X-ray Scattering: Liquid Metal/Vapor Interfaces P.S. Pershan
SEAS & Dept of Physics, Harvard Univ., Cambridge, MA, US
• I: Liquid Metal/Vapor Interfaces
• II: Examples from experiments done by our group and others.
• III: Open questions on surface freezing of liquid metals (Mechler)
Pershan/LAMXIV
Our Group.
• Colleagues (~20 years)
Pershan/LAMXIV
Balagurusamy, V. S. K.Berman, E. √√Deutsch, M. DiMasi, E. Fukuto, M. Gebhardt , J. Gog, T. Graber, T. Grigoriev, A.
Huber, P. Kawamoto, E. H. Kuzmenko, I. Lin, B. H. Magnussen, O. M. √√Mechler, S.Meron, M. Ocko, B. M. Pontoni, D.
Regan, M. J. Sellner, S.Shpyrko, O. G. Steimer, C. Stoltz, S.Streitel, R. Tostmann, H. √√Yahel, E
Harvard, Non-Harvard, Beam Line√√ Speakers at LAMXIV
Fresnel X-ray Reflectivity
Pershan/LAMXIV
ε ≈1 − ρ∞r0λ2 πRF (Qz ) ≈ Qc 2Qz( )
4
Qc2 ≈ r0λ
2 π( )r∞
Qz = 4π λ( )sinα
:
Qx ≈ 2π λ( )α α −β[ ]
α ≤10° Qx ≤0.01Å−1
Diffuse scattering:
Grazing Incidence Diffraction(GID)
Pershan/LAMXIV
Qxy ≈ 4π λ( )sinθDiffuse Scattering at Larger θ ≤20°
Qxy < 3Å−1
2D Bragg Peaks
Real Liquid Surfaces
Pershan/LAMXIV
Φ Qz( )2
Surface Structure
Φ Qz ,Qxy( )2
Thermal capillary waves CW Qz ,
rQxy ,T( )
R Qz( )=RΦ Qz( ) Φ Qz( )2CW Qz,0,T( )Reflectivity
€
α =β
Diffuse Scattering
ds d 2rQxy~Φ Qz.
rQxy( )
2CW Qz,
rQxy,T( )α ≠β
orθ ≠ 0
Qxy ≤0.01Å−1
or
Qxy~{0.1 to 3 or 4 Å−1}
Hg
In
GaHg: Magnussen et al. (1995).Ga: Regan et al.(1995)In: Tostmann et al.(1999)
Type I: Elemental LiquidLayer Response of Bulk Susceptibility
Pershan/LAMXIV
Φ Qz( ) ≈1
ρ∞
dz−∞
+∞
∫ d ρ z( ) dz⎡⎣ ⎤⎦exp iQzz⎡⎣ ⎤⎦
Metallic Liquids (D’Evelyn & Rice ‘83)
R Qz( )=RΦ Qz( ) Φεff Qz,T( )2
whεrε Φεff Qz,T( )2=Φ Qz( )
2CW Qz,0,T( )
Type II: Surface Adsorption(Ga-Bi alloy) Bulk Phase Coexistence
Pershan/LAMXIV
Nattland &Freyland, ’94Chatain & Wynblatt, ‘96P. Huber,’03
γ ~ dz Δg c( ) +12
κdcdx⎡⎣⎢
⎤⎦⎥
2⎧⎨⎪⎩⎪
⎫⎬⎪⎭⎪
∫ Surface Tension
Gibbs: < 1900Butler: ’35Egry: ‘05
1)rBi−rich > rGα−rich
2)γBi−rich <γGα−rich
Electron Density
ξ
d
Influence Parameter: κ → Δg c( ) = κd2cdz2x →
d vs T Calphad Initiative(data)Gibbs free energy density: Δg c( )
TypeIIIa: Surface Phase Transition2 Phase Binary Solution
Pershan/LAMXIV
BilayerMonolayer
Liquid
Shpyrko et al. Science 313, 77 (2006) vol. 313 (5783)Mechler et al. LAMXIV (2010)
2D Au-Si Crystals+Layer
γPb 458( ) < γ Ga 718( )
γSi 865( ) < γ Au 1189( )
Au-Si Eutectic
Is this Gibbs?
Yang et al. PRB. 62, 13111 (2000)
Gibbs AdsorptionPb-monolayer on Ga
2D Crystal.
GID Scattering
Type IIIb: Phase Transition(Insoluble Monolayer)
Pershan/LAMXIV
Kraack et al. The Structure and Phase Diagram of Langmuir Films ofAlcohols on Mercury. Langmuir 20, 5386 (2004)
CH 3 CH2[ ]n−2( )CH2OH
GIDR Qz( ) RΦ Qz( ) r z( )
Φ Qz( )
Structure Factor &Thermal EffectsDebye-WallerCapillary Waves
Pershan/LAMXIV
h =kBT2πγ
Qz2
d 2srQ( )
dQxy2
~ds
rQ( )
dQxy2
Φ
ΦrQ( )
2 1
Qxy2−h
Qx = 2π λ( ) cosβ −cosα[ ]
R Qz( )
h Qx( )2
~κBT γQx2 for QΔεβyε >Qx >~cm
−12D
CW Qz ,T( )= d 2rQxy ds d 2
rQxy⎡⎣ ⎤⎦Rεsoλution∫
= ΔQRεsoλution QΔεβyε⎡⎣ ⎤⎦hOR εxπ −Qz
2Σ2⎡⎣ ⎤⎦Debye-Waller
R Qz( )=RΦ Qz( ) Φ2CW
Diffuse Scat: In
~0.01Å-1
Debye-Waller Demonstration
Pershan/LAMXIV
R Q z( )RΦ Qz( )
= Φ Qz( )2CW (Qz,T)
Ga vs. T
GaIn
Hg
In
Ga Ga In
R Qz( )RΦ Qz( )CW (Qz,T)
=Φ Qz( )2
Distorted Crystal Layer Model
Pershan/ESRF
Φ Qz( ) = Qzdexp −σ 0
2Qz2 / 2⎡⎣ ⎤⎦
1− exp iQzd⎡⎣ ⎤⎦exp −σ 2Qz2⎡⎣ ⎤⎦
r z( )ρ ∞( )
=d
σ n 2πexp − z + nd( )2 / 2σ n
2( )⎡⎣ ⎤⎦n=0
∞
∑
s n2 = σ 0
2 + nσ 2
DCM (Magnussen ’95)
s 0 ,σ , & dOnly 3 Adjustable Parameters
n=0 1 2 3 ...
~ 1 s
Elemental Liquid Metals Studied
Pershan/ESRF
K Ga In Sn Bi HgDCM DCM DCM +1 +1 ?
☐ ☐
• Why are 1st Layers for Bi and Sn different from K, Ga and In?
Sn
Mol. Dynamic. SimulationsCalderín et al. PRB,80,115403 (2009)
Φ QZ( )2
No BumpBump
R Qz( )
RΦ Qz( )CW T( )=Φ
rQ( )
2
Bi is like Sn! Why is Hg so different?
Eutectic Alloys
Pershan/ESRF
J. W. Gibbs <1900Surface Adsorption: A/B AlloyIf Surface Tension: γA > γB Surface is Rich in “B”.
AxB1-x γ(A)/γ(B) ΔH*
(mixing)Concentration of Surface Layers
1st 2nd 34d
GaxBi1-x 718/378=1.90 +4 Liquid-Liquid Phase Sep.
Ga83.5In16.5 718/556=1.29 +5 97%In
In78Bi22 556/378=1.47 -1 35%Bi
Sn57Bi43 560/378=1.48 +1 96%Bi 25%Bi 53%Bi
Au71Sn29 1100/560=1.96 -10 96%Sn <1%Sn 24%Sn
Au72Ge28 1100/621=1.77 -21 No Gibbs Adsorption
Au82Si18 1100/865=1.27 -30 4-layers, 2DXtal (AuSi2)
Pd81Ge19 1500/621=2.4-44
~40 Å wetting layer (No Measureable Gibbs Adsorption)
9th Int. Conf on Surf. X-ray and Neutron Scan (Taiwan, Jul.’06). 15
Gibbs Surface Adsorption(BiSn)
γBi=378, γSn=560, Alloy: Bi and Sn
γ(Bi)≈ 398γ(Sn)≈ 567 dyne/cm
Energy Dispersion: Bi:L3 f(E)
Adsorption
Scat. Ampl.
Surface Freezing Au82Si18Eutectic
Pershan/LAMXIV
Si Au
T/γ~0.8
Bragg PeaksLT: Bilayer XtalHT: MonolayerLL: Liquid
Mechler (LAMXIV)
Gallium T/γ~0.56
2D-Crystal Rigidity
Rigidity Reduces
Debye-Waller
AuGe Eutectic(Should be Similar to Au-Si)
Pershan/ESRF
γ(Au)/γ(Si or Ge) ΔH
Au72Ge28 1100/621=1.77 -21
Au82Si18 1100/865=1.27 -30Au-Si Au-Ge
• Au-Ge is Different from Au-Si
• No Surface Freezing
• Why?
Au-Si
Surface Frozen Ge≤6.5 atm%
2D GID Scans
Pasturel et al. Structure- Liquid Au-Si - molecular dynamics. PRB (2010)
Upmanyu et al. (in preparation): NESub surface Si enrichment!Si (Surface) (Au-Si) (bonding)
Surface Freezing of Au82Si18 and Glass Forming!(Mechler)
Pershan/LAMXIV
Glass Former
Au-Si
Not A Glass Former
Au-Ge
Glass Former
Glass Former
Pd-Si Pd-Ge
Summary•Elemental metals Surface induced layering.•Simplest Distorted Crystal Model (Ga,In, K)
Debye-Waller Effects of Thermal Capillary Waves Near surface deviations from DCM (Sn, Bi). •Other Metal/Vapor Interfaces
2 Phase Binary Alloys (Ga-Bi, Ga-Pb, Ga-Tl)Gibbs Adsorption, Wetting, 2D Crystals
Langmuir Monolayers on Hg (Deutsch)•Unexplained behavior of Au82Si18 (Mechler)
Eutectic 2D Surface phase transitions for Au-Si•New Results I: Au-Cu-Si: (Mechler: LAMXIV)•New Results II: Liquid Ge: No Layering (Private Discussion: Mechler and Yahel)
•New Results from Others:Liquid Metal/Solid: (Deutsch: LAMXIV)
Pershan/ESRF
