SINGLE GRAIN BOUNDARY MIGRATION

V. Paidar, S. KadeCkovfi, P. Lej6ek

Institute o f Physics, Czeehosl. Aead. SeL, Na Slovanee 2, 180 40 Praha 8, Czeehoslovakia

Various driving forces which cause migration of grain boundaries in bicrystals are discussed. The analysis of experimental data for migration of symmetrical tilt grain boundaries 37 ~ <001) E5 in Fe-3 wt. ~ Si bicrystals indicates that the migration velocity is proportional to the driving force only for relatively fast boundary movement. The observed deviation from linearity might be related to segregation of impurities at the grain boundary.

1. INTRODUCTION

Plastic deformation of polycrystalline materials at high temperatures is strongly affected by grain boundary mobility. In particular, recrystallization processes depend substantially on migration characteristics of grain boundaries. It is well known that the properties of grain boundaries vary significantly in a non-trivial way with the boundary type. The anisotropy of grain boundary properties can be studied under well defined experimental conditions on bicrystalline samples.

The motion of a single grain boundary is still a complicated process which ls inflnenced by various effects due to different structural features of the moving bound- ary (behaviour of grain boundary dislocations, drag by segregating impurities and solute atoms etc.). In this paper the driving forces which can cause the movement of the grain boundary in bicrystals will de described and the results of experiments investigating the grain boundary migration in Fe-3 wt. ~o Si bicrystals will be analysed.

2. DRIVING FORCES

When the distribution of dislocations and dislocation walls separating mosaic blocks in the component crystals of bicrystal is homogeneous on both sides of the grain boundary, the main driving force for boundary migration is a reduction of the grain boundary energy due to decreasing surface area of the moving boundary. A difference in surface tension of free surfaces possessing different crystallographic orientations may cause another driving force acting on the grain boundary. The effect of side free surfaces on boundary migration can be studied in the experimental arrangement suggested in [1]. The grain boundary motion which takes place at high temperatures may be influenced by diffusion of impurities and solute atoms that segregate to the boundary. If the diffusion of impurities at certain temperature is faster than the motion of the grain boundary in the case of low driving forces, the distribution of impurities around a boundary gives a negligible drag force. However,

4 '70 Czech. J. Phys. B 38 (1988)

V. Paidar et al.: Single grain boundary migration

if the boundary migrates with a higher velocity at the same temperature, the impurity atoms are not able to attain an equilibrium distribution and it results in the drag force acting against the driving force. At sufficiently high velocities of migrating boundary, the impurity atmosphere bas no time to be formed and the boundary motion will not be influenced by impurity segregation. This is the case of large driving forces. Hence to study the effect of segregation on grain boundary motion it is essential to carry out experiments at a wide range of driving forces.

FS ,Q_~

ci GB

Fig. 1. Threcdifferentconfigurationsofmigratinggrainbound- aries: a) reversed-capillary technique, b) direct-capillary (wedge) technique, c) constant driving force technique. GB

denotes grain boundaries and FS free surfaces.

Three different regimes of grain boundary migration can be employed [2, 3]. For reversed-capillary technique (fig. la) the driving force, F, due to the reduction of the grain boundary area is a decreasing function of the migration distance, a, and depends on the angle, OE, of the initial boundary plane to the free surface

(1) F = \ ~ 7 2 O E 1 a

where y is the boundary energy. For direct-capillary technique (fig. lb) the driving force increases with the migration distance

(2) F - R - - a

where R defines the initial position of the grain boundary. Finally, for constant driving force technique (fig. lc)

(3) F 27 nd

where d denotes the width of disappearing narrow grain. The grain boundary energy in expressions (1)-(3) was assumed to be a constant, however, it may vary with the orientation of the boundary normal.

Czech, J, Phys. B 38 (1988) 471

E Paidar et al.: Single grain boundary migration

3. RESULTS AND DISCUSSION

A modified reversed-capillary technique was used in our experiments [1]. Kinetics of grain boundary migration were analysed in detail for two different orientations of grain boundary normal in [4]. Measured dependences of the migration distance, a, on the anneafing time, t, at four different temperatures were interpreted assuming that the migration velocity is proportional to the acting driving force determined by the shape of the moving grain boundary. Because of equivalent orientations of external free surfaces on studied samples, the driving force resulting due to free surfaces is equal to zero. It is important to note that fluctuations of migration velocity due to changes of mosaic block structure swept by the grain boundary are suppressed in the a(t) dependence. The motion of a grain boundary can be locally retarded by dislocation walls on the rear side of the boundary or accelerated by the walls in front of the moving boundary. However, in order to check the assumption of the linear dependence of migration velocity on driving force let us plot the velocity determined from two successive positions of the boundary as a function of the ratio F/? calculated from equation (1). The angle OE was 45 ~ in our experiments. It is done in fig. 2. In spite

106[ ' 1373K '

/ /

[]/ 10-8 1223 ~/Lj

/ [ ]

I i

102 FI~' [rr�9 1] 103

Fig. 2. The dependence of the migration velocity, v, on the ratio of the driving force, F, and the grain boundary energy, ?, measured at four different tempera- tures for symmetrical tir grain boundaries 37 ~ (001)

25 in Fe-3 wt. % Si bicrystals.

of a relatively large starter of experimental data it is seen that the migration velocity, v, is proportional to the driving force, F, at temperature above 1273 K. The positions of eorresponding full lines in fig. 2 were determined from a(t) dependences [4]. However, at 1223 K for low migration velocities in particular there is a clear devia- tion from the linear relationship between v and F (full line). The data are better approximated assuming that v is proportional to F z (dashed line).

A possible reason for the observed deviation from linear behaviour might be segregation of impurities discussed above. It would mean that segregation does not

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V. Paidar et aL: Single grain boundary migration

affect grain boundary motion if the migration velocity is higher than certain critical value for each temperature. On the other hand segregation effects related to diffusion of impurities would modify the boundary motion at low velocities for small driving

forces. To prove this hypothesis further experiments are desirable.

Reeeived 25 September 1987

Referenees

[1] LejEek P., Kade~kov~i S., Paidar V.: Annealing Processes- Recovery, Recrystallization and Grain Growth. 7th Riso Int. Symp. Metall. Mater. Sci., Riso, 1986, p. 437.

[2] Masteller M. S., Bauer C. L.: Recrystallization of Metallic Materials. Dr. Riederer Verlag GmbH, Stuttgart, 1978, p. 251.

[3] Kopetskii Ch. V., Shvindlerman L. S.: High Purity Metals, Nauka, Moseow, 1976, p. 73 (in Russian).

[4] Lejœ P., Paidar V., Grabski M. W.: J. Phys. (Paris) to be published.

Czech. J. Phys, B 38 (1988) 473