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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 2
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)
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 3
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!
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 4
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).
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 5
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!
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 6
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 7
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!
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 8
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)∫
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 9
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 10
Surface Structure
€
(Qz ) 2 ~ A2 + B2 + 2AB cos QzD[ ] R(Qz ) =R(Qz) (Qz)
2
Structure Factor
Reflectivity
Grazing Incidence Diffraction
Qxy ≈2ksinθ
Layers
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 11
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 12
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⎡⎣ ⎤⎦
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 13
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 14
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:
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 15
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 16
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 17
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 18
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).
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 19
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 20
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 21
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 22
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 23
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 24
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.
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 25
Surface Freezing AuSiGe Eutectics
Au82Si18
1st Order
Transition
R/RF
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 26
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 27
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 28
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.
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 29
Silicon vs Germanium
Au-Si-Ge Eutectics u)/ Si)Au82Si18 1100/86Au81.9Si17.3Gε 0.8Au77Si9Gε14
Au72Gε 28 1100/621
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 30
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?
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 31
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?
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 32
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
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 33
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!
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 34
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!