high temperature capillarity in metal systems: insights ......
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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)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 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
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Wetting & Spreading
• Classical applications– Joining– Adhesion– Encapsulants– Lubrication
• Modern applications– Photolithography– Microcontact printing– Microfluidics
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
NiCu System
• Model system has well characterized thermodynamic properties
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Brazing Simulation
Liquid CuSolid Ni (100)
d = 11 nm
T = 1750K
Ni (100)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Laminar Flow Velocity Profile
P2ηl
(d2/4 - y2)vx(y) =
Psim = 835 bar
Pmodel = 750 bar
• Flow profile agrees with capillarity based model
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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 =
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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!)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Model for Influence of Dissolution
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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.
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Dissolution Driving Force
µ!
Liquid Solid
Freeenergy
Conc.
Pure liquid represents thecase of infinite drivingforce, V=Vo
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Dissolution for Varying Liquid Composition
Compositionsstudied, T=1750 K
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Dissolution Simulations
20x20 unit cells
Ni solid
Ni solid
Cu-Ni liquid
• Extract rate from early t slope
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Dissolution Rate
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
Test for Arrhenius Behavior of V0
V0
Ea = 2.9 eV(close to value for
self-diffusion in Ni)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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
• For T = 1750 K dissolutive case, Qdiss ~ 0.24 J/m2 (comparedto γLcosθ = 0.49 J/m2)
• For T = 1500 K dissolutive case, Qdiss ~ 0.01 J/m2 (comparedto γLcosθ = 0.35 J/m2)
6th International Symposium on Contact Angle, Wettability, and AdhesionUniversity of Maine - Orono; July 14 - 16, 2008
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