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Indentation-size-effects-on-the-creep-behavior-of-nanocrystalline-tetragonal-Ta-films_2009_Scripta

Indentation size e?ects on the creep behavior of nanocrystalline

tetragonal Ta ?lms

Z.H.Cao,a P.Y.Li,a H.M.Lu,a Y.L.Huang,b Y.C.Zhou b and X.K.Meng a,*

National Laboratory of Solid State Microstructures and Department of Material Science and Engineering,Nanjing University,

22Hankou Road,Nanjing 210093,People’s Republic of China

Faculty of Materials and Photoelectronics Physics,Xiangtan University,Xiangtan 411105,People’s Republic of China

Received 6October 2008;revised 31October 2008;accepted 11November 2008

Available online 27November 2008

Nanoindentation creep tests were carried out at maximum indentation loads from 500to 9000l N to study the indentation size e?ects (ISEs)on the creep behavior of nanocrystalline tetragonal Ta ?lms.The experimental results show that the hardness,creep strain rate and stress exponent are all indentation size-dependent.The ISE on the creep behavior is explained by grain boundary di?usion and sliding,and self-di?usion along the indenter/specimen interface and along the free surface of specimen.ó2008Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.

Keywords:Nanoindentation;Creep;Nanocrystalline materials;Ta

The mechanical behavior of nanocrystalline

materials has been investigated extensively since these materials often exhibit a prominent size e?ect.For example,the inverse Hall–Petch relation of nanocrystal-line metal has been found by a number of researchers [1–3],and the strength of ?lm metals is known to scale inversely with the ?lm thickness [4–6].Moreover,another important issue is the indentation size e?ect (ISE)of mechanical behavior in nanometer-and submi-cron-scaled nanoindentation testing [7–10].The size dependence of mechanical behavior is generally thought to be related to the inherent length scale.

In previous reports,creep results of nanocrystalline Cu,Al and Ni indicate that both hardness and creep strain rate have a remarkable ISE [11–13].Furthermore,a signi?cant size dependence of strain rate sensitivity,namely the strain rate sensitivity being higher at smaller indentation size,has been found in nanocrystalline and single-crystal Ni 3Al [14].In addition to experimental re-sults,it has also been found that the hardness decreases with increasing indent depth during atomistic simula-tions [15]and with an analytical model [16].Pure Ta and Ta-based alloys have been widely applied as di?u-sion barriers in ballistic rockets and spacecraft due to their excellent properties.The mechanical properties of

nanocrystalline Ta and its alloys have been investigated widely [17,18].It has been found that the hardness of tetragonal Ta ?lms with a grain size of 32.3nm reaches about 15GPa [19].Moreover,nanocrystalline tetrago-nal Ta exhibits negative strain rate sensitivity in nanoin-dentation tests [20].However,the creep behavior of nanocrystalline Ta ?lms during nanoindentation at room temperature has not been investigated in detail.The present study is performed to investigate the ISEs on the creep behavior of nanocrystalline tetragonal Ta ?lms by the nanoindentation technique.

Tetragonal Ta ?lms were deposited on Si(111)sub-strate under pure argon gas by DC magnetron sputter-ing at room temperature using a 99.95%purity Ta target.The base pressure of the sputtering chamber was kept at 6.2?10à5Pa,while the working pressure was 1.4Pa.The sputtering power was about 280W.The deposited rate was kept at about 50nm min à1,and the deposition time was 40min for an estimated ?lm thickness of about 2l m.The structure of as-deposited Ta ?lms was characterized by X-ray di?raction (XRD)and transmission electron microscopy (TEM).

The nanoindentation tests were carried out at room temperature using a TriboIndenter (Hysitron Inc.)with a Berkovich diamond indenter where the nominal tip ra-dius of curvature,R ,was about 150nm.Consequently,the minimum depth for self-similar indentation is esti-mated to be about 9nm,which is calculated from the equation R (1àsin70.3°)=0.06R [8].The displacement

*Corresponding author.Fax:+862583595535;e-mail:

mengxk@https://www.wendangku.net/doc/3b9516581.html,

Available online at https://www.wendangku.net/doc/3b9516581.html,

Scripta Materialia 60(2009)

415–418

https://www.wendangku.net/doc/3b9516581.html,/locate/scriptamat

and load resolutions of the instrument were0.1nm and

100nN,respectively.In order to avoid any substrate

e?ect,the indentation depth was controlled below1/10 of the?lm thickness.The creep properties of Ta?lms

were characterized under a constant loading rate _P?5000l N sà1with the holding load ranging from 500to9000l N.The holding time was kept for40s

and then the samples were unloaded to10%of the max-

imum load and were held constant for thermal drift cor-rection.Finally,the indenter was withdrawn to zero load.The hardness measurements were performed at loads ranging from500to9000l N almost without load holding.Indentation at each load was repeated at least 10times.

The XRD spectrum of an as-deposited Ta?lm is

shown in Figure1.The(002)and(004)peaks of b phase at33.6°and70.8°are found in the as-deposited nanocrystalline Ta?lm.The XRD results clearly indi-cate that b phase is the only phase in the?lm.The aver-age grain size of the Ta?lm is about10nm,determined using the Scherrer method[21].A typical planar view of a TEM image of the Ta?lm is shown in Figure2a, where corresponding selected-area electron di?raction (SAED)pattern is presented in the bottom right corner. It is found that the Ta?lm is composed of equiaxed nanocrystalline grains.A detailed lattice image is shown in Figure2b,from which the grain size distribution is determined to be from3to8nm.The grain size deter-mined by TEM should be more accurate than that of XRD.

For a self-similar indenter,the indentation strain rate _e and the stress r in the depth-sensing indentation tech-nique obey the following relations[22,23]

_e?1

;r?

A c

;e1T

where P is indentation load,h is the instantaneous in-denter displacement,t is time and A c is the contact area. To calculate the displacement rate,_h?dh=dt,the inden-ter displacement vs.time curve at constant indentation load can be?tted by the following empirical law[8]:

hetT?h itaetàt iTbtkt;e2Twhere h i,a,t i,b and k are?tting constants.The function in Eq.(2)is found to accurately?t to the creep curves at all indentation loads.An example of an experimental result(P max=500l N)and?tting curve is shown in Figure3.

Figure4a shows variations in creep depth during the holding period as a function of time in the nanoindenta-tion creep tests.The data also show that for each load there is an initial abrupt increase in creep depth,fol-lowed by a stage with a smaller rate of increasing creep depth.The initial stage is known as transient creep and the later corresponds to steady-state creep.The changes of hardness and creep depth with the indentation loads are shown in Figure4b.The creep depth increases from 6.3to15.6nm with the increasing indentation load from 500to9000l N.The hardness,on the other hand,was determined by means of the Oliver–Pharr method[24]. The e?ect of creep on the hardness is avoided since load holding is not performed during the hardness measure-ment.Consequently,the resultant hardness is believed to be the intrinsic strength of nanocrystalline tetragonal Ta?lms.It is found that the hardness of nanocrystalline tetragonal Ta?lms decreases slightly from14.1to 12.8GPa with the increasing indentation load or indent depth,which shows a mild ISE.The hardness in the present work is much lower than that of tetragonal Ta ?lm with32.3nm grain size in Ref.[19].It is suggested that the inverse Hall–Petch relation occurs as the aver-age grain size of Ta?lm decreases to below10nm. The grain boundary di?usion or grain boundary

sliding Figure1.The XRD spectrum of nanocrystalline tetragonal Ta?lms

grown on Si

substrate.

Figure2.Plane-view TEM images of a nanocrystalline tetragonal Ta

?lm:(a)bright-?eld image and SAED pattern,and(b)lattice

image.

Figure 3.Experimental and?tted creep curve of nanocrystalline

tetragonal Ta?lms at500l N.The obtained?tting parameters are

h i=25.8,a=2.8,t i=0.1,b=0.2and k=0.02.

416Z.H.Cao et al./Scripta Materialia60(2009)415–418

instead of dislocation pile-up may be responsible for the softening behavior.In addition,the high volume frac-tions of grain boundary or triple junctions and the lower density of geometrically necessary dislocation in a nano-crystalline metal are believed to weaken the ISE of hard-ness [25].Similar results have also been found in a number of other materials including nanocrystalline and single-crystalline Ni 3Al and Cu [14,26,27].

Based on the relationship between indenter geometry and the related mechanical property,the creep strain

rate _e

has typically been de?ned as instantaneous dis-placement rate/instantaneous displacement or _h

=h [22].The creep stain rate _e

is calculated by Eq.(1),which is shown in Figure 5.For all maximum indentation loads,

each _e

decreases to a stable value in the steady-state creep stage with prolonged holding time.As is shown in the magni?ed curve in the right top corner of

Figure 5,the steady _e

decreases from 1.5?10à3to 5.0?10à4s à1when the indentation load increases from 500to 9000l N,exhibiting a strong ISE.This behavior was also found in the nanoindentation creep study of

nanocrystalline Ni ?lms [28].The intense change of _e

indicates that the creep behavior is dominated by di?er-ent mechanisms at di?erent indentation loads or inden-tation depths.

To further investigate the creep mechanism of nano-crystalline tetragonal Ta ?lms,the relation of ln(strain rate)vs.ln(stress)is plotted in Figure 6a.Thus,the stress exponent n can be determined through the slope of the curves.In the case of each curve under di?erent indenta-tion loads,n decreases to a steady-state value with the elapsing of holding time.For example,at 500l N,the

n at the beginning of the load hold is about 16.5,but it decreases toward a steady-state value of about 4.3.The value of 4.3at the steady-state creep stage can be regarded as the valid n of the whole creep process.Fig-ure 6b shows that the steady stress exponent n increases dramatically with the enhanced indentation load or indent depth,and exhibits a strong ISE.Spontaneously,the creep strain rate sensitivity m (m =1/n [23])decreases with enhanced indentation load.This ISE on n was also found in previous reports [14,28].

It is well known that dislocations and grain bound-aries (GBs)are the most popular di?usion paths under creep deformation.For coarse crystalline metals,dislo-cation climb is often the main creep mechanism,while the creep behavior of nanocrystalline metals may be dominated by GB di?usion and GB sliding [29,30].The di?erent creep mechanism can be re?ected by the magnitude of the steady stress exponent n .Figure 6b shows that n increases from 4.3to 24with the indenta-tion load increasing from 500to 9000l N,and the cor-responding m changes from 0.23to 0.04.Moreover,_e

is up to about 1.5?10à3to 5.0?10à4s à1

.The high _e

and low n indicate that GB di?usion and sliding are the dominant creep mechanisms for all indentation loads.It is noted that another creep mechanism may act for low indentation loads or shallow indentation depths.The critical indentation depth for self-di?usion along the indenter/specimen is about 30nm for ultra-?ne-grained Cu in the literature [31].For example,the small indent penetration depth at the 500l N is below 28nm and is very close to the specimen surface.Thus,the self-di?usion along the indenter/specimen interface and along the free surface of the specimen will play an important role during creep process [32,33].This is also demonstrated by the low n of about 4.3and the high m of about 0.23.This di?usion process will be weakened as the indenter penetrates far away from the free surface of specimen since the di?usion length l will be much longer with increasing indentation depth.As indentation load increased to 3000l N with about 80nm indentation depth,n increased to about 17.9.Finally,n increases to about 24at 9000l N which is approximately six times higher than that at 500l N.As is discussed above,the dislocation pile-up is ruled out by the softening hardness behavior.Consequently,GB di?usion and sliding are still the dominant creep mechanisms even at 9000l N in-dent load with about 200nm indentation depth.

In summary,we have carried out nanoindentation creep tests on the nanocrystalline tetragonal Ta ?lms at maximum indentation loads from 500to 9000l

Figure 4.(a)Creep responses of nanocrystalline tetragonal Ta ?lms at maximum indentation loads from 500to 9000l N.(b)Variations in hardness and creep depth with di?erent indentation loads at room

temperature.

Figure 5.Variations in creep strain rate with holding time at maximum indentation loads from 500to 9000l

Figure 6.(a)The plots of ln(strain rate)vs.ln(stress)at di?erent maximum indentation loads.(b)Variations in stress exponent and creep strain rate sensitivity with di?erent maximum indentation loads.

Z.H.Cao et al./Scripta Materialia 60(2009)415–418417

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This work was supported by the State Key Program for Basic Research of China(Grant No. 2004CB619305),the Natural Science Foundation of China(Grant No.50571044,50831004,BK2006716), the Postdoctoral Science Foundation of China(Grant No.20070410326),and the Jiangsu Planned Projects for Postdoctoral Research Funds(Grant No.0701029B). [1]A.Giga,Y.Kimoto,Y.Takigawa,K.Higashi,Scripta

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