The Structure Liquid Surfaces

P. S. Pershan

DEAS & Dept . Of Physics, Harvard Univ.

Cambridge, MA 02421

DMR-0124936; NSF 03-03916; DE-FG02-88-ER45379

O. Shpyrko, A. Grigoriev, R. Streitel, P. Pershan, B. Ocko, and M. Deutsch,” Surface Freezing and Quasi-2D Phase Transitions in Binary Metal Liquids,” (March APS 2005)

O. G. Shpyrko, A. Y. Grigoriev, R. Streitel, D. Pontoni, P. S. Pershan, M. Deutsch, B. M. Ocko, B. Lin, M Meron, T. Graber, J. Gebhardt, "Atomic-scale surface demixing in a eutectic liquid BiSn alloy.Phys. Rev.Lett. "Submitted (2005).

Other Principal Collaborators: J. Als-Nielsen, E. DiMasi, E. Kawamoto, O. Gang, P. Huber, O. Magnussen, K. Penanen, M. Regan, ,M.Schlossman, D.Schwartz, H. Tostmann,

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Condensed Matter: 20th CenturySolids:

•Bulk (3d) Structure Band Gaps, exotic Fermi

Surfaces, etc•Surfaces (2d) Localized Electron States, physisorption, metal/semiconductor interface (rectification), etc.

Liquids: Absence of Structure Less Phenomena•Bulk (3d): Liquid Structure Factor•Surfaces (2d): Surface tension, Langmuir monolayers, wetting. Ancient History of Liquid Surfaces:Pliny the Elder (~50 AD) & Ben Franklin Surfactants (oil) calm water surface waves

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Footprint of whale (biomaterial on surface of sea). http://web.mit.edu/1.63/www/ (Chiang C, Mei and T. R Akylas

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Modern Era of Surface ScienceRef: A. Zangwill, Physics at Surfaces (Cambridge University Press,1988)

True emergence of solid state surface physics: Electron Spectroscopy (Brundle, 1974) & Auger Spectroscopy (Harris, 1974) followed by STM, AFM, etc •••• Synchrotron: SSRL(1973), NSLS (1984), APS (1998) ••••

X-rays & Surfaces (Solid): •Reflectivity (Parratt ’54) •Grazing Incidence Diffraction(GID) (Marra, Eisenberger, Cho ’79) New tool: probe buried interfaces and structure far below the surface (i.e. GaAs-Al interface)

Liquid Surfaces: Reflectivity: Als-Nielsen and Pershan ‘82 (Liquid Crystal)&’85 (Water):GID: Dutta ‘84 (Langmuir monolayer on water).

THIS TALK: X-RAY AND LIQUID SURFACES

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X-Rays and Solid Surfaces

kiks

αi

αs

2θ

RF (Qz ) =Qz− Qz

2 −Qc2

Qz + Qz2 −Qc

2

2

→Qc2Qz

⎛

⎝⎜⎞

⎠⎟

4

Qc2 ~ "electrondensity"

Qx

Qy

Qz

Truncation Rods from Crystal Surface

Bragg Scattering From Crystal

αi = α s & θ = 0

orrQxy = 0

Fresnel Reflectivity from Flat Surface A. H. Compton and S. K. Allison ‘35:

Surface Information: Intensity along truncation rodsExtra Peaks due to Surface Phases

(reconstruction)

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Liquid vs Solid Surfaces

Qx

Qy

Qz

Langmuir MonlayerSurface Freezing

etc

Liquids: Bulk Liquid Diffuse Scattering

dσdΩ

≈dσodΩ

⎛⎝⎜

⎞⎠⎟

Φn,m(Qz)2δ(

rQxy−

rQm,n)

n,m∑3d Crystal

dσdΩ

≈dσodΩ

⎛⎝⎜

⎞⎠⎟Φ0,0 (Qz)

2 δ(rQxy)

If Liquid Surface was FLAT Specular would be the Only Truncation Rod

Surfaces ARE NOT FLAT!

Liquid Surface Information:Surface Structure Factor Φ(Qz)Extra peaks due to Langmuir monolayer or

Surface Frozen phases.

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Surface Roughness

dσdΩ

~ d2rrxy exp −

Qz2

2h(

rrxy)−h(0)⎡⎣ ⎤⎦

2⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫ exp irQxy •

rrxy⎡⎣ ⎤⎦

For a solid:

exp[-Qz2<h(0)2>

rxy

exp[-Qz2<h(0)2-h(rxy)h(0)>]

Fourier Transform

δ (rQxy ) Φ(Qz )

2exp −Qz

2 h(0)2⎡⎣ ⎤⎦Reflectivity Structure Factor + Debye -Waller

h(r)h(0)

Δφ=Qz[h(r)-h(0)]

αi

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dσdΩ

~  d2

rrxy

rxyη

⎡

⎣⎢⎢

⎤

⎦⎥⎥∫ exp i

rQxy •

rrxy⎡⎣ ⎤⎦

~1

Qxy2−ηδ (Qxy )

Fluctuations of Surface of Bulk Liquid

Energy

Area=12

gρmass +γqxy2

{ }h(r)2

h(r)2π/qxy

h(0)2 −h(rxy)h(0) ~kBT2πγ

qxydqxy1

qxy2 1−J 0 (rxyqxy)⎡⎣ ⎤⎦0

qmax∫ ≈kBT2πγ

ln rxyqmax⎡⎣ ⎤⎦

qmax~1/Atomqgravity ≈ gρmass γ ~1 / mm

exp −Qz2 h(0)2 −h(rxy)h(0)⎡

⎣⎤⎦~1 rxy

η η =kBT

2πγQz

2

Not δ(Qxy)

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Effect of Resolution

αs

αi

(2π/λ)Δα s

ΔQxyScan Detector αs

Solid Liquid

Intensity vs Qxy

Qxy Qxy

Increasing Qz or

η ~ Qz2

Liquid: Large αi  ~Capillary Effects Dominate

Solid: Effect of Resolution on R(Qz) is Minor

Liquid: Small αi  ~Nearly Solid Like

Solid Liquid

Intensity vs Qxy

Qxy Qxy

ΔQxy

dσdΩ

~1

Qxy2−η

Small angles liquids are like solids / large angles they are not!

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Simulated Detector Scan

The Liquid Surface Reflectometer

HasyLab: Als-Nielsen, Christensen, Pershan, PRL (`82).

NSLS: X22B, X19C

APS: CHEMMATCARS, CMC, CAT

ESRF: ID15A (Alternate Design) H. Reichert ‘03

Δαs

w

h

h sin(α s)Δα s

Qx

Qy

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Data for Water with increasing α

R(qz )

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are needed to see this picture.

Qy(1/Å)

Qz (or αi Increasing

0.3 Å-1 to 1 Å-1

η  Increasing0.08 to ~ 1

Shpyrko, Fukuto, Pershan, Ocko, Gog, I. Kuzmenko, Deutsch,,Phys. Rev. B (2004).

CMC CAT

Peak vanishes for slight increase in Qz

dσ dΩ~Qxy2−η

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Surface Induced Layering: Φ(Qz)

Nematic Surface Smectic-A Order

S(rQ) ~

1

1+ξ⊥2Q⊥

2 +ξ//2 Qz−Q0( )

2

z

ξ//(T ) ≈ ξo T − TNA TNA( )−0.71±0.04

Ψ(z) ~ Ψ 0 sin Q0z( )exp−z

ξ //(T )

⎡

⎣⎢

⎤

⎦⎥

Surface Induced SmecticIsotropic/Nematic/Smectic-A

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Nematic Phase: 1st Observed Surface Induced Layering

First Data (Pershan, Als-Nielsen.PRL, ‘84)

RF(Qz)

T-TNA

0.05 C2.811.6

1/WidthSurface vs.Bulk

ξ//(T ) ≈ ξo T − TNA TNA( )−0.71±0.04

ρ(

rr ) = Bs exp −iQ0z − z ξ⎡⎣ ⎤⎦

|Φ(Qz)|2

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Reflectivity & Surface Structure Factor (Layers)

Structure Factor

Φ(Qz)|2Thermal Factor

R(Qz) =

RF(Qz)

Simple Surfac

e

€ 

Φ(Qz ) ≡1

ρ Bulkdz

∂ ρ(z )

∂z eiQz •z

∫

Surface Structure Factor

α

D

•When do surface layers appear?

•Quantitative Measure of Φ(Qz)!

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

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Density Profile vs DepthSolid-liquid interface

Hard wall

Molecular SimulationsG. A. Chapela, G. Saville, S. M. Thompson, and J. S. Rowlinson, "Computer simulation of a gas-liquid interace",J. C. S. Faraday Trans II 73, 1133 (1977).

Lennard-Jones (12,6) molecules

Accepted Lore: Density Profile at Free Surface is Monotonic

Liquid Crystals are Different:• Why?• What else is different?

Liquid vapor

interface

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Simple Thoughts on Surface Layering

Order Parameter ρ(r): Electron, Mass, or Particle Density

ρ(r)ρ(0) ~ ρ02 exp[−iQ0r − r ξ ]Bulk (3d)Correlation Function:

Characteristic Wavevector: Q0 & Correlation Length: ξ

Bulk Susceptibility: Zsurf(Q0ξ)

ρ(

rr ) = Bs exp −iQ0z − z ξ⎡⎣ ⎤⎦

Bs =Zsurfh(z=0)Surface Induced Layering:

Surface Field: h(z=0)

<h2>1/2

D

<h2>1/2

D

h2 1/2

D

u

Translation Energyvs

Entropy

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In Plane Surface Order

Langmuir Monolayeron H2O or Hg

2D Liquid 2D Crystal

Surface Freezing2D Surface Crystal

SubSurface3D Liquid

Long Chain AlkanesMetallic Alloys

Solid/Liquid Interface•Commensurate/Incommensurate 2d•Layering

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Digest of Liquid Surface Order

Layering In-Plane Surface Order

Nematic/Isotropic Liquid Xtal

Yes No

Microemulsions Yes NoLong Chain Alkanes,

Alcohols, etcNo Yes

H2O No NoElemental Liquid Metals Yes NoAlloys of Liquid Metals Yes Yes

Langmuir Monolayers No Yes

Experiments:

Simulations:Atom & Small-Non-Metallic Molecules

No No

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Why are Liquid Metals Different?

Simuation (Lennard-Jones Liquids) D'Evelyn & . Rice, J. Chem. Phys., 1983.

For Metals Particle-Particle Interactions

Change Across 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

This influences the structure of the surface!

Goal: Measure Intrinsic Surface Structure Factor Φ(Qz)

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Typical Liquid Metal Measurements

Hg

In

Ga

Effect of T (Liquid Ga)

R(Qz )

RF(Qz )⇒ Φ(Qz)

2Θ(Qz,T)

Structure FactorThermal Factor

Observe Apparent Difference

• Magnussen, Ocko, Regan, Penanen, PershanM. Deutsch ,PRL (1995).• Regan, Kawamoto, Pershan, Maskil, Deutsch, Magnussen, Ocko, L. E. Berman, PRL (1995).• Tostmann,DiMasi, Pershan, Ocko, Shpyrko, M. Deutsch, PRB (1999).

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Removal of Thermal Factor

R(Qz )

RF(Qz )×Θ(Qz,T)⇒ Φ(Qz)

2

Liquid Ga

1

ρbulk

∂ ρ(z)∂z

=12π

dQz  Φ(Qz)e−iQzz∫

Electron Density Profile

Indium T- effects removed& not removed

Ga & In with T-effects removed

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Metallic Layering Is not Due to High Surface Tension

R/(RF x Thermal) for Ga, In and K

γ In(~550mN/m)Ga(~750mN/m)K(~100mN/m)H2O(73mN/m)

H2O vs K

H2O vs Liquid Metals

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Gibbs Absorption: GaBi Alloy

2PhaseLiquid/Liquid

2 PhaseLiquid/Solid Bi

GaBi

γ(Bi)= 398 mN/mγ(Ga)=750 mN/m

Monolayer of Bi Coats Liquid SurfaceThick Wetting Layer of Bi-Rich Liquid vs Temperature

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olloq. Jun’05Liquid Metals of Electronic Interest (I): BiSn O. G. Shpyrko, A. Y. Grigoriev, R. Streitel, D. Pontoni, P. S. Pershan, M. Deutsch, B. M. Ocko, Meron, B. Lin .Phys. Rev.Lett. "Submitted (2005).Energy Dispersive Reflectivity

142 °C

Tm=138°C

γ(Bi)≈ 398γ(Sn)≈567 dyne/cm

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Liquid Metals of Electronic Interest (II)

Au80.5Si19.5 eutectic alloyR(qz )

RF (qz )×Θ(qz,T )= Φ(qz)

2

Detector (αS)-ScanAlloy is Liquid γ=780 dynes/cm

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Surface Phase Transition vs T

Reflectivity/(RF)2 Phases

Simple Layering Model

(i.e. Ga or In)

γ 1200 dyne/cm

γ 718 dyne/cm

Not Divided by Thermal

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Model Density Profiles AuSi(Preliminary)

High T Phase

Low T Phase

Typical ProfilesGa & In

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2D Order of Surface Phases (GID)

Truncation Rod Monolayer

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In-plane structure model: AuSi2 Low Temperature Phase

7.4

9.4

12 atoms:4 Au, 8 Si

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AuSi, AuGe vs Elements

AuSi ~ 10 x AuGe & elements

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The Future

The Buried Liquid/Solid InterfaceEffects: •Layering induced by

hard wall!•Surface induced in-plane

order! Crystal

Liquid

Problems with conventional approach:

•Absorption in Liquid

•Bulk Diffuse Scattering ~2 to 3 mm

0.1° to 10°

Path/2

Path > 20 mmGa Abs. Length 0.05mm(10 KeV)

0.13mm(30KeV)

Si Abs. Length ~17 mm(70 Kev)

H. Reichert, et a;/ Physica B-Condensed Matter (03).

van der Veen and Reichert, MRS Bulletin (04).

Single Xtal Si

Footprint

Beam Height ~10 mPath ~ 5 mm

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Summary

Solid vs Liquid Surfaces Reviewed X-ray Methods of Surfaces

Special Requirements of LiquidsCARS, -CAT, CMC

Surface Roughness: Capillary Waves Examples of Liquid Surface Order Liquid Metals vs Non-Metals Alloys: AuSi >10 x Others: Surface

Freezing Future: Buried Interfaces (Not DONE

@APS)