High Temperature Capillarity in Metal Systems: Insights ... Presentations/Contact6_2008_EWebb_High… · High Temperature Capillarity in Metal Systems: Insights from Atomic Modeling

6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008

High Temperature Capillarity inMetal Systems: Insights from

Atomic Modeling

J. J. Hoyt, McMaster University

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the UnitedStates Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Edmund B. Webb III, Sandia National Laboratories

For more information: Acta Materialia, 56 1802 (2008)


Outline

• Introduction: High temperature wetting and spreading• liquid metals on metals (also oxides/ceramics)• reactive wetting models / experiments

• Enhanced reactive wetting in a brazing geometry• Cu(l) entering pore in Ni• model for rate of substrate dissolution• connecting free energy of dissolution to spreading kinetics

• Conclusions and outlook


Wetting & Spreading

• Classical applications– Joining– Adhesion– Encapsulants– Lubrication

• Modern applications– Photolithography– Microcontact printing– Microfluidics


High Temperature Capillarity

• Welding, brazing, and soldering used for centuries to join metalsand metals and oxides (ceramics)

• construction, auto manufacturing, (micro)electronics, jewelry

• Braze/Solder melts at lower T than materials to be joined

• Reactions between the liquid braze/solder and the solid materialsresult in strong mechanical bonding (also hermeticity)

• Despite centuries of application, underlying phenomena stillunclear (empirical engineering)


Modeling Wetting in Metal Systems

• Classical atomistic simulations• Molecular Dynamics - real space, real time atomic trajectories• Monte Carlo - equilibrium properties (phase diagrams)

• Realistic interatomic potentials for metals (EAM)

• We’re examining liquid Cu infiltrating a pore in Ni

Ei = Fi(ρi) + ½ Σ Φij(Rij)j≠i

ρi = Σ ρj (Rij)j≠i

a


NiCu System

• Model system has well characterized thermodynamic properties


Brazing Simulation

Liquid CuSolid Ni (100)

d = 11 nm

T = 1750K

Ni (100)


Brazing Simulation

• Substrate dissolution observed during infiltration - how does thiseffect wetting kinetics?

T = 1750K, t ~ 2 ns T = 1500K, t ~ 1.5 ns

Withdissolution

Nodissolution


Porous Metal Infiltration - Brazing

• What is the flow profile for liquid infiltration into a pore?

l

d

θ

viscosity

pressure

P2ηl

(d2/4 - y2)vx(y) =

x

y

Milner, 1958: Poiseuille flow … Assume NoDissolution


Laminar Flow Velocity Profile

P2ηl

(d2/4 - y2)vx(y) =

Psim = 835 bar

Pmodel = 750 bar

• Flow profile agrees with capillarity based model


Porous Metal Infiltration - Brazing

• How fast does liquid metal penetrate a pore?

Milner, 1958:

l

d

θ

viscosity

liquid surface tensionpressure

dγLcosθ3η

t=Pd2

6ηtl2 =


Computing the Contact Angle• Regardless of dissolution, we assume the solid/liquid interfaceremains flat near the contact line

• Compute the position of the front as a function of y (shown byblack points below in figs on left); fit either linear (near contact line)or circular (entire front) in figs on right

T = 1750 K Dissolutive System

In this geometry,two methods give

similar results(not so for sessile

drops!)


Contact Angle with Time

• T = 1750 K• ND : θ ≈ 58o

• D : θ ≈ 45o

• T = 1500 K• ND : θ ≈ 64o

• D : θ ≈ 62o

γ = 738 mJ/m2 (T=1500 K)γ = 698 mJ/m2 (T=1750 K)

η = 2.8 cP (T=1500 K)

η = 2.2 cP (T=1750 K)


Infiltration Rate

dγLcosθ3η

tl2 =

l2 = 44 Å/ps t (ND)

(a) and (b): T = 1500 K

l2 = 47 Å/ps t (D)

l2 = 42 Å/ps t (ND)l2 = 45 Å/ps t (D)

Fits

Theory

(c) and (d): T = 1750 K

Fits

Theory

l2 = 62 Å/ps t (ND)l2 = 125 Å/ps t (D)

l2 = 60 Å/ps t (ND)l2 = 80 Å/ps t (D)


Infiltration Rate

d (γLcosθ + Qdiss)3η

t=l2

• Qdiss is an energy related to dissolution

• For T = 1750 K dissolutive case, Qdiss ~ 0.24 J/m2 (comparedto γLcosθ = 0.49 J/m2)

• Energy of dissolution plays significant role in determiningwetting kinetics at sufficiently high T


Model for Influence of Dissolution


Model for Dissolution Rate

Proposal: Velocity of dissolving interface is given by:

[ ])/exp(1)( kTTVVo

µ!""=

Chemical potential of base metal atom in the solid minus that in the liquid

This relationship has been established for the solidification rate as a function ofundercooling in pure metals.


Dissolution Driving Force

µ!

Liquid Solid

Freeenergy

Conc.

Pure liquid represents thecase of infinite drivingforce, V=Vo


Dissolution for Varying Liquid Composition

Compositionsstudied, T=1750 K


Dissolution Simulations

20x20 unit cells

Ni solid

Ni solid

Cu-Ni liquid

• Extract rate from early t slope


Dissolution Rate


Test for Arrhenius Behavior of V0

V0

Ea = 2.9 eV(close to value for

self-diffusion in Ni)


Arrhenius Behavior for V0

• Arrhenius behavior of V0 explains significant effect ofdissolution whereas the effect was negligible at T = 1500 K

• Ea = 2.9 eV means Qdiss at T = 1500 K should be roughly 1/20of the value at T = 1750 K




Conclusions

• Infiltration rate of liquid Cu through a channel obeys l2~t law;kinetics enhanced due to dissolution of base metal at T = 1750 K

• Dissolution rate of base metal obeys:

[ ])/exp(1)( kTTVVo

µ!""=

• V0 exhibits Arrhenius behavior; at high enough dissolution rate, Qdissincreases driving force for infiltration

• Dissolution is a reaction for which the ‘reaction volume’ canincrease significantly with increasing reaction rate AND thishappens on a time scale comparable to the time for liquid to advanceacross surface

Documents

High Temperature Capillarity in Metal Systems: Insights ... Presentations/Contact6_2008_EWebb_High… · High Temperature Capillarity in Metal Systems: Insights from Atomic Modeling