Point defects in Ni2Si: 63Ni diffusion and differential scanning calorimetry study of quenched-in vacancies

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Point defects in Ni Si: 63Ni diffusion and differential 2 scanning calorimetry study of quenched-in vacancies

A. Jennane , E.H. Sayouty , J. Bernardini &

G. Moya

Published online: 14 Nov 2010.

To cite this article: A. Jennane , E.H. Sayouty , J. Bernardini & G. Moya (1997) Point defects in Ni Si: 63Ni diffusion and differential 2 scanning calorimetry study of quenched-in vacancies, Philosophical Magazine Letters, 76:1, 33-40, DOI: 10.1080/095008397179354

To link to this article: http://dx.doi.org/10.1080/095008397179354

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P

M

L

, 1997, V

76, N

1, 33± 40

Point defects in Ni

Si:

Ni diffusion and differential scanning calorimetry study of quenched-in vacancies

By A. J

§, E. H. S

, J. B

and G. M

§

²

Laboratoire de Physique NucleÂaire, Faculte des Sciences d’AõÈ n-Chock, BP 5366, Casablanca, Maroc

³

Laboratoire de MeÂtallurgie associe au CNRS (UMR 6518 ) , Faculte des Sciences de St JeÂroÃme, 13397 Marseille, Cedex 20, France

§Laboratoire de Physique des MateÂriaux (EA 882 ) , Faculte des Sciences de St JeÂroÃme, 13397 Marseille, Cedex 20, France

[Received 28 January 1997 and accepted 28 February 1997]

A

No curvature is observed in the Arrhenius plot for nickel volume di€ usion coe cients measured up to T

0 ´ 94T

in Ni

Si using

Ni as a tracer.

Di€ erential scanning calorimetry performed on the same samples, quenched from 820 and 1015

C, reveals two annealing stages, in good agreement with a previous positron annihilation study. The activation energy and the order of the reaction for each stage have been determined. At low temperatures, the activation energy of the stage centred at about 180

C ( 1 ´ 1

0 ´ 1 eV ) is integrated as the nickel monovacancy migration energy. It is assumed that the second stage, centred at about 380

C, corresponds to the break-up of vacancy clusters; its activation energy ( 2 ´ 6

0 ´ 1 eV ) is in agreement with that measured for nickel bulk di€ usion ( 2 ´ 42

0 ´ 04 eV ) .

§

1. I

That point defects in¯ uence many physical properties of crystalline materials and are responsible for di€ usion-controlled processes, which often govern solid-state reactions, is now well accepted. Little information, however, has been obtained on these defects in intermetallic compounds apart from tracer di€ usion measurements (Mehrer 1996 ) . Bulk di€ usion of nickel in the intermetallic compound Ni

Si has been investigated (Ciccariello et al. 1990 ) using the

Ni radiotracer and the sectioning technique between 647 and 910

C (0 ´ 5 < T / T

< 0 ´ 7 ) . The value of the activation energy (Q

= 2 ´ 48 eV ) is in agreement with a vacancy mechanism. It is the purpose of the present paper to obtain a better characterization of the vacancy defects present after quenching in this compound using di€ erential scanning calorimetry (DSC ) as previously done for the compound

-NiSb (Jennane et al. 1992 ) . Such a kinetic study allows one to determine the reaction order and the activation energy of the di€ erent stages which occur during the temperature scan. To discuss the di€ usion mechanism of nickel, ® rstly the vacancy concentrations on the nickel and silicon sublattices have been evaluated using Miedema’s (1979 ) theory and secondly di€ usion experiments of

63

Ni have been carried out at temperatures higher than 0 ´ 7T

where T

is the melting temperature.

0950± 0839/97 $12´00

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§

2. E

Polycrystalline Ni

Si compounds were obtained by levitation melting from pure nickel and silicon (see Ciccariello et al. (1990 ) for details ) . Samples with speci® c dimensions were prepared by electro-erosion, mechanically polished and successively annealed at 1100

C for 1 h and at 700

C for 14 h in quartz tubes under a pure argon atmosphere before being slowly cooled in the furnace. To avoid any contact between the sample and the quartz, the former was placed on a small plate of alumina.

2.1. Non-equilibrium technique: differential scanning calorimetry

Many investigations have shown that kinetic parameters such as the activation energy E

of a thermally activated process can be evaluated from anisothermal measurements, performed by DSC for instance, as reliably as from isothermal mea- surements. This point, which was controversial (Brown 1988 ) , has been previously discussed in detail (Jennane et al. 1992, Sassi et al. 1993 ) . Brie¯ y, DSC measures a thermal ¯ ux as a function of temperature which varies linearly with time. When only one kind of defect is eliminated, the energy released q ( t ) at time t can be written:

q ( t ) = Q ( 0 ) - ^{Q ( t )} , ^{( 1 )}

where the stored energy Q ( t ) is given by:

Q ( t ) = D H

C ( t ) . ( 2 )

In eqn. (2 ) , C ( t ) represents the concentration of the remaining free defects at time t whose enthalpy of formation is D H

. When t = 0 , ^{Q ( 0 ) = D H}

^{C ( 0 ) where C ( 0 ) is}

the initial relevant defect concentration. Thus the thermal ¯ ux released by a sample during an anneal is de® ned by

dq

dt ⁼ - ^dQ _dt ^{( t ) =} - ^{D H}

^dC _dt ^{( t ) . ( 3 )}

In eqn. (3 ) , dC ( t ) /d t may be identi® ed with the rate of a chemical reaction of mth order. So

dC ( t )

dt ⁼ - ^k [ ^{C ( t )} ]

^,

where k is the rate constant . When the annealing is performed at a constant heating rate a = dT /d t, one can write

dq

dT ⁼ - ^dQ _dT ⁼ - ^{D H}

^dC _dT ^{= D H}

_a ^kC

^{. ( 4 )}

For low or average heating rates, the term dq /dT can be assimilated to the de¯ ection at any point on the thermogram and the quantity of heat released between two temperatures T

and T, where T is the temperature of the sample at the annealing time t, and is given by

[ ^{D q ( T )} ] _T ^T

⁼ ò

^{dT dq dT = -} D H

ò

^{dC dT dT = -} D H

[ ^{C ( T ) - C ( T}

⁾ ] ^.

If T

is the temperature when the relevant defect becomes mobile, then C ( T

) _< C ( 0 )

and

34 A. Jennane et al.

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q ( T ) = D H

[ ^{C ( 0 ) - C ( T )} ] ^{= D H}

^C _Â ^{( T ) ,}

where C Â ^{( T )} is the defect concentration eliminated at the temperature T. So q ( T ) is equal to A ( T ) , the partial area under the thermogram between temperatures T

and T . In the same way, the total heat e€ ect linked to the total elimination of defects during an isochronal anneal, which appears as a peak occurring between the temperatures T

and T

on the thermogram, may be written as

q ( T

) = D H

C Â ^{( T}

^{) =} D H

C ( 0 ) = Q ( 0 ) .

Q ( 0 ) is equal to A ( T

) , the total area under the peak while Q ( T ) = Q ( 0 ) - ^{q ( T ) is}

equal to A ( T

) - ^{A ( T ) .}

Thus, it follows from eqn. (4 ) that, for any annealing time t where the temperature is equal to T ,

k

= d q

( ) dT ^{a C}

^-

^{[ [ A A ( ( T T}

^{) ) ] -}

^{- A}

^{( T ) ]}

^{. ( 5 )} Since the annealing process is thermally activated, the reaction rate constant k

may be written as a function of temperature in the following way:

k

= k

exp - ^E

k

T

( ) ^{, ( 6 )}

where k

is the frequency factor, k

is the Boltzmann constant and E

is the activation energy for the annealing process.

Samples (5 mm in diameter, 0 ´ 8 mm thick and with mass about 80 mg ) were put in a vertical furnace for 2 h at the quench temperature T

before rapid quenching in salt water at 0

C by gravity (quenching rate about 10

C s ^-

) . Then the quenched sample was placed in the crucible of the laboratory cell of a Perkin± Elmer di€ erential scanning calorimeter. The other cell contained a reference sample, pre-annealed at 850

C for 14 h under argon, to obtain a reliable base line.

Ni

Si samples were quenched from T

= 820 and 1015

C. To measure the ¯ ux linked to the stored energy release, thermograms were produced by linearly scanning the temperature from room temperature to 550

C under ¯ owing argon.

2.2. Equilibrium technique: diffusion of

Ni

Details of this technique have been given by Ciccariello et al. (1990 ) .

Ni di€ u- sion was performed in quartz tubes under a pure argon atmosphere in pre-heated furnaces and rapidly stopped, at the end of the annealing period, by cooling the quartz tubes with water. Before the di€ usion treatment the samples (1 ´ 5 mm in diameter and 2 mm thick ) were pre-annealed at the intended di€ usion temperature to ensure that the defects are in equilibrium. After the di€ usion treatment, the side edges and back surface were ground o€ for a distance of several di€ usion lengths to minimize the e€ ect of possible side or back di€ usion on the radioactive counting.

The remaining procedures were sectioning, weighing and counting out as usual in radiotracer experiments. Penetration pro® les were obtained by a mechanical section- ing technique. As the

Ni tracer (speci® c activity about 6 mCi mg ^-

) is a soft

emitter (67 keV ) , the A

residual activity of the samples at di€ erent depths x was detected using a low-

-background detector and the di€ usion coe cients D of nickel were determined from the slopes of the curves of ln A

= f ( x

) .

Point defects in Ni

Si 35

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§

3. E

3.1. Differential scanning calorimetry results

Figure 1 shows the thermograms for Ni

Si samples quenched from T

= 820

C and T

= 1015

C (heating rate a = 20

C min ^-

) . One observes two energy release peaks, centred around 180 and 380

C respectively. The two peaks have the same shape, which indicates the same order of reaction (Wang et al. 1984 ) . The rate constants were determined by ® tting successively the two experimental thermograms with the ® rst-order ( m = 1 ) and second-order ( m = 2 ) kinetic test corresponding to eqn. (4 ) . When the rate constants are extracted assuming that m = 2, the data points are well ® tted by a straight line on a logarithmic plot. The Arrhenius plots of the rate constants corresponding to the two annealing stages carried out for T

= 1015

C are shown in ® gs. 2 and 3. The activation energies E

and E

for peaks 1 and 2 and determined from eqn. (6 ) are equal to 1 ´ 1 6 0 ´ 1 and 2 ´ 6 6 0 ´ 1 eV respectively. It is worth noting that, when the reaction order is known, E

can also be determined

36 A. Jennane et al.

Fig. 1

Release rate of stored energy for specimens quenched from T

820

C and T

1015

C (heating rate a

20

C min

) .

Fig. 2

Arrhenius plot of the rate constants for the low-temperature annealing stage ( T

1015

C ) .

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(Granato and Nilan 1965 ) from the half-width D T

of the peak of the thermograms by the relation

E

= B k

T

D T

, ^{( 7 )}

where T

corresponds to the maximum of the peak and B to a constant depending on the order of the reaction; as B = 2 ´ 9 when m = 2 (Iwata and Nihira 1976 ) , one

® nds by using eqn. (7 ) that E

= 1 ´ 03 eV and E

= 2 ´ 7 eV, con® rming both the order of the reaction and the energies previously determined by the rate-constant method.

3.2. Radio-tracer diffusion results

Three measurements of nickel di€ usion have been performed at high tempera- tures (0 ´ 84 < T / T

< 0 ´ 94 ) to complete those previously reported by Ciccariello et al. (1990 ) . As expected for di€ usion by a single mechanism in an homogeneous material, the pro® les are well ® tted by the solution of Fick’s second law relative to a di€ usion from an instantaneous source (® g. 4 ) . All the relevant parameters asso- ciated with these measurements are presented in the table. The di€ usion coe cients D are plotted in the Arrhenius diagram, drawn in ® g. 5, where the values previously published by Ciccariello et al. (1990 ) are also reported. It can be observed in this

® gure that all the coe cients ® t well a single Arrhenius plot leading to a di€ usion activation energy Q

= 2 ´ 42 6 0 ´ 04 eV.

Point defects in Ni

Si 37

Fig. 3

Arrhenius plot of the rate constants for the high-temperature annealing stage (T

1015

C ) .

Diffusion coefficients of nickel in Ni

Si.

(

T C ) (cm ^D

s

) ¹⁰

4

( Dt )

(cm )

1058 1 ´ 06 ´ 10

27 ´ 63

1183 6 ´ 54 ´ 10

68 ´ 62

1207 1 ´ 02 ´ 10

85 ´ 70

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§

4. D

Before interpreting the existence of two stages in the DSC thermograms, let us recall that these two recovery stages have also been observed in a previous positron annihilation spectroscopy (PAS ) study of quenched Ni

Si samples (Jennane et al.

1994 ) . DSC peaks are slightly shifted to higher temperatures (about 50 K ) because the heating rate (20

C min ^-

) is much higher than that used in the PAS experiments (1 ´ 68

Cmin ^-

) . From Miedema’s (1979 ) model, vacancy formation energies of 0 ´ 93 and 1 ´ 64 eV are predicted for the nickel and silicon sublattices respectively which implies a ratio C

( Ni ) /C

( Si ) = 700 at 1015

C, that is thermal vacancies are mainly formed on the nickel sublattice.

38 A. Jennane et al.

Fig. 4

Penetration profiles of

Ni in Ni

Si samples.

Fig. 5

Arrhenius plot of the

Ni lattice diffusion coefficients in Ni

Si ( j ) , from Ciccariello et al.

(1990 ) ; ( m ) , present results.

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No curvature is present in the Arrhenius plot of ln D = f ( _{1 /T} ) for the nickel di€ usion, and so the presence of divacancies can be ruled out. Thus the migration of this complex defect cannot be assumed to explain the ® rst peak detected on the DSC thermograms as claimed by Wang, Shimotomai and Doyama (1983 ) for NiAl com- pounds. Taking this and the value of the reaction order (m = 2 ) into account, we propose the following.

(a ) In the first stage, at low temperatures, nickel vacancies agglomerate to form divacancies as precursors of very small clusters. The activation energy E

= 1 ´ 1 eV can be identified with the migration energy D H

of quenched Ni monovacancies.

(b ) In the second stage, at high temperatures, the clusters become unstable; they break up, releasing their vacancies which rapidly annihilate at the sinks of the crystal. The activation energy E

= 2 ´ 6 eV is in effect very close to the diffusion activation energy (2 ´ 42 eV ) which is identified with that necessary to break up the clusters (Meshi 1965, Moser 1977 ) . The slight difference (0 ´ 18 eV ) might indicate that in an ordered compound a cluster mainly formed with one kind of vacancy cannot disappear without modifiyng both the sublattices.

The present value of D H

is in agreement with that measured for pure nickel (Khama and Sonnberg 1981, Wang et al. 1984, Cochrane et al. 1984 ) and the ratio D H

/ Q

= 0 ´ 44, determined from the present DSC and radio-tracer measure- ments is comparable with that for Ni

Al (Hancock 1971 ) and pure nickel (Bron® n et al. 1975 ) which supports a vacancy mechanism. On the atomic scale this agreement is well understood by the structure (Tu et al. 1975 ) of the

-Ni

Si (structure, C23;

type, PbCl

) where nickel atoms form continuous zigzag chains, allowing nickel atom di€ usion on its own sublattice.

From the approximate relation:

Q

< D H

+ D H

, ^{( 8 )}

one can estimate D H

to be about 1 ´ 40 eV, which is higher than the value calcu- lated from Miedema’s theory. Using this value, the nickel vacancy atomic concen- tration would be 8 ´ 3 ´ 10 ^-

for T

= 1015

C. Such a concentration is too low ® rst to be measured by DSC and second to explain the saturated positron spectra previously observed (Jennane et al. 1994 ) for Ni

Si samples quenched from a lower temperature ( T

= 905

C ) . To reach a vacancy concentration of about 10 ^-

which saturates the positron spectrum, a value at least equal to 1 ´ 14 eV, in agreement with Miedema’s value (0 ´ 93 eV ) , must be assumed. The apparent small discrepancy between the two values of 1 ´ 14 and 1 ´ 40 eV could be linked to a variation in the correlation factor with temperature, the variation of which is not taken into account in the approximate relation (8 ) .

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40 Point defects in Ni

Si

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