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www.helsinki.fi/yliopisto
Nanoacoustic guided
waves
Dr. Ari Salmi
24.1.2014 1
www.helsinki.fi/yliopisto
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!
24.1.2014 3
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
24.1.2014 4
What are the ultrasonic
characteristics of the pulses
generated by an OPT?
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Guided waves
24.1.2014
Matemaattis-luonnontieteellinen tiedekunta /
Henkilön nimi / Esityksen nimi 5
• 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
24.1.2014 6
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
24.1.2014 7
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
24.1.2014 8
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
24.1.2014 9
Dispersion curves
http://www.waterworld.com/content/dam/WWI/Volume%2027/Issue%203/z1206WWIfl03.jpg
• Detection of defects
• Polytec commercial device
• Detection of impacts
24.1.2014 10
Practical use: Lamb waves
• Rayleigh
• Scholte
• Stoneley
24.1.2014 11
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
24.1.2014 12
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
24.1.2014 13
Guided waves in complex
structures: pipe
• Ph.D. thesis: K. L. J. Fong (2005)
24.1.2014 14
Example: Multiple roundtrips
24.1.2014 15
Guided waves in complex
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
24.1.2014 16
Circumferential order
• Lowe et al., Ultrasonics 1998
• Detection of notches in oil pipes
• L-modes
24.1.2014 17
Practical use: Tube waves
• Quasi-A0 modes at high frequencies
• Due to difference of curvature, energy concentrates
on the outer surface
• ”Curved Rayleigh modes”
24.1.2014 18
Guided waves in complex structures:
Whispering gallery mode
• Solid spheres: Rayleigh waves (naturally collimated)
• Tsukahara et al., APL 2000 & 2003
• Line source
24.1.2014 19
Guided waves in complex
structures: spheres
• Ultrasonic gas sensor
• Yamanaka et al., IEEE trans. Ult. 2006
24.1.2014 20
Practical use: waves on spheres
• Some differences
• High frequencies required to achieve meaningful fd
products
• Elasticities very high wave velocities very high
24.1.2014 21
Guided waves in nanoscale
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Nanoplates
(Plate-like structures with a thickness in the range of nm)
24.1.2014
Matemaattis-luonnontieteellinen tiedekunta /
Henkilön nimi / Esityksen nimi 22
• Nardi et al., Proc. SPIE 8681, 2013
• Generate SAWs (Rayleigh waves) on thin film-substrate
structures
• Measure mechanical properties of the thin films
24.1.2014 23
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
24.1.2014 24
Nanometrology by surface
acoustic waves (SAWs)
• 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
24.1.2014 25
Nanometrology by surface
acoustic waves (SAWs)
• Probe pulse
• Extreme ultraviolet (30 nm wavelength)
• Diffracts from the nanograting
‒ displacement from the diffraction pattern
24.1.2014 26
Nanometrology by surface
acoustic waves (SAWs)
• 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
24.1.2014 27
Nanometrology by surface
acoustic waves (SAWs)
• Results: both SAWs and longitudinal waves (LAW)
visible
24.1.2014 28
Nanometrology by surface
acoustic waves (SAWs)
• Results: SAW velocity approaches the Rayleigh
velocity of silicon when wavelength is increased
24.1.2014 29
Nanometrology by surface
acoustic waves (SAWs)
• Higher harmonics of the surface wave
24.1.2014 30
2nd order SAW?
• Results: Calculated isotropic Young’s moduli match
nanoindentation results quite well
• Both LAW and SAW velocities considered
24.1.2014 31
Nanometrology by surface
acoustic waves (SAWs)
• Hurley et al., Applied Physics Letters 2008
• 22 GHz surface waves
24.1.2014 32
Even higher frequency SAW’s
• Siemens et al., Applied Physics Letters 2009
• 50 GHz surface waves
‒ 125 nm wavelength
24.1.2014 33
Even higher frequency SAW’s
• Nardi et al., Applied Physics Letters 2012
• 100 GHz surface waves (theoretical)
‒ 63 nm wavelength
24.1.2014 34
Even higher frequency SAW’s
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Tubular structures on the
nanoscale
Rod/tube like structures with a nanometer radius
24.1.2014
Matemaattis-luonnontieteellinen tiedekunta /
Henkilön nimi / Esityksen nimi 35
• Carbon nanotubes
• Nanowires (aspect ratio > 20)
• E.g. Gold
• Nanorods (aspect ratio ~5)
• E.g. ZnO
24.1.2014 36
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)
24.1.2014 39
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
24.1.2014 40
Sound propagation in MWCNTs
• Mante et al., Nano Letters 2013 (February)
• AlN/GaN nanowire superlattices
• Coherent guided acoustic phonons (CGAPs)
24.1.2014 41
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
Sound propagation in nanowires
• 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
24.1.2014 43
Info: Sound propagation in
periodic structures
• This unit cell in case of water can be plotted in a
momentum space unit cell (|kL| ≤ π)
24.1.2014 44
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!
24.1.2014 45
Info: Brillouin zone
• Two modes detected (at 25 GHz and 60 GHz)
• Negative dispersion @ 60 GHz
• Times of arrival match the expected ones
24.1.2014 46
Sound propagation in nanowires
• 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!
24.1.2014 47
Sound propagation in silica
microwires
• Absorbed and emitted phonons have different
energy
• For example, Santori et al., Nature Photonics 2012
24.1.2014 48
Stokes scattering
• Measurement of the SAWs with Brillouing scattering
• Stimulated Brillouin scattering (phonons from the light)
• The surface wave visible!
24.1.2014 49
Sound propagation in silica
microwires
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Take-home
24.1.2014
Matemaattis-luonnontieteellinen tiedekunta /
Henkilön nimi / Esityksen nimi 50
• 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