AB INITIO STUDY OF ADHESION TO ALUMINUM

Newton Ooi: newton.ooi@asu.edu

Computational Materials Science Group of Dr. James Adams

http://ceaspub.eas.asu.edu/cms/

APS 4 Corners Meeting: October 24-25, 2003

ALUMINUM

• Properties– Thermal and electrical conductor– Forms stable oxide– Low cost and low weight– Ductile– No magnetic properties

• Uses– Microelectronics– Structural materials in vehicles and

buildings– Packaging for food and drinks

Al circuit board

Al sheet rolling

PROBLEMS WITH USING AL

• Poor surface properties– Soft and low hardness– Abrades and wears easily– Low melting point friction welding occurs with other materials– Sticks to opposing tool pieces

• Requires use of coatings or lubricants in many forming processes – Welding– Cold/hot rolling– Drilling or riveting– Extrusion

• Determine adhesion between Al and coating/lubricant

ADHESION TO ALUMINUM

• Measure with wetting experiments– Oxidation and surface contamination– No insight into atomic bonding– Difficult to quantify results

• Examine by computer simulation– No concern about oxidation and contamination– Find ideal work of adhesion

work of separation– Assumes no plastic deformation– Complex interfacial bonding & geometry need reliable quantum mechanical

approaches

• We have examined adhesion of Al to following materials:– Common coatings: CrN, VN, WC, diamond…

– Native oxide: Al2O3

– Common lubricants: graphite

WORK OF SEPARATION

= +

E2

2

E1

1

A

ET

AEEEW Ts /2121

DENSITY FUNCTIONAL THEORY

Kinetic energy of

non-interacting electronsElectrostatic

energyExchange

correlation energy

Potential energy of non-interacting electrons

• Total energy is functional of electron density

• Proposed first by Thomas and Fermi in 1920s

• Current model proposed by Hohenberg, Kohn and Sham in 1960s and applicable to ground state

• Replace many-electron Schrödinger equation with single particle Kohn-Sham (KS) equation

METHODOLOGY

• Software: Vienna Ab initio Software Package (VASP)– Fortran 90 code for Unix / Linux

– Born – Oppenheimer approximation

– Plane wave basis set to span Hilbert space

– Pseudopotentials to represent ion – electron interactions

– Super cell method 3D periodic boundary conditions

– Variational method with free energy as variational quantity

– Exchange – correlation energy: LDA or GGA

– VASP website: http://cms.mpi.univie.ac.at/vasp/

• Simulation procedures– Bulk calculations

– Surface calculations

– Interface calculations

– Calculate work of separation

– Analyze atomic and electronic structure of interface

j

riGGeA

*

Aluminum FCC Cell

BULK CALCULATIONS

• Find irreducible Brillouin zone

• Plane wave convergence to minimize basis set

• Calculate energy (enthalpy) as function of volume

– Fit to equation of state

– Determine cohesive energy, bulk modulus and lattice constants

– Select pseudopotential for surface calculations

Aluminum data a (Å) Ec (eV) V (Å3) Bo (GPa)

LDA : GGA 3.971 : 4.039 -4.22 : -3.72 15.66 : 16.47 82.55 : 72.75

Experiment 4.045 -3.39 16.60 72.2

-3.8

-3.7

-3.6

-3.5

-3.4

-3.3

-3.2

-3.1

-3.0

0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35

Volume / Equilibrium Volume

en

erg

y /

ato

m (

eV

)

• Construct surface slabs to make interfaces with

• Determine irreducible Brillouin zone

• Vacuum convergence to reduce interaction between adjacent slabs

• Calculate surface energy via surface thickness convergence

• We used equation of Boettger: PRB 49, 23 (1994) 16798

SURFACE ENERGY CALCULATIONS

2ns 2

n

2

1NN HHHH

Cell

Vacuum

Slab

INTERFACE CALCULATIONS

• Generate periodic interfaces– With or without vacuum?– Sandwich or bi-layer?– Lattice mismatch?– Interface registry?– Determine equilibrium interfacial separation

• Relax interface and isolated slabs to minimal energy geometries• Calculate work of separation• Analyze interfacial geometry and structure• Electronic structure analysis

– Charge density plots– Electron localization function

CREATE INTERFACES

• Vacuum or not?– Vacuum allows more room for

atoms to relax increases accuracy

– Vacuum must be populated by plane waves increases calculation cost

• Bi-layer or sandwich?– Dipoles must cancel– All interfaces must be identical in

geometry and composition– Mirror/inversion symmetry

requirements

INTERFACE GEOMETRY

• Matching up surfaces

• Minimize lattice mismatch

• Al(111) – graphite (0001)

• Interface registry or coherency

• Fully coherent to fully incoherent

• C = black and Al = gray

Al – Graphite charge density

Abrupt change at interface = negligible Al – graphite bonding

Al – Graphite ELF

• ELF (Electron Localization Function) measures the Pauli exclusion principle

• Different bonding types are differentiated by color – Red areas bonding pairs localized bonding covalent

– Blue to green unpaired electrons or vacuum

– Yellow to orange metallic bonding

SUMMARY

• Adhesion to aluminum increases with the polarity of opposing material polarity increases bond formation

• Graphite has lowest adhesion to aluminum• Adhesion at interface proportional to the surface energies of

contacting surfaces surface reactivity• DFT adhesion calculations give results in good agreement with

available experimental data

System Experiment Ws (J/m2) Calculated Ws (J/m2)

Al – Al2O3 1.13 1.06

Al – graphite 0.1 – 0.4 0.2 – 0.35

FUTURE WORK

• Aluminum – Diamond-like carbon (DLC)

– Influence of surface stresses in carbon

– Effect of sp3/sp2 bonding ratio in carbon

– Surface termination

• Aluminum – BN– Hexagonal or cubic BN– Surface stoichiometry:

B or N or BxNy

ELF of 64-atom DLC cubic supercell with gray iso-surface of 0.53

CREDITS

• Acknowledgements– Dr. J. B. Adams– Dr. D. J. Siegel– Dr. L. G. Hector and Dr. Y. Qi at General Motors– Members of my research group– NCSA at UIUC for computational resources– NSF for funding under grant DMR 9619353 – Georg Kresse and authors of VASP

• References– Siegel, Hector, Adams. PRB 67 (2003) 092105– Kittel. Introduction to Solid State Physics: 7th Edition 2000 John Wiley & Sons– Ooi, Adams, Singisetti. Physica Status Solidi B 239 (2003) 44– Adams et al. Journal of Nuclear Materials 216 (1994) 265– Landry et al. Mat. Science and Engineering A254 (1998) 99– www.accelrys.com– www.webelements.com