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Materials Science and Engineering A 460–461 (2007) 7–13

Sintering and grain growth kinetics of ball millednanocrystalline nickel powder

Bharat B. Panigrahi ∗,1

Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India

Received 14 July 2006; received in revised form 28 December 2006; accepted 11 January 2007

bstract

Detailed studies on the sintering and grain growth of ball milled nanocrystalline nickel power were carried out. The analysis of grain coarseningrocess was found to be very helpful for understanding the sintering mechanisms. The explosive grain growth was observed at higher temperaturend the activation energy of grain growth increased with increasing temperature. The grain boundary diffusion was identified as grain growth

echanism at lower temperatures. This powder showed very low activation energy of sintering (66.2 ± 3 kJ mol−1). The surface diffusion was

ound as dominating mechanism through out the sintering. At higher temperatures lattice diffusion was found to be controlling both, sintering andrain growth. 2007 Elsevier B.V. All rights reserved.

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eywords: Sintering; Dilatometry; Diffusion; Grain growth; Neck ratio

. Introduction

Nanocrystalline powders (NP) have been the subject of con-iderable experimental work in recent years [1–3]. Severalynthesis techniques have been developed and each techniqueives nanocrystalline samples with a specific microstructure, andence with potentially different properties. NP shows a largepecific surface area and a high defect density (especially inilled powders), which can act as an additional driving force

uring sintering. These powders were reported to sinter at muchower temperatures, as low as 0.2–0.3Tm (Tm is melting tempera-ure) and to show a high sintering rate [3,4]. However, the grainrowth is a major concern during sintering of NP and hence,he grain size dependent parameters [5], such as diffusivitiesnd activation energies would be continuously changing throughut the process. Due to lack of clear understanding of diffusionehaviours, their sintering mechanisms have been remained con-

roversial. NP tends to yield relatively low activation energy ofintering [3,4]. The mass flow mechanism, such as, grain rota-ion (GR) and grain sliding, which are not normally observed

∗ Tel.: +82 42 868 5499; fax: +82 42 868 5032.E-mail addresses: panigrahi14@yahoo.com, pani@kriss.re.kr.

1 Present address: Division of Advanced Technology, Korea Research Institutef Standards & Science, Daejeon 305-340, Korea.

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921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2007.01.035

n normal powder, were reported in nano powders to controloth, sintering and grain growth [6–9]. Recently, Panigrahi etl. [4] was reported a gradual change in sintering mechanismsith increasing temperatures in nanocrystalline titanium. They

howed that sintering initially started with dislocation motionnd particle slidings, followed by the grain boundary diffusionGBD) at moderate temperatures and volume diffusion (VD)long with GR dominated the sintering at higher temperatures.

Nanocrystalline nickel (n-Ni) has attracted much attentionue to its commercial importance and several works wereeported on its synthesis and grain growth behaviour. The n-i was reported to show a high grain growth with increasing

emperatures [10–17]. In electrodeposited n-Ni, Klement et al.10] observed grain growth up to about 250 nm at 593 K andobayashi et al. [17] reported the grain size exceeding over500 nm at 1073 K. Ball milled n-Ni was reported to show rel-tively higher thermal stability up to about 600 K compared tohe nanostructured Ni prepared by sever plastic deformation orhemical route [11,16]. Few studies were reported [7,18] on theintering behaviour of n-Ni powders. Andrievski [7] observedhe formation of non uniform microscopic pores during sinter-ng of nanocrystalline nickel, which after piled up, led to the

articles rearrangements and slidings. Ragulya and Skorokhod18] employed a rate controlled sintering technique on n-Nio achieve density level up to 99% with relatively little grainrowth.

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B.B. Panigrahi / Materials Science a

It appears that most of the reported studies on sinteringnd grain growth of n-Ni were carried out independently whileeglecting the effect of grain growth (occurring simultaneously)n sintering behaviour. Present investigation attempts to under-tand the sintering kinetics of ball milled n-Ni using dilatometricintering and its grain growth kinetics. Efforts have been made tovaluate the sintering mechanisms and the influence of the grainrowth on the same through the grain size dependent sinteringaps.

. Experimental

The n-Ni was prepared by high energy ball milling from325 mesh high purity (99.7%) nickel powder. The ball to

owder ratio (weight) was 10:1 using WC balls (∼10 mmiameter) and vial (250 ml), with rotating speed of 300 rpm,illing was done for 35 h. To avoid agglomeration or clogging

f powders during milling, toluene was added to the vials prioro milling. Average grain size (crystallite size) was found to be2 nm, calculated through the X-ray diffraction (XRD) analysis19]. The transmission electron microscopy study of the milledowder revealed, the particles were mostly in the range of0–60 nm in size (Fig. 1).

Powder was compacted in a steel die (7.94 mm diameter)y applying uniaxial compaction pressure of about 250 MPa.he L0/d0 ratio (where L0 is the length and d0 is the diameter)f the green compact was about 0.55 and the average densityf about 5.8 g cm−3 (∼65% theoretical). Sintering of the com-acts was carried out in a high sensitivity (±0.5 �m) dilatometricystem (Shimadzu DT30 Thermal Analyzer, Japan) under highurity argon (further purified by passing over titanium turningseated at 1000 ◦C). Compacts were heated with a heating rate

◦ −1

f 10 C min to various temperatures: 300, 400, 600, 800 and000 ◦C for an isothermal holding time of 60 min. The sampleas allowed to cool in the furnace. The dimensional changes (in

he axial direction) throughout the thermal cycle were recorded

Fig. 1. TEM micrograph of the 35 h milled Ni powder.

talrQwt

F

gineering A 460–461 (2007) 7–13

ontinuously on a strip chart recorder. For the grain growthtudy additional sets of samples were sintered for 0 min (at theoment when temperature reached to set point), 10 and 30 min

nder identical conditions. The grain size (crystallite size) of theintered sample was measured by XRD method.

. Results and discussion

.1. Grain growth

The sample shows explosive grain growth up to 1036 nm at273 K (Fig. 2). This result was not much surprising; as suchrowth was earlier reported by others also [10–17]. The grainrowth behaviour of nanocrystalline material was reported tobey the law [20,21]:

m − Gm0 = Kgmt (1)

here G0 is the initial grain size, G the grain size at time t, mconstant and Kg is the grain boundary mobility parameter. Ifm0 is negligible compared with Gm, Eq. (1) becomes

n(G) = 1

mln(t) + 1

mln(Kgm) (2)

Further, the Kg is a temperature dependent parameter, givens

g = K0 exp

(− Qg

RT

)(3)

here K0 is a constant, Qg the activation energy for the grainoarsening, R the universal gas constant and T is the temperature.ig. 3 shows the logarithmic plot of G versus t to obtain the valuesf m, which was found to vary from 3.9 to 5.3 with increasingemperatures. The plot of ln Kg versus 1/T was shown in Fig. 4nd it was found that data points do not follow single straightine fit. Thus the data was fitted for two separate temperature

anges for determining activation energies of grain growth, i.e.

g1 (for 573–873 K) and Qg2 (for 873–1273 K). In the presentork, Qg1 was found to be 111.7 ± 6 kJ mol−1. Interestingly,

he activation energy of grain boundary (GB) self-diffusion was

ig. 2. Measured grain size as a function of temperature and isothermal time.

B.B. Panigrahi / Materials Science and Engineering A 460–461 (2007) 7–13 9

Fv

r1Twdiw

3

Wctbis(�

tr

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Fe

Fig. 5. Dilatometric sintering curves of the n-Ni powder compacts. Curves couldbe divided in three regions: (1) constant rate heating, (2) isothermal zone, and(3) cooling zone.

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ig. 3. Log–log plots of grain size and time for obtaining the values of m atarious temperatures.

eported [22] to be 115 kJ mol−1 and Qg was reported [15] to be02.5 kJ mol−1 which was attributed to the GBD mechanism.he Qg2 was found to be 266.4 ± 8 kJ mol−1 (in the presentork) which was close to the activation energy of lattice selfiffusion (271 kJ mol−1 [22]). It appears that the grain growths initially controlled by GBD but at higher temperatures VDould be the grain growth mechanism.

.2. Sintering and activation energy

Dilatometric plots of the samples have been shown in Fig. 5.hen the heating was started, sample did not show any signifi-

ant thermal expansion, the sintering line moved almost horizon-ally and at about 200 ◦C, it started shrinking slowly, followedy a rapid shrinkage. Shrinkage rate slowed down gradually dur-ng isothermal holding. When the furnace was switched-off, ithowed continuous contraction. Most of the samples showedFig. 6) nearly isotropic shrinkage [(�L/L0)/(�d/d0) ∼= 1, whereL is change in length and �d is change in diameter]. The sin-

ered density increased gradually with temperature (Fig. 6) andeached up to 94.2% (theoretical) at 1273 K.

The linear shrinkages from the dilatometric curves were mea-ured by usual method [4,23] and shown in Fig. 7. The activation

ig. 4. Arrhenius plot of Kg and temperature for determining the activationnergies of grain growth.

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Fa

ig. 6. Densities and relative dimensional changes [ratio of the axial (�L/L0)o radial (�d/d0) shrinkage] after sintering for 60 min (RT, room temperature).

nergy (Q) for the sintering was estimated using the followingquation [24,25]:

nQ

n Y = C0 − n ln T −

RT+ n ln t (4)

here Y is �L/L0, C0 the constant containing physical parame-ers and n is an exponent. The value of n could be obtained from

ig. 7. Measured shrinkages from dilatometric curves as a function of temper-ture and isothermal time.

10 B.B. Panigrahi / Materials Science and Engineering A 460–461 (2007) 7–13

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ig. 8. Log–log plots of linear shrinkage vs. isothermal time to obtain the valuesf n and C.

he slope of the plot of ln(Y) versus ln(t) (Fig. 8). The valuef n was found to be decreasing and the intercept, C (obtainedrom the plots of Fig. 8) was found to be increasing graduallyith increasing temperatures (Fig. 9). According to Eq. (4), the

ntercept (C) would be given as

= C0 − n ln T − nQ

RT(5)

From Eq. (5), the plot of C versus n/T (Fig. 10) would yieldslope equal to Q/R. The Q was found to be 66.2 ± 3 kJ mol−1

hich was much smaller than the reported activation energiesf the self-diffusions (SD, GBD or VD) of polycrystalline NiAppendix A). The activation energy of grain boundary selfiffusion in n-Ni was reported to be 46 kJ mol−1 for a veryow temperature range (293–473 K) by Bokstein et al. [26] ando other diffusion data are available at the moment for n-Ni.his caused difficulty in identifying the densification mecha-ism. Thus, to evaluate the sintering mechanism, attempts wereade through the kinetic models of Ashby [27] analogous to the

uthor’s earlier works [4].

.3. Analysis of mechanism through sintering models

Ashby [27] proposed equations to predict theoretically theeck growth rate (x/t, where x is neck size and t is time) during

ig. 9. Dependence of slope n and intercept C (obtained from Fig. 8) on theemperature.

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ig. 10. Arrhenius plot of C vs. n/T to determine the activation energy ofintering.

intering, using bulk material properties and diffusivity data. Tose these models, the measurements of neck size between parti-le couples are required. Since, the powder does not comprise ofono-sized particles, measuring the neck size accurately in thene and irregular shaped particles would be extremely difficult.nstead of neck growth rate (x/t), those equations can be pre-ented in terms of rate of change of neck ratio [r = (x/a)/t, whereis the particle radius] also. The value of r can be obtained from

he linear shrinkage with a good approximation [4,23,28] as

= x/a

t= (2Y )1/2

t(6)

The Ashby’s [27] equations for different mechanisms can beiven in terms of r, as:

(i) Surface diffusion (SD) from the surface source:

rs = 2δsDsFK31

a(7)

ii) VD from a surface source:

rv1 = 2DvFK21

a(8)

ii) VD from sources on the GB:

rv2 = 4DvFK22

a(9)

iv) GB transport from sources on the GB:

rb = 4δbDbFK22

xa(10)

v) Vapour transport from a surface source:

rvp = PvFK1

a

(Ω

2πΔ0kT

)1/2

(11)

here δs is the effective surface thickness, δb the effective grainoundary thickness, Ds, Db, Dv are the surface diffusion (SD),BD and VD coefficients, respectively; F the γsΩkT, γs is the

urface free energy, Ω the atomic volume, k the Boltzmann’s

B.B. Panigrahi / Materials Science and Engineering A 460–461 (2007) 7–13 11

Table 1Experimental and predicted rates (r) for 0 min shrinkage data

Temperature(K)

Mean particlesize (nm)

Experimental r(cm cm−1 s−1)

Predicted r (cm cm−1 s−1) for various mechanisms

rs rv1 rv2 rb rvp

573 44 7.20 × 10−4 6.58 × 10−3 2.08 × 10−10 4.91 × 10−10 3.05 × 10 1.16 × 10−24

673 66 1.20 × 10−3 8.04 × 10−4 3.71 × 10−9 1.06 × 10−8 1.16 1.24 × 10−20

−3 10−2 −6 −5 −14

1 10−2

1 10−2

ct

i

Fsr

873 97 1.10 × 10 1.06 ×073 138 9.90 × 10−4 5.59 ×273 414 8.60 × 10−4 3.10 ×

onstant, K1 and K2 are the curvature differences and Δ0 is theheoretical density.

The necessary physical data for the calculations were shownn Appendix A. The predictions of sintering rates (r) were car-

rasn

ig. 11. Contour plots of the predicted rates (r), in z-axis, for the mechanisms rs, rv1 anhrinkage data as a function of particle size and temperature. The contour lines haveange of experimentally observed rates. Grain growths at 0, 10 and 30 min (isotherma

5.91 × 10 1.78 × 10 1.15 1.50 × 105.89 × 10−4 1.62 × 10−3 9.73 × 10−1 8.76 × 10−11

3.69 × 10−3 8.87 × 10−3 1.37 × 10−1 1.33 × 10−8

ied out first for the measured particle size using x/a obtainedt 0 min. The predicted rates for various mechanisms have beenhown in Table 1. For determining the mass transport mecha-ism, the predicted rates were compared (an order of magnitude)

d rv2 for 0 min (a, b and c, respectively) and for 30 min (d, e and f, respectively)been leveled with their values (cm cm−1 s−1). The hatching patterns show thel holding) have also been shown.

1 nd Engineering A 460–461 (2007) 7–13

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2 B.B. Panigrahi / Materials Science a

ith the experimentally obtained rates (also shown in the sameable). A careful observation of Table 1 indicates that SD mecha-ism (rs), matches closely (within one order of magnitude) withxperimental rates at lower temperature range (573–873 K). Thewo lattice diffusion mechanisms (rv1 and rv2) seem to have val-es near to experimental rates at higher temperatures only (1073nd 1273 K). The rest of the mechanisms, rb, and rvp show aarge deviation (by three or higher orders) from experimentalates. For a clear understanding of the process, the predictedates for each mechanism were represented through the three-imensional contour plots as a function of particle size andemperature. As indicated by Table 1, only dominating mech-nisms (rs, rv1 and rv2) have been presented here for detailednalysis in the form of contour plots (Fig. 11). These maps areignificantly different than the sintering diagram of Ashby [27]as a function of temperature and neck ratio for a single par-icle size). In the present map (Fig. 11), the particle size washown in x-axis and temperature was shown in y-axis whereashe predicted rates were shown in z-axis (perpendicular to thelane of paper). Using the x/a data obtained at 0 and 30 min,he rates were predicted for a wide range of assumed particleizes (ranging from 10 to 1050 nm) as shown in Fig. 11(a)–(f).he predictions for a large range of particles were carried out

o consider the effect of non-homogeneous particle sizes andrain growth on sintering rates. The predicted rates, which havehe values in the experimental range, were marked by hatchingdiagonal line patterns). The measured grain size after sinteringor 0, 10 and 30 min were also shown in the respective figures.

The SD seems to be controlling the process during initialeating (Fig. 11(a)). The grain sizes measured at 0 min were verylose to the predicted r. The VD mechanisms (rv1 and rv2) seemo operate above 873 K (Fig. 11(b) and (c)) as the measured grainizes are located in the predicted range of rv1 and rv2. When theates were predicted for 30 min (Fig. 11(d)–(f)), the rates movedignificantly towards larger particle size and showed relativelylower rate (compared to 0 min rates). The retardation of theintering rate with longer holding time could be attributed toeck growth and the grain coarsening process. Clearly, at higheremperatures, mechanism seems to transform from SD to VD.

For the coarse size nickel powders, the SD and GBD wereeported as dominating sintering mechanisms earlier by othernvestigators [30,31]. It is not sure; the reason of this contra-ictory result is because of reduction in grain size alone (in theresent case) or ignoring the effect of the grain growth whilenalyzing the sintering kinetics by them [30,31]. To clarify thisontroversy, an attempt was made to predict rate (r) throughnother GBD based model (Appendix B) for second stage sin-ering. The rates were predicted for 0 and 30 min, both yieldedimilar results (rates for 30 min is shown in Fig. 12). It is interest-ng to note that predicted rates (within one order of magnitude)ere in the range of initial particle size at higher temperatures,ut they were deviated significantly from the grain growth line.his reveals that if the grain growth effect is not considered,

BD would be emerging as dominating mechanism at higher

emperature range.The milled powder is expected to have a large amount of

efects and dislocations. The dislocation densities of n-Ni were

vGSs

ig. 12. Predicted rates (r) for GBD mechanism (for the sintering stage 2) bysing x/a of 30 min. The hatching pattern shows the experimental rate rangewithin one order of magnitude).

eported [12,29] to be 1011 and 5 × 1011 cm−2. Thus the move-ents of the existing dislocations and possibly generation of

ew dislocations due to the extreme curvature at the neck aseported by others [6–8], could possibly led to GR in the presentystem also. It seems that GR might have a significant influencen both sintering as well as on grain growth in n-Ni. However,he direct observation or the quantitative estimation of densifi-ation and grain growth caused by GR could not be made in thisnvestigation.

. Conclusions

Sintering and grain growth of nanocrystalline nickel powderere analysed. Both, grain growth and sintering mechanismsere found to be changing at higher temperatures. At lower

emperature range the surface diffusion and grain boundary dif-usion were found as mechanisms of sintering and grain growthespectively. At higher temperature lattice diffusion was foundo be controlling both, sintering and grain growth process.

cknowledgements

Prof. M.M. Godkhindi, Prof. I. Manna, Indian Institute ofechnology Kharagpur (where the experimental works werearried out) and the financial assistance received from DSTGovernment of India) under the Young Scientist FellowshipFast Track) scheme (sanction letter no.: SR/FTP/ETA-4/2003), are gratefully acknowledged. Author wishes to thankr. S.J. Cho and Dr. M.C. Chu (KRISS, Daejeon, Korea).

ppendix A

Properties of polycrystalline nickel [22,28]: γs = 1860 eargsm−2, Ω = 1.09 × 10−23 cm3, Δ0 = 8.9 g cm−3, Tm = 1726 K,requency factor for SD (δsD0s) = 4.4 × 10−8 cm3 s−1, acti-

ation energy for SD = 199.0 kJ mol−1, frequency factor forBD (δbD0b) = 3.5 × 10−11 cm3 s−1, activation energy forD = 115.0 kJ mol−1, frequency factor for VD = 6.0 × 10−1 cm2

−1, activation energy for VD = 271.0 kJ mol−1, frequency fac-

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B.B. Panigrahi / Materials Scienc

or for vaporization = 7.5 × 109 g f cm−2, activation energy foraporization = 401.0 kJ mol−1.

ppendix B

Equation for neck ratio growth rate by GBD for second stageintering [27]:

b2 =(

1

16a

)DBδBFK3

3

loge(xfK3/2) − 3/4(B.1)

here K3 is similar to K1, K2, and xf = 0.74a.

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