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www.helsinki.fi/yliopisto

Nanoacoustic guided

waves

Dr. Ari Salmi

24.1.2014 1


Additional details /

nanoultrasonic imaging

24.1.2014

Matemaattis-luonnontieteellinen tiedekunta /

Henkilön nimi / Esityksen nimi 2

• Sun et al., APL 2001

• Change the delay between the pump and the probe

pulses

• measure transmission coefficient of the probe pulse

as a function of delay (delay generated with translation

stages)

‒ No picosecond scope needed!

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How does one measure picosecond

ultrasound in practice?

• Chern et al., Physical Review B, 2003

• Not the same system, but similar

• 0.7-0.9 THz -3 dB band

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What are the ultrasonic

characteristics of the pulses

generated by an OPT?


Guided waves

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• Waves propagating along a structure

• Guided by the boundaries of the material

• Guided wave testing: probe long distances along the

guiding structure

• Most commonly used: Lamb waves

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Guided waves

http://www.ndt.net/article/wcndt00/papers/idn508/fig1.gif

• Important factors:

• Attenuation in length direction

• Displacement direction

‒ Affects pickup and launch

• Velocity

‒ Different modes travel at different velocities

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Guided waves: modes

http://www.twi.co.uk/news-events/connect/november-december-2012/driving-inspection-around-the-bend/

• Two different types

• Symmetric

• Asymmetric

• Solutions to two Lamb equations

• Has to be solved numerically

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Guided waves: Lamb waves

http://www.me.sc.edu/Research/lamss/research/Waves/img004.jpg

http://www.ndt-

ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/plateW

aves.gif

• Describe the propagating modes

• Phase/group velocity as a function of frequency

• Thickness dependent

• Obtained as a solution to Lamb dispersion equations

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Dispersion curves

http://www.waterworld.com/content/dam/WWI/Volume%2027/Issue%203/z1206WWIfl03.jpg

• Detection of defects

• Polytec commercial device

• Detection of impacts

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Practical use: Lamb waves

• Rayleigh

• Scholte

• Stoneley

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Interface waves

http://geophysics.geoscienceworld.org/content/69/2/330/F1.large.jpg

http://earthquake.usgs.gov/learn/glossary/images/rayleigh_web.jpg

• Curved surfaces cause the modes to change

• Quasi-plate modes

• Difference in curvature between inner and outer

surfaces

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Complex geometries: Curvature

• Cylindrical geometry

• Plate in the longitudinal direction

• Ultrasound propagation depends on the frequency

• At high frequencies, gives rise to a problem: multiple

roundtrips

• Solved by signal processing

‒ Pre-information on the structure

‒ Differential measurements

• Lamb modes

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Guided waves in complex

structures: pipe

• Ph.D. thesis: K. L. J. Fong (2005)

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Example: Multiple roundtrips

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structures: pipe / rod

http://www.guided-nde.com/_mgxroot/gw-modes.jpg https://workspace.imperial.ac.uk/nde/Public/Thesis-IC-Zheng-Fan-Final.pdf

• At low frequencies, modes differ from Lamb modes:

• Torsional T(0,y)

• Flexural F(x,y)

• Longitudinal L(0,y)

• The (x,y) notation: x is the circumferential order and

y the ’order’ of the mode

• Changes in amplitude as a function of radial

direction

• Shin et al., 1999

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Circumferential order

• Lowe et al., Ultrasonics 1998

• Detection of notches in oil pipes

• L-modes

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Practical use: Tube waves

• Quasi-A0 modes at high frequencies

• Due to difference of curvature, energy concentrates

on the outer surface

• ”Curved Rayleigh modes”

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Guided waves in complex structures:

Whispering gallery mode

• Solid spheres: Rayleigh waves (naturally collimated)

• Tsukahara et al., APL 2000 & 2003

• Line source

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structures: spheres

• Ultrasonic gas sensor

• Yamanaka et al., IEEE trans. Ult. 2006

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Practical use: waves on spheres

• Some differences

• High frequencies required to achieve meaningful fd

products

• Elasticities very high wave velocities very high

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Guided waves in nanoscale


Nanoplates

(Plate-like structures with a thickness in the range of nm)

24.1.2014



• Nardi et al., Proc. SPIE 8681, 2013

• Generate SAWs (Rayleigh waves) on thin film-substrate

structures

• Measure mechanical properties of the thin films

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Nanometrology by surface

acoustic waves (SAWs)

• Sample used: 50-100 nm thick SiC:H films deposited

on silicon substrates

• Metallic periodic nanostructures on the surface

• These absorb the pump pulse (800 nm, d = 500 µm,

fluence 10 mJ/cm2

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• The metallic structures are the transducers

• Absorb the pump pulse and expand from the

temperature

• Frequency adjustable by the period

• Also longitudinal waves generated from the film

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• Probe pulse

• Extreme ultraviolet (30 nm wavelength)

• Diffracts from the nanograting

‒ displacement from the diffraction pattern

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• How do you get an EUV beam?

• Rundquist et al., Science 1998

• Ti:SA laser @ 800 nm

• Use higher harmonic generation in a gas (argon)

• Ionization of gas atoms in a tight focus

• Change gas pressure to adjust the phase between the

light and emitted soft x-rays

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• Results: both SAWs and longitudinal waves (LAW)

visible

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• Results: SAW velocity approaches the Rayleigh

velocity of silicon when wavelength is increased

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• Higher harmonics of the surface wave

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2nd order SAW?

• Results: Calculated isotropic Young’s moduli match

nanoindentation results quite well

• Both LAW and SAW velocities considered

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• Hurley et al., Applied Physics Letters 2008

• 22 GHz surface waves

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Even higher frequency SAW’s

• Siemens et al., Applied Physics Letters 2009

• 50 GHz surface waves

‒ 125 nm wavelength

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• Nardi et al., Applied Physics Letters 2012

• 100 GHz surface waves (theoretical)

‒ 63 nm wavelength

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Tubular structures on the

nanoscale

Rod/tube like structures with a nanometer radius

24.1.2014



• Carbon nanotubes

• Nanowires (aspect ratio > 20)

• E.g. Gold

• Nanorods (aspect ratio ~5)

• E.g. ZnO

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Tubular structures in nanoscale

• Carbon nanotubes are over 40 years old

• First paper out 1952

• Up to date, no experimental paper exists studying

propagating waves on CNT’s

• Only temperature conductivity via phonons

• Many theoretical papers

24.1.2014 37

Sound propagation in carbon

nanotubes

• Heireche et al., Physica E 2008

• Nonlocal Timoshenko beam model

• Local vs nonlocal

• Nonlocal theory of elasticity: stress at x is a functional of

the strain field at every point of a body

• Local (classical) theory -> only strain at x matters

24.1.2014 38

Sound propagation in SWCNTs

x

• Phase velocity vs local or nonlocal elasticity

• F mode

• Scale parameter e0a (a = internal characteristic length)

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Sound propagation in SWCNTs

• Yoon et al., JAP 2003

• Critical frequencies after which several speeds of sound

coexist (several modes)

‒ Van der Waals forces between the tubes make them vibrate

together

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Sound propagation in MWCNTs

• Mante et al., Nano Letters 2013 (February)

• AlN/GaN nanowire superlattices

• Coherent guided acoustic phonons (CGAPs)

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Sound propagation in nanowires

• CGAPs have a peculiar dispersion relation

• In circular GaN nanorods (d = 75 nm), quite normal

• In superlattices, the modes fold into a Brillouin zone

24.1.2014 42


• James et al., JASA 1995

• Take 1-D column of water, assume that it is comprised

of periodic units of length L

• From dispersion relation ω(k) plot has two straight

lines

• From periodicity propagation can be described as an

unit cell

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Info: Sound propagation in

periodic structures

• This unit cell in case of water can be plotted in a

momentum space unit cell (|kL| ≤ π)

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Info: Sound propagation in

periodic structures

• This momentum space unit cell is a Brillouin zone

• Propagation of waves can be completely

characterized by their behavior in a single zone!

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Info: Brillouin zone

• Two modes detected (at 25 GHz and 60 GHz)

• Negative dispersion @ 60 GHz

• Times of arrival match the expected ones

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• Beugnot et al., arXiv 10.1.2014

• ~micrometer diameter optical fibers

• Light propagating in the fiber generates surface

waves

• GAWBS and SBS well known

• SAWBS!

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Sound propagation in silica

microwires

• Absorbed and emitted phonons have different

energy

• For example, Santori et al., Nature Photonics 2012

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Stokes scattering

• Measurement of the SAWs with Brillouing scattering

• Stimulated Brillouin scattering (phonons from the light)

• The surface wave visible!

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Sound propagation in silica

microwires


Take-home

24.1.2014



• Most of the work in nanoplates and rods

• No work on propagating modes on nanospheres

• No work on Scholte or Stoneley waves

• Some work on whispering gallery modes (only in

resonance lecture on trapped modes)

• Propagation velocities very high

• Guided sound excitation very hard at the moment

24.1.2014 51

Take-home: Nanoacoustic

guided waves

nanoacoustic guided waveselectronics.physics.helsinki.fi/wp-content/uploads/2014/... · 2017. 3....

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