x-ray liquid surface: experimental variety of liquid metal/vapor interfaces
DESCRIPTION
X-ray Scattering: Liquid Metal/Vapor Interfaces P.S. Pershan SEAS & Dept of Physics, Harvard Univ., Cambridge, MA, US. X-ray Liquid Surface: Experimental Variety of Liquid Metal/Vapor Interfaces Open questions on surface freezing of liquid metals. Our Group . Colleagues (~20 years). - PowerPoint PPT PresentationTRANSCRIPT
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X-ray Scattering: Liquid Metal/Vapor Interfaces P.S. Pershan
SEAS & Dept of Physics, Harvard Univ., Cambridge, MA, US
• X-ray Liquid Surface: Experimental• Variety of Liquid Metal/Vapor
Interfaces • Open questions on surface freezing of
liquid metals
Pershan/SNIP
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Our Group.
• Colleagues (~20 years)
Pershan/SNIP
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
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Liquid Surface Reflectometer
Pershan/SNIP
1982: Hasylab1986: NSLS2002: APS
Q
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Fresnel X-ray Reflectivity
Pershan/SNIP
ε ≈1 − ρ∞r0λ2 π Qc
2 ≈ r0λ2 π( )r∞
Qz = 4π λ( )sinα
Qx ≈ 2π λ( )α α −β[ ]
α ≤10° ,λ ~1.5Å→ Qx ≤0.01Å−1
Diffuse scattering:
R Qz( )= Qz − Qz2 −Qc
2( ) Qz + Qz2 −Qc
2( )2
Qz ≥5Qc ⇒ RF(Qz)≈ Qc 2Qz( )4
If Qz <Qc ⇒ R Qz( )≈1
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Grazing Incidence Diffraction(GID)
Pershan SINP
Qxy ≈ 4π λ( )sinθDiffuse Scattering at Larger θ ≤20°
Qxy < 3Å−1
2D Bragg Peaks
Qz ≤Qc
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Real Liquid Surfaces
Pershan/SNIP
F Qz( )2
Surface Structure
F Qz ,Qxy( )2
Thermal capillary waves CW Qz ,
rQxy ,T( )
R Qz( )=RF Qz( ) F Qz( )2CW Qz,0,T( )Reflectivity
€
α =β
Diffuse Scattering
ds d 2rQxy~F Qz.
rQxy( )
2CW Qz,
rQxy,T( )α ≠β
orθ ≠ 0
Qxy ≤0.01Å−1
or
Qxy~{0.1 to 3 or 4 Å−1}
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Surface Structure Factor
Pershan/LAMXIV
sSurface Roughness (atomic scale)
Molecular Size aa >s ⇒ Lαyεring
Dielectric Liquids s > a⇒ NoLayering
LiquidCrystals1982
R Qz( )=RF Qz( ) F Qz( )2CW Qz,0,T( )
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Pershan/SNIP).
8
Free Surfaces of Non-Metallic vs Metallic Liquids(Layered)
Simuation (Lennard-Jones Non-Metallic 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 induces Layer Structure of LM Surface!Goal: Measure Intrinsic Surface Structure Factor F Qz( )
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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
F Qz( ) ≈1
ρ∞
dz−∞
+∞
∫ d ρ z( ) dz⎡⎣ ⎤⎦exp iQzz⎡⎣ ⎤⎦
Metallic Liquids (D’Evelyn & Rice ‘83)
R Qz( )=RF Qz( ) Fεff Qz,T( )2
whεrε Fεff Qz,T( )2=F Qz( )
2CW Qz,0,T( )
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Type II: Surface Adsorption(Ga-Bi alloy) Bulk Phase Coexistence
Pershan/SNIP
Nattland &Freyland, ’94Chatain & Wynblatt, ‘96P. Huber,’03
g ~ dz Δg c( ) +12
κdcdx⎡⎣⎢
⎤⎦⎥
2⎧⎨⎪⎩⎪
⎫⎬⎪⎭⎪
∫ Surface Tension
Gibbs: < 1900Butler: ’35Egry: ‘05
1)rBi−rich > rGα−rich
2)gBi−rich <gGα−rich
Electron Density
ξ
d
Influence Parameter: κ → Δg c( ) = κd2cdz2x →
d vs T Calphad Initiative(data)Gibbs free energy density: Δg c( )
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TypeIIIa: Surface Phase Transition2 Phase Binary Solution
Pershan/SNIP
BilayerMonolayer
Liquid
Shpyrko et al. Science 313, 77 (2006) vol. 313 (5783)Mechler et al. PRL (sub 2010)
2D Au-Si Crystals+Layer
gPb 458( ) < γ Ga 718( )
gSi 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
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Structure Factor &Thermal EffectsDebye-WallerCapillary Waves
Pershan/SNIP
h =kBT2πγ
Qz2
d 2srQ( )
dQxy2
~ds
rQ( )
dQxy2
F
FrQ( )
2 1
Qxy2−h
Qx = 2π λ( ) cosβ −cosα[ ]
R Qz( )
h Qx( )2
~κBT gQx2 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( )=RF Qz( ) F2CW
Diffuse Scat: In
~0.01Å-1
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Debye-Waller Demonstration
Pershan/SNIP
R Q z( )RF Qz( )
= F Qz( )2CW (Qz,T)
Ga vs. T
GaIn
Hg
In
Ga Ga In
R Qz( )RF Qz( )CW (Qz,T)
=F Qz( )2
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Distorted Crystal Layer Model
Pershan/SNIP
F 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
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Elemental Liquid Metals Studied
Pershan/SNIP
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)
F QZ( )2
No BumpBump
R Qz( )
RF Qz( )CW T( )=F
rQ( )
2
Bi is like Sn! Why is Hg so different?
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Eutectic Alloys
Pershan/SNIP
J. W. Gibbs <1900Surface Adsorption: A/B AlloyIf Surface Tension: gA > gB Surface is Rich in “B”.
AxB1-x g(A)/g(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)
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Pershan/SNIP 17
Gibbs Surface Adsorption(BiSn)
gBi=378, gSn=560, Alloy: Bi and Sn
g(Bi)≈ 398g(Sn)≈ 567 dyne/cm
Energy Dispersion: Bi:L3 f(E)
Adsorption
Scat. Ampl.
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Surface Freezing Au82Si18Eutectic
Pershan/SNIP
Si Au
T/γ~0.8Gallium T/γ~0.56
2D-Crystal Rigidity
Rigidity Reduces
Debye-Waller
Bragg PeaksLT: Bilayer XtalHT: MonolayerLL: Liquid
Mechler (LAMXIV)
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Thickness of the surface crystals
LT: destructive interference → bilayer crystalline phase, d≈ 3.31 Å
HT: atomic monolayer crystalline phase
LT HT
Pershan/SNIP
Intensity distribution of Bragg reflections along qzTruncation rod:
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thermal height-height fluctuations
Structure factor: electron density profile
Surface crystals exhibit bending rigidity,
Quenching of short wavelength capillary waves
No effect on long wavelength capillary waves
Effect of surface crystals on capillary wave spectrum
Reflectivity of liquid surface:
For LT surface phase ( ):
Diffuse scattering under grazing incidence
bending rigiditysurface tension
h qxy( )2
~1 gθxy2 1+ K g( )
2 θxy2( )⎡⎣ ⎤⎦
−1
Pershan/SNIP
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Self consistent density profile
Constraints for density profiles: LT: Bilayer and DCM HT: Monolayer and DCM LL: Monolayer and DCM, qmax
Bending rigidity essential for a more physical picture of surface structure
}+ allow qe to vary
R/RF
LT: HT: for HT, LT and LL
Density profiles
LT
HT
LL
Pershan/SNIP
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AuGe Eutectic(Should be Similar to Au-Si)
g(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)
Pershan/SNIP
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Surface Freezing of Au82Si18 and Glass Forming!
Glass Former
Au-Si
Not A Glass Former
Au-Ge
Glass Former
Glass Former
Pd-Si Pd-Ge
Pershan/SNIP
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Surface freezing in liquid Au-Cu-Si-Ag-Pd
2D crystalline monolayer on the liquid surface !
R/Rf @1.4 Å-1
GID
Cooling
Heating
Heating
LT (694K)
LL (704K)
GIDTrunc. Rod @ 1.65 Å-1
Lattice: single hexagonal layer (a= 4.4Å)Superstructure ?
Pershan/SNIP
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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
•Unexplained behavior of Au82Si18
Eutectic 2D Surface phase transitions for Au-Si•New Results I: Au-Cu-Si-Ag-Pd: •New Results II: Liquid Ge: No Layering
Pershan/SNIP