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

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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

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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

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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

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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

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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)

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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

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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

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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)

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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

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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)

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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

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