however I want to take more data in 100 ~ 500 MPa range to confirm, as the red and black "peaks" are suspicious.
I finished connecting all OSEM input /output cables to the breakout cable.
Aggregating all good measurements for MG, FQ based on the criteria for "good" discussed in Elog 950, we plot to have visual comparison for dynamic modulus amongst the three samples tested so far. From a rough look, the loss modulus of amorphous materials (FQ, MG) are more "linear" than that of Cu in static stress sweep. Also notice that there seems to be a consistent increase in storage modulus in all samples. From the basic linear fitting, amplitude measurements of FQ, MG, Cu_saturate all have a slope of ~ 0.15 e3. If we understand why "good" is good, and taking enough measurements on FQ to confirm the consistency, we might be able to use it as a calibration line.
I estimated the optical path length based on Yuji's work (LIGO_T1400600-v1), and set up the input steering mirrors accordingly as shown in the figure. The beam needs to travel 3.11 meter to achieve ~ 300 um beam waist at the end mirrors. Unfortunately I under-calculated the length on breadboard at the begining (and didn't notice it until just now..), so the path is now 10 cm longer than expected.
After hours of painful alignement on this 12 d.o.f. flying board, knocking off only one magnet (A), I finally overlapped the splitting beams and saw fringes on both photodiodes, with everything dampped except for A, the breadboard horizontal in plane direction.
I was having a hard time last week locking the Michelson. Yesterday with remote help from Gabriele, we noticed that the first problem is the wrong sign. By inputing a 1000 count offset at the Coil input the two blades were driven in opposite direction, so the servo is loop actually not doing anything to cancel the displacement difference. We resolved the issue by changing the sign of Z2 coil output, while also changing the sign of Z2 ctrl output to compensate for the sign of the entire damping loop. Gabriele also pointed out the second problem where the lock filter had double pole at 10 Hz that limited the bandwidth, eating up too much phase, so we moved the double pole up to 100 Hz. Then we were probably sensing too much correction due to the high frequency noise, so we moved it down to 50 Hz, and the Michelson is locked with gain of 10.
I further pushed the zero down to 40Hz (red curve) because it seems to give more stable lock (50Hz green).
Since the Michelson is very sensitive to environmental noise i.e. seismic, acoustic, air current noise, I left it locked overnight for a better investigation of the error signal spectrum.
Late Elog but on Monday (Elog 965) I left around 6:30pm and the Michelson lost lock in 1.5 hr).
I plotted three spectrum 6:30 to 7:00pm (purple) 6:30 to 7:30pm (blue) and 12:00 to 12:30am (green), calibrated with the non-linear inversion of the Michelson fringe:
The fringes were becoming faster and the former lock scheme no longer works. Using the good part of single blade transfer function I measured, we fitted for the differential blade model, in unit of um/uN. Optical gain is calculated to be 5.61 mW/um using peak to peak SERV_IN1 reading of 0.95 mW. Using plant model -- multiplication of differential blade model and optical gain, in unit of mW/uN -- we designed in sisotool the new compensator. However using this lock filter we are still not able to lock the interferometer.
We start to question if there's anything really wrong with the alignment. By comparing the shadow sensor signals (blue curve damped, red undamped) with the locked ones (green) we clearly see a difference. Then we noticed the board is badly sagged probably due to creep, and is definitely touching down. We are going to re-adjust the OSEM positions to try solving this problem.
[Gabriele, Xiaoyue] Today we leveled the second stage up by shortening the suspension wires to solve the touch-down problem. Before putting effort to re-alignment, we marked the stage and board positions, and we are leaving it suspended in current status for a night to see if there's any more sagging.
I wrapped up my recent literature review on mechanical properties i.e. internal friction and acoustic emission of materials, and discussed about possible insights on crackling-noisy materials candidates according to the investigation. The summary is uploaded to DCC-T1500225.
Today I put the order for our next testing blade materials on McMaster-Carr: General Purpose 1074/1075 Spring Steel, Spring-Tempered Strips- Unpolished (cold rolled). I picked heat treated ones with spring quality, and since the price is relatively cheap, I purchased four different thickness 9074K34, 9074K39, 9074K45, 9074K633
Once the materials are arrived they will be sent to machine shop for wire Electrical Discharge Machining (EDM) cut. I am already in cue and the lead time is approximately two weeks from now.
The yield strength of this general purpose steel is not rated but we can infer an approximate value from its hardness (rockwell hardness C44). From the conversion CHART the estimated tensile yielding is 205,000 psi = 1.4 GPa. Then I did some simple calculation about the applied stress on blade if we load 2.2 kg mass (the mass we are loading to the maraging steel blade now) according to the ordered strip thickness.
If the approximation is not too bad, we can have three sets of static load spanning 54 ~ 92 % of yielding without machining new blocks of mass.
[Saikanth, Xiaoyue] We aligned the Michelson by tweaking the first incoming mirror, one arm end mirror, and the two stearing mirrors before PDs. The photodiodes were initially saturated so we rotated the waveplate to dump enough power until seeing half power decrease when blocking one arm. The SP / AP PDs are reading power 4.46V / 5.12V with contrast defects of 90.1% / 95.3%. We can adjust the incoming beam polarization to balance the two arms better.
Yesterday we locked the Michelson again using the designed filters. From the error signal spectrum we saw most RMS comes from 10 Hz motion. We injected more noise in low frequency by adding complex pair poles at 5 Hz, Q = 2 and complex zeros at 50 Hz, Q = 1 ro shape the noise, and measured the open loop transfer function. We also add in SERV_OUT to measure plan transfer function for filter design.
Checking in foton the lock filters (no compensator) + plant for the expected response, we saw that more phase margin was needed to increase the low frequency gain. we switched off ELP100 (the 100 Hz low pass filter) to gain more phase and saw no significant change in the peak to peak value of the control signal, which means we were not saturating with the high frequency correction. Then since we want to correct more for low frequency motion, we designed boost with complex poles at 1 Hz, Q = 1, zeros at 10 Hz, Q = 1, gainning 1 at high frequency and ramping up in low frequency. Then most of the RMS comes from frequency peak ~ 8 Hz, so we add res8 with resonance gain at 8 Hz, Q = 10, 20 dB. After boosting, the error signal is having a 2% peak to peak amplitude compared to the unlocked state. We checked the error signal spectrum and it's largely improved at low frequency.
Then we want to take care of the high frequency 2nd order structure at 152 Hz.
We first measured the plant and fit for the new compensator, substitute if for the old comp152. We checked the error signal spectrum and compare with the one with no compensator but a notch filter at 152 Hz, it turned out that the notch filter works better -- it has a similar spectrum but with less correction.
The servo filters is now modified to be:
The next step is to investigate the intensity noise.
[Kla, Xiaoyue] We fabricated more ~ 500 nm Cu pillars and did DMA tests. This time we decided to extend our load sweep to post yield so we have retrospect of the real yielding strength for each pillar. Also we make sure of a good contact and alignement that can induce dislocation avalanches post yielding. In future study we will further increase the static load resolution (step numbers).
In the analysis I calibrated the storage and loss modulus based the average phase shift ~ 5 deg in MG, FQ data (elog 955). The calibrated data gives mostly positive loss modulus all the way up to yield. However my analysis so far is still not convincing because of the emergent negative loss modulus. I plan to "clean up" the raw data by passing it through a low pass filter and look into single cycles instead of the overall demodulation at 1 Hz to see the time evolution of hysteresis behavior.
As suggested by Gabriele, before looking into single cycles of my load and displacement measurements I took a look at the sinusoidal fit residual. The attached are three sample analysis. For each one I plotted the raw load, displacement data (blue) and their fit (red) in Fig 1, 2. The yielding point is marked by the deviation from linear increase in displacement. The time evolution of the fit residuals for both load and displacement are plotted in Fig. 3, 4. There are time dependent features showing up even in "elastic" regime without discernible nonlinearity, and they are becoming more evident when approaching the quasi-static yielding.
This suggests that the former 1 Hz sinusoidal fit for the entire 15-second segment is not accurate enough to describe the time-variant oscillations.
It should be noted that the load and displacement residuals are highly correlated. As far as I am concerned, this is due to the fact that we prescribed only the voltage applied to the capacitive (drive) plates, and the actual load applied to the sample is dependent on the displacement of the central (driven) plate.