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Liquid Metal SurfacesP. S. Pershan
SEAS & Dept of Physics, Harvard Univ., Cambridge, MA, USA
• Colleagues
Pershan/ESRF
Balagurusamy, V. S. K.Berman, E. Deutsch, M. DiMasi, E. Fukuto, M. Gebhardt , J. Gog, T. Graber, T. Grigoriev, A.
Huber, P. Kawamoto, E. H. Kuzmenko, I. Lin, B. H. Magnussen, O. M. Mechler, S.Meron, M. Ocko, B. M. Pontoni, D.
Regan, M. J. Sellner, S.Shpyrko, O. G. Steimer, C. Stoltz, S.Streitel, R. Tostmann, H. Yahel, E
Harvard, Non-Harvard, Beam Line
Reflectivity
Pershan/ESRF
1st Synchrotron Studies: Liquid Crystal Surfaces
Reflectivity
Normalized
Liquid Crystal: Isotropic/Nematic/Smectic-A Surface Induced
Smectic
z
Idea! Als-Nielsen, Christensen, Pershan,(1982)
Tilt Monochromator to Steer beam downward by Horizontal liquid surface.
Kinematics & Reflectivity: Flat Surface
Pershan/ESRF
RF Qz( ) ≈ Qc 2Qz( )4
Fresnel
Reflectivity
Temperature Dependence of Liq. Xtal Surface.
ΔQxySlit
rki = 2π λ( ) xcos −zsin[ ]
ΔQxySlit = k2 sin β ΔβΔθ
Resolution:
Reflectivity:Flat Surface
=β & 2θ = 0rQxy = 0
dσrQ( )
dQxy2 =
dσrQ( )
dQxy2
F
ΦrQ( )
2δ 2
rQxy( )
Fresnel
Reflectivity ⇒ d2
rQxyδ
2 (rQxy) =1AQxy
Slit
Qxy=0∫Not True for Liquids
Electron Density(Liq. Xtal)
Φ Qz( ) ≈1
ρ∞
dz∫∂ < ρ z( ) >
∂ze−iQzz
Structure Factor
z
x
No Layering for Water and Simple Liquids
Pershan/ESRF
A. Braslau et al. PRL (1985).
Molecular SimulationsChapela et al. (1977)
Hard WallLayerFree Surface ✕ Layers
RF Qz( )
Surface Roughness
u
al
δu<l Surface Defines a Layerδu≥a Surface Does Not
Define a
Layer
Liquid Crystal Simple Liquid
Free Surface of Liquid Metal: Hard Wall
Pershan/ESRF
Metallic Liquids (D’Evelyn & Rice ‘83)
Suppression of Local Fluctuations Local Hard Wall.
Layers
Vapor: Neutral AtomsLiquid:
Positive Ions in Sea of Negative Fermi Liquid
Interface
Hg
In
GaHg. Magnussen et al. (1995).Ga Regan et al.(1995).
Goal: Measure Electron/Atom Density Profile!
Capillary Waves & Thermal Roughness
Pershan/ESRF
Rough Phase Shift
δϕ r
rxy( ) = Qzδurrxy( )
d 2σrQ( )
dQxy2
~dσ
rQ( )
dQxy2
F
ΦrQ( )
2d2rrxye
irQxy •rxye
iQz u(rrxy)−u(0)⎡⎣
⎤⎦∫
d 2rQxy
d 2σrQ( )
dQxy2AQxy
Slit
Qxy=0
∫ ~dσ
rQ( )
dQxy2
F
ΦrQ( )
2CW η,ΔQxy
Slit( )
d 2 r
rxyei
rQz •rxy∫ ~δ 2
rQxy( )
Flat surface:(Qz <<1)
d 2r
Qxy
d 2σrQ( )
dQxy2AQxy
Slit
Qxy=0∫ ~dσ
rQ( )
dQxy2
F
ΦrQ( )
2Signal
u
rrxy( )−u 0( )⎡⎣ ⎤⎦
2~
kBT2πγ
ln(rxyQxymax)2D Liquid Surface Sinha et al.’88
d 2 r
rxyei
rQxy •rxy e
iQz u(rrxy )−u(0)⎡
⎣⎢⎤⎦⎥∫ ~
ηQxy
2−η⎛
⎝⎜⎞
⎠⎟η =
kBT
2πγQz
2
AQxySlit =k2 sinβΔβΔθ
Capillary Effects: H20 & Ga
Pershan/ESRF
log R Qz( ) RF Qz( )⎡⎣ ⎤⎦≈Log exp −Qz2σ cap
2( )⎡⎣ ⎤⎦
σcap2 ≈
kBT2πγ
Qz2 ln Qmax ΔQxy
Slit( ) Slits
5.0 mm2.0 mm0.8 mm
Water (Schwartz ’90):
(Qz) for Liquid Ga (Regan, ’96)
ρEff z,T( ) / ρ ∞
ρ z( ) / ρ ∞
R Qz( ) RF Qz( ) =Φ Qz( )2CW η,ΔQxy
Slit( )
η =kBT
2πγQz
2
R Qz( ) RF Qz( )CW(η,ΔQxySlit) ≈Φ Qz( )
2
η ~ (0.5 to0.9)
Diffuse Scattering Surface Tension(γ)
Pershan/ESRF
d 2σrQ( )
dQxy2
~dσ
rQ( )
dQxy2
F
ΦrQ( )
2 1
Qxy
2−ηη =kBT
2πγQz
2
rQxy > ΔQxy
Compare Ga/In
Hg
In
Ga
Diffuse Scattering for In ≠
Compare (z) In Ga
Solid LineNo Adjustable Parameters
Simplest Surface Structure Model
Pershan/ESRF
ρ z( )
ρ ∞( )=
d
σ n 2πexp − z + nd( )
2/ 2σ n
2( )⎡⎣
⎤⎦
n=0
∞
∑
σ n2 = σ 0
2 + nσ 2
DCM (Magnussen ’95)
Φ Qz( ) =1
ρ ∞( )dz
−∞
+∞
∫∂ ρ z( )
∂zexp −iQzz[ ]
= Qzd exp iQzdj⎡⎣ ⎤⎦exp −σ n2Qz
2 / 2⎡⎣ ⎤⎦n=0
∞
∑
= Qzdexp −σ 0
2Qz2 / 2⎡⎣ ⎤⎦
1− exp iQzd⎡⎣ ⎤⎦exp −σ 2Qz2⎡⎣ ⎤⎦
Elemental Liquid Metals Studied
Pershan/ESRF
K Ga In Sn Bi Hg
DCM DCM DCM +1 +1 ?
☐ ☐
No Bump/Bump
Measureable Difference in 1st
Layer
•Why are 1st Layers for Bi and Sn different from K, Ga and In?•Why is Hg different from all others?
R Qz( )RF Qz( )CW η,ΔQxy
Slit( )= Φ
rQ( )
2
Eutectic Alloys
Pershan/ESRF
J. W. Gibbs ~1920Surface Adsorption: A/B AlloyIf Surface Tension: A > B Surface is Rich in “B”.
AxB1-x γA)/γB) ΔH*
(mixing)Concentration of Surface Layers
1st 2nd 34d
GaxBi1-x 718/378=1.90 +4 Liquid-Liquid Phase Sep.
Ga83.5In16.5 718/556=1.29 +5 97%In
In78Bi22 556/378=1.47 -1 35%Bi
Sn57Bi43 560/378=1.48 +1 96%Bi 25%Bi 53%Bi
Au71Sn29 1100/560=1.96 -10 96%Sn <1%Sn 24%Sn
Au72Ge28 1100/621=1.77 -21 No Gibbs Absorption
Au82Si18 1100/865=1.27 -30 4-layers, 2DXtal (AuSi2)
Pd81Ge19 1500/621=2.4-44
~40 Å wetting layer (No Measureable Gibbs Absorption)
*(kJ/mol)Takeuchi and Inoue, Mater. Trans. 46 (2005)
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 12
Gibbs Surface Adsorption(BiSn)
Bi=378, Sn=560,
Alloy: Bi and Sn
γ(Bi)≈ 398γ(Sn)≈567 dyne/cm
Energy Dispersion: f(E)
Adsorption
Scat. Ampl.
R/RF
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 13
Surface Freezing Au82Si18Eutectic
2D Surface Crystals:
Grazing Incidence Diffraction
1st OrderTransition
R/RF × 20 DCM
DCM
There is no theoretical
explanation!
AuGe Eutectic(Should be Similar to Au-Si)
Pershan/ESRF
γ(Au)/γSi or Ge) ΔH
Au72Ge28 1100/621=1.77 -21
Au82Si18 1100/865=1.27 -30Au-Si Au-Ge
f`(E) @AuL3-Edge
11.0
5 ke
v
11.9
15 k
ev
1. Bumphigher density in 1st layer.
2. No Energy effect Ge in 1st layer ≤40atm%.
•Small Gibbs (Different from Au-Sn, etc)!•No Enhanced Layering or 2D order(Different from Au-Si)!
Au-Si
×0.82
AuSiGe-Ternary Eutectic
Pershan/ESRF
Au Si
Ge
EutecticLine
Surface Frozen Ge≤6.5 atm%
What is the physics of the cross over from Si type to Ge type surface between 2.5 atm% and 6.5 atm%?
18atm%Si
Time average 0.8atm%Ge
0% Si
Pd81Ge19(Dec.’08)
Pershan/ESRF
Au82Si18 Pd81Ge19
Glass former
yes better
H -30 -44
Expected same 2D surface order for Pd81Ge19 as Au82Si18! Not found; however, something new! Metallic Clusters (Giant Unit Cells)
Small angle oscillations! Ref: Urban &Feuerbacher, J.Non-Crys.Sol.(04)
Quenched Icosahedral Clusters
Others: NaCd2 30Å YbCu4.5 44-49Å Al3Mg2 28Å
14nm
Mg32(Al,Zn)49
Preliminary fit.
~4%
ρρ ∞
Summary• Metal/Vapor InterfaceAtomic Layering:
• Surface Structure Factor - Φ(Qz): Measurement affected by thermal roughness. Requires knowledge of surface tension.
• Surface tension: measured with diffuse scattering:
• Surface tension effect demonstrated for Ga/In
• Subtle differences in elemental surfaces (Ga, In, K vs. Sn, Bi vs Hg)
• Alloys: Surface tension vs. Enthalpy of MixingGibbs absorption is not simple. No reliable theory.
• Au82Si18 anomalously strong layering and 2D order.Why are Au82Si18, Au72Ge28 and Pd81Ge19 all different?
• Need for THEORY!
• New Result (Preliminary): Surfaces & Icosahedral Metallic Clusters
Pershan/ESRF