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CORRELATION BETWEEN THE BOUNDARY ENERGY AND PRECIPITATION IN COPPER-[011]
SYMMETRIC TILT BOUNDARIES
R. Monzen, K. Kitagawa, H. Miura, M. Kato, T. Mori
To cite this version:
R. Monzen, K. Kitagawa, H. Miura, M. Kato, T. Mori. CORRELATION BETWEEN THE BOUND- ARY ENERGY AND PRECIPITATION IN COPPER-[011] SYMMETRIC TILT BOUNDARIES.
Journal de Physique Colloques, 1990, 51 (C1), pp.C1-269-C1-274. �10.1051/jphyscol:1990142�. �jpa-
00230301�
COLLOQUE D E P H Y S I Q U E
Colloque Cl, suppl6ment a u n O l . T o m e 51, janvier 1990
CORRELATION BETWEEN THE BOUNDARY ENERGY AND PRECIPITATION IN COPPER-[Oll]
SYMMETRIC TILT BOUNDARIES
R. MONZEN, K. KITAGAWA, H. MIURA', M. KATO* and T. MORI*
Department of Mechanical Systems Engineering. Kanazawa University,
~ o d a t s u n o , Kanazawa 920, Japan
Department of Materials Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan
Abstract
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T h e misorientation angle dependence of density and volume of BCC precipitates on symmetric [Oll] tilt boundaries in a Cu-Fe-CO alloy has been studied to examine a correlation between the boundary precipitation and the boundary energy or the angle of the precipitate habit plane against the boundary plane. In general, the lower the boundary energy, the smaller the number and volume of the boundary precipitates.The minimum of the density and volume occurs where the cusps of the boundary energy exist; 0=70.5O (C3) and 130' (Ell). It has been found that the boundary energy plays a strong role in governing the boundary precipitation.
1
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INTRODUCTIONPrecipitates of a second phase are often formed preferentially on grain boundaries.
Examining polycrystalline samples of Al-Zn-Mg, Unwin and Nicholson have found that the density of the MgZn2 precipitates is lower on the boundaries with smaller C values (high coincidence boundaries)/l/. Butler and Swann conducted in situ observation of the same precipitation with a high voltage electron microscope and reached a similar conclusion/2/. The recent study of Czurratis, Kroggel and Lgffer for a similar alloy showed that the precipitate density in coincidence boundaries increases with increasing C values/3/. Although the energy of a boundary is not determined only by the C values, it is usually assumed that smaller C boundaries have lower energies. In classical theory, the nucleation rate of precipitates on a boundary is an increasing function of the boundary energy. In addition to the role of energy, we must consider those of solute segregation and diffusivity on grain boundaries when we discuss precipitation on grain boundaries. These properties also depend on the character of a boundary. Intuitively considered, a low energy boundary has a less disturbed structure than a high energy boundary. It appears that a larger degree of segregation and more enhanced diffusivity is achieved on a boundary with a larger energy or a higher C value/4-7/. These effects also promote the precipitation on boundaries. Thus, the results of Unwin and Nicholson and Butler and Swann can be expected without much reservation.
However, the study of Le Coze, Biscondi, Levy and Goux does not support this simple expectation/8/. Using bicrystals of A1-Cu with controlled orientations, they observed the precipitation of the 8 phase on the boundaries whose energies had be-en determined. On symmetric [001] tilt boundaries, the precipitate density changed with the misorientation angles sensitively in the range where the boundary energy is almost constant. 'Moreover, on symmetric [Oll] tilt boundaries, the maximum densities were achieved on the boundaries, C3 {l111 and C11 {113}, which have the minimum energies (cusps). The boundaries with larger energies had lower densities of the precipitates. Park and Ardell examined the precipitation on boundaries in Al-Zn-Mg and reached a conclusion that the crystallographic orientation of
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990142
Cl-270 COLLOQUE DE PHYSIQUE
the precipitates with respect to the boundaries determined the frequency of the boundary precipitation/9/. A theory also exists that a precipitate variant whose habit plane makes the smallest angle to a boundary plane is most favorably nucleated/lO,ll/. In short, the subject of the grain boundary precipitation has not been completely understood yet.
Considering the above situations, we studied the boundary precipitation in a'Cu-Fe-CO alloy, using bicrystals with controlled orientations. This alloy has two advantages to examine this subject. When aged at suitable temperatures, BCC precipitates containing Fe and C O are formed on grain boundaries/l2/. The precipitates exhibit the Kurdjumov-Sachs orientation relationship to one of the abutting grains. The {lll)f//{llO)b plane which defines the Kurdjumov-Sachs relationship of the plane forms an almost flat habit plane. Thus, varying the crystallographic orientation of a boundary, we can systematically change the angle between the habit plane and boundary. In some special cases, we can also fix this angle while changing the character of boundaries. The energy of a boundary in Cu can also be determined with sufficient accuracy by the method adopted by Miura et al, as reported in this conference.
Therefore, seeking a correlation between the precipitate density and the habit plane angle or the boundary energy, we can examine the boundary precipitation and discuss what principally determines this phenomenon.
2 - EXPERIMENTAL
As fully described by Miura, Kato and Mori in this conference report, the relative energy of a boundary in Cu can be determined by measuring the shape of a Si02 particle on the boundary. Bicrystals with symmetric [Oil] tilt boundaries of a Cu-O.OG%Si alloy were grown with the Bridgman method. The bicrystals were internally oxidized to form Si02 particles at 1273K for 24hr and subsequently degassed. Thin foils made from the internally oxidized bicrystals and containing boundaries were observed by transmission electron microscopy (TEM).
The shape of Si02 particles on a boundary was measured and the boundary energy, relative to the (isotropic) interfacial energy of Cu-Si02, was calculated.
Similar bicrystals of a Cu-1.4%Fe-O.6ZCo alloy were grown. After the solution treatment at 1273K for Zhr, the bicrystals were aged at 873K for lhr. BCC Fe-CO precipitates were formed by this aging. The density and size of BCC boundary precipitates on grain boundaries were determined by TEM. Examples o f TEM pictures are shown in Figs. l(a) and (b). Figure l(a) is an edge-on observation of a [Oil] tilt boundary with the misorientation angle 0=14O0.
As seen here, the boundary precipitates have almost flat habit planes in a grain to which those precipiwes have the Kurdjumov-Sachs relationship. Near the boundary, there exists a well defined precipitate free zone, beyond which a large number of fine coherent FCC precipitates are formed. After tilting a sample so that a boundary became inclined to the electron beam, the distribution of boundary precipitates was observed as shown in Fig. l(b).
About five foils were examined to determine the density of the BCC precipitates on a single boundary.
Identical experiments were performed on bicrystals with [001] twist boundaries. This was to extract only a role of the character of a boundary, by keeping the inclination of the habit plane of precipitates fixed to the boundary.
-X+. ,
"'i
Fig. 1 - (a) BCC Fe-CO precipitates on a symmetric [011] tilt boundary of Cu-1.6Fe-0.4Co (0=140°). Edge-on observation. (b) A similar boundary to that in (a) is examined from an oblique direction.
3 - RESULTS AND DISCUSSION
Figure 2 shows the boundary energy y against the misorientation angle 8 of symmetric [011] tilt boundaries in Cu. Each experimental point is the average of the values determined by about twenty Si02 particles and is bounded by the standard deviation. The y ( 0 ) curve in Fig. 2 is similar to that reported for A1 by Hasson and Goux/l3/. As observed in Al, three clear cusps exist at 8=4O0 ( C 9 ) , 70.5' (C3) and 130" (C11). However, the scatter of the data is smaller in the present measurement. Moreover, the present method has an advantage that the so-called torque term need not be included in the determination of the boundary energy.
The density D of the BCC precipitates in Cu-Fe-CO on [Oll] tilt boundaries is shown against the misorientation angle 8 in Fig. 3. Also in this figure it is seen that the boundaries with 8=4O1, 70.5' and 130' have minimum densities, the existence of the cusps in the D (8) curve. Although the cusp at 8=4O0 cannot be claimed strongly because of the scatter of the data, those at 8=70.5" and 130' are definite. That is, the density of the boundary precipitates shows local minima at the boundaries which accompany the energy cusps in the y (8) curve. For completeness, we present the width of precipitate free zones and the average volume of precipitates against the misorientation angle in Figs. 4 and 5. The general shapes
Fig. 2
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Theboundaries of
Misorientation Angle (deg.)
A
5
Y
r
[Oll] tilt
:
I : ::
; : : !-
. - 1 A-
--- h7 W C 3
-
C-
c - - -- - - -
- g 2 5 E
hl - v - - (1uU-J-0 m - c9 0
Z m G g
n s u
I Y Y ' ? ' ? ? f I
II
1 I , 1 1 1
Fig. 3 - Density of Fe-CO precipitates against the misorientation angle of symmetric [Oil]
tilt boundaries (Cu-Fe-CO)
.
F
Misorientation Angle ( deg. )
boundary energy against the misorientation angle for symmetr Cu.
COLLOQUE DE PHYSIQUE
Misorientation Angle (deg. )
Fig. 4 - Width of precipitate (Fe-CO) free zones (PFZ) against the misorientation angle (symmetric [Oil] tilt boundaries).
Misorientation Angle ( d e g . )
Fig. 5
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Volume of a boundary Fe-CO precipitate against the misorientation angle (symmetric [Oil] tilt boundaries).of Figs. 3-5 are similar. The sharp cusps at 8=70.5O and 130' are clearly seen in Figs. 4 and 5 , although the cusp at 0=40° in Fig. 4 is somewhat shadowed. The comparison of Fig. 4 with Figs. 3 and 5 shows that the width of precipitate free zones is closely associated with the density and growth of boundary precipitates. It is obvious that the precipitates with larger density and volume cause a larger width of precipitate free zones. The observation of Figs.
3-5 agrees with that by Unwin, Lorimer and Nicholson/l4/. There is a strong correlation between the boundary precipitation and energy. Qualitatively, the lower the boundary energy, the lower the precipitate density. This is opposite to the observation by Le Coze et al, in particular, the case of [Oll] tilt boundaries/8/. The present observation qualitatively agrees, in appearance, with that by Unwin and Nicholson and Butler and Swann who reported almost no precipitation on low C boundaries (high coincidence boundaries)/l,2/. However, what we would like to stress here is that the minimum density of precipitates occurs on the boundary with the minimum energy. Needless to say, the density does not correlate well only with the C values. For example, the energy is almost zero on C3, 0=70.5O while it is substantially large on 13, 8=110°. Corresponding to this, the precipitate density on the 0=110° boundary is large. A similar argument is given to the Cl1 boundary which is achieved by 0=51° and 0=130°. A higher density of precipitates is observed on the e=51° boundary which has a larger boundary energy than the 0=130° boundary. Butler and Swann argued that the
retardation of precipitation on high coincidence boundaries is not caused primarily by low energies possessed by these boundaries/2/. Without going into detail, the results shown in Figs. 2 and 3 are likely to refute the above reasoning. Summarizing the above discussion, it is our contention that the boundary energy is a principal factor determining the frequency of boundary precipitation. It may directly govern the energetics of nucleation or may be a measure with which diffusivity or segregation on a boundary increases. In fact, Herveuval et a1 observed the minimum of diffusivity at 0=70.5" (C3) and 0=130° (111) in symmetric [Oil]
tilt boundaries of Al, although they detected another minimum at 0=110° (13)/4/.
Next, let us examine the effect of the angle between the habit plane of precipitates and the boundary plane. It has been found that the variants of BCC precipitates predominantly formed on a boundary are those whose habit planes make the smallest angle to the boundary/l2/.
This was also the case in the present study. Thus, the positive role of the habit plane angle in determining boundary precipitation certainly exists. There aFe ranges of 8 which can be accounted for possibly by this effect of the smallest angle of the habit plane. As simple geometry shows, in symmetric [Oil] tilt boundaries, ar35.3"-8/2 when 8<70.5" and a=8/2-35.3"
when 0>70.5'. Let us compare the two regions near 0=0° and 180". The precipitate density in the region near 0=0° is higher than that in the region near 0=180°. a is larger near 8=18O0.
However, Sn most ranges of 8, the effect of the boundary energy is overwhelming. In the extreme case of 0=70.5" (13), the precipitate density is practically zero while a i s the smallest there. The energy of the 8=70.5' boundary can be taken zero compared with the energies of other boundaries for all practical purposes. Furthermore, the presence of the minimum density on the 40' and 130° boundaries cannot be explained simply by the dependence of a on 8. a changes monotonically around 8=40° and 130". These facts indicate that if the effect of the boundary energy acts in opposite direction against that of the habit plane angle in promoting or retarding the boundary precipitation, it is the boundary energy that principally governs the precipitation.
The principal role for the boundary energy to determine the boundary precipitation was also examined by using [001] twist boundaries. These boundaries are parallel to (001) to which all the habit planes of BCC boundary precipitates incline by a constant angle, 54.7".
The energies of [OOl] twist boundaries in Cu have already been determined as a function of the twist (misorientation) angle 0i15/: The boundary energies have minima (cusps) at 8=13O (141), 23" (113), 28" (117), 37" (15) and possibly 44' (129). Figure 6 shows the density of precipitates on [001] twist boundaries against the twist angle. Corresponding to the energy cusps, the density of the boundary precipitates becomes minimum at these special boundaries.
That is, there is a direct correlation between the precipitate density and energy in the [001]
twist boundaries.
The comparison between the [Oil] tilt and [001] twist boundaries in the boundary precipitation, Figs. 3 and 6, merits some discussion. In both types of boundaries, the boundary having an energy cusp has a sharply small density of precipitates compared with its nearby boundaries. However, the largest density in the [Oil] tilt boundaries is approximately twice as large as that in the [OOl] twist boundaries. These boundaries have energies close to that of random boundaries. In this connection, one may consider the possible role of a which affects the boundary precipitation in addition to the boundary energy. As far as physically existing boundaries are concerned, a is smaller in the [Oil] tilt boundaries than in the [001]
Misorientation Angle ( d e g . )
Fig. 6
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Density of boundary BCC Fe-CO precipitates against the misorientation angle of [001]twist boundaries of Cu-Fe-Co.
Cl-274 COLLOQUE DE PHYSIQUE
twist boundaries. However, it appears more plausible that the atomistic structure of a boundary plays a more significant role. Except for the 0=70.5' (13) boundary, the symmetric [Oil] tilt boundaries always contain steps on an atomistic scale. These steps are likely to serve for the sites where the precipitate nuclei are formed. On the other hand, the [001]
twist boundaries do not contain such steps if the boundaries are ideally constructed. Thus, the number of the nucleation sites is smaller in the [001] twist boundaries. Qualitatively, this accounts for the difference in the magnitude of the largest densities between Figs. 3 and 6.
4
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SUMMARYThe boundary precipitation of BCC precipitates in a Cu-Fe-CO alloy was examined in conjunction with the boundary energy and the crystallography of the precipitates, using symmetric [ O l l ] tilt boundaries. There was a good correlation between the density of the precipitates and the boundary energy: In general, the larger the boundary energy, the larger the density of the boundary precipitates. The precipitate density became minimum at the misorientation angles of 70.5' (13) and 130' (111) where sharp energy minima (cusps) were also observed. Although the angle between the habit plane of the precipitates and t.he boundary showed some effect on the preference of the precipitation, it is the boundary energy that principally governs the boundary precipitation.
Acknowledgement
This research was partly supported by a Grant-in-Aid for Scientific Research from the Ministy of Education, Science and Culture (No. 63550533).
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