Transcript Diapositiva 1

Otto Stern (Sohrau 1888 – Berkeley 1969)
Nobel Laureate 1943
Otto Stern, O.R. Frisch, I. Estermann
(Hamburg, 1929-1933)
He
2
4.542
[Å] 

1
k[Å ]
Ei [meV]
k  ( K, k z ) k f  ki
K  G
G
2
(m, n)
a
a
NaCl(001)
“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)
I00
J. E. Lennard-Jones and A. F. Devonshire, Nature 137 (1936) 1069.
INELASTIC SCATTERING
Gas – Surface Interactions:
INELASTIC RESONANCES
- energy transfer
- sticking (adsorption)
Lattice vibrations (phonons)
J.M. Jackson and N.F. Mott, Proc. Roy. Soc. A 137 (1932) 703: Quantum DWBA
kf
d 2( 1 )

dE f dΩ f
kiz
v
2
F fi  uQv
 n(
V ( z)  Ao exp( z)
Qv
)  ( E f -Ei - Qv )   1  n(Qv ) ( E f -Ei  Qv ) 
pi  πkiz /β,
1/ 2
 sinh 2 p f sinh 2 pi 


F fi 
2
2

sinh p f  sinh pi 
4 p f pi

p 2f  pi2
p f  πk fz /β
e-W (Q,  i )
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
v
3Trel
v

v
5T0
v
 0.5%  Trel  25 mK
v
High-resolution diffraction
Supersonic He-atom beam sources
Time-of-flight spectroscopy
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
Phonon dispersion curves
Forces between atoms
Forces between ions and electrons
(electron-phonon interaction)
& electronic susceptibility
inelastic He atom scattering excites phonons
phonon excitations probe interatomic forces
Surface waves
Lord Rayleigh (1887)
Irpinia 1980 (Polo Sismico Alberto Gabriele,
FCCSEM Erice)
Surface phonons 1: from 3D lattice to slab
1
 2
1
 3
  0  lj
u(l )u( j )  lj
u(l )u( j )u(k )  ...
2
rl r j
6
rl r j rk
 2
 R l , j 
 rl  r j
 M l u (l, t )   j R (l, j)u ( j, t )
interatomic
potential
force constant
matrix
harmonic
eq. of motion
rl  r(l1 l2 l3,) = l1a1 + l2a2 + l3a3 + d()
rl  r(l1 l2 l3,) = l1a1 + l2a2 + d(l3,)
u (l , t )  u (l3 , Q ) exp[iQ  (l1a1  l2a2 )  iQv t]
3D
2D slab
Bloch waves
2
l3 ' ' R (l3 , l3 '  ' ; Q)u (l3 '  ' , Q )  M lQ
 u  (l3 '  ' , Q )
secular equation
…to a slab of
Nz layers
Surface phonons 2:
from one monolayer…
TOF spectrum
Energy-transfer spectrum
2 2
 E 
(ki  k 2f )  Q
2m
K  K i  K f  G  Q
K i  ki sin  i
K f  k f sin  f
scan curves for 90° geometry
 2ki2
 E 
2m
2



K
1  tan2 i 1 
 

Ki  




HAS versus theory
NaF(001)
LiF(001)
theory: Green Function
surface dynamics + DWBA
scattering theory
end of lecture 3
Metals:
Skin & Bones I
Cu(111)
HAS
Longitudinal
resonance
Rayleigh
wave
Anomalous longitudinal resonance
Cu(111) HAS data
C. Kaden et al. PRB (1992)
Cu(001)
a giant resonance
G. Benedek et al. PRB 1993
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
E  Eion  F[n(r)]   v ion (r)n(r)d 3r
v ion (r)  l v l (r  rl  u(l ))
nl r    C l Y r  rl 
C (l)  C0, (l)  c (l)
Equilibrium:
 E  c l   0
 Γ, l , 
E  Eo 
1
R l , l u l u l 

2 l ,l 


1




T
l
,
l


T





 l '  , l  u l c l  


l

,
l

2
1
  l ,l j H   ' l , l  '  c l c l  '  .
2

2 E
 2 Eion
 2 vl ( r - rl )
3
R (l , l ' ) 

  ll '  d r n( r )
u (l )u (l ' ) u (l )u (l ' )
r r
ion
 R
(l , l ' )  R0el, (l , l ' ) .
T  l , l    2 E  u l   c l 
1
3
d
r    E  n r  u l   Y r  rl 

V
  d 3r   v I r   u l   Y r  rl  ,

H ' l , l  '   2 E  c l   c ' l  '



1
3 3
2

d
r
d
r

E  nr  nr Y r  rl Y r  rl  '  ,

2
V
Adiabatic condition
c   H 1T u
Secular equation
2
ion
el
1 


M Q
u
Q
ν

(
R

R

TH
T ) uQν 

0
Dynamic electron density oscillations
 n( r )   d 3r ( r, r)l  vion ( r) /  rl  u(l )
Non-local dielectric response (susceptibility)
1
3
3

H 
' (l , l  ' )    d r d rY (r  rl )  (r, r)Y' (r  rl ' ' ).
Density-functional Hellmann-Feynman vs. Multipole expansion
occ
R (l , l ' )  2
el
vk
occ
 2 vion ( r )
 vk  vion ( r )
 vk
 vk  2
 vk  c.c.
u (l ) u (l ' )
vk u (l ) u (l ' )
k Kohn-Sham wavefunctions:
occ
  vk vk n(r)
vk
occ

vk
occ

vk
2
 2 vion ( r )

vion ( r )
 vk
 vk   d 3r n( r )
 R0el
u (l ) u (l ' )
u (l ) u (l ' )
 vk  vion ( r )
 n( r )  vion ( r )
 vk  c.c.   d 3r
u (l ) u (l ' )
u (l ) u (l ' )
  d 3r d 3r '
 vion ( r )
 v (r' )
 (r, r ' ) ion
u (l )
 u ( l ' )
  TH 1T 
parametrized ME method
Ion-core
displacements
ME
DFPT
Electron density
oscillations
Metals: Skin & Bones II
HAS  hole-electron pairs!
1D conductor
electron-hole excitations
Peierls instability
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).
The Cavendish He3 SpinEcho Apparatus
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
First tests for He3 Spin-Echo:
- Bound states of He3 on LiF(001)
- Surface Transport Measurements
using Quasi-elastic Helium Atom
Scattering (QHAS)
back to Frisch &
Stern!
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).
atom microscope
4He
gas jets
atom interferometry
cluster, droplets at 0.37 K
4He
liquid jets
nano-scale superfluididity
targets for high-energy physics
targets for laser accelerators (e.g., for hadrotherapy)
superfluid 4He (p-H2) clusters inside 3He droplets
jets from expansion of solid 4He: the geyser effect
Grenoble - 9
SUPERSONIC CLUSTER BEAM DEPOSITION
at the Department of Physics, University of Milano
SOURCE CHAMBER
DEPOSITION CHAMBER
quartz MB sample manipulator
TOF-MS
CHAMBER
He line
PMCS
cluster beam
substrate
time of flight
mass
spectrometer
to
pulsed
power
supply
target
2000 l/s diff.
pump
cluster
assembled film
700 l/s diff.
pump
500 l/s turbo
pump
something more on inelastic atom scattering:
Giorgio Benedek J. Peter Toennies
Helium Atom Scattering Spectroscopy
of Surface Phonons
Springer-Verlag
Berlin Heidelberg New York 2007
end of lecture 4