Introduction to Nanomechanics (Spring 2012)
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Transcript of Introduction to Nanomechanics (Spring 2012)
Introduction to Nanomechanics(Spring 2012)
Martino Poggio
Preliminary Logistics and Introduction
Course outline and expectations; What is nanomechanics? Why study
nanomechanics?
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People
• Course Leader/Lectures: – Martino Poggio
• Teaching Assistants/Exercise Sessions: – Michele Montinaro– Fei Xue– Gunter Wüst– Jonathan Prechtel
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Format and requirements
• Language: English• Prerequisites: Physics III; course-work in solid- state
physics and statistical mechanics• Lectures: 10-12 on Tues. (21.02-29.05.2012)• Exercise Sessions: 13-14 on Wed.• Assignments: exercises and reading of current papers• Final paper: 4-5 page report on significant
experimental paper due on 29.06.2012• Grading: Pass/fail
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Literature
• Foundations of Nanomechanics, A. N. Cleland (Springer, 2003)
• Fundamentals of Statistical and Thermal Physics, F. Reif (McGraw-Hill, 1965)
• Original papers from Nature, Science, Physical Review Letters, Applied Physics Letters, Review of Scientific Instruments, Physics Today, etc.
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Websitehttp://poggiolab.unibas.ch/NanoMechSpring2012.htm
• Overview• Format and Requirements• Schedule
– Lecture content– Exercise session
• Documents (PDF)– Optional reading
• Documents (PDF)
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http://poggiolab.unibas.ch/NanoMechSpring2012.htm
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http://poggiolab.unibas.ch/NanoMechSpring2012.htm
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What is nanomechanics?
• Well… it’s the study of the mechanical properties of very very small things
• A nanometer is 10-9 meters1 nm = 0.000000001 m100,000 nm ≈ diameter of a human hair1 nm ≈ diameter of 10 atoms
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Red blood cell10 mm
DNA2.5 nmH atom50 pm
Visible light0.4 - 0.8 mm
Proton1.75 fm
Matterhorn1.0 km
Size scales
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mmm fm103 m109 m 10-15 m106 m
pm10-12 m
nm10-9 m
Mm kmGm mm10-6 m10-3 m100 m
BIG small
The sun
1.4 Gm1.2 Mm
Basel
Lecce
Average man1.75 m
Dog flea2 mm
(Macro)mechanics
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mmm fm103 m109 m 10-15 m106 m
pm10-12 m
nm10-9 m
Mm kmGm mm10-6 m10-3 m100 m
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Nanomechanics
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How is nanomechanics different than (macro)mechanics?
• Thermal fluctuations significantly affect the motion of small bodies
• Quantum mechanical fluctuations affect the motion of even smaller bodies
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Brownian motion
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Fat droplets suspended in milk through a 40x objective. The droplets are 0.5 - 3.0 mm in size.
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Thermal energy
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Tkvm B23
21 2
Particle mass
Boltzmann constant
TemperatureMean square velocity
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Brownian motion
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taTk
r B
2
Viscosity of medium
Mean square displacement(a measure of the size of the fluctuations)
Particle radius
Elapsed time
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Cantilever
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x
F
Spring constant
3
3
lwtk
kxF
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Cantilever
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x
F
kxF
Tkxk B21
21 2
Mean square displacement
kTk
x B2
3
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wtlTkx B
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1st mode
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(Macro)mechanics
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L = 2 mw = 100 mmt = 50 mmESS = 200 GPa
3
3
4L
Ewtk
k = 78 kN/m
xth = 0.2 pm
for T = 300 K
Tkk
xx Bth 2
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L = 120 mmw = 3 mmt = 100 nmESi = 169 GPa
Nanomechanics
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3
3
4L
Ewtk
k = 73 mN/m
xth = 8 nm
for T = 300 K
Tkk
xx Bth 2
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Quantum fluctuations
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mxZPF 2
Zero point fluctuations
Planck constant
Resonant frequencyMass
mkxZPF
2
2wtlxZPF
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(Macro)mechanics
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l = 2 mw = 100 mmt = 50 mmESS = 200 Gpar = 7.85 g/cm3
k = 78 kN/m
xZPF = 0.2 amxZPF = 0.2 x 10-18 m
4lwtm r
m = 20 kg
3
3
4lEwtk
mkxZPF
2
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L = 120 mmw = 3 mmt = 100 nmESi = 169 Gpar = 2.3 g/cm3
Nanomechanics
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3
3
4lEwtk
k = 73 mN/m
m = 20 pgmk
xZPF2
xZPF = 0.2 pmxZPF = 0.2 x 10-12 m
4lwtm r
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Carbon nanotube
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m = 10-21 kg = 2 x 500 MHz
xZPF = 4 pmxZPF = 4 x 10-12 m
mkxZPF
2
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Quantum fluctuations of a drum
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Lehnert, 2011
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Why study nanomechanics?
• Link between classical mechanics and statistical mechanics
• Link between classical mechanics and quantum mechanics
• Smaller sensors are more sensitive
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What is nanomechanics good for?
• Smaller sensors are more sensitive!
– Measurement of displacement– Measurement of mass– Measurement of force– Measurement of charge– Measurement of magnetic moment
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Atomic force microscopy (AFM)
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10 nm
Giessibl, 2000
Si (111) (AFM)
Folks, 2000
Magnetic Bits (MFM)
10 mm
DNA (AFM)
Hamon, 2007500 nm
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Scanning tunneling microscopy (STM)
Eigler, 1993
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Quantum effects
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Schwab et al., 2000 Decca, 2003
Quantum of Thermal Conductance Casimir Force Measurement
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Weighing a single atom
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Zettl, 2008
Measuring a single electron spin
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Rugar, 2004
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Nano-magnetic resonance imaging (nanoMRI)
50 nm
Degen, 2009
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Cantilever Basics (statics)
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