surface structure and chemical composition of liquid metal alloys

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 LatticeExtensive 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 −12

ΦAA + 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

ρE 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!

jp − φs ~1λ

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

ε (z)∫


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

cosα = ε χosα`Snell’s LawCritical Angle:cos2 αχρit =ε oρ 1−αχρit

2 =1−4πρbulkε2 μω 2

αχρit2 =4πρbulkρεl

2

RF (Qz ) = (α − α 2 −αχρit2 ) (α + α 2 −αχρit

2 )2

→ α χρit 2α( )4

Fresnel Reflectivity From A Structureless Flat Surface

Qz = 4π l( )sinαQc = 4π l( )sinαχ ≈0.03−0.08Å−1


Surface Structure

€

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

2

Structure Factor

Reflectivity

Grazing Incidence Diffraction

Qxy ≈2ksinθ

Layers


X-ray Scattering Experiments

α ≈α s & θ ≈ 0Qxy ≈0 Qz ≈ 4π l( )sinα

Specular Reflectivity

GIDQxy ~ sinθ ≠0

R Qz( )=R Qz( ) Qz( )2


SurfaceRoughness

Solids

h(r)h(0)

Δj=Qz[h(ρ)-h(0)]

αi

dsdΩ

~(Qz)2 d2ρρxy εxπ −

Qz2

2h(ρρxy)−h(0)⎡⎣ ⎤⎦

2⎡⎣⎢⎢

⎤⎦⎥⎥∫ εxπ i

ρQxy•

ρρxy⎡⎣ ⎤⎦

Solid

rxyxSuρf

exp[−Qz2 h 0( )2 ]

1 d 2rrxy exp[i

rQxy • rrxy ] =d 2(

ρQxy)∫

Fourier Transform Effect of RoughnessDebye-Waller

dsdΩ

~ Qz( )2d 2(

ρQxy)εxπ −Qz

2 h(0)2⎡⎣ ⎤⎦


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

h(r)2π/θxy

EnergyArea

=12

ρμ αss+θxy2

{ } h ρθxy( )2

qmax~1/Atom

qgravity ≈ ρμαss ~1 / μμ

exp −Qz2 h(0)2 −h(ρxy)h(0)⎡⎣ ⎤⎦~1 ρxy

hr >> 1/qmax

dsdΩ

⇔ds

d2 ρQxy

~ d2ρρxy εxπ −Qz

2

2h(ρρxy)−h(0)⎡⎣ ⎤⎦

2⎡⎣⎢⎢

⎤⎦⎥⎥∫ εxπ i

ρQxy•

ρρxy⎡⎣ ⎤⎦

h<<1

h∼1

Solid

rxy1/qmax

Qz<<1 or h<<1 Solid Like

Otherwise, h~1 Very Different

h(0)2 −h(ρxy)h(0) ≈kBT2π

ln ρxyθμ αx⎡⎣ ⎤⎦ h =kBT2πγ

Qz2


ds

A0d2Qxy

≈Qχ

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 d 2

ρQxy( )εxπ −Qz

2 h(0)2⎡⎣ ⎤⎦

Solid

Liquid: Diffuse Scattering vs Specular Reflection.

h =kBT2πγ

Qz2

dsdΩ

~ d2ρρxy εxπ −Qz

2

2h(ρρxy)−h(0)⎡⎣ ⎤⎦

2⎡⎣⎢⎢

⎤⎦⎥⎥∫ εxπ i

ρQxy•

ρρxy⎡⎣ ⎤⎦

1 / rxyh → ds dΩ ~1 Qxy

2−h

Q(Qz ,T )ds

A0d2Qxy

≈Qχ

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 Qxy

θμ αx

⎛⎝⎜

⎞⎠⎟h h

2πQxy2

⎛⎝⎜

⎞⎠⎟

Liquid

No True Specular Reflection for Liquids:


Solid vs Liquid I (Reflectometer)

Solid:

Qmax~ 2 to 3 Å-1 E~10 keV θ~1

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, μ-CAT

ESRF: ID10B & ID15A (Alternate Design)

H. Reichert ‘03

ResolutionΔQy << 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/l)[cos(αI)-cos(αs)]

Qz (or αi)Increasing

0.3 Å-1 to 1 Å-1

hIncreasing0.08 to ~ 1

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

CMC CAT

Peak vanishes for slight increase in Qz

ds dΩ ~Qxy2−h 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)2Q(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 )×Q(Qz, T)

⇒ (Qz)2

Liquid Ga

1ρbulk

∂ ρ(z)∂z

=12π

dQz (Qz)ε−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 )×Q(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

1stLαyερ 2nd 3ρd

Gα83.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-G εEutεχtiχsAu82Si18 1100/86=1.27Au81.9Si17.3Gε 0.8

2ΔSuρfαχεCρystαl(AuSi2)Anoμ αlouslyStρonLαyερin

Au77Si9Gε14

Au72Gε 28 1100/621=1.77ModεstoρNoSuρfαχεEnhαnχεμ εntNoρμ αlSuρfαχεLαyερin


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

dsA0d

2Qxy

≈Qχ

2Qz

⎛⎝⎜

⎞⎠⎟

4

(Qz)2 Qxy

θμ αx

⎛⎝⎜

⎞⎠⎟h h

2πQxy2

⎛⎝⎜

⎞⎠⎟

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 1100/86Au81.9Si17.3Gε 0.8Au77Si9Gε14

Au72Gε 28 1100/621


Reflectivity of the Au-eutectics

Au-Si-Ge Eutectics u)/ Si)Au82Si18 1100/86Au81.9Si17.3Gε 0.8Au77Si9Gε14

Au72Gε 28 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 ⇒ Suρfαχε Oρdερ

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!

surface structure and chemical composition of liquid metal alloys

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