Diffusion species in pipe diffusion for orowan loop climb in a Cu-SiO2 alloy

Scripta

METALLURGICA

Vol. 15, pp. 5 5 5 - 5 5 8 , Printed in U . S . A .

1981

Pergamon P r e s s Ltd. All r i g h t s r e s e r v e d

DIFFUSION SPECIES IN PIPE DIFFUSION FOR OROWAN LOOP CLIMB IN A Cu-SiO 2 ALLOY

Michio Okabe, Munetaka Koda and T. Mori Department of Materials Science and Engineering Tokyo Institute of Technology 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan

(Received

March

]0,

1981]

INTRODUCTION It appears generally agreed that softening on low temperature annealing after work hardening in dispersion strengthened alloys is induced by climb and disappearance of Orowan loops caused by pipe diffusion along the cores of the loops (1-3). The climb rate of an Orowan loop was analysed on the basis of the pipe diffusion (3,4) and was successfully applied to understanding of annealing after work hardening and recovery creep in dispersion strengthened alloys (3-7). In these studies, it was tacitly assumed that the diffusion species were the matrix atoms when a quantitative discussion was made in the estimation of the softening and creep rates. In our view, however, this assumption is not necessarily axiomatic nor has it ever been justified experimentally. In a contimuun approach, the origin of the internal stress responsible for work hardening is the existence of misfit between a dispersoid and a olasticaIly deforming matrix (8-10). Then, the loss of the internal stress is understood to be caused by a decrease in the misfit. In principle, the change in the misfit can be brought about by the diffusion of either the matrix or the dispersoid element (Ii). In fact, discussions on the softening were once made by referring to a work (12), in which the diffusion of [;iO2 constituents along the Cu-SiO2 interface was measured by use of spheroidization of Si02 particles with lumps (13,14). Although the identification of the diffusion species does not alter the analyses of the softening and creep in character, in order to complete the mechanism of the pipe diffusion along an Orowan loop it is desirable to know whether the matrix atoms or the dispersoid constiuents diffuse in the process of the dislocation climb. In the present study, this problem was solved experimentally and will be reported in the following. EXPERIMENTAL PROCEDURE Single crystals of a Cu-SiO 2 alloy were utilized because of the almost perfect spherical shape of the SiO2 particles. The method of the specimen preparation was identical to that reported previously (3). The volume fraction and the average diameter of the SiO 2 particles were 0.005 and 75.4 nm, respectively. The specimens with the dimension of 2.6 mar, x 0.7 L~nn x 59.1 mm had the initial tensile direction that inclined by 47.0 ° to the primary slip direction, [i01], and by 44.0 ° to the normal of the slip plane, (iii). To produce the Orowan loops without forming prismatic loops and still to observe the particle shape change caused by diffusion on annealing if the diffusion species were constituents of Si02, several cycles of deformation and subsequent annealing were given to a specimen; in one cycle a specimen was strained at 77 K by glide strain of ~ 4 % and annealed for 1 h at 473 K. This straining condition insures that glide dislocations leave essentially only the Orowan loops around the SiO2 particles (13) and the annealing eliminates the Orowan loops (3). Examination of the specimen elongation and orientation after a total of 3 6 . 1 % glide strain showed that the deformation occurred only on the primary slip system. This foils were made out of the deformed and annealed specimens with

555 0036-9748/81/050555-04502.00/0 Copyright (c) 1 9 8 1 P e r g a m o n Press

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a standard method and were observed under a 200 kV electron microscope with a b e a m parallel [i21]. EXPERIMENTAL

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RESULTS

If the diffusion species are the constituents of SiO2, a Si02 particle after deformation and annealing would be observed as shown in a solid line in Fig. i, where the original spherical shape of the particle is depicted by a dotted line. The angle e of the axis of the ellipsoid from the slip derection [i01] and the aspect ratio al/a 2 are given, respectively, in terms of the total glide strain y as

0=~ 1

tan

-12

~

- -

i

al = ( ye cos 0 + 2 T sin0 cos@ + i a2 y2 sin20 _ 2 y sin0 cos'0+ 1 ) -~ On the contrary, if the climb of an Orowan loop is caused by the diffusion of the matrix atoms, the shape of the Si02 would remain unchanged and spherical. In Fig. 2 are shown electron micrographs from the specimens, (a) before deformation and (b) after ii cycles of deformation and annealing, the total glide strain being 3 6 . 1 % . It is clear that the shape of the Si02 particles is not changed by deformation and annealing. This is further demonstrated by Fig. 3, where histograms showing the distribution of the particles with the particular aspect ratios are given for several total glide strains. The aspect ratio was measured by assuming Eq. (i). For reference, the hypothetical values of the aspect ratio in the case of the SiO 2 diffusion are shown in Fig. 3 by arrows, corresponding to Eq. (2). Even though the Si02 particles are not perfectly spherical, we can definitely conclude that the shape of the particles after deformation and annealing is the same as that before deformation and that the diffusion species responsible for the climb of the Orowan loops are Cu atoms. DISCUSSION AND CONCLUSION First, we discuss the motivation of the present study. It might be argued that diffusion species are no doubt matrix atoms because the plastic deformation is brought about by dislocations gliding in the matrix. This reasoning is not well founded as will be described in the following. Suppose we have a dispersed particle which is highly resistant to plastic deformationfor an unspecified reason but has a high diffusion constant, for example, because of its low melting point. Then, we would naturally consider that a decrease in misfit produced by the matrix plastic deformation will be induced by the diffusion of the particle. Secondly, we may have to discuss whether an Orowan loop is in contacton the matrix-particle interface or is repelled by some distance from the interface. The detailed discussion on this problem requires atomistic consideration on the core structure of the dislocation. Here, however, we will employ the elasticity approach. The elastic constant of Cu is larger than that of Si02. Thus, there is no reason to consider that a dislocation is repelled from the interface. We would also like to point out the possibility that a loop is attracted to a particle even when the particle has a larger elastic modulus. The attractive force comes from a fact that a loop surrounding a particle has the shortest line energy when it is at the interface. Although a quantitative discussion is not possible at the present moment, we can show the importance of the elastic strain energy associated with dislocation loops around a particle. Instead of a single discrete loop, let us consider several dislocation loops surrounding a particle and smear out these dislocations. Then, the elastic strain energy can be calculated by giving a misfit strain in a closed domain bounded by the smeared dislocation loops (15). It can be easily shown that the elastic strain energy is an increasing function of this closed domain. The particle can be assumed to be plastically nondeforming and the situation where the domain becomes smaller than the particle is physically unconceivable. Therefore, the minimum of the elastic strain energy is achieved when the closed domain defined by the smeared loops coincides with the particle. This corresponds to the case that the discrete loops are in contact to the particle. Next, we consider a starting point in the present study; softening of a work hardened dispersion strengthened alloy is caused by loss of Orowan loops by pipe diffusion. Although this has been fairly well established (1-3), a diffusion mechanism was once doubted on the ground that the information on the interfacial diffusion of Si02 in a Cu-SiO2 alloy (12) could not account for the observed softening (13). This is natural because not only the diffusion

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path but also the diffusion species are different in the softening and the change in tile shape of SiO2 particles. Finally, we repeat the conclusion that in a Cu-SiO 2 alloy, the climb of an Orowan loop occurs by the Cu atom diffusion along the dislocation loop pipe, as assumed previously (3,5,7). REFERENCES (i) (2) (3) (4) (5) (6) (7) (8) (9) (i0) (11) (12) (13) (14)

P.M. Hazzledine and P.B, Hirsch, Phil. Mag., 30, 1331(1974). D. Gould, P.B. Hirsch and F.J. Humphreys, Phil. Mag., 30, 1353(1974). T. Mori and iI. Tokushige, Acta metall., 25, 635(1977). M. Okabe and T. Mori, Acta metall., 27, 1373(1979). T. Mori and T. Mura, Acta metall., 26, 1199(1978). T. Mori and T. Osawa, Phil. Mag. A, 40, 445(1979). M. Okabe, T. Mochizuke and T. Mori, Phil. Mag. A, 41, 615(1980). K. Tanaka and T. Mori, Acta metall., 18, 931(1970). L.M. Brown and W.M. Stobbs, Phil. Mag., 23, 1185(1971). L.M. Brown, Acta metall., 21, 879(1973). T. Mori, M. Okabe and T. Mura, Acta metall., 28, 319(1980), W.M. Stobbs, Phil Mag., 3-0, 1073(1973). L.M. Brown and W.M. Stobbs, Phil. Mag., 344, 351(1976). L.M. Brown, Proc. 5th Int. Conf. Strength of Metals and Alloys, p.1551, Pergamon Press, Oxfocd(1979). (]5) K. Tanaka, K. Narita and T. Mori, Acta metall., 20, 297(1972).

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O~

Oi

FIG. i

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OROWAN

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(a)

Vol.

(b)

FIG. 2 Electron micrographs viwed from the [121]. (a) Undeformed. (b) After Ii cycles of deformation and annealing ( y = 0.36 ).

~ (a) 8 61

Y=0 0

(b)

y=OI

40 2 80

=

60 40 20 0 80 ( e ) 60 40 20 0 0.95 I 0

"Z

Aspect

.

"

095 I 0 I 05

I 05 Ratio,

m/a2

FIG. 3 Particle shape distribution. (a) Undeformed. (b)~(e) After several cycles of deformation and annealing.

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