MIGRATION OF DIFFERENTLY ORIENTED GRAIN BOUNDARIES MEASURED ON Fe-3wt%Si 37° <001> BICRYSTALS

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MIGRATION OF DIFFERENTLY ORIENTED GRAIN BOUNDARIES MEASURED ON Fe-3wt%Si 37°

BICRYSTALS

P. Lejček, V. Paidar, M. Grabski

To cite this version:

P. Lejček, V. Paidar, M. Grabski. MIGRATION OF DIFFERENTLY ORIENTED GRAIN BOUND-

ARIES MEASURED ON Fe-3wt%Si 37° BICRYSTALS. Journal de Physique Colloques, 1988, 49

(C5), pp.C5-587-C5-592. �10.1051/jphyscol:1988573�. �jpa-00228070�

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JOURNAL D E PHYSIQUE

Colloque C5, supplbment au n O I O , Tome 49, octobre 1988

MIGRATION OF DIFFERENTLY ORIENTED GRAIN BOUNDARIES MEASURED ON Fe-3wt%Si 37"

<001> BICRYSTALS

P. L E J ~ E K , V. PAIDAR and M.W. GRABSKI"

Institute of Physics, Czechoslovak Academy of Sciences, N A Slovance 2.

180 40 Praha 8, Czechoslovakia

" ~ n s t i t u t e of Materials Science and Engineering, Warsaw University of Technology, Narbutta 85, PL-02-524 Warsaw, Poland

&sun& - Nous avons etudi& l'effet de l'orientation de la normale au joint

de flexion (37'<001>) sur la migration des des joints de grains les bicristaux Fe-3%Si en poids. La vitesse de migration est proportionelle B la force motrice si la temperatures et les forces motrices imposees sont suf f isament &levees. L' energie d' activation de la migration des joints symetriques est egale 3.7 eV/at, tandis que pour les joints asydtriques elle est 1 eV/at seulement.

Abstract - The dependence of the grain boundary migration on the orientation of the boundary surface was investigated on Fe-3wt%Si bicrystals with 37'<001> tilt grain boundary. It was found that the migration velocity is proportional to the driving force at sufficiently high temperatures and for large values of the imposed driving force. The emigration activation energy is 3.7 eV/at for symmetrical boundary while it is only about leV/at for asymmetrical one.

1. INTRODUCTION

The properties of grain boundaries, which are related to mechanical behaviour of polycrystals, strongly depend on the grain boundary type. It has been shown recently I11 that such quantities as yield stress do not depend only on the grain size, as considered in the Hall-Petch formula, but are affected in a comparable extent by grain boundary types. A pronounced dependence of the grain boundary sliding rate on the misorientation of grains is known for symmetrical bicrystals .with the <001> rotation axis 121. The effect of misorientation on the mobility of migration boundaries has been demonstrated already in 131. It followed from the analysis of experimental data for <001> tilt boundaries in lead that the activation energy of migration is lowest for the grain misorientation close to special grain boundaries. The effect of grain orientation on the grain boundary mobility in aluminium bicrystals was investigated systematically in [ 4 , 5 1 . The motion of single grain boundary was studied under the action of constant driving force. In this experimental arrangement the migration boundary has a half- cylindrical shape, i.e. the normal to the boundary plane varies +90' with respect to the direction of motion.

In spite of an important role which grain boundary migration plays in various metallurgical processes, such as grain growth, recrystallization, high temperature plastic deformation, superplasticity etc., the understanding of boundary migration is still incomplete 161. The reason is that it is not easy to conduct experiments under fully defined conditions on samples where all the influences affecting the grain boundary motion are controlled. Since the 'mving boundary interacts with dislocations, other crystal defects and impurities, the distribution of crystal imperfections in the boundary vicinity should be observed.

In the present paper which is a part of a larger project of the investigation of mechanical properties of bicrystals C7, Sittner and Paidar, to be published], the effect of the grain boundary plane orientation on the mobility of the boundary is addressed. In comparison with the effect of the crystal misorientation much less attention has been given in literature to the influence of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988573

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C5-588 JOURNAL DE PHYSIQUE

the orientation of the boundary plane normal on the migration rate. In C81 the mobilities of tilt and mixed segments of the grain boundary possessing a chosen misorientation were measured. It was found that the activation energy for grain boundary migration is slightly lower for mixed than for tilt boundaries, the mixed orientation was near to twist boundary.

In order to study the effect of grain boundary plane orientation on migration, it is desirable to keep the boundary nearly planar. Various boundary shapes used to measure the migration of individual grain boundaries in bicrystals are discussed in [9,101. It is possible to use the wedge technique with a small angle of the wedge-shape specimen. However, as the contracting grain can shrink too fast due to the increasing driving force it is not easy to choose appropriate annealing times. It should be noted that the moving boundary segment is never nearly planar for the constant driving force technique. In the case of reversed- capillary technique 1111, the driving force decreases with increasing grain boundary displacement, and hence this technique can be applied without difficulties even if the magnitude of the migration rate cannot be evaluated a p r i o r i , In our measurements we used used the reversed-capillary technique with rectangular samples having the initially planar grain boundary intersecting diagonally the sample under the angle of 45'. This geometry limits the variation of the migrating boundary normal to tlie range of 45' only, two boundary segments migrating in the opposite directions can be measured simultaneously and the effect of free surfaces on the moving boundary can be tested. The experiments were carried out for two orientations of the grain boundary plane for the 2=5 tilt boundary (37"11001).

Preliminary results on the migration of symmetrical grain boundary has been presented in t 121.

3. RESULTS 2. EXPERIMERTAL

The specimens used in the present study were prepared from Fe-3wt%Si bicrystals, 13 mm in diameter, grown by floating zone technique 1131. Two kinds of 1=5 bicrystals characterized by the 37*[1001 rotation were chosen: (a) bicrystals with the spm&rical tmxxbrg lying on the C013) type planes of both component crystals, and (b) bicrystals with the aspn&xical

boundarv

lying on the ( 0 1 14) and (0 20 23) crystallographic planes of respective crystals. the boundary orientation in this case is inclined 22.5' to the symmetrical orientation and is situated in the middle between two symmetrical orientations of the boundary planes on (013) and {012>.

2 R

The disc of the geometry shown in Fig. 1 with z=3 mm, 2D=8 mm and a=45"

The annealed boundary was composed of an initial planar part and of an approximately circular arc. Jo faceting under the resolution of an optical microscope was found. The circular segment was nearly tangential to the initial straight segment and perpendicular to the side free surface. As it is seen from Fig.2, the orientations of the boundary at the points of their exits to the side

I

were spark-cutted, grinded and chemically polished in a mixture HF

&;

<& ^GB

^(13%)

⁺

^H,D, (1+4). To study the grain boundary migration, each specimen was

6

annealed at a chosen temperature in

d

the range 1223 to 1273 K for a defined

2D

period of time. The heating and

z

cooling were rather quick ( 2 K/s and

10 k/s, respectively) so that the boundary movement during these processes may be neglected. After Fig. 1. Geometry of specimens etching of the boundary (and also of

the dislocation microstructure) in a solution of 3%HH1YOZ in etylalcohol and observation, the specimen was repolished and repeatedly annealed at the same temperature for the next defined period of time.

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free surface were {012) and (0 20 23)/(0 1 14) for initially symmetrical and asymmetrical boundary respectively. the variation of the length of the circular boundary segment, 1, can be expressed as a function of the measured displacement

(0B)J 1051)

Fig.2. Orientation relation in (a) syrmnetrical and (b) asymmetrical bicrystals.

Face surfaces of both component crystals A and B are of the same orientation distance, a. When the migrating segments meet at the centre of the sample their curvature is p=D/cosa and the corresponding displacement distance can be denoted as a,=((l/sina)-1)p. two different regimes of the grain boundary migration have to be distinguished, When a<a, :

and when a>a,:

where b denotes the following function of a

b = cota - a/6 (3)

For the angle a equal to 45', the geomtrical factor f is 0.27 and a,/D is 0.586.

The driving force of the grain boundary energy per unit area of the moving boundary

Therefore, the quantity expressed by the equations (1) and (2) is a negative ratio of the driving force and boundary energy. The dependence of Fly on the displacement a/D is shown in Fig.3 for both regimes of grain boundary migration. Our experimental data were collected mostly during the first regime when the driving force is inversely proportional to a, according to (4) and (1).

The experimental data have been analysed assuming that the migration velocity, v, can be written as:

v = da/dt = ME'" (5 1

where M is grain boundary mobility which depends on annealing temperature, T. Then the displacement distance, a, is a function of the annealing time, t:

where the exponent is n = l/(mtl) and

C = M*(yf)'-n/n"

When the migration velocity is proportional to the driving force, then m=1, n=1/2 and the energy can be determined experimentally:

n

= cZ/2f (8)

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Fig.4 Time dependence of the boundary displacement, a, for (a) symmetrical and (b) asymmetrical boundary corresponding to a different temperatures

5

2

FIT'F>

1 ⁰ ^l

^--- ^'

^I ^h

'

The isothermal time dependences of the boundary displacement, a, are plotted in Fig.4. The condition of the proportionality between migration velocity and driving force is fulfilled in the most cases and the values of the exponent n are then in the range from 0.46 to 0.51 (full lines in Fig.4). Only in the case of the lowest mobility (at 1223 K for both boundaries) the values of this exponent are reduced to about 1/3 (dashed lines in Fig.4). The reduction indicates a change of the migration mechanism which will not be considered in the analysis of experimental results in this paper. From the data complying with the parabolic law,the values of the product I11 were calculated according to the eqs. (6) and (8).

Fig.3. The dependence of the driving force divided by the boundary energy,

F / y , on the relative displacement a/D

migration

for the two according regimes to of eq. grain (1) and boundary (2)

o

az

04 0.6 O.ealD 1

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These data for both kinds of the migrating boundary are presented in Table 1 and in Fig.5. It is apparent that the data for the symmetrical boundary can be well represented by Arrhenius equation:

M = M, exp(-Q/kT) (9)

with the constant activation energy of grain boundary migration, Q=3.7 eV/at. The data for the asymmetrical boundary exhibit much greater scatter. If we assume the Arrhenius equation to be also fulfilled, the activation energy is about 1.0 eV/at.

-19

-

069 072 075 078 081 W Fig.5 Temperature dependence of the product My, D

-

symmetrical boundary,

'

T

.

- asymmetrical boundary Table 1. Values of My for symmetrical and asymmetrical boundaries.

The activation energy for grain boundary migration was evaluated assuming that the boundary energy does not depend on temperature. It was further assumed that the boundary migration is not affected by the tension of free surfaces. In all cases the face surfaces have the same orientation (100) in both grains. The side surfaces have the same orientation {021> only for bicrystals with the symmetrical boundary (Fig. 2a) while there are differently oriented side surfaces on bicrystals with the asymmetrical boundary (Fig. 2b). The difference in surface tension should be detected in our experimental arrangement where it acts in the opposite way on two boundary segments which migrate simultaneously. However, no systematic difference between the upper and lower migrating segments in Fig.2b has been found. It may mean that surface energies for free surfaces near to (011) and (001) are of comparable magnitude. The migration activation energy for 37'<001> grain boundaries in the f.c.c. metals: Pb and A1 (0.2 ev/at and 0.7 eV/at, respectively 13.41 ) is substantially lower than corresponding activation energy for bulk self - diffusion (1.1 eV/at and 1.5 eV/at, respective] y [ 141 ) , and in Pb it is of the same magnitude as the activation energy for grain boundary self - diffusion C151. The orientations

T IK1 1373 1323 1273 1233

My Em2/s symmetrical boundary

2.94 x lo-=

6. 72 x

1.79 x

6.40 x lo-"

asymmetrical boundary 1.42 x 10-lC' 1.46 x lo--'"

7.34 x lo-"

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of the migrating grain boundary in C3,41 were not specified. The value of migration energy of 1 eV/at for our asymmetrical boundary 37'<001> in b.c.c Fe

-

3wt%Si alloy is comparable with the energy for grain boundary self-diffusion in polycrystalline a-Fe (1.45 eV/at [I51 ) . It is again substantially lower than the energy for bulk self-diffusion in a-Fe (2.6 eV/at [ 141 ) . However, in spite of the fact that the mobility of our symmetrical boundary is essentially higher than for asymmetrica:l one, the migration activation energy for symmetrical boundary is surprisingly large (3.7 eV/at). The dependence of grain boundary energy on the plane orientation is not taken into account in our considerations here.

Nevertheless, is should be noted that the twin boundary on {Ill) with 2=3 in aluminium is totally immobile even when annealed for extended periods of time just below the melting point 1161. Obviously, the explanation of the complex dependence of grain boundary migration on all the geometrical parameters of the gtain boundary still requires further research.

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^{in press}

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