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 Introduction to Nanomechanics

Format and requirements Language: English Prerequisites: Physics III; course-work in solid- state physics and statistical mechanics Lectures: on Tues. ( ) Exercise Sessions: on Wed. Assignments: exercises and reading of current papers Final paper: 4-5 page report on significant experimental paper due on Grading: Pass/fail Introduction to Nanomechanics

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. Introduction to Nanomechanics

Website Overview Format and Requirements Schedule – Lecture content – Exercise session Documents (PDF) – Optional reading Documents (PDF) 6Introduction to Nanomechanics

Introduction to Nanomechanics7

Introduction to Nanomechanics8

What is nanomechanics? Well… it’s the study of the mechanical properties of very very small things A nanometer is meters 1 nm = m 100,000 nm ≈ diameter of a human hair 1 nm ≈ diameter of 10 atoms 9Introduction to Nanomechanics

Red blood cell 10  m DNA 2.5 nm H atom 50 pm Visible light  m Proton 1.75 fm Matterhorn 1.0 km Size scales Introduction to Nanomechanics10 mmmfm 10 3 m10 9 m m10 6 m pm m nm m MmkmkmGm mm m10 -3 m10 0 m BIG small The sun 1.4 Gm 1.2 Mm Basel Lecce Average man 1.75 m Dog flea 2 mm

(Macro)mechanics 11 mmmfm 10 3 m10 9 m m10 6 m pm m nm m MmkmkmGm mm m10 -3 m10 0 m Introduction to Nanomechanics Nanomechanics

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 12Introduction to Nanomechanics

Brownian motion 13 Fat droplets suspended in milk through a 40x objective. The droplets are  m in size. Introduction to Nanomechanics

Thermal energy 14 Particle mass Boltzmann constant Temperature Mean square velocity Introduction to Nanomechanics

Brownian motion 15 Viscosity of medium Mean square displacement (a measure of the size of the fluctuations) Particle radius Elapsed time Introduction to Nanomechanics

Cantilever 16 x F Spring constant Introduction to Nanomechanics

Cantilever 17 x F Mean square displacement Introduction to Nanomechanics

1 st mode 18Introduction to Nanomechanics

(Macro)mechanics 19 L = 2 m w = 100 mm t = 50 mm E SS = 200 GPa k = 78 k  m x th = 0.2 pm for T = 300 K Introduction to Nanomechanics

L = 120  m w = 3  m t = 100 nm E Si = 169 GPa Nanomechanics 20 k = 73  m x th = 8 nm for T = 300 K Introduction to Nanomechanics

Quantum fluctuations 21 Zero point fluctuations Planck constant Resonant frequency Mass Introduction to Nanomechanics

(Macro)mechanics 22 l = 2 m w = 100 mm t = 50 mm E SS = 200 Gpa  = 7.85 g/cm 3 k = 78 k  m x ZPF = 0.2 am x ZPF = 0.2 x m m = 20 kg Introduction to Nanomechanics

L = 120  m w = 3  m t = 100 nm E Si = 169 Gpa  = 2.3 g/cm 3 Nanomechanics 23 k = 73  m m = 20 pg x ZPF = 0.2 pm x ZPF = 0.2 x m Introduction to Nanomechanics

Carbon nanotube 24 m = kg  = 2  x 500 MHz x ZPF = 4 pm x ZPF = 4 x m Introduction to Nanomechanics

Quantum fluctuations of a drum 25 Lehnert, 2011 Introduction to Nanomechanics

Why study nanomechanics? Link between classical mechanics and statistical mechanics Link between classical mechanics and quantum mechanics Smaller sensors are more sensitive 26Introduction to Nanomechanics

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 27Introduction to Nanomechanics

Atomic force microscopy (AFM) nm Giessibl, 2000 Si (111) (AFM) Folks, 2000 Magnetic Bits (MFM) 10  m DNA (AFM) Hamon, nm Introduction to Nanomechanics

Scanning tunneling microscopy (STM) 29 Eigler, 1993 Introduction to Nanomechanics

Quantum effects 30 Schwab et al., 2000 Decca, 2003 Quantum of Thermal ConductanceCasimir Force Measurement Introduction to Nanomechanics

Weighing a single atom 31 Zettl, 2008

Measuring a single electron spin 32 Rugar, 2004 Introduction to Nanomechanics

33 Nano-magnetic resonance imaging (nanoMRI) 50 nm Degen, 2009 Introduction to Nanomechanics

Cantilever Basics (statics) 34Introduction to Nanomechanics