G

CM

a

ARRA

KGGBA

1

pomimtrueotoob

g

(((((

0d

Materials Science and Engineering A 512 (2009) 82–86

Contents lists available at ScienceDirect

Materials Science and Engineering A

journa l homepage: www.e lsev ier .com/ locate /msea

rain growth and twin formation in boron-doped nickel polycrystals

handra S. Pande ∗, M. Ashraf Imamaterials Science and Technology Division, Naval Research Laboratory, Washington, DC 20375, USA

r t i c l e i n f o

rticle history:eceived 21 October 2008eceived in revised form 7 January 2009

a b s t r a c t

Formation of annealing twins and its relation to grain growth is investigated. Our previous studies haveestablished a relation between twin density, grain size, and temperature. A model of the mechanism of

ccepted 14 January 2009

eywords:rain growthrain boundariesoron dopingnnealing twins

their formation based on the emergence of Shockley partial loops on consecutive {1 1 1} planes dur-ing grain migration has also been developed previously. This model can satisfactorily explain someexperimental and theoretical results found over the years. In this paper we provide additional experi-mental evidence in support of our model by investigating twin formation in boron-doped nickel. We findthat boron addition slows down grain growth, though the kinetics of grain growth remains parabolic.There is a drastic reduction in twin density due to boron addition especially around a boron content of∼200 ppm.

. Introduction

Annealing twins were first observed over 80 years ago, by Car-enter and Tamura [1]. Since then annealing twins have beenbserved in a variety of deformed and subsequently annealed f.c.c.aterials (for a review see Ref. [2]). Twinning affects properties

n a variety of material, including such technologically importantaterial as superalloys, whose fatigue behavior at high tempera-

ure is drastically affected by the presence of twin interfaces. Theole of twinning in recrystallization and grain growth is well doc-mented. For example Gertsman et al. [3] have concluded that thevolving grain boundary distribution could only be due to a resultf evolving multiple annealing twins. Therefore, a knowledge ofwin density, twin and grain boundary interfaces, and their effectn the development of microstructure can be very useful. In viewf their importance annealing twins have been extensively studiedoth theoretically and experimentally [2].

The important factors determining twinning frequency duringrain growth are [2,4]:

1) grain size D,

2) temperature T and time of annealing t,3) velocity of grain boundary migration,4) grain boundary energy,5) twin boundary energy (or stacking fault energy).

∗ Corresponding author. Tel.: +1 202 767 2744; fax: +1 202 767 2623.E-mail address: pande@anvil.nrl.navy.mil (C.S. Pande).

921-5093/$ – see front matter. Published by Elsevier B.V.oi:10.1016/j.msea.2009.01.030

Published by Elsevier B.V.

Other factors often not usually considered carefully are:

(1) texture,(2) prestrain or prior deformation,(3) inclusions.

There are very few systems where all these factors have beentaken into account in a detailed investigation. Pande et al. [4], havecarried out a systematic study of the formation of annealing twinsin pure nickel as a function of annealing conditions. Based on theseobservations they have proposed three basic rules for the develop-ment of annealing twins. These are:

(1) twins are produced by grain boundaries when they are migrat-ing,

(2) number of twins produced is proportional to the distance ofmigration,

(3) number of twins produced is also proportional to driving forcefor migration.

It was shown [4,5] that these postulates lead to a simple relationbetween twin density p and grain size D as:

p = B

Dlog

D

Do(1)

here p is the number of twin interfaces per unit length. (It is oftenmeasured by measuring the number of intersections by twin inter-faces on a line of a given length. It is related to number of twins pergrain.) B is a constant, and Do can be identified from Eq. (1) as thevalue of grain size when p = 0.

C.S. Pande, M.A. Imam / Materials Science a

feBwrFtaaawbr

tutmlbepcasgmtucmtd

pemTbaabfiflob

Fig. 1. A generalized plot of twin density as a function of grain size.

The simple relation (1) is able to explain our observation in Niairly well. The constant B is in general material dependent and isxpected to depend strongly on stacking fault energy of the system.ecause of the simplicity of the expression (1), it can be checkedith data from various researchers, obtained from different mate-

ials and in a variety of conditions over a wide range of grain sizes.ig. 1 shows such a plot where normalized twin density p/p0 is plot-ed against normalized grain size, D/D0. Hu and Smith [6] data is fornnealed alpha brass, Baro and Gleiter [7] data is for Cu–3 wt.% Al,nd Charnock and Nutting [8] data is for 80/20 brass. A fairly goodgreement with Eq. (1) is noted. Note the range of grain sizes overhich Eq. (1) appears to be applicable. However, the fit appears to

e better because of the data from various materials cover differentanges in grain size.

Several models of twin nucleation and growth have been pos-ulated [9–12], but there has been no single model, which is as yetniversally accepted. Gleiter [9] proposed an atomistic model forhe formation of annealing twins based on “growth accidents” of

igrating grain boundaries and developed an equation to calcu-ate the twin density. He predicted that twin density dependedoth on the grain size and temperature. This is not borne out byxperiments even after the use of values for some of the variousarameters, which now seem incorrect [13]. Pande et al. [4,5] con-lusively showed by experiments and by Eq. (1) that irrespective ofny combinations of annealing temperature and time, once a grainize is achieved by annealing, twin density is given by that value ofrain size. Li et al. [13] showed recently that Gleiter’s formulationay in fact be consistent with our experiments if one calculates

he annealing twin density in Cu–3 wt.% Al bronze and pure Cusing the complete equation and more recent values of materialonstants. Gleiter’s model then shows that density depends pri-arily on the grain size with little dependence on the annealing

emperature, etc., in agreement with our results. Any temperatureependence is through its effect on grain size.

One obvious question in the study of annealing twins is the rolelayed by twin boundary energy and stacking fault energy (the twonergies are usually related). Since we did not, in our experiments,easure these parameters we do not know their role precisely.

hey can in principle also be introduced in the theory preferablyy a microscopic theory of twin formation. We have proposed suchmicroscopic theory previously based on the idea that annealing

nd deformation twins are identical crystallographically [14]. Theyoth consist of stacking fault on consecutive {1 1 1} planes. Theseaults are produced by the glide of Shockley partials. Based on this

dea, a microscopic model for the formation of annealing twins in.c.c. crystals was proposed [14]. It was argued that Shockley partialoops nucleate on consecutive {1 1 1} planes by growth accidentsccurring on migrating {1 1 1} steps associated with a moving grainoundary. The higher the velocity of the boundary, higher the steps

nd Engineering A 512 (2009) 82–86 83

associated with twin density. The absence of twin in high stackingfault energy materials and influence of temperature on twin densitycan be rationalized in terms of the model. This model is consistentwith our previous work [4,5]. Further evidence could in principlebe obtained by precise high-resolution studies of twin nucleationin f.c.c. materials. This has as yet not been performed. Another testof the mechanism would be as follows: the critical assumption inthe model is that any increment in twin density is proportional tothe driving force of the migrating boundary. Changing the drivingforce without significantly affecting the other pertinent parame-ters such as grain size can test this result. It is known [15] thatthe driving force of the migrating boundaries can be substantiallychanged by the addition of impurities. (For a detailed discussion onthe role of impurities in grain boundary migration see Refs. [16,17].)Twin densities then should be dependent on trace impurities. Wehave therefore studied extensively the role played by small addi-tions of boron in the formation of annealing twins. These resultsare presented in this paper. Preliminary analysis indicates that theresults are also consistent with our previous understanding of theformation of these twins.

2. Experimental

Nickel, nominally 99.9 pct pure, was used in this investigation.Trace impurities, in weight percent, consisted of A1 0.02 pct, Bi 0.02pct, Cr 0.01 pct, Cu 0.01 pct, Fe 0.04 pct, Mg 0.01 pct, Mn 0.09 pct, Si0.01 pct, and Ti 0.006 pct. Boron-doped nickel samples were madeby arc melting. Samples containing 175, 241, 385 and 601 ppm boronwere prepared. These samples were given the following thermo-mechanical treatment sequence before final annealing: (a) straightrolled 50 pct to 6.4-mm thickness, (b) annealed for 35 min at 600 ◦Cin hydrogen atmosphere, (c) cross-rolled 50 pct to 3.2-mm thick-ness, (d) straight rolled 50 pct to 1.6-mm thickness, and finally, (e)diagonally rolled 50 pct to 0.8-mm thickness. The rolling betweenintermediate anneals was done to avoid strong texture effects.After that the 12 mm × 0.8 mm sizes were prepared for final heattreatment. These heat treatments were carried out under vacuum(10−5 Torr or better) at temperatures ranging from 750 to 1200 ◦Cand time ranging from 2 min to 100 h. After heat treatment, one faceof each specimen was carefully ground to approximately half theinitial width of the specimen followed by metallographic polishingand etching to reveal the microstructures. Metallographic parame-ters, such as grain size, twin density, and twin width, were evaluatedusing linear analysis based on Smith and Guttman’s procedure [18].To facilitate accurate and statistically meaningful counting of thenumber of intersections of a random line with the grain boundariesand twin boundaries, a specially designed system for data acqui-sition and analysis was used. This system is computer aided andoperator interactive.

Measurement of twin density (p) and grain size (D), was done asfollows: number of intersections of a random line of unit lengthwith two-dimensional feature in three-dimensional structure isexactly half the surface to volume ratio, i.e. if

• L = total length traversed,• G = total number of grain boundaries intercepted,• M = number of twin boundaries intercepted,• then: grain size D = L/G,• twin density (p) = M/L, i.e. number of twin intersections per unit

length, and

number of twinsgrain

(N) = D(

M

L

)=

(L

G

)·(

M

L

)

= M

G(if grain shapes do not change) (2)

84 C.S. Pande, M.A. Imam / Materials Science a

Fig. 2. (a) A plot of square of grain size as a function of time at constant temperatureas indicated. (b) A plot of square of grain size as a function of time at constanttemperature as indicated. (c) A plot of square of grain size as a function of time atconstant temperature as indicated. (d) A plot of square of grain size as a function oftime at constant temperature as indicated.

nd Engineering A 512 (2009) 82–86

Transmission electron microscopy was done on some typicalspecimens, to determine the nature of twin and grain boundaries,and segregation, if any of boron, at the grain boundaries.

3. Results

Average grain sizes, D, were measured as a function of timeand temperature, for both pure nickel and also boron-doped nickel.These results are plotted in Fig. 2 as D2 vs. time t. It is seen thatfollowing relation between D and t is obeyed closely:

D2 − D21 = Kt (3)

where K and D21 are constants and can be obtained from the slope

and the intercept of the straight line in Fig. 2. It is also seen thatthe slope depends on the temperature of annealing, but the rela-tion (3) is obeyed for all temperatures. D1 should be same for alltemperatures. It is seen that it is approximately but not exactly so.It is interesting to note that the time exponent is same for all thecases independent of annealing temperature.

Theory [16,17] indicates that the following relation should relateK to temperature of annealing:

K = KO exp(

− Q

RT

)(4)

where Q is the activation of the process, R is the gas constant, andKO is a constant.

If this relation is true, a plot of log K vs. 1/T should be a straightline, and the activation energy of Q can be obtained from the slopeof this line. In Fig. 3 we have plotted log K as a function of 1/T for purenickel as well as for boron-doped nickel. It is seen that a straight lineis obtained in all cases. From the slope, we have obtained activationenergy for this process for boron-doped nickel for several values ofboron content.

In Fig. 4, we have plotted the activation energy, Q, as functionof the boron content in the nickel. It is seen that activation energyincreases with increasing boron content in a smooth fashion, show-ing a gradual increase in Q, and indicating a gradual slowing downthe grain boundary migration with increasing boron content.

Fig. 5 shows a plot of N, the number of twins/grain as a func-tion of grain size for several boron content (Note: N is number oftwins/grain whereas p is twin density. The two are of course related,

N = pD). It is seen that N is not a monotonically increasing functionof grain size. Instead N dips for a grain size of about 200 �m, andthen either increases or stays roughly level. A similar situation isseen in the plot of N vs. boron content (Fig. 6), for several tempera-tures of annealing. N dips to a low value for a boron content of about

Fig. 3. A plot of log K (obtained from Fig. 1) as a function of inverse square of tem-perature in Kelvin.

C.S. Pande, M.A. Imam / Materials Science and Engineering A 512 (2009) 82–86 85

Fig. 4. A plot of activation energy as function of the boron content in the nickel.

Fc

2c

bcaaotT

F

Fig. 7. Electron micrograph showing twins (at T1, T2 and T3) and grain boundary (atG). The twin T3 is attached to the grain boundary. Notice the twin length is almostvertical to grain boundary.

ig. 5. A plot of number of twins per grain as function of grain size for several boronontent in nickel.

00 ppm, then increases or stays level. The two curves N vs. boronontent, and N vs. grain size, appear to be similar.

Fig. 7 is a typical electron micrograph showing twins, grainoundary and segregation of boron at grain boundaries. The boronontent of the specimen in Fig. 7 was 385 ppm. The length of twinsre roughly at right angle to the boundary contrary to the model

ssumed by Glieter [9]. However we cannot rule out Gleiter’s modeln this basis. Similar to Fig. 7, Fig. 8 is again showing features ofwins, grain boundary and segregation of boron at grain boundaries.he boron content of the specimen in Fig. 8 was 601 ppm.

ig. 6. A plot of number of twins as function of the boron content in the nickel.

Fig. 8. Electron micrograph showing twins (at T) and grain boundary (at G). Boronprecipitation at grain boundary is also seen.

4. Discussion and conclusions

It is hoped that results reported here, provides further insightfor the mechanism of growth of annealing twins, as it relatesto the growth of twins with the migration of grain boundaries.The presence of boron in nickel slows down the migration of theboundaries, as seen by the smooth increase in activation ener-gies with boron content (see Fig. 4). But this is not sufficient toexplain our results. An additional effect is present, as seen from thefact that N is minimum for a certain grain size or boron content(see Figs. 5 and 6, respectively). It is not yet clear what pre-cisely this additional effect is. Preliminary transmission electronmicroscopy revealed the presence of some boron-rich precipitatesnear the grain boundaries (see Figs. 7 and 8) for higher boron con-tent (>200 ppm) specimens. One way to reconcile our results withour previous model is to assume that boron not only slows downthe grain boundary migration but also, prevents the migrationof steps on the grain boundaries, thereby preventing the nucle-ation of twins. Such poisoning of twin nucleation does not needa large boron content, and indeed it might saturate for a small

boron content, sufficient to cover a nanolayer of the grain bound-aries. Nucleation of a boron-rich precipitates may interfere with thepoisoning of steps at higher boron content. This explanation is nec-essarily tentative and needs further experimental and theoreticalinvestigation.

8 ience a

ftdinbi

bimbtbigt

tuddistii

ttatmmig‘tdaE

[[[[[[

[

[17] A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials, Clarendon Press,

6 C.S. Pande, M.A. Imam / Materials Sc

Randle et al. [19] have recently investigated annealing twinormation in nickel and its relationship with grain growth. Theyentatively conclude that twin formation can take place indepen-ently of grain growth. They find that once a certain density of twins

s reached, it is not changed further by grain growth. Our results areot entirely in agreement with these conclusions, but it is possi-le that the results of the two studies can be reconciled by further

nvestigations.Song et al. [20] studied the behavior of random high-angle grain

oundaries of a Pb-base alloy during thermo-mechanical process-ng and heat treatment using electron back-scattered diffraction

ethod. Repetitive thermo-mechanical processing was found toe effective in increasing the fraction of special boundaries, andhis was attributed to interactions associated with annealing twinoundaries. Evidence was found that annealing twin formation

nvolves grain boundary migration presumably leading to grainrowth. This result agrees with our results, but contradicts withhe conclusions in Ref. [19].

Choudhury and Jayaganthan [21] investigated the grain migra-ion of bicrystal boundaries with of mobile and immobile impuritiessing Monte Carlo simulation with the energetics of the systemescribed by Potts’ model in both two dimension and three-imensional cases. They showed that the grain pinning effect

ncreases with increase in percentage of impurities. It was alsohown that the maximum grain pinning is possible only up to cer-ain percentage of impurities and beyond which it does not have anynfluence consistent with our observations. This is what we observen boron-doped nickel.

Finally, we reconcile our observations with two ‘microscopic’heories of twin formation [9,14]. One major difference betweenhe two models is that Gleiter’s model envisages twin nucleationt a small glancing angle to the migrating grain after boundary, i.e.he nucleating twin is almost parallel to the boundary, whereas our

odel [14] assumes twin formation almost at right angle to theigrating boundary. In practice we find that both type of anneal-

ng twins are found in nickel. Gleiter’s model if correctly appliedives twin density solely determined by grain size (see Eq. (1)). Our

microscopic’ model [14], so far makes no quantitative prediction ofwin density, but appears to be consistent with all the observationsescribed here. It thus appears that both models are equally valid,nd may be subsets of a more comprehensive model consistent withq. (1).

[[[[

nd Engineering A 512 (2009) 82–86

In summary, we find that small additions of boron slow downgrain growth, though kinetics of growth remain approximatelyparabolic. There is a drastic reduction in twin density for a spe-cific boron content of ∼200 ppm. This value perhaps is a function ofgrain size. Activation energy of grain growth increases with increas-ing boron content. The present results are all consistent with theauthors’ model of annealing twin formation.

Acknowledgements

The authors are grateful to Dr. Jerry Feng for advice and sup-port and Mr. S. Smith for technical assistance. The authors are alsograteful to Mr. Nabil Ashraf for assistance in the preparation of thispaper.

References

[1] H. Carpenter, S. Tamura, Proc. Roy. Soc. A 113 (1926) 161.[2] M.A. Meyer, C. McCowan, in: C.S. Pande, D.A. Smith, A.H. King, J. Walter

(Eds.), Proceedings of an International Symposium on “Interface Migrationand Control of Microstructure”, held in conjunction with ASM’s MetalsCongress and TMS/AIME Fall Meeting, September 17–21, Detroit, MI, USA, 1984,p. 99.

[3] W.Y. Gertsman, K. Tangri, R.Z. Valiev, Acta Metall. Matter 42 (42) (1994)1785.

[4] C.S. Pande, M.A. Imam, B.B. Rath, in: C.S. Pande, D.A. Smith, A.H. King, J. Walter(Eds.), Proceedings of an International Symposium on “Interface Migration andControl of Microstructure”, held in conjunction with ASM’s Metals Congressand TMS/AIME Fall Meeting, September 17–21, Detroit, MI, USA, 1984, p. 125.

[5] C.S. Pande, M.A. Imam, B.B. Rath, Met. Trans. A 21A (1990) 2891.[6] H. Hu, C.S. Smith, Acta Metall. 4 (1956) 638.[7] G. Baro, H. Gleiter, Z. Metallkd. 63 (1972) 661.[8] W. Charnock, J. Nutting, Met. Sci. J. (1967) 78.[9] H. Gleiter, Acta Metall. 17 (1969) 1421.10] G. Gindraux, W. Form, J. Inst. Met. 101 (1973) 85.11] S. Dash, N. Brown, Acta Metall. 11 (1963) 1067.12] M.A. Meyers, L.E. Murr, Acta Metall. 26 (1978) 951.13] Q. Li, J.R. Cahoon, N.L. Richards, Scripta Mater. 55 (2006) 1155.14] S. Mahajan, C.S. Pande, M.A. Imam, B.B. Rath, Acta Mater. 45 (1997) 2633.15] L.E. Murr, Interfacial Phenomena in Metals and Alloys, Addison-Wesley, Read-

ing, 1975, p. 204.16] G. Gottstein, L.S. Shvindlerman, Grain Boundary Migration in Metals: Thermo-

dynamics Kinetics, Applications, CRC Press, Boca Raton, FL, 1999.

Oxford, 1995.18] C.S. Smith, L. Guttman, Trans. Am. Inst. Min. Met. Eng. 197 (1953) 81.19] V. Randle, P.R. Rios, Y. Hu, Acta Mater. 58 (2007) 130.20] K.H. Song, Y.B. Chun, S.K. Hwang, Mater. Sci. Eng. A 454–455 (2007) 629.21] S. Choudhury, R. Jayaganthan, Mater. Chem. Phys. 109 (2008) 325.