Growth of α-Fe-Co particles on [001] symmetric tilt boundaries in Cu bicrystals

Scripta Materialia.

Vol. 37, No. 10, pp. 1505-1510. 1997 Elsevicr Science Ltd Copyright 0 1997 Acta Metallurgica Inc. Printed in the USA. All rights reserved I359-6462/97 S 17.00 + .OO

PI1 s13594462(97)00296-0

GROWTH OF cc-Fe-Co PARTICLES ON [OOl] SYMMETRIC TILT BOUNDARIES IN Cu BICRYSTALS T. Echigo and R. Monzen Department of Mechanical Systems Engineering, Kanazawa University, 2-40-20 Kodatsuno, Kanazawa 920, Japan (Received May 15, 1997) (Accepted July 9, 1997)

oductioq Much theoretical work has been done on the growth of precipitate particles on a grain boundary (l-4). It has been shown that the mean particle radius r increases with increasing aging time t as r-4”. This result was derived from the assumption that solute atoms diffuse on two-dimensional grain boundaries. On the other hand, a few experiments have been reported on the growth of boundary particles. Butler and Swamr (5) examined the growth of boundary MgZn, particles in an Al-Zn-Mg alloy. They obtained the relationship r” = Kt, where K is the rate constant, with n having values between 3 and just over 4 depending on the misorientation angle of the two abutting grains. Czurratis et al. (6) revealed using the same alloy system that r is proportional to t”4 for particles on random high-angle boundaries. They also obtained an activation energy (1.8 eV) for the particle growth from the slope of a plot of lo@ against 1IT, where T is the aging temperature. Recently, using orientation-controlled bicrystals, Fujii et al. (7) investigated the growth of a-Fe-Co precipitate particles on [Ol I] symmetric tilt boundaries with misorientation angles of u = 5-50.5” in a CuFe-Co alloy aged at 873K. The development of precipitate-free zones (PFZs) during aging also was examined. They showed that the power n for f’ = Kf varied systematically from 3 to 5 as the misorientation increases from IO to 50.50, while the relationship d2-t held between the width d of PFZs and aging time t for all the bicrystals investigated. The change in the n values was explained reasonably by considering the relative contribution of bulk diffusion and dislocation pipe diffusion towards the particle growth. It is well known that bulk diffusivity decreases remarkably with decreasing temperature in comparison with grain-boundary diffusivity. This means that the relative contribution of the bulk diffusion towards the growth of r-Fe-Co particles on a boundary should become smaller as aging temperature becomes lower. Therefore, it is very probably that, if aging temperatures lower than the temperature of 873K, adopted by Fujii et al. (7), are chosen, 0 would become closer to 4, independent of the boundary character. With this in mind, the coarsening of boundary a-Fe-Co particles is investigated for various [OOl] symmetric tilt boundaries in Cu-Fe-Co alloy bicrystals aged between 673 and 723K. Furthermore, the activation energy for the particle growth is estimated as a function of the misorientation angle.

1505

1506

GROWTH OF a-Fe-Co PARTICLES

Vol. 37, No. 10

Bicrystals, lmm thick, of a Cu- 1.4mass%Fe-0.6mass%Co alloy containing various [00 I] symmetric tilt boundaries with misorientation angles 0 = 9-80” were grown by the Bridgman method using two seed crystals. Hereafter, a bicrystal with the misorientation angle 0 and its grain boundary will be expressed as a 8 bicrystal and a 0 boundary, respectively. The bicrystals were aged at 673,698 or 723K for various time periods ranging from 40 to 216h after a solution treatment at 1253K for lh. The size of a-Fe-Co precipitate particles formed on grain boundaries was examined on a transmission electron microscope (Hitachi H-800; 2OOkV)after making thin foils. For each boundary and aging condition, about 30 particles were observed with a beam parallel to [OOl]. Results a-Fe-Co particles precipitated on all the boundaries examined. However, coherent y-Fe-Co particles in grains were too small to be detected by transmission electron microscopy. Accordingly, PFZs could not be identified on both sides of all the boundaries. To examine the shape of the a-Fe-Co particles, the same particles were observed from several different directions by tilting thin foils. The boundary particles were nearly spherical (lens like), independent of misorientation angle, aging temperature and time. This is consistent with the results of previous studies obtained using the same Cu-Fe-Co alloy system aged at 873K for Ih (8, 9). This also is in contrast with the observation by Fujii et al. (7) that the shape of a-Fe-Co particles on [Ol l] symmetric tilt boundaries after long aging over 1h at 873K depends on the misorientation angle: on 10 and 15” boundaries the particles are nearly spherical, whil’e on 20 and 50.5” boundaries they are rod like. Figure 1 shows the mean particle radius r as a function of aging time t for 56” bicrystals aged at 673, 698 and 723K. An almost linear relationship can be seen between r and t when plotted on logarithmic scales. This indicates that r is nearly proportional to t”“. From the slope of the straight line drawn by the least-squares method, n can be obtained for each boundary and aging temperature. The calculated values of n are listed in Table 1. For all the boundaries, n is very close to 4 irrespective of aging temperature. The value of n = 4 agrees with the value obtained theoretically (l-4).

5o I 8 =56’

Aging Time,

t /set

Figure 1. Change in the mean particle radius with aging time for a 56’ boundary aged at 723,698 and 6733.

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GROWTHOF a-Fe-Co PARTICLES

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TABLE 1 Calculatedn Value for Each Boundary Aged at 723,698 and 673K n

Misoricntntion Angle (degrees)

-

Aging Temperature (K) 123

698

613

9

3.8

3.8

4.1

14

3.8

4.2

4.2

22

4.0

3.9

4.1

28

3.9

4.0

4.2

30

3.9

4.0

4.1

36

3.9

3.9

4.2

48

4.0

4.0

4.0

53

3.9

3.9

4.1

56

3.9

4.1

4.2

63

3.8

4.1

4.1

68

3.9

3.9

4.1

74

3.8

4.0

4.1

80

3.8

3.8

4.2

According to Ardell(3), the kinetics of particle growth on high angle-grain boundaries is given as r4-r 4 = 0

k-t,

(1)

where 80CD~o&u(r+)~~ K= 3GRTv (4)

Here o is the particle-matrix interfacial energy per unit area, C is the solute concentration, o is the width of the gram boundary, R is the molar volume of the precipitate, Do is the pre-exponential factor of grainboundary diffusivity, Q is the activation energy of grain-boundary diffusion, G is a constant related to the alloy system, +(I$)> and ~(4) are constants which depend on the volume fraction 4, and RT has its usual meaning. On the basis of eq. (2), log(KT/C) was plotted against l/T, as exemplified in Fig. 2. K was calculated by the least-squares method from plots of # against t. We also adopted C = 70,SO and 90 moUm’ at 673, 698 and 723K, respectively (10). For all the boundaries, a straight line could be drawn and the activation energy Q was estimated from its slope. The values of Q are given against the misorientation angle 0 in Fig. 3. Q is plotted downwards in this figure. The Q values change between 0.9 and 1.4 eV, depending on the misorientation angle.

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GROWTH OF a-Fe-Co PARTICLES

I

I

I

I

1.40

1.35

Vol. 37, No. IO

I

1.45

1.50

1

l/T/10-3K-’ Figure 2. Plot of log(KTIc) against l/Tfor 9,48,56 and 74” boundaries.

Discussion It is known that the activation energy of grain-boundary diffusion is approximately 50 to 70% of that of bulk diffusion (11). Since the values of the activation energies in Fig. 3 are much smaller than that (2.2 eV) of the bulk diffusion of Fe or Co in Cu, they can be reasonably identified as the activation energies for grain-bounds di~sion of solute. The dependence of Q on 9 in Fig. 3 is nonmonotonic; cusps exist near e = 28.1 o ( I: 17 ), e = 36.9” (~5) e = 53.2” (X5), 0 = 61.9” (E 17) and 8 = 73.7” (X2.5).The variation of Q with e does not follow the same trend as the grain-boundary diffusion of Zn in [OOl] symmetric tilt boundaries of Al (12, 13). Aleshin et al. (12) measured the activation energy of diffusion for boundaries with e = 10-45”. There were minima at e = 23..5”,28.5” and 37”. The dependence of the gram-bo~da~ difmsivity on e reported by Biscondi (13) showed no clear cusps. However, intuitively speaking, boundary diffusion in a high-energy boundary is expected to take place more easily than that in a low-energy boundary since the atomic I

, t

10

I

I

20

1

28.1

36.9

El7

x5

I

30

Mi~o~ent~on

I

53.2 25

I

,

40

60

Angle,

,

61.9 El7

I

60

I

I

73.7 x.25

I

70

t

60

B /deg.

Figure 3. Measured activation energy Q plotted against the misorientation angle 8.

GROWTH OF a-Fe-Co PARTICLES

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TABLE 2 Numerical Values Used for the Calculation of the Pre-Exponential factor D, G ** 3 3

*o-44

0

n

OW

(m3/mol)


v(4)

0s

71x104

'10338

* 18

in the former is considered to be more random and disturbed. Actually the position of the cusps in Fig. :3coincides with that of the boundary energy cusps in Cu (14). Therefore we conclude that a higher-energy boundary has a higher diffusivity. From eq. (2) and Fig. 3, the pre-exponential factor D,, was calculated for all boundaries. In this calculation, we used the numerical values listed in Table 2. D,, was independent of the aging temperature. The calculated values of Do at 723K are shown against the misorientation angle 0 in Fig. 4. D, is plotted downwards in this figure. The D, values range from lo-* to 1W5m*/s, depending on the misorientation angle. These values are smaller than that (-lo4 m%) for bulk diffusion of Fe or Co in Cu. Furthermore, the comparison of Fig. 4 with Fig. 3 reveals that the larger the Q value, the larger is the Do value. If grain-boundary diffusion occurs by a vacancy exchange model, the pre-exponential factor is written as D,=exp {(A$ + ASJR } from the work by Balluffi (16). Here A$ is the vacancy formation entropy and A& is the vacancy migration entropy. Moreover, according to Shewmon (17), the following empirical relationship often holds; AS,+ A&,-Q/T,,,, where T, is the melting point. From these equations, it can be seen that larger Q results in larger D,. This relationship is also the case in the present study, as shown in Figs. 3 and 4. arrangement

Conclusions

The kinetics of the coarsening of a-Fe-Co precipitate particles on different [OOl] symmetric tilt boundaries has been investigated using Cu-Fe-Co alloy bicrystals aged at 673,698 and 723K. The conclusions of this study are summarized as follows.

10-g

r

I

I

I

1

I

I

I

-i

c-4-

28.1 36.9 Zl7 t5

E

\

<

532 I5

61.9 Zl7

13.1 Z25

10-8:

5 iii LL. to-7 2 E g k

106"

723K

b

a

10-5 0

I 10

I

1

I

I

I

,

I

1

20

30

40

50

60

70

60

90

Misorientation

Angle,

B /deg.

Figure 4. D,,plotted against the misorientation

angle 8.

1510

(1)

(2)

GROWTH OF a-Fe-Co PARTICLES

Vol. 37, No. 10

The aging time t dependence of the mean particle radius r can be represented by J’ = Kr, where K is a constant. The power n is 4 irrespective of misorientation angle and aging temperature. This value is in agreement with the growth theories of boundary particles (1-4). The measured activation energy Q and calculated pre-exponential factor D, of grain-boundary diffttsivity against misorientation angle curves display several cusps and these curves are analogous to the boundary energy against misorientation angle curve. A higher-energy boundary has a higher diffusivity with a smaller value of Q and a smaller value of Do. Acknowledgments

Thanks are due to the Industrial Research Institute of Ishikawa whose transmission electron microscope was used for the microscopic observation. Mr. J. Nakayama also is acknowledged for his experimental assistance. References I.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

M.V. Speight, Acta metah. 16, 133 (1968). H.O. Kirchner, Metall. Trans. 2,2861 (1971). A.J. Ardell, Acta metall. 20,601 (1972). R.D. Vengrenovitch, Acta metall. 30, 1079 (1982). E.P. Butler and P.R. Swarm, Acta metall. 24,343 (1976). P. Czurratis, P. Kroggel and H. Loffer, 2. Metallk. 79,307 (1988).. T. Fujii, M. Moriyama, M. Kato and T. Mori, Phil. Mag. A 68, 137 (1993). R. Monzen and K. Kitagawa, Scripta metall. 22, 173 (1988). R. Monzen, K. Kitagawa, M. Kato and T. Mori, J. Japan Inst. Metals 54, 1308 (1990). G. Tammann and W. Oelsen, Z. Anorg. U. Allg. Chem. 186,38 (1930). H. Gleiter and B. Chalmers, Prog. Mater. Sci. 16, 77 (1972). A.N. Aleshin, B.S. Bokstein and L.S. Shvindlerman, Sov. Phys. Solid State 19,205l (1977). M. Biscondi, in Physical Chemistry of the Solid States: Applications to Metals and Their Compounds (edited by P. Lacombe), p. 225, Elsevier Science Publishers, Amsterdam (1984). T. Mori, T. Ishii, M. Kajihara and M. Kato, Phil. Mag. lett. 75,367 (1997). T. Fujii, M. Kato and T. Mori, Mater. Trans., Japan Inst. Metals 32, 229 (1991). R.W. Balluffi, Metall. Trans. A 13,2069 (1982). P.G. Shewmon, Diffusion in Solids, McGraw-Hill, NewYork (1963).