Self Organized Criticality noise in metals and advanced hinges collective dislocation effects Riccardo DeSalvo Sannio University riccardo.desalvo@unisannio.it Riccardo.desalvo@gmail.com

The problem with Dislocations Collective dislocation activity in metals breakdown the linearity of springs 1/f noise produced Effects evident at low frequency, present everywhere This affects the performance of Seismic attenuators Seismic sensors What to do?

Dislocations basics Dislocations cannot end inside a crystal Extend across the entire grain Mostly move freely across crystal Internal tensions pull them straight Bent by stresses Cannot cross other dislocations Get pinned at various intervals by point defects like impurities, atomic vacancies, … Or on other dislocations A. Granato, et al., “Theory of mechanical damping due to dislocations”, Jour. Of Appl. Phys., vol 27, n 6, p583-593, 1956

Dislocations new understandings Can turn around a pinning point Cannot turn around other dislocations Often the dislocation free length is more limited by entanglement than by pinning

Dislocations new understandings Therefore dislocations will pileup, entangle and disentangle as a consequence of stress variations

Dislocations new problems IF entanglement and disentanglement are permitted the ensuing free length changes will cause the following instabilities:  Young’s modulus  Equilibrium point  Loss mechanisms LIGO-P1000105

Self Organized Criticality is a property of dynamical systems SOC important facts Self Organized Criticality is a property of dynamical systems a driving force is needed Per Bak 1996 How nature works: The Science of Self-Organized Criticality

SOC properties => Does not follow our beloved linear rules ! ! Movement of entangling dislocations is intrinsically Fractal => Does not follow our beloved linear rules ! ! => Avalanches induce random motion => 1/f noise at all frequencies

Experiment exploring SOC THE GAS-EMAS filter A “microscope” for mesoscale effects see LIGO-G1000990 LIGO-P1000105 Class. Quantum Grav. 26 (2009) 204018

Effects of dislocation S O C

Hysteresis equal noise ! ! ! Actuator force [mN] Temperature [oC] Thermal or position drifts generate hysteresis! Hysteresis proceeds by avalanches  1/f noise

Low frequency instability 65 kg payload can fall indifferently up or down NOT CREEP, NOT a GRAVITY DRIVEN EFFECT It is the Young’s Modulus that Suddenly fails! instability region mm starting from ~ 0.2 Hz

Anomalous Hysteresis at lower frequency Residual elasticity from crystal Change of equilibrium point from disentangled, re-entangled Network of dislocations

Controlling hysteresis Forced, slowly decaying oscillations successfully smooth out critical slope and eliminate hysteresis Same tune 0.15 Hz

Controlling hysteresis  controlling noise Bring the system away from the critical slope means: to Eliminate the source of avalanching!

Frequency (Young's modulus) dependence from. oscillation amplitude Drops with oscillation amplitude as dictated by SOC

Excess Dissipation at larger oscillation amplitude increases with oscillation amplitude as dictated by SOC

Big problem Downconversion thermal drifts + microseismic peak resonance downconversion low microseismic activity => low downconversion

Summary of Consequences Hysteresis indicates something is shifting in the material. Run-offs, changing Young’s modulus, new loss mechanisms An avalanche dominated 1/f noise is expected Should extend up to the smallest (fastest) event (MHz) Should extend down to the largest avalanche (mHz)

Ways out SOC noise is a dynamic effect It needs a power source to generate critical slope No power source, eventually no SOC noise

Ways out Keep system quiet, avoid thermal variations completely block dislocations Use materials without dislocations Use mechanics insensitive to dislocations dilution Avoid flexures => knife edge hinges an example

A high precision mechanical ground rotation sensor V. Dergachev, M. Asadoor, A. Bhawal, R. Desalvo, C. Kim, A. Lottarini, Y. Minenkov, C. Murphy, A. O’Toole, G. Pu, A. Rodionov, M. Shaner DCC: LIGO-G1001051-v3

Motivation: Advanced LIGO Active isolation requirements Requirements are more than an order of magnitude more strict than existing tiltmeter performance. Lantz, B., et al. (2009). “Requirements for a Ground Rotation Sensor for Advanced LIGO." Bulletin of the Seismological Society of America 99(2B): 980-989.

Mechanical tiltmeter Adjustable LVDT position sensors weights for tuning mechanical properties LVDT position sensors Pivot point built as a knife edge on anvil, both of tungsten carbide feedback actuators

Knife-edge hinge 2525

Hysteresis measurement hysteresis virtually eliminated lower noise performance achieved

Exponential decay keeps phase through excitations Seismic event Continuing sinusoidal fit across excitation pulses

Better performance achieved !

What is still needed to achieve the LIGO requirements ? lower instrumental noise, limiting performance at high frequencies. in vacuum operation to improve performance at low frequencies lower resonant frequency (longer balance) . . . .

The key point By designing a geometry not sensitive to dislocation SOC noise Tiltmeter performance drastically improved Will the GW interferometer seismic attenuation need the same ?