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?

Introduction to Nanomechanics 3

People

• Course Leader/Lectures: – Martino Poggio

• Teaching Assistants/Exercise Sessions: – Michele Montinaro– Fei Xue– Gunter Wüst– Jonathan Prechtel

21.02.2012


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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6

Websitehttp://poggiolab.unibas.ch/NanoMechSpring2012.htm

• Overview• Format and Requirements• Schedule

– Lecture content– Exercise session

• Documents (PDF)– Optional reading

• Documents (PDF)

Introduction to Nanomechanics21.02.2012


http://poggiolab.unibas.ch/NanoMechSpring2012.htm

21.02.2012

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

9Introduction to Nanomechanics21.02.2012

Red blood cell10 mm

DNA2.5 nmH atom50 pm

Visible light0.4 - 0.8 mm

Proton1.75 fm

Matterhorn1.0 km

Size scales

21.02.2012 Introduction to Nanomechanics 10

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

11

mmm fm103 m109 m 10-15 m106 m

pm10-12 m

nm10-9 m

Mm kmGm mm10-6 m10-3 m100 m


Nanomechanics

12

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


Brownian motion

13

Fat droplets suspended in milk through a 40x objective. The droplets are 0.5 - 3.0 mm in size.


Thermal energy

14

Tkvm B23

21 2

Particle mass

Boltzmann constant

TemperatureMean square velocity


Brownian motion

15

taTk

r B

2

Viscosity of medium

Mean square displacement(a measure of the size of the fluctuations)

Particle radius

Elapsed time


Cantilever

16

x

F

Spring constant

3

3

lwtk

kxF


Cantilever

17

x

F

kxF

Tkxk B21

21 2

Mean square displacement

kTk

x B2

3

32

wtlTkx B


1st mode


(Macro)mechanics

19

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


L = 120 mmw = 3 mmt = 100 nmESi = 169 GPa

Nanomechanics

20

3

3

4L

Ewtk

k = 73 mN/m

xth = 8 nm

for T = 300 K

Tkk

xx Bth 2


Quantum fluctuations

21

mxZPF 2

Zero point fluctuations

Planck constant

Resonant frequencyMass

mkxZPF

2

2wtlxZPF


(Macro)mechanics

22

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


L = 120 mmw = 3 mmt = 100 nmESi = 169 Gpar = 2.3 g/cm3

Nanomechanics

23

3

3

4lEwtk

k = 73 mN/m

m = 20 pgmk

xZPF2

xZPF = 0.2 pmxZPF = 0.2 x 10-12 m

4lwtm r


Carbon nanotube

24

m = 10-21 kg = 2 x 500 MHz

xZPF = 4 pmxZPF = 4 x 10-12 m

mkxZPF

2


Quantum fluctuations of a drum

25

Lehnert, 2011


26

Why study nanomechanics?

• Link between classical mechanics and statistical mechanics

• Link between classical mechanics and quantum mechanics

• Smaller sensors are more sensitive


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


Atomic force microscopy (AFM)

28

10 nm

Giessibl, 2000

Si (111) (AFM)

Folks, 2000

Magnetic Bits (MFM)

10 mm

DNA (AFM)

Hamon, 2007500 nm


29

Scanning tunneling microscopy (STM)

Eigler, 1993


Quantum effects

30

Schwab et al., 2000 Decca, 2003

Quantum of Thermal Conductance Casimir Force Measurement


Weighing a single atom

31

Zettl, 2008

Measuring a single electron spin

32

Rugar, 2004


33

Nano-magnetic resonance imaging (nanoMRI)

50 nm

Degen, 2009


34

Cantilever Basics (statics)


introduction to nanomechanics (spring 2012)

Documents

mode18 introduction

thermal physics

study nanomechanics

solidstate physics

nanomechanics different

applied physics letters

thermal fluctuations

m106 mpm10