Transcript Document

Tetra Point Wetting at the Free Surface of a Binary Liquid Metal
Patrick Huber, Oleg Shpyrko, Peter Pershan, Holger Tostmann*, Elaine DiMasi**, Ben Ocko**, Moshe Deutsch***
Department of Physics, Harvard University, Cambridge MA, U.S.A.
*University of Florida, Gainesville, FL, ** Brookhaven National Lab, Upton, NY, *** Bar-Ilan University, Tel Aviv
X-ray reflectivity measurements
X-ray reflectivity from GaBi at T=200°C
(X22B NSLS, CMC-CAT APS)
0
10
beam-bending
monochromator
-1
10
-2
liquid metal
sample
(  * , T )  plane
Scattering geometry
270
Consolute Point
TC
10
synchrotron beam,
horizontal
Our measurements of the microscopic structure of the wetting film in combination with the
known bulk thermodynamics allow calculations of liquid-liquid interfacial tensions and the
extraction of information on the surface potential.
(c, T )  plane
-3
10
qZ
kin
-4
1x10
liquid-liquid coexistence
liquid-liquid coexistence, metastable
liquid-solid coexistence
250
kout
-5
1x10
-6
10
z
consolute
point
260
-7
10
<
=
=
>
TM
Temperature [°C]
Scattering setup
Temperature T
We present x-ray reflectivity measurements from the free surface of a gallium-bismuth (Ga-Bi)
alloy over a temperature range from T = 200°C up to T=280°C. We found a continuous
formation of a wetting film at the surface driven by the phase transition of first order in the
bulk at the monotectic temperature TM = 222°C. The observed wetting scenario is closely
related to triple point wetting known from one component systems and properly described as
complete wetting at a solid-liquid-liquid-vapor tetra point [1,2].
Microscopic View on Tetra Point Wetting
X-ray reflectivity
Abstract
240
230
monotectic
point
220
210
-8
surface height
tracking
Bulk thermodynamics
10
0.00
0.50
0.75
1.00
1.25
1.50
200
-1
-0.10
-0.15
-0.20
-0.25
Concentration of Gallium
1.6
T > TC (regime III):
• Free Energy G(c,T) available from CALPHAD project [4]
homogeneous
regime III: Gibbs adsorbed monolayer of pure Bi.
1.4
1.2
1.0
0.8
0
20
40
60
80
100
4.0
regime II: Thick wetting film of the heavier Bi-rich phase
intrudes between the low density, Ga-rich phase
and the vapor phase in defiance of gravity. [5,6]
1.6
3.5
Consolute Point
regime I: Gibbs adsorbed monolayer of pure Bi. [6,7]
Tmono < T < TC (regime II):
Ga-rich
relative Electrondensity sub
Bi-rich
3.5
1.4
1.2
2.0
1.5
280°C - regime III
225°C - regime II
200°C - regime I
3.0
218.0°C
2.5
R/RF
1.6
222.0°C
3.0
z [Å]
4.0
1.0
1.0
0.5
2.5
0.8
20
40
60
80
0.0
100
R/RF
0
z [Å]
TM
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
10
20
-1
qz [Å ]
2.0
30
40
50
60
70
z [Å]
1.5
1.6
T < Tmono (regime I):
relative Electrondensity sub
Temperature T
-0.05
(Bi-Ga) [kJ/mol]
relative Electrondensity sub
• Phase diagram measured with calorimetric methods by P. Predel [3]
0.00
qz [Å ]
Bulk structure  surface structure
relative Electrondensity sub
• Binary liquid metal with miscibility gap and monotectic point
TC
0.25
Ga-rich
1.4
1.2
1.0
• Transition pinned at bulk first order transition (monotectic point).
0.5
• Correctly described as complete wetting at a solid-liquid-liquid-vapor tetra point. [2]
(Phenomenon related to well known triple point wetting for one component systems. [1])
1.0
0.0
solid Bi
0.8
0
20
40
60
80
0.0
100
z [Å]
0.2
0.4
0.6
0.8
1.0
-1
qz [Å ]
Concentration of Gallium
()

experiment mean field,
gradient theory
 ()
2
cap
thermal fluctuations,
capillary wave theory
minimize
J/mol
J/mol
d
c(z)
g


dz2
2
excess ( c ( z ) )
c
intrinsic liquid-liquid interfacial profiles
calculate
1.0
Free Energy
Based on thermochemical datasets
Concentration of Gallium
0.9
Common tangent construction
for T=150°C
0.8
0.7
222°C
230°C
238°C
246°C
254°C
258°C
0.6
0.5
0.4
0.3
-150-120 -90 -60 -30 0
30 60 90 120 150 180
z [Å]
extract
 2 int r ( ),  ( )   2 cap ( ( ))
Deter m
1
 c(z) 
  A N   gexcess (c(z))    
 dz
2  z 
2
i nation of gradient param eter 
interfacial excess energy
interfacial tension [mN/m]
 
2
int r
• Experimental data indicate film structures dominated by density gradients.
- In contrast to the frequently used “homogeneous slab” models.
- but in agreement with density functional calculations for wetting in binary systems at hard walls. [7]
35
30
• Wetting scenario in Ga-Bi analogous to behavior in Ga-Pb system. [12]
liquid-liquid interfacial tension of Ga-Bi
25
20
15
10
5
References
Gradient Theory
Two-Scale Factor Universality [9]
0
[1] R. Pandit, M. E. Fisher, Physical Review Letters 51, 1772 (1983)
0.0
0.1
0.2
0.3
0.4
0.5
[2] S. Dietrich and M. Schick, Surface Science 382, 178 (1997)
(TC-T)/TC
liquid-liquid interfacial tension of Ga-Pb
interfacial tension [mN/m]

2
obs
1.4
• Preliminary analysis suggests: short-range, screened Coulomb interactions + long-range,
van-der-Waals like dispersion forces are necessary to explain evolution of profiles confirming
modern treatments of interactions in metals. [11]
Gradient Theory for the liquid-liquid interface [8]
interfacial roughness
1.2
[3] P. Predel, Zeitschrift für Physikalische Chemie Neue Folge 24, 206 (1960)
70
[4] L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams, Academic Press, NY (1970)
60
[5] D. Nattland, S. C. Muller, P. D. Poh, Freyland W., Journal of Non-Crystalline Solids 207, 772 (1996)
50
[6] H. Tostmann, E. DiMasi, O. G. Shpyrko, P.S. Pershan, B.M. Ocko, M.Deutsch, Physical Review Letters 84, 4385 (2000)
40
[7] N. Lei, Z. Q. Huang, and S. A. Rice, Journal of Chemical Physics 104, 4802 (1996)
30
[8] H.T. Davis, Stastical Mechanics of Phases, Interfaces, and Thin Films, Wiley-VCH, NY (1996)
20
[9] H. Kreuser and D. Woermann, Journal of Chemical Physics 98, 7655 (1993)
10
Gradient Theory
f it to measurements [10]
[10] M. Merkwitz, J. Weise, K. Thriemer, Hoyer W., Zeitschrift Fur Metallkunde 89, 247 (1998)
0
0.0
0.1
0.2
(TC-T)/TC
0.3
0.4
0.5
[11] N. W. Ashcroft, Philosophical Transactions of the Royal Society of London Series a 334, 407 (1991)
[12] P. Wynblatt and D. Chatain, Berichte der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 102, 1142 (1998)