Non-Harvard Collaborators:

Ben Ocko, Elaine DiMasi, Olaf Magnussen Physics Dept. Brookhaven National Laboratory

Moshe Deutsch: Bar Ilan University, Israel

Binhua Lin, Mati Meron, Tim Graber, Jeff Gerbhardt, Advanced Photon Source

Harvard Students/Postdocs

Alexei Grigoriev, Patrick Huber, E.H. Kawamoto, Holger Tostmann,

Mike Regan, Oleg Shpyrko.

The Surface Structure of Liquid Metals and Alloys

Support: DE-FG02-88-ER45379/NSF- DMR-0124936

* Current associates are underlined

Oleg Shpyrko

Liquid Surfaces: Metals/Non-Metals Are Different

For Metals Particle-Particle Interactions Change Across The Surface

D'Evelyn & . Rice, J. Chem. Phys., 1983. 78: p. 5225.

This influences the structure of the surface!

Interactions are Same in Vapor and Liquid

Dielectric Liquids

Vapor: Neutral Atoms

Liquid: Positive Ions in Sea of Negative Fermi Liquid

Different Interactions

Metallic Liquids

Non-Metal Liquids

Predictions of Monte Carlo Calculations

Average Density <(z)> vs Distance From Surface(z)

Chapela & Saville, 1978

Hard Wall = > Layers

Free SurfaceNo-Layer

D'Evelyn & Rice, 1983

Metallic Liquids: Layers @Free Surface

Liquid/Vapor Surface Structure Factor (Qz)

X-ray Reflectivity: R(Qz) & (Qz)

Quantitative Measure of (Qz)!

€

(Qz ) ≡1

ρ Bulkdz

∂ ρ(z )

∂z eiQz •z

∫

Surface Structure Factor

α

D

Prediction: Constructive InterferenceQz=(4)sin α =(2/D)

R(Qz)~|(Qz)|2

QzSurface Normal Wave vector Transfer

Measured

Hg (1995)

Ga (1996)

In (1999)

Hg

In

Ga

Note Difference

Thermal Effects on Reflectivity

R(Qz) =

Ideal Flat Surface:

Fresnel

RF(Qz)

Structure Factor

(Qz)

Thermal Factor

Differential Cross Section:

dσdΩ

~ dxe−Qz

2 h(x)2−h(x)h(x')eiQx[x−x']∫

Thermal Roughness Phase Shifts

eiQz h(x)−h(x') ⎡

⎣ ⎢ ⎤ ⎦ ⎥ ≈e

−Qz2 h(x)2−h(x')h(x)

Qx

Parallel Surface Wave Vector Transfer

Liquid vs Solid SurfacesdσdΩ

~ dxe−Qz

2 h(x)2 −h(x)h(x')eiQx[x−x']∫

R(Qz ) ~ dQx dσdΩ

(Qx.Qz)Resol∫

Depends on

Resolution

Liquid

Liquid Surface

•2D SurfaceTension •Gravity(|x-x’|~mm)

dσdΩ

(Qx,Qz)

Solid

Independent of

Resolution

Resolution

Measure of Structure Factor Requires Thermal Effects be Removed

R(Qz) =

Ideal Flat Surface:

Fresnel

RF(Qz)

Structure Factor

(Qz)

Thermal Factor

(Qz,T)

R(Qz) dσdΩ

~ 1 Qx( )2−η

Large (T/Qz2

••• No specular peak if η~2!•••

η ~kBT

2πγQz

2

Surface Tension

R(Qz )

RF(Qz )×(Qz,T)⇒ (Qz)

2

To Understand Thermal EffectsDiffuse Scattering From Liquid Surface

Qx=(2)[cos α-cos ]

Qz=(2)[sin α+sin ]

Diffuse Scattering for Liquid Indium

Solid Lines: Theory Known Surface Tension is Only Adjustable

Parameter

Demonstration of Thermal Removed: Liquid Gallium

Electron Density: Ga and In

Average Electron Density Indium (with/without T effects).

1

bulk

∂ (z)∂z

=12

dQz (Qz)e−iQzz∫

Electron Density Profile

R(Qz )

RF(Qz )×(Qz,T)⇒ (Qz)

2R(Qz )

RF(Qz )⇒ (Qz)

2(Qz,T)

Issue 1 What other metals can be studied?

Element Tm (K) Tm/ P_melt(mm)Ga 302.93 718 0.42Hg 234.28 498 0.47 1.2E-06Sn 505.118 560 0.90In 429.32 556 0.77K 336.8 388 0.87 ~1.0E-6Zn 692.73 782 0.89 2.2E-01Al 933.52 914 1.02Cu 1356.6 1303 1.04 9.7E-04Cd 594.1 570 1.04 1.1E-01Bi 544.5 378 1.44Li (Chemistry) 453.69 398 1.14Au 1337.58 1169 1.14 1.6E-05Tl 576.7 464 1.24Pb 600.64 458 1.31

η (i.e. T/) must be small

P & T : low enough for UHV(Hg, K, Na are special)

Measurement of Potassium

Good: Oxides Dissolve in Bulk LiquidClean SurfaceBad: Low η at layering peak is large, R(Qz) too small

R(Qz )

RF(Qz )⇒ (Qz

2(Qz,T)R(Qz )

RF(Qz )×(Qz,T)⇒ (Qz

2

Ga

In

K

Maximum Qz~0.85QPeak

Data Layering in K is same as Ga, In.

ηD

ebye

-Wal

ler

X 1

0-2

R(Qz) R(Qz )

RF(Qz )×(Qz,T)⇒ (Qz)

2

Possible Model Spacing of 1st Layer Reduced~10%

Anomalous Layering of Liquid Sn Surface

BumpNot seen in

Ga,In

Bump Surface Density Is Higher Than Bulk!

GaK

H2O

R(Qz )

RF(Qz )×(Qz,T)⇒ (Qz)

2

Is there experimental evidence that dielectric liquids are not layered?

Water: dynes/cm K: 1 dynes/cm

R(Qz)

R(Qz)/RF(Qz)

Water does not show indication of surface layering!

If we can’t study other pure metals, what can we do?

•Alloys•Surface Chemistry of Liquid Metals (oxidation)

Surface: Heavier Bi rich liquid

Bulk: lighter Ga rich liquid!

GaBi:

Binary Phase

Diagram

Bi Ga

Thickness of heavier Bi rich layer.

Short Range Wetting

Keep Looking: i.e. Alloys for Electronics Example: AuSi Low Temperature Eutectic

AuSi Diffuse ScatteringAlloy is Liquid =780 dynes/cm

R(Qz )

RF(Qz )×(Qz,T)⇒ (Qz)

2

Summary

1- To Measure Liquid Surface Structure Factor |(Qz)|Effects of Capillary Waves.

2- |(Qz)| of Free Surface of Liquid Metals Exhibits Atomic Layering!

3- Water does Not! What about other non-metallic liquids.

4- Surfaces of Liquid Alloys: Interesting Physics Sn: Anomalous Surface GaBi: Short Range WettingAuSi: Enormously Intense

Future