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Intermetallics 17 (2009) 962–964

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Intermetallics

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Interdiffusion and activation energy in Ti3Au phase with A15 crystal structure

A.K. Kumar, A. Paul*

Department of Materials Engineering and Centre for Electronics Design and Technology, Indian Institute of Science, Bangalore 560012, India

a r t i c l e i n f o

Article history:Received 24 March 2009Received in revised form14 April 2009Accepted 15 April 2009Available online 28 May 2009

Keywords:B. DiffusionA. Intermetallics, miscellaneousD. Defects: point defectsG. Superconducting applications

* Corresponding author. Tel.: þ91 8022933242; faxE-mail address: aloke@materials.iisc.ernet.in (A. P

0966-9795/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.intermet.2009.04.005

a b s t r a c t

The knowledge of diffusion parameters, such as integrated diffusion coefficient and the activation energyfor diffusion is important to understand the growth rate of the product phase and the atomic mechanismof diffusion. These parameters are determined in Ti3Au phase with A15 crystal structure. The calculateddiffusion parameters will help in validating the theoretical analysis on defect structure of the phase.

� 2009 Elsevier Ltd. All rights reserved.

There is a renewed interest to study diffusion and defectstructure of intermetallic compounds with A15 crystal structure,since most of them possess superconductivity. Experimental dataon diffusion parameters, which help to validate the theoreticalanalysis on defect structure, are available only in few systems likeV3Ga [1] and V3Si [2]. Theoretical analysis on defect structures isconducted in Nb3Sn compound, which has the same crystal struc-ture by Besson et al. [3]. They found that even at stoichiometriccomposition high concentration of antisite defects are present atelevated temperature. Further, vacancies present on the sublatticefor major element (Nb) are much higher than the vacancies presenton the sublattice for minor element (Sn). Following they predictedthat Nb diffusion rate must be much higher than the diffusion rateof Sn in the Nb3Sn phase. They also calculated the integrateddiffusion coefficient and determined the activation energy ofdiffusion for comparison with the experimental results to validatethe theoretical analysis. Unfortunately there are no reliable exper-imental data available in this system. Numerous articles are avail-able on the growth kinetics of the Nb3Sn phase [4–6]. However, itwas not possible to determine the diffusion parameters in theseexperiments, since the experiments were conducted with the aimto replicate the bronze technique (interaction between Nb andCu(Sn) bronze alloy, where Nb3Sn grows at the interface). This isnot an ideal methodology to determine the diffusion parameters tovalidate the theoretical analysis conducted in a binary Nb–Sn

: þ91 802360 0472.aul).

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system. At present, we are trying to determine the diffusionparameters in this system. The present article’s aim is to determinethe diffusion parameters in another A15 intermetallic compound,Ti3Au, which has the same crystal structure. The parameterscalculated in this study will help to compare the data available inother systems. This will further help to understand the atomicmechanism of diffusion and defect concentrations in A15 inter-metallic compounds, since different systems will have differentconcentrations of structural defects.

In this study diffusion couple technique is used to determine theintegrated diffusion coefficient and activation energy. Titaniumwith the purity of 99.98 wt% and gold with the purity of 99.99 wt%are used in this study to make the end members. An alloy withphase mixture of Ti3Au and TiAu (average composition of Ti-34 at.%Au) was prepared by arc melting. Further it was equilibratedat 1175 �C for 24 h under vacuum (w10�6 mbar). Slices withdimension of around 7� 7�1 mm were cut by slow speed dia-mond saw and bonding faces were ground and polished followingstandard metallographic preparation up to 1 mm finish. Polishedspecimens of the alloy and pure Ti were then clamped together andannealed at five different temperatures in the temperature range of1000–1200 �C for 24 h in vacuum (w10�6 mbar). After the experi-ment, bonded specimens were cross-sectioned by slow speed dia-mond saw and again standard metallographic preparation wasfollowed. The interdiffusion zone was examined by scanning elec-tron microscope (SEM) and composition profile was measured withattached energy dispersive spectrometer (EDS).

SEM image of the interdiffusion zone of the diffusion coupleannealed at 1050 �C for 24 h is shown in Fig. 1a and corresponding

7.0x10-4 7.5x10-4 8.0x10-410-17

10-16

10-15

10-14

(Ti-34 at.%Au) / Ti diffusion couple

1/T (K-1

)

kp

(m

2/s

)

Fig. 2. The parabolic growth constant of the product phase calculated at differenttemperatures is shown.

A.K. Kumar, A. Paul / Intermetallics 17 (2009) 962–964 963

average composition profile is shown in Fig. 1b. It should be notedhere that we have presented the average alloy composition used asone of the end members, which is used to calculate the diffusionparameters. Significant penetration of Au in the Ti end member wasfound. The parabolic growth constant (kp) of the product phase wascalculated from the measured layer thickness (Dx) and annealingtime, t following

Dx2 ¼ 2kpt (1)

The parabolic growth constant data calculated at differenttemperatures are plotted in Fig. 2. Further, the activation energy, Q(J/mol) for the growth was calculated from

kp ¼ kopexp

��Q

RT

�(2)

where kpo is the pre-exponential factor, R (¼8.314 J/mol K) is the gas

constant and T is the temperature in Kelvin. The activation energyfor the growth was found to be 222 kJ/mol. However, it should benoted that parabolic growth constant is not a material constant anddepends on the end member composition. So it is necessary todetermine the diffusion parameters and the activation energy fordiffusion, which will shed light on the growth kinetics irrespectiveof the end member composition and the atomic mechanism ofdiffusion.

Since the phase (Ti3Au) of interest grows with very narrowhomogeneity range following the phase diagram [7], it is not

Fig. 1. (a) Interdiffusion zone of the diffusion couple annealed at 1050 �C for 24 h isshown. Unaffected part of the Ti end member is beyond the limit of micrograph, (b) theaverage composition profile is shown. The average composition of the alloy, which isused to calculate the diffusion parameter, is presented.

possible to measure the vanishingly small concentration gradientto calculate the interdiffusion coefficient. For this kind of cases,Wagner [8] introduced the concept of integrated diffusion coeffi-cient ð~DintÞ; which is basically the interdiffusion coefficient, ~Dintegrated over the homogeneity range and can be expressed as

~Dbint ¼

ZN00i

N0i

~DdNi ¼ ~DDNbi (3)

where Ni is the composition of element i and DNib¼Ni

00�Ni

0is the

homogeneity range of the product phase, b (in our case it is Ti3Au).The integrated diffusion coefficient of a phase b from the compo-sition profile can be measured from Ref. [9]

~Dbint ¼

�Nb

i � N�i

��Nþi � Nb

i

�Nþi � N�i

Dx2

2t

þ Dx2t

264Nþi � Nb

i

Nþi � N�i

ZxI

�N

Vbm

Vm

�Ni � N�i

�dx

þNb

i � N�iNþi � N�i

ZþN

xII

Vbm

Vm

�Nþi � Ni

�dx

375 (4)

where Nib is the average/stoichiometric composition of the product

phase, Ni� and Ni

þ are the composition of the unaffected left- andright-hand side of the end member. Vm is the molar volume. Molarvolume of the product phase, Ti3Au (Vb

m¼ 9.95 cm3/mol) iscalculated from the lattice parameter data available in Ref. [10].Further, molar volume at different composition in Ti(Au) wasconsidered following Vegard’s law from the knowledge of themolar volume of pure elements (VTi

m¼ 10.64 and VAum¼ 10.21

cm3/mol). The integrated diffusion coefficient of the product phasecalculated at different temperatures is shown in Fig. 3. Further, theactivation energy for diffusion is calculated following

~Dbint ¼ Doexp

��Q

RT

�(5)

7.0x10-4 7.5x10-4 8.0x10-410-17

10-16

10-15

10-14

1/T (K-1

)

(Ti-34 at.%Au) / Ti diffusion couple

Din

t (m

2/s)

~

Activation energy, Q = 219kJ/mole

Fig. 3. The integrated diffusion coefficient at different temperature is plotted followingArrhenius equation.

A.K. Kumar, A. Paul / Intermetallics 17 (2009) 962–964964

where Do (m2/s) is the pre-exponential exponent. The activationenergy for diffusion is calculated to be 219 kJ/mol. This indicatesthat diffusion occurs by lattice mechanism. It should be noted herethat we have conducted experiments at a particular annealing timeonly. Since the experiments are conducted at relatively hightemperatures, there is no doubt about the lattice diffusion

controlled process and thickness versus time plot is not necessary.This is further supported from the activation energy for diffusioncalculated, which indicates that lattice diffusion is operative.

Acknowledgment

A. Paul would like to acknowledge the financial support receivedfrom CSIR, India (No. 22(409)/06/EMRII) for this research work.

References

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