9th int. conf on surf. x-ray and neutron scan (taiwan, jul.’06). 1 surface structure and chemical...

9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 1

Surface Structure and Chemical Composition of Liquid Metal Alloys

P. S. PershanHSEAS & Dept. of Physics, Harvard Univ.

I. Liquid Surfaces: Basic IdeasII. Experimental Methods for Studying Liquid

Surfaces

III.Liquid MetalsIII.Simple Surfaces: Ga, In, K, Hg(?)IV.Subtler Sufaces: Sn, BiV. Alloys: Gibbs Adsorption, SnBi, AuSnVI.Au-Eutectics: Surface Crystals

HSEAS


ColleaguesV. Balagurusamy, R. Streitel, O. Shpyrko, P. S. Pershan, M.

Deutsch, and B. Ocko, "Surface X-ray Scattering Studies of Liquid AuSn alloy ",Phys. Rev. B, (2006), to appear..

G. Shpyrko, R. Streitel, V. S. K. Balagurusamy, A. Y. Grigoriev, M. Deutsch, B. M. Ocko, M. Meron, B. H. Lin, and P. S. Pershan, "Surface crystallization in a liquid AuSi alloy",Science 313, 77 (2006).

O. G. Shpyrko, A. Y. Grikgoriev, R. Streitel, D. Pontoni, P. S. Pershan, M. Deutsch, and B. M. Ocko, "Atomic-scale surface demixing in a eutectic liquid BiSn alloy."Phys. Rev. Lett. 95, 106103 (2005).

•Grigoriev, O. G. Shpyrko, C. Steimer, P. Pershan, B. Ocko, M. Deutsch, B. Lin, M. Meron, T. Graber and J. Gebhardt "Surface Oxidation of Liquid Sn", Surf. Sci. 575, 3, 223 (2005).

•G. Shpyrko, A. Grigoriev, C. Steimer, P. S. Pershan, B. Lin, M. Meron, T. Graber, J. Gerbhardt, B. M. Ocko, and M. Deutsch, "Anomalous layering at the liquid Sn surface",Phys. Rev. B 70, 224206 (2004).

Stefan Sellner (New to Group)


Modern Era of Surface Science:

Solid Surfaces• Electron Spectroscopy (Brundle, 1974) & Auger Spectroscopy (Harris, 1974) followed by STM, AFM, etc

•Coincidentally:Synchrotron: SSRL(1973), NSLS

(1984), APS (1998)

•Synchrotron Radiation Enabled First Atomic Scale Studies of Liquid Surfaces

But these techniques can not be used on Liquids!


Solid vs Liquid SurfacesNon-metallic, Atomic, H2O, etc

Free Surface:Defined by OnlyGravity & Surface Tension

ρ(z)

z

Liquid Solid Surface:Defined by Hard Wall

Liquid Surfaces: Most of What We Know Molecular Simulations

Solid Surface:Defined by Rigid Lattice

Extensive Studies: Reconstruction, etc

Width of Interface Surface

Tension

Properties of

Interfaces

Hard Wall Atomic Layering

Long Wavelength Capillary Fluctuations

(To be discussed later).


Free Surfaces: Induced Order:

When? Properties?Liquid Crystals:

Fluctuations <<Molecular Size

Different Interactions Suppress Local FluctuationsLocal Layering

Vapor: Neutral Atoms

Liquid: Positive Ions in Sea of Negative Fermi Liquid

Metallic Liquids (D’Evelyn & Rice ‘83)

Goal : Measure surface induced order!


Surface Tension vs Interfacial Structure

Heuristic Discussion: Young, Poisson, etc. ~1800

Nearest Neighbor Attractive Interaction: -

Number of Neighbors for Bulk Atom:ZB

Enthalpy per Bulk Atom;- ZB

Number of Neighbors for Surface Atom: ZS<ZB

Enthalpy per Surface Atom; - ZS

Surface Enthalpy: Enthalpy= - ZS-(- ZB)

=+ (ZB-ZS)>0

S`

Fluctuations of Surface Atoms: ZS`≠ZS

Interfacial Structure Total= Enthalpy+ Entropy


Liquid Metal AlloysJ. W. Gibbs ~1920

A/B Alloy If Surface Tension: A

> B

Surface Rich in “B”.Eutectic Alloys

AB −1

2ΦAA + ΦBB( ) > 0

Immiscible SolidRepulsive Pair-wise

Interactions

Surface Layering, Adsorption & 2D Ordering!Approx. Theories of Surface: Guggenheim(1944), Defay-Prigogine

(1950), Strohl-King(1989)

dμ dT =−S

Entropy of Mixing!


How Liquid Surfaces Have Been Studied!

• Surface Tension• Ellipsometry: Drude (1889)

For nearly 200 Years:Measured Integrated Properties of Interface

More Recent: •Non-Linear Optics (Sum/Difference Frequency)

P(ω3)i = χ ω3;ω2 ,ω1( )i, j,k E(ω) j

rE ω( )k

j,k∑Local Property:

Requires Non-Trivial Theory

~200 years with little progress in understanding.X-rays now yield atomic structure Hope for Theory!

φp − φs ~1

λdz

ε (z) − ε liquid( ) ε (z) − ε vapor( )

ε (z)∫


X-Ray Reflectivity: Basicsε =1− 4πρ∞e2 mω 2 ≈ 1−10−5

cosα = ε cosα`Snell’s LawCritical Angle:cos2αcrit =ε or 1−αcrit

2 =1−4πρbulke2 mω 2

αcrit2 =4πρbulkreλ

2

RF (Qz ) = (α − α 2 −αcrit2 ) (α + α 2 −αcrit

2 )2

→ α crit 2α( )4

Fresnel Reflectivity From A Structureless Flat Surface

Qz = 4π λ( )sinαQc = 4π λ( )sinαc ≈0.03−0.08Å−1


Surface Structure

€

(Qz )2

~ A2 + B2 + 2AB cos QzD[ ] R(Qz ) =RF (Qz) (Qz)

2

Structure Factor

Reflectivity

Grazing Incidence Diffraction

Qxy ≈2ksinθ

Layers


X-ray Scattering Experiments

α ≈α s & θ ≈ 0Qxy ≈0 Qz ≈ 4π λ( )sinα

Specular Reflectivity

GID

Qxy ~ sinθ ≠0R Qz( ) =RF Qz( ) Qz( )

2


SurfaceRoughness

Solids

h(r)h(0)

Δφ=Qz[h(r)-h(0)]

αi

dσdΩ

~(Qz)2 d2rrxyexp −

Qz2

2h(

rrxy)−h(0)⎡⎣ ⎤⎦

2⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫ exp irQxy •

rrxy⎡⎣ ⎤⎦

Solid

rxyξSurf

exp[−Qz2 h 0( )2 ]

1

d 2 rrxy exp[i

rQxy •

rrxy ] =δ 2 (

rQxy)∫

Fourier Transform Effect of RoughnessDebye-Waller

dσdΩ

~ Qz( )2δ 2 (

rQxy)exp −Qz

2 h(0)2⎡⎣ ⎤⎦


Liquid RoughnessS. K. Sinha et al Phys. Rev. 38, 2297 (1988).

h(r)2π/qxy

Energy

Area=12

gρmass +qxy2

{ } hrqxy( )

2

qmax~1/Atom

qgravity ≈ gρmass ~1 / mm

exp −Qz2 h(0)2 −h(rxy)h(0)⎡

⎣⎤⎦~1 rxy

ηr >> 1/qmax

dσdΩ

⇔dσ

d2 rQxy

~ d2rrxyexp −Qz2

2h(

rrxy)−h(0)⎡⎣ ⎤⎦

2⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫ exp irQxy •

rrxy⎡⎣ ⎤⎦

η<<1

η∼1

Solid

rxy1/qmax

Qz<<1 or η<<1 Solid Like

Otherwise, η~1 Very Different

h(0)2 −h(rxy)h(0) ≈kBT2π

ln rxyqmax⎡⎣ ⎤⎦η =

kBT

2πγQz

2


dσA0d

2Qxy

≈Qc

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 δ 2

rQxy( )exp −Qz

2 h(0)2⎡⎣ ⎤⎦

dσA0d

2Qxy

≈Qc

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 δ 2

rQxy( )exp −Qz

2 h(0)2⎡⎣ ⎤⎦

Solid

Liquid: Diffuse Scattering vs Specular Reflection.

η =kBT

2πγQz

2η =kBT

2πγQz

2

dσdΩ

~ d2rrxyexp −Qz2

2h(

rrxy)−h(0)⎡⎣ ⎤⎦

2⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫ exp irQxy •

rrxy⎡⎣ ⎤⎦

1 / rxyη → dσ dΩ~1 Qxy

2−η

Θ(Qz ,T )

dσA0d

2Qxy

≈Qc

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 Qxy

qmax

⎛

⎝⎜⎞

⎠⎟

η η2πQxy

2⎛

⎝⎜⎞

⎠⎟dσ

A0d2Qxy

≈Qc

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 Qxy

qmax

⎛

⎝⎜⎞

⎠⎟

η η2πQxy

2⎛

⎝⎜⎞

⎠⎟

Liquid

No True Specular Reflection for Liquids:


Solid vs Liquid I (Reflectometer)

Solid:

Qmax~ 2 to 3 Å-1 E~10 keV θ1

Als-Nielsen, ‘82

Solid Specular Reflectiv

ty:Rotate Sample!

Liquid:

Liquid: Scan Incident

Beam/Sample Height


Liquid Surface Reflectometer

HASYLAB: BW1

NSLS: X22B, X19C

APS: CHEMMATCARS, CMC, μCAT

ESRF: ID10B & ID15A (Alternate Design)

H. Reichert ‘03

Resolution

ΔQy << ΔQx

Δαs

w

h

h sin(α s)Δα s

Qx

Qy

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


Data for H2O

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Qy(1/Å)=(2π/λcos(αI)-cos(αs)]

Qz (or αiIncreasing

0.3 Å-1 to 1 Å-1

ηIncreasing0.08 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 Δαs

w

h

h sin(α s)Δα s

Qx

Qy


Typical Liquid Metal Measurements

Hg

In

Ga

Effect of T (Liquid Ga)

R(Qz )

RF(Qz )⇒ (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).


Removal of Thermal Factor

R(Qz )

RF(Qz )×Θ(Qz,T)⇒ (Qz)

2

Liquid Ga

1

ρbulk

∂ ρ(z)∂z

=12π

dQz (Qz)e−iQzz∫

Electron Density Profile

ρ(z)>

Ga & In with T-effects removed

ρ(z)> Indium T- effects Not Removed

T-effects Removed


Metallic Layering Is not Due to High

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

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

H2O vs Liquid Metals

H2O

K


Anomalous Layering of Liquid Sn

R(Qz) R(Qz )

RF(Qz )×Θ(Qz,T)⇒ (Qz)

2

BumpNot seen in Ga,In

Bump Surface Density Is Higher Than Bulk!

No Theoretical Explanation Why Sn Should be This Way !

1st Layer is~10 % Thinner


Anomalous Layering of Liquid Sn &Bi

Bi: Equal Spacing

Bi: ~8%

Higher

DensityModel

Properties:

Number of Atoms 1st layer vs others

ΔZ/Z

Spacing of 1st layer vs others

Δd/dK Ga In Sn Bi Hg

ΔZ/Z +8%

Δd/d -10%

NoTheory


Liquid Metal AlloysJ. W. Gibbs ~1920

A/B AlloySurface AdsorptionIf Surface Tension: A > B

Surface is Rich in “B”.

Approx. Theories of Surface: Guggenheim(1944), Defay-Prigogine (1950), Strohl-King(1989)

There is No Serious Theory of Effects to be Described!

Concentration of Surface Layers A1-xBx

1stLayer 2nd 3rd

Ga83.In16. 718/6 =1.29 97%In In78Bi22 6/378 =1.47 3%Bi Sn7Bi43 60/378 =1.48 96%Bi 2%Bi 3%BiAu71Sn29 1100/60=1.96 9.8%Sn <1%Sn 24%Sn

Au-Si-GeEutecticsAu82Si18 1100/86=1.27Au81.9Si17.3Ge0.8

2 D SurfaceCrystal(AuSi2)AnomalouslyStrongLayering

Au77Si9Ge14

Au72Ge28 1100/621=1.77ModestorNoSurfaceEnhancementNormalSurfaceLayering


Gibbs Surface Adsorption(BiSn)

Bi=378, Sn=560, Alloy: Bi and Sn

(Bi)≈ 398(Sn)≈567 dyne/cm

Energy Dispersion: f(E)

Adsorption

Scat. Ampl.


Surface Freezing AuSiGe Eutectics

Au82Si18

1st Order

Transition

R/RF


Grazing Incidence Diffraction

Electron Density

High T

Low T

Au82Si18 Continued

Standard

Low THigh T

Qz Dependence of Bragg PeakProv

es 2D

2D Surface Crystals


Au82Si18 Continued: 2D-Liquid

dσA0d

2Qxy

≈Qc

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 Qxy

qmax

⎛

⎝⎜⎞

⎠⎟

η η2πQxy

2

⎛

⎝⎜⎞

⎠⎟dσ

A0d2Qxy

≈Qc

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 Qxy

qmax

⎛

⎝⎜⎞

⎠⎟

η η2πQxy

2

⎛

⎝⎜⎞

⎠⎟

Diffuse Scattering From H2O

Diffuse Scattering From

Au82Si18


Why?? Au82Si18

• There is no theoretical explanation!• Some Speculations!

2-X. Li et al "Gold as hydrogen. … bonding in disilicon gold clusters Si2Aun -(n=2,4), J.P.Chem A 109(‘05).

3- J. Weissmuller, "Reduced Short-Range Order in Amorphous-Si/Au-Alloys",J. Non-Cryst. Solids 142(‘92). •Si1-xAux: Covalent Metallic vs x. Possible Surface •Network with Covalent Structure

1- Gibbs: Si should adsorb to surface.


Silicon vs Germanium

Au-Si-Ge Eutectics u) / Si)Au82Si18 1100/86Au81.9Si17.3Ge0.8Au77Si9Ge14

Au72Ge28 1100/621


Reflectivity of the Au-eutectics

Au-Si-Ge Eutectics u) / Si)Au82Si18 1100/86Au81.9Si17.3Ge0.8Au77Si9Ge14

Au72Ge28 1100/621

Why are AuSi and AuGe eutectics different? Could it be that Si is more covalent?


Another Mystery Surface Tension and Order

d dt=−SA > 0SA < 0 ⇒ SurfaceOrder

Croxton, Stat. Mec. of the Liq. Surf. (1980).

C. J. Aidinis,..”.. liquid metal field ion emitter for the production of Si ions",Microelec. Eng. 73-74(‘04).

V ∝

0.8%Ge: Nearly Same as 0% Ge- But Differences (next)

Croxton’s Idea?


GID: Au81.9Si17.3Ge0.8

0.8% Ge: GID Scans Fluctuate

0% Ge: GID Scans Reproduceable

Average

0.8%Ge: Fluctuating Coarse PowderPartial Powder Average

0%Ge: Fine Powder

Lattices are Identical


Temperature Range Au81.9Si17.3Ge0.8 vs Au82Si18

Au82Si18

18°C

Solid Melting

Layering Transition

Temperature Range

0% Ge 360 C 371.2 C 11.2 C 0.8%Ge 363 C 389 C 26 C

Ge has a major effect!

Why! No Explanation!


SummaryI. Liquid vs Solid Surfaces

Capillary Roughness vs Rigid Lattice Different Experimental Methods

II. No True Reflectivity from Liquid Surfaces

Experiments on WaterIII.Liquid Metals

Simple (Ga, In, K, Hg) Anomalous (Sn, Bi) Gibbs Adsorption (SnBi) Surface Freezing (AuSiGe Eutectics)

IV. Need for Theory!

9th int. conf on surf. x-ray and neutron scan (taiwan, jul.’06). 1 surface structure and chemical...

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