Otto Stern (Sohrau 1888 – Berkeley 1969) Nobel Laureate 1943

Otto Stern, O.R. Frisch, I. Estermann (Hamburg, 1929-1933)

He

NaCl(001)

[meV]

542.4

][Å

2[Å]

1iEk

),(2

GG K

),K(k

nma

kkk ifz

a

“These experiments are of interest not only because of

their confirmation of the predictions of quantum mechanics,

but also because they introduce the possibility of applying

atom diffraction to investigations of the atomic constitution

of surfaces.”

(T. M. Johnson, Phys. Rev. 37 (1931) 847).

Bound-state resonances

Frisch-Stern (1933)

J. E. Lennard-Jones and A. F. Devonshire, Nature 137 (1936) 1069.

I00

Gas – Surface Interactions:

- energy transfer

- sticking (adsorption)

INELASTIC SCATTERING

INELASTIC RESONANCES

)()(1)-()( QQQQ

212

vifvvifvQvfiiz

f

ff

)(

-EEn-EEnk

dΩdE

dvk

uF

Lattice vibrations (phonons)

)exp()( zAzV o

),(e4

2 sinh2sinh

sinhsinh

2/1

22

22

i-Wpp

pp

pp

pp

if

if

if

i

f

fi

QF

/βπkp/βπkp fzfizi ,

J.M. Jackson and N.F. Mott, Proc. Roy. Soc. A 137 (1932) 703: Quantum DWBA

L.D. Landau, Phys. Z. Sowjet. 8 (1935) 489.B.L. Bonch-Bruevich, Usp. Fiz. Nauka 40 (1950) 369

Classical

Rarified Gas Dynamics

Supersonic Molecular Beams

Supersonic nozzle beam sources

05

3

v

v

T

Trel

v

mK25%5.0v

v

relT

Supersonic He-atom beam sourcesTime-of-flight spectroscopy

High-resolution diffraction

J. P. Toennies: HUGO (MPI-SF, Goettingen)

Angular distributions

Diffraction

Inelastic processes: - inelastic bound state resonances

- kinematical focussing

- surfing

Time of Flight (TOF) Inelastic scattering

Phonons

via the mechanical action (Pauli repulsion) on the electron density

Forces between atoms

Forces between ions and electrons (electron-phonon interaction)

& electronic susceptibility

Phonon dispersion curves

phonon excitations probe interatomic forces

inelastic He atom scattering excites phonons

Surface waves

Lord Rayleigh (1887)

Irpinia 1980 (Polo Sismico Alberto Gabriele, FCCSEM Erice)

Surface phonons 1: from 3D lattice to slab

...)()()(6

1)()(

2

1 32

0

kjljl ljljkjljl

uuurrr

uurr

jlRrr jl

,2

),(),(),( tjujlRtluM jl

rl r(l1 l2 l3,) = l1a1 + l2a2 + l3a3 + d()

rl r(l1 l2 l3,) = l1a1 + l2a2 + d(l3,)

]aaQ[ Q ) Q21 tillilutlu v )(exp),(,( 213

),''(),''();'',( 32

333''3 QQQ Q luMlullR ll

interatomicpotential

force constant matrix

harmonic eq. of motion

3D

2D slab

Bloch waves

secular equation

Surface phonons 2: from one monolayer…

…to a slab of Nz layers

TOF spectrum

Energy-transfer spectrum

scan curves for 90° geometry

fffiii

fi

fi

kKkK

kkm

E

sinsin

)(2

222

QGKKK

Q

22

22

1tan12 i

ii

K

K

m

kE

HAS versus theory

theory: Green Function surface dynamics + DWBA

scattering theory

LiF(001)

NaF(001)

end of lecture 3

Rayleighwave

Longitudinalresonance

Metals:

Skin & Bones I

Cu(111)

HAS

Anomalous longitudinal resonance

Cu(111) HAS dataC. Kaden et al. PRB (1992)

G. Benedek et al. PRB 1993

Cu(001)a giant resonance

There is something fundamental in the anomalous longitudinal resonance

A feature common to all metal surfaces

A strong amplitude in HAS but weak in EELS

Unphysical fitting with force-constant models

The Multipole Expansion (ME) Method

rdnnFEE ionion 3)()()]([ rrr v

))(()( ll llion urrr vv

)()()( ,0 lclClC

,Γ,0 llcE

Equilibrium:

ll YlCn rrr

.'',2

1

,',2

1

,2

1

, '

,

,

jll

ll

llo

lclcllH

lclullTllT

lulullREE

,

1

,

3

3

2

lI

l

Ylurd

YlunErdV

lcluEllT

rrrv

rrr

,1

'',

'233

2

'2

'

ll YYnnErdrdV

lclcEllH

rrrrrr

.)',()',(

)r-r()r(

)'()()'()()',(

,0

23

'

22

llRllR

rrnrd

lulu

E

lulu

EllR

elion

llll

ion

v

Adiabatic condition uc TH 1

νTTHRRνM elion QuQu )( 10

2Q

Secular equation

Dynamic electron density oscillations

l lion lrdn )(ur/)r()r,r()r( 3 v

Non-local dielectric response (susceptibility)

).(),()( )',( '''331

' ll YYrdrdllH rrrrrr

Density-functional Hellmann-Feynman vs. Multipole expansion

..)'(

)r(

)(2

)'()(

)r(2)',(

kk

k

kk

2

k cclulululu

llRocc

vv

ionvocc

vv

ionv

el

vv

k Kohn-Sham wavefunctions: )(rkkk

nvv

occ

v

elionocc

vv

ionv R

lulunrd

lulu 0

23

kk

2

k )'()(

)r()r(

)'()(

)r(

vv

TTHlulu

dd

lulu

nrdcc

lulu

ionion

ionocc

vv

ionv

133

3

kk

k

)'(

)'r()'r,r(

)(

)r('rr

)'(

)r(

)(

)r(..

)'(

)r(

)(

vv

vv

parametrized ME method

Ion-coredisplacements

Electron density oscillations

ME

DFPT

Metals: Skin & Bones II

1D conductor

Peierls instability

electron-hole excitations

HAS hole-electron pairs!

The Helium-3 Spin-Echo Spectroscopy

P. Fouquet, A.P. Jardine, S. Dworski, G. Alexandrowicz, W. Allison and J. Ellis

"Thermal energy 3He spin-echo spectrometer for ultrahigh resolution surface dynamics measurements“

Rev. Sci. Inst. 76, 053109 (2005).

Parameter Value

Total scattering angle 44.4 degrees

3He Angular Resolution 0.1 degree

Nominal beam energy 8 meV

Measured beam intensity 1e14 atoms/second

Beam diameter at target 2 mm

Energy resolution (QE peak width) 20 neV

Scattering chamber base pressure 2e-10 mbar

Sample manipulator 6 axis, titanium

Sample manipulator resolution 0.003 degrees

Sample heating Radiation / E-beam

Sample cooling Liquid Nitrogen or Helium

Sample temperature range 55 K - >1200 K

The Cavendish He3 Spin-Echo Apparatus

First tests for He3 Spin-Echo:

- Bound states of He3 on LiF(001)

- Surface Transport Measurements using Quasi-elastic Helium Atom Scattering (QHAS)

A.P. Jardine, S. Dworski, P. Fouquet, G. Alexandrowicz, G.Y.H. Lee, D.J. Riley, J. Ellis, W. Allison, "Ultrahigh resolution spin-echo measurement of surface

potential energy landscapes", Science 304, 1790-1793 (2004).

back to Frisch & Stern!

4He liquid jets

cluster, droplets at 0.37 K

nano-scale superfluididity

targets for high-energy physics

targets for laser accelerators (e.g., for hadrotherapy)

4He gas jets

atom microscope

atom interferometry

superfluid 4He (p-H2) clusters inside 3He droplets

jets from expansion of solid 4He: the geyser effect

PMCS substratecluster beamtime of flight

mass spectrometer

quartz MB

2000 l/s diff. pump

500 l/s turbo pump

700 l/s diff. pump

He line

sample manipulator

target cluster assembled film

to pulsed power supply

SOURCE CHAMBERDEPOSITION CHAMBER TOF-MS

CHAMBER

SUPERSONIC CLUSTER BEAM DEPOSITION at the Department of Physics, University of Milano

Grenoble - 9 

Giorgio Benedek J. Peter Toennies Helium Atom Scattering Spectroscopy

of Surface Phonons

Springer-VerlagBerlin Heidelberg New York 2007

something more on inelastic atom scattering:

end of lecture 4

JPT

Bibi Bortolani