F ree E nergyB ased o n therm o che m ical d a tasets

J/m ol

Tetra Point Wetting at the Free Surface of a Binary Liquid MetalTetra Point Wetting at the Free Surface of a Binary Liquid MetalPatrick HuberPatrick Huber, Oleg Shpyrko, Peter Pershan, Holger Tostmann*, Elaine DiMasi**, Ben Ocko**, Moshe Deutsch***, Oleg Shpyrko, Peter Pershan, Holger Tostmann*, Elaine DiMasi**, Ben Ocko**, Moshe Deutsch***

Department of Physics, Harvard University, Cambridge MA, U.S.A.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 *University of Florida, Gainesville, FL, ** Brookhaven National Lab, Upton, NY, *** Bar-Ilan University, Tel Aviv

AbstractWe 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].

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.

X-ray reflectivity measurements  Microscopic View on Tetra Point Wetting 

Gradient Theory for the liquid-liquid interface [8]

References

[1] R. Pandit, M. E. Fisher, Physical Review Letters 51, 1772 (1983)

[2] S. Dietrich and M. Schick, Surface Science 382, 178 (1997)

[3] P. Predel, Zeitschrift für Physikalische Chemie Neue Folge 24, 206 (1960)

[4] L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams, Academic Press, NY (1970)

[5] D. Nattland, S. C. Muller, P. D. Poh, Freyland W., Journal of Non-Crystalline Solids 207, 772 (1996)

[6] H. Tostmann, E. DiMasi, O. G. Shpyrko, P.S. Pershan, B.M. Ocko, M.Deutsch, Physical Review Letters 84, 4385 (2000)

[7] N. Lei, Z. Q. Huang, and S. A. Rice, Journal of Chemical Physics 104, 4802 (1996)

[8] H.T. Davis, Stastical Mechanics of Phases, Interfaces, and Thin Films, Wiley-VCH, NY (1996)

[9] H. Kreuser and D. Woermann, Journal of Chemical Physics 98, 7655 (1993)

[10] M. Merkwitz, J. Weise, K. Thriemer, Hoyer W., Zeitschrift Fur Metallkunde 89, 247 (1998)

[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) 

Bulk thermodynamics• Binary liquid metal with miscibility gap and monotectic point

• Phase diagram measured with calorimetric methods by P. Predel [3]

• Free Energy G(c,T) available from CALPHAD project [4]

Bulk structure surface structure 

• Transition pinned at bulk first order transition (monotectic point).

• 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])

• 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]

• 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]

• Wetting scenario in Ga-Bi analogous to behavior in Ga-Pb system. [12]

regime III: Gibbs adsorbed monolayer of pure Bi.

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]

regime I: Gibbs adsorbed monolayer of pure Bi. [6,7]

T > T (reg im e III):C

h o m o g e n eo u s

T m o n o < T < T (reg im e II): C

T < T m ono (reg im e I):

G a-rich

so lid B i

B i- rich

G a- rich

C o n so lu te P o in t

Tem

pera

ture

T

C o n c e n tra tio n o f G a lliu m

T C

T M

J/m

ol

C o m m o n ta n g e n t c o n s t ru c tio nfo r T = 1 5 0 °C

S c a tte rin g se tu p(X 2 2 B N S L S , C M C -C AT A P S )

X -ra y re fle c tiv ity fro m G a B i a t T = 2 0 0 °C

b e a m -b e n d in gm o n o c h ro m ato r

sy n c h ro tro n b e a m ,h o riz o n ta l

su rface h eig h ttrac k in g

l iqu id m e ta lsam p le

z

0.00 0.25 0.50 0.75 1.00 1.25 1.5010-8

10-7

10-6

1x10-5

1x10-4

10-3

10-2

10-1

100

X-r

ay r

efle

ctiv

ity

qz [Å-1]

S ca tte r in g g e o m e try

kin

q Zk out

0 20 40 60 80 1000.8

1.0

1.2

1.4

1.6

rela

tive

Elec

trond

ensi

ty su

b

z [Å]

0 20 40 60 80 1000.8

1.0

1.2

1.4

1.6re

lativ

eEl

ectro

nden

sity

su

b

z [Å]

0 20 40 60 80 1000.8

1.0

1.2

1.4

1.6

rela

tive

Elec

trond

ensi

ty su

b

z [Å]

0.0 0.1 0.2 0.3 0.4 0.5

0

5

10

15

20

25

30

35

liquid-liquid interfacial tension of Ga-Bi

Gradient Theory Two-Scale Factor Universality [9]

inte

rfac

ial t

ensi

on [

mN

/m]

(TC-T)/T

C

0.0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

70

liquid-liquid interfacial tension of Ga-Pb

Gradient Theory f it to measurements [10]

inte

rfac

ial t

ensi

on [

mN

/m]

(TC-T)/T

C

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

280°C - regime III 225°C - regime II 200°C - regime I

qz [Å-1]

R/R

F

0 10 20 30 40 50 60 700.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

rela

tive

Ele

ctro

nden

sity

su

b

z [Å]

200

210

220

230

240

250

260

270

0.00 -0.05 -0.10 -0.15 -0.20 -0.25

Tem

pera

ture

[°C

]

monotecticpoint

consolutepoint

(Bi

-Ga

) [kJ/mol]

liquid-liquid coexistence liquid-liquid coexistence, metastable liquid-solid coexistence

C o n so lu te P o int

Tem

pera

ture

T

C o n cen tra tio n o f G alliu m

T C

T M

p laneT ),( *planeTc ),(

< = = >

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

218.0°C

222.0°C

R/R

F

qz [Å-1]

-150-120 -90 -60 -30 0 30 60 90 120 150 1800.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

intrinsic liquid-liquid interfacial profiles

Con

cent

ratio

n of

Gal

lium

z [Å]

222°C 230°C 238°C 246°C 254°C 258°C

dz

zzc

zcgNA excess

2)(

21

))((

m ea n f ie ld ,grad ien t theory

th e rm a l f lu c tu a tio n s ,cap illa ry w ave theory

e x p e rim e n t

Det

e rm

i nat

ion

o f g

r adi

ent p

aram

eter

in terfa cia l rou g h n ess

in terfa cia l ex cess en erg y

m in im ize

e x trac t

c a lcu la te

)()( 2int

22 caprobs

))(()() ,( 2in t

2 capr

czcg

d zzcd e x c e s s

) )(()(

2

2