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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Introduction to Nanomechanics 4

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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Introduction to Nanomechanics 5

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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Introduction to Nanomechanics 8

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

14

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

16

x

F

Spring constant

3

3

lwtk

kxF

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Cantilever

17

x

F

kxF

Tkxk B21

21 2

Mean square displacement

kTk

x B2

3

32

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

25

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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