Introduction to Nanomechanics
(Spring 2012)
Martino Poggio
Preliminary Logistics and
Introduction
Course outline and expectations;
What is nanomechanics? Why study
nanomechanics?
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 solidstate 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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Website
http://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 meters
1 nm = 0.000000001 m
100,000 nm ≈ diameter of a human hair
1 nm ≈ diameter of 10 atoms
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Size scales
Visible light
0.4 DNA
- 0.8 mm
Matterhorn Basel 2.5 nm
1.0 km
RedThe
Hblood
atom
suncell
Proton
50 mm
pm 1.2
10
Average
Mm man
1.75
fm
1.4 Gm 1.75 m
Lecce
Dog flea
2 mm
BIG
small
109 m
106 m
103 m
100 m
10-3 m
10-6 m
10-9 m
10-12 m
10-15 m
Gm
Mm
km
m
mm
mm
nm
pm
fm
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(Macro)mechanics
Nanomechanics
109 m
106 m
103 m
100 m
10-3 m
10-6 m
10-9 m
10-12 m
10-15 m
Gm
Mm
km
m
mm
mm
nm
pm
fm
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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 bodies
smaller
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Brownian motion
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
Particle mass
Boltzmann constant
1
3
2
m v  k BT
2
2
Mean square velocity
Temperature
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Brownian motion
Mean square displacement
(a measure of the size of the fluctuations)
r
2
 k BT 
t
 
  a 
Viscosity of medium
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Elapsed time
Particle radius
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Cantilever
F
x
F  kx
Spring constant
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k
Introduction to Nanomechanics
wt
l
3
3
16
Cantilever
F
k BT
x 
F  kxk
x
2
3
1 2 2
1 l
xk x kBT k B3T
2
2 wt
Mean square displacement
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1st mode
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(Macro)mechanics
L=2m
w = 100 mm
t = 50 mm
ESS = 200 GPa
k
xth = 0.2 pm
Ewt 3
for T = 300 K
4L3
k = 78 kN/m
xth 
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x
2

kB
T
k
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Nanomechanics
L = 120 mm
w = 3 mm
t = 100 nm
ESi = 169 GPa
k
xth = 8 nm
Ewt 3
for T = 300 K
4L3
k = 73 mN/m
xth 
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x
2

kB
T
k
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Quantum fluctuations
Zero point fluctuations
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xZPF 

2mmk

x ZPF 
l
Mass
wt
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Planck constant
Resonant frequency
2
21
(Macro)mechanics
l=2m
w = 100 mm
t = 50 mm
ESS = 200 Gpa
r = 7.85 g/cm3
k
xZPF = 0.2 am
xZPF = 0.2 x 10-18 m
Ewt 3
4l 3
k = 78 kN/m
m
rlwt
4
xZPF 

2 mk
m = 20 kg
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Nanomechanics
L = 120 mm
w = 3 mm
t = 100 nm
ESi = 169 Gpa
r = 2.3 g/cm3
k
xZPF = 0.2 pm
xZPF = 0.2 x 10-12 m
Ewt 3
4l 3
k = 73 mN/m
m
rlwt
4
xZPF 

2 mk
m = 20 pg
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Carbon nanotube
m = 10-21 kg
 = 2 x 500 MHz
xZPF = 4 pm
xZPF = 4 x 10-12 m
xZPF 
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
2 mk
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Quantum fluctuations of a drum
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)
Si (111) (AFM)
Giessibl, 2000
DNA (AFM)
10 nm
Magnetic Bits (MFM)
Hamon, 2007
500 nm
Folks, 2000
10 mm
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Scanning tunneling microscopy (STM)
Eigler, 1993
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Quantum effects
Quantum of Thermal Conductance
Schwab et al., 2000
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Casimir Force Measurement
Decca, 2003
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Weighing a single atom
Zettl, 2008
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Measuring a single electron spin
Rugar, 2004
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Nano-magnetic resonance imaging
(nanoMRI)
Degen, 2009
50 nm
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Cantilever Basics (statics)
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