α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εF ο υο υο υο υο υ n δ εδ εδ εδ εδ ε r ’ s δ α ψ δ α ψ δ α ψ δ α ψ δ α ψ S ρ ερ ερ ερ ερ ε c i ααααα l I s s u εεεεε

I S S U E N O . 3 0 9 • O C T O B E R 2 0 0 9 • 1 1 5

D I F F U S I O N I N C U ( A L ) S O L I D S O L U T I O N

A . L a i k a n d K . B h a n u m u r t h y

M a t e r i a l s S c i e n c e D i v i s i o n

ABSTRACT

The solid state diffusion characteristics in the Cu(Al) solid solution phase, was investigatedin the temperature range of 1023–1223 K, us ing s ingle phase bulk d i f fus ion couples ,between pure Cu and Cu- 10 at.% Al . The interdif fus ion coeff ic ients, D , were calculatedusing Boltzmann–Matano method and Hal l ’ s method from the concentrat ion prof i les ofthe couples acquired us ing EPMA. The calculated interdi f fus ion coeff ic ients (D ) rangedbetween 1.39 X 10

-14 and 3.97 X 10

-13 m2/s in the temperature range of 1023 to 1223 K.

The composition and temperature dependence of D were established. The activation energyfo r i n te rd i f fu s ion va r i e s f rom 123 .1 to 134 .2 k J /mo l i n the concent ra t ion range1 at . % ≤≤≤≤≤ CAl ≤≤≤≤≤ 9 at . %. The impur i ty d i f fus ion coeff ic ient of Al in Cu, i s determined byextrapolat ing the interd i f fus ion coeff f ic ient va lues , to inf in i te d i lut ion of the a l loyi.e CAl → 0 and its temperature dependence was also established. The activation energy forimpur i ty d i f fus ion of Al in Cu was found to be 137.1 kJ /mol.

M r. A r i j i t L a i k i s t h e r e c i p i e n t o f t h e D A E Yo u n g E n g i n e e r A w a r d

f o r t h e y e a r 2 0 0 7

Introduction

The Cu-rich side of the Cu-Al system, finds commercialapplication in the form of aluminium bronzes, whichare Cu-based alloys containing up to 16% Al. Thesealloys are considered as potential materials for a widevariety of applications, due to their corrosion resistanceand exceptionally high strength [1]. The Cu-sideterminal solid solution is single phase Cu(Al) (α-phase)and can dissolve up to 19.7 at. % of Al and can bestrengthened by cold working. Additions of certainelements, such as cobalt and nickel render these single-phase binary alloys, age-hardenable. The Cu(Al) solidsolution takes part in two solid state reactions in thesystem i.e. a eutectoid reaction β ↔ γ1 +Cu(Al) at567 °C and a peritectoid reaction Cu(Al) + γ1 ↔ α2

[2]. These reactions being solid state in nature, theirkinetics are essentially controlled by the diffusionbehaviour of the participating phases.

It is worth noting, that Sprengel et al [3] showed thatthe interdiffusion coefficients obtained from diffusioncouple consisting of multiple phases, differ from thoseconsisting of a single-phase. Kim and Chang [4] havereported a large difference in the activation energyfor interdiffusion, determined by multi-phase diffusioncouples and single-phase diffusion couples, in the NiAlphase. The large difference in the activation energycould be due to the fact, that phase boundariesformed in multi-phase diffusion couples, influencethe diffusion flux to a large extent. The phaseboundaries act both as source and sink for point

1 1 6 • I S S U E N O . 3 0 9 • O C T O B E R 2 0 0 9

α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εD R . H O M I B H A B H A C E N T E N A R Y Y E A R

defects and the grain boundaries in an intermediatephase, formed during annealing, may alter the overalldiffusion rate in the system. Therefore, the diffusioncoefficients calculated from such experiments, are nottruly representative.

Besides, no published data for tracer diffusivity ofaluminium (DAl) in Cu is available. It is worthmentioning here, that this is due to the experimentallimitations in determining the impurity diffusioncoefficient of Al in Cu, primarily due to non-availabilityof suitable radioactive isotope of Al, which could beused as tracer. The only isotope which is suitable forsuch experiments is 26Al (t1/2 = 0.75 X 106 yr), whichhas low specific activity and is extremely expensive.The production and isolation of the 26Al isotope,required for the radio-tracer diffusion experiments, isextremely difficult [5] and can be achieved through a(p,pn) nuclear reaction, with naturally occurring 27Alin a cyclotron [6]. However, the impurity diffusioncoefficient of Al can also be determined, fromconcentration-dependent interdiffuson coefficients,using diffusion couples experiments. Recently suchstudies on binary systems Ni-Al [7] and Zr-Al [8] havebeen reported.

The present study reports a detailed investigation ofthe diffusion behaviour in the fcc Cu(Al) solid solution,in the concentration range 0 ≤≤≤≤≤ CAl ≤≤≤≤≤10 at.% Al in thetemperature range of 1023 to 1223 K. The impuritydiffusion coefficient of Al in Cu, is determined byextrapolating the interdiffusivity values, to infinitedilution of the alloy i.e. CAl → 0 and its temperaturedependence was also established.

Experimental procedure

A dilute alloy of nominal composition Cu-10 at. %Alwas prepared by vacuum induction melting, usingpure (99.9%) Cu and pure (99.95%) Al. Rectangularpieces of size 10 X 8 X 3 X mm3 were cut from therolled Cu-Al alloy and pure Cu and were encapsulatedin quartz tubes in He atmosphere and annealed at1223 K for 72 h. The 10 X 8 mm2 surfaces of thesamples were prepared, to a metallographic

finish of 0.25 µm. The diffusion couples were madeby keeping the polished surfaces of the pure Cu andthe Cu-10 at. %Al alloy pieces in contact with eachother, under a pressure of about 5 MPa in an Inconeldie and then heating in vacuum better than 10"3 Pa at1223 K for 1 h. Chemical analysis using EPMA acrossthe interface of the as-bonded couples, showed anegligible diffusion width. The couples were thensealed in quartz capsules in He atmosphere anddiffusion-annealed isothermally, for different timeintervals, in a preheated resistance heating furnace,in the temperature range 1023–1223 K for 24–72 h.The details of the heat treatment schedule of theisothermal diffusion annealing are given in Table 1.The cross-sections of the couples were prepared to0.25 µm finish using standard metallographictechniques as described earlier. The polished surfacesof the couples were etched with an etchant with thecomposition: 5 parts water, 5 parts ammoniumhydroxide and 2 parts hydrogen peroxide to revealthe microstructure.

The cross-sections of the polished samples werecharacterized using an optical microscope and anelectron probe microanalyzer (CAMECA SX100)equipped with three wavelength dispersivespectrometers. The operating voltage and beam currentwere kept at 20 kV and 20 nA respectively. Pure Cuand pure Al were used as standards for the analysis.Lithium fluoride and thallium acid pthalate(TAP)crystals were used, for diffraction of Cu-Kα and Al-Lαlines respectively. The standard PAP correction

Table 1: Heat treatment schedule for the diffusioncouples

Couple Temperature TimeNo. [K] [hrs]

1 1023 722 1073 623 1123 484 1173 365 1223 24

α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εF ο υο υο υο υο υ n δ εδ εδ εδ εδ ε r ’ s δ α ψ δ α ψ δ α ψ δ α ψ δ α ψ S ρ ερ ερ ερ ερ ε c i ααααα l I s s u εεεεε

I S S U E N O . 3 0 9 • O C T O B E R 2 0 0 9 • 1 1 7

programme was used for atomic number (Z),absorption (A) and fluorescence (F) corrections.Quantitative analysis on point-to-point basis was doneat a regular interval of 1-2 µm, by scanning the sampleacross the bonding interface, to determine theconcentration profile. For each sample, at least threescans were taken at different locations, to confirmthe consistency of the concentration profiles.

Results and Discussion

Interdiffusion in the Cu(Al) phase

Fig. 1 shows a typical concentration profile for thecouple annealed at 1223K. The plot shows typicallysolid solution type of concentration penetration curveacross the interface. The concentration profiles for allthe couples are of the same nature and isrepresented by Fig. 1. During the process of annealing,the initial compositions of the individual pieces ofthe couples are preserved at the ends, thereby fulfillingthe requirement of infinite geometry. The interdiffusioncoefficients for various compositions, within thediffusion zone for all the diffusion couples, werecalculated by using the Boltzmann-Matano method[9,10] and Hall’s method [11]. The interdiffusioncoefficients (D) calculated ranges between1.39 X 10-14 and 3.97 X 10-13 m2/s in the presenttemperature range of annealing.

The interdiffusion coefficients were calculated atcompositions alloy, ranging from 0.5 at. % to 9.5 at.% at intervals of 0.5 at. %. The concentrationdependence of interdiffusion coefficients at varioustemperatures by Boltzmann-Matano method ispresented in Fig. 2. The interdiffusion coefficients atvarious temperatures are fitted in a cubic relation ofthe type:

D = a + b CAl + c CAl2 + dCAl

3

Fig. 1: Concentration profile across the interface of Cu/Cu-10 at. % Al couple annealed at 1223K for 24 h.

Fig. 2: Concentration dependence of interdiffusioncoefficient in Cu(Al) solid solution at varioustemperatures

The values of the parameters a, b, c and d for varioustemperatures are given in Table 2.

Such enhancement in the interdiffusion coefficientD of the terminal solid solution, with the addition ofAl was reported in other systems as well. For example,increase in the interdiffusion coefficient in the β-Zr(Al)solid solution phase was observed in single phase [8]as well as in multiphase [12] diffusion coupleexperiments. Similar behaviour was reported in theβ-Ti(Al) solid solution phase by Hirano and Iijima [13].Addition of Al to Cu decreases the solidus temperatureline in the Cu–Al phase diagram [2]. The activationenergy of diffusion is directly related to the solidustemperature [14]. Therefore, with increase in Alconcentration, solidus temperature and henceactivation energy decreases and the diffusivityincreases.

1 1 8 • I S S U E N O . 3 0 9 • O C T O B E R 2 0 0 9

α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εD R . H O M I B H A B H A C E N T E N A R Y Y E A R

In order to establish the temperature dependence ofthe interdiffusion coefficient D, the logarithmic valuesof D (ln D) is plotted against the reciprocal of theabsolute temperature (T) of diffusion annealing forvarious compositions in Fig. 3. A linear relationshipin this plot shows, that D follows an Arrhenius typeof relationship, D = D0 exp(-Q/RT). The pre–exponential factor (D0) and the activation energy (Q)were evaluated at various compositions, in the range1 at. % ≤≤≤≤≤ CAl ≤≤≤≤≤ 9 at. % from the values of slope andintercept of the plots in Fig. 3. The values are tabutaledin Table 3. The activation energy for interdiffusion, Q,varies between 123.1 ± 3.9 to 134.2 ± 3.9 kJ/molin this concentration range.

Impurity diffusion of Al in Cu

According to the Darken’s relation [15], theinterdiffusion coefficient in an infinitely dilute solidsolution, corresponds to the impurity diffusioncoefficient of the solute in the solvent matrix. Theimpurity diffusion coefficient of Al in Cu phase wasdetermined, by extrapolating the D values in the range0 ≤≤≤≤≤ CAl ≤≤≤≤≤ 1 at. %, calculated by Hall’s method, toinfinite dilution, i.e., CAl→0. In the narrowcomposition range 0 ≤≤≤≤≤ CAl ≤≤≤≤≤ 1 at. %, D bears a linearrelationship of the type D = a + b CAl. Here the

impurity diffusion of Al in Cu is denoted as (CAl

= 0). Table 4 shows the values of at various

temperatures of investigation. The logarithm of (CAl

= 0) is plotted against the inverse of absolute

Table 2: Values of the parameters a, b, c and d in therelation D = a + b CAl + c CAl

2 + d CAl3 (CAl is in at. %).

Fig. 3: Temperature dependence of interdiffusioncoefficient, D, at various concentrations of Al

Table 3: Pre-exponential factor, D0, and activationenergy, Q, for interdiffusion in the Cu(Al) solid solutionphase at various compositions of Cu and Al

Table 4: Impurity diffusion coefficients of Al in Cu.

Temperature a b c d X10-4

[K]

1023 -29.54 0.24 -0.03 16.211073 -30.48 0.04 0.01 -15.021123 -30.74 0.01 0.01 -10.631173 -31.75 0.14 -0.01 7.021223 -31.93 0.09 -0.01 5.04

Composition Al Pre-exponential factor Activation

[at. %] (D0 X 108) [m2/s] energy [kJ/mol]

1 4.88 129.5

2 7.01 131.9

3 8.22 132.8

4 9.60 133.6

5 10.83 134.2

6 9.68 132.5

7 9.97 132.3

8 8.58 130.4

9 3.82 123.1

Temperature Impurity diffusivity[K] DAl

Cu [m2/s]

1023 1.4823 X 1013

1073 5.7903 X 10"14

1123 4.4646 X 1014

1173 1.6261 X 1014

1223 1.3582 X10"14

α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εF ο υο υο υο υο υ n δ εδ εδ εδ εδ ε r ’ s δ α ψ δ α ψ δ α ψ δ α ψ δ α ψ S ρ ερ ερ ερ ερ ε c i ααααα l I s s u εεεεε

I S S U E N O . 3 0 9 • O C T O B E R 2 0 0 9 • 1 1 9

temperature in Fig. 4. The frequency factor D0 andthe activation energy QAl have been estimated by fittinga straight line to the data points in Fig. 4, by linearregression method. The activation energy of impuritydiffusion is 137.1±4.0 kJ/mol. The temperaturedependence can be expressed by an Arrhenius relation:

m2/s.

activation energy for interdiffusion varies from 123.1to 134.2 kJ/mol in this composition range. Theimpurity diffusion coefficient of Al in Cu is determinedby extrapolating the interdiffusion coefficient valuesto infinite dilution of the alloy i.e CAl→0. Thetemperature dependence of the impurity diffusion

coefficient of Al in Cu was established and the

activation energy for impurity diffusion of Al in Cu,was found to be 137.1±4 kJ/mol.

Acknowledgements

The authors are grateful to Dr A. K. Suri, DirectorMaterials Group and Dr. G. K. Dey, Head MaterialsScience Division, for their support andencouragement.

References

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2. J. L. Murray, in: Binary Alloy Phase Diagrams,edited by T. B. Massalski, H. Okamoto, P. R.Subramanian and L. Kacprzak, 2nd Edn., ASMInternational, Materials Park, OH (1990) pp. 141-143.

3. W. Sprengel, N. Oikawa, H. Nakajima,Proceedings of the Workshop on Defects,Dynamics and Diffusion in Intermetallics, Vienna,Austria, 1994.

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Vol. 31A (2000) p. 1519.

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Fig. 4: Temperature dependence of impurity diffusivityof Al in Cu.

Summary

The interdiffusion coefficient for the fcc Cu(Al) solidsolution phase was determined, in the temperaturerange of 1023–1123 K, using single phase bulkdiffusion couples, between pure Cu/Cu- 10 at.% Alalloy. The interdiffusion coefficients, D, calculatedusing Boltzmann–Matano method and Hall’s method,were found to range between 1.39 X 10

-14 and 3.97

X 10-13

m2/s in this temperature range. Thecomposition and temperature dependenceof the interdiffusion coefficient (D) wereestablished. The interdiffusion coefficient (D) wasfound to follow a cubic relation of the typeD = a + b CAl + c CAl

2 + d CAl3 with the concentration

of Al in the range 1 at. % ≤≤≤≤≤ CAl ≤≤≤≤≤ 9 at. %.The interdiffusion coefficient (D) shows anArrhenius type of temperature dependence and the

1 2 0 • I S S U E N O . 3 0 9 • O C T O B E R 2 0 0 9

α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξα β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξφ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εψ ζ α β χ δ ε φ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ ε φ γ η ι ϕ κ λ μ ν ο π θ ρ σ τ υ ϖ ω ξ ψ ζ α β χ δ εD R . H O M I B H A B H A C E N T E N A R Y Y E A R

Mr. Arijit Laik joined from the 43rd batch of BARC Training School in Metallurgy discipline and

was awarded the Homi Bhabha Prize. His research interest is mainly solid state diffusion in

metals and alloys. His other research interests are metal-ceramic reactions, dissimilar materials

joining and materials characterization using electron probe microanalysis. He has more than 30

research publications.

Dr. K. Bhanumurthy joined the 24th batch of BARC Training School. His research interest

includes interdiffusion studies in metals and alloys, similar and dissimilar materials joining

using advanced solid state processes, friction stir welding, materials characterization, phase

diagrams study and evaluation. He has more than 110 research publications.

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