Microstructural evolution of a heavily cold-rolled CuCr in situ metal matrix composite

Microstructural evolution of a heavily cold-rolled CuCr in situ metal matrix composite

ELSEVIER Materials Science and Engineering A212 (1996) 149-156 A Microstructural evolution of a heavily cold-rolled Cu-Cr in situ metal matrix comp...

4MB Sizes 16 Downloads 59 Views

ELSEVIER

Materials Science and Engineering A212 (1996) 149-156

A

Microstructural evolution of a heavily cold-rolled Cu-Cr in situ metal matrix composite Y. Jin, K. Adachi, T. Takeuchi, H.G. Suzuki National Research Institute Jbr Metals, 1-2-1 Tsukuba 305, Japan

Received 9 November 1995: in revised form 11 January 1996

Abstract

The microstructural evolution of a Cu-15wt.%Cr in situ metal matrix composite has been investigated by means of scanning electron microscopy, analytical transmission electron microscopy, high resolution electron microscopy and energy-dispersive X-ray spectrometry. It is found that the dendritic Cr and equiaxed Cr in the as-cast state are mostly deformed into Cr ribbons after cold rolling to 89.8% reduction in thickness. In these heavily deformed Cr ribbons, ellipsoidal Cu-rich clusters with size around 1 nm were observed which have the same lattice as the Cr ribbons but different Cu concentrations from each other. Lattice distortion also exists around these Cu-rich clusters, though its extent varies depending on the Cu concentration in each cluster. Keywords: Cu -Cr composite; Electron microscopy;Cold-rolled microstructure; Precipitation

1. Introduction

A new generation of Cu conductive materials [1-7], which are distinguished by possessing both high strength and good conductivity, can be developed within the frame of metal matrix composite (MMCs). In contrast with previous generations, these materials contain an amount of secondary element far exceeding that element's solubility in the Cu matrix. These secondary elements form dendrites during casting, which can be deformed into fibres (for wire) or ribbons (for sheet) by further extensive cold working to reinforce the whole material. Terminologically, this kind of material is generally referred to as an "in situ metal matrix composite" [1-4,8-10]. Among these materials, C u - C r in situ MMCs appear very promising for their economic potential in the electrical and electronic industries. Heavy cold working is a very important intermediate step in processing in situ MMCs. It not only deforms dendrites into fibres but also enhances the migration of solute atoms by producing a large amount of vacancies through dislocation movement [11-13]. Unlike the similar C u - N b binary alloy system, the solubility of Cu in Cr was generally believed to be negligible from room temperature to as high as 1076 °C [14]. However, Takeuchi et al. [15] reported a concentration of about 1 0921-5093/96/$15.00 © 1996-- Elsevier Science S.A. All rights reserved PH S0921-5093(96)10194-5

at.% Cu in extracted Cr dendrites. Adachi [16] recently found that the lattice parameters of Cr ribbons in MMCs decrease with increasing aging temperature, as studied by the X-ray technique. These new facts indicate that the solubility of Cu in Cr may not be negligible and early-stage precipitation may occur as a result of the heavy cold-working process. In addition to the terms " G u i n i e r - P r e s t o n (GP) zone" [17] and "short-range-ordered (SRO) structure" [18,19], "solute-rich cluster" [20-23] has become popular recently in the description of the early-stage precipitation phenomenon. In contrast with GP zones, solute-rich clusters are also available for the case where early-stage precipitates transform directly to stable phases without first becoming intermetastable phases. Unlike SRO structures, solute-rich clusters do not produce periodic diffuse diffraction streaks (or spots) and thus cannot be detected by the selected area diffraction (SAD) technique. Theoretically, the cluster dynamics approach [24,25] has also proved successful in the interpretation of the phase separation phenomenon. In this work we have investigated the microstructure of a Cu-15wt.%Cr in situ metal matrix composite in both as-cast and heavily cold-rolled states by means of scanning electron microscopy (SEM), analytical transmission electron microscopy (TEM), high resolution electron microscopy (HREM), energy-dispersive X-ray

150

Y. Jin et al. / Materials Science and Engineering A212 (1996) 149-156

spectrometry (EDS) and computer-aided image simulation.

2. Experimental details The cast ingot was prepared by arc melting high purity Cu and Cr in a vacuum furnace. Its chemical composition (wt.%) was found to be 14.97 Cr, 0.002 Ca, 0.003 S, 0.006 N and 0.047 O with the balance Cu. The original plate cut from the ingot was cold rolled eight times to a total thickness reduction of 89.8%. The SEM samples were prepared by the conventional mechanical polishing method and etched in an aqueoous solution of 15 vol.% HC1, 5 vol.% H2SO 4 and 10 vol.% HNO3. The TEM samples were prepared by both ionthinning and electronic polishing methods. The ionthinned samples were prepared in a Gatan-600 ion-milling machine at liquid nitrogen temperature with an accelerating voltage of 5 kV, a gun current of 0.5 mA and an incident angle of 8°. The electronically polished samples were prepared in a Fischione 130 electronic polishing machine below - 4 0 °C with a current of 40 mA. The electrolyte for polishing was composed of 25 vol.% HNO 3 and 75 vol.% CH3OH. The SEM observation was conducted in a JSM-5400 scanning electron microscope with an accelerating voltage of 30 kV. The analytical TEM observation was conducted in a JEM-2000FXII transmission electron microscope equipped with a W I N D O W T M EDS system with a regular Be window detector at an accelerating voltage of 160 kV. The H R E M observation was carried out in a JEM-2000EXII transmission electron microscope with accelerating voltage of 200.kV. The H R E M image simulation was performed with the commercial software package MACTEMPAS. Unit cells with large repeat distance in the beam direction were divided into several slices according to the multislice method [26].

Fig. 1. SEM backscattered electron images (reverse mode) of (a) dendritic Cr and (b) equiaxed Cr in as-cast state; (c) and (d) are enlarged photographs showing respective details. of equiaxed Cr is smaller, in the range 10-20 ~tm. With even larger magnification, as demonstrated in the backscattered electron images of regular mode (Fig. 2(a)) and reverse mode (Fig. 2(b)), eutectic Cr (C) was observed in the Cu matrix (B) between dendritic Cr (A). By further deep etching, as shown in the secondary electron image (Fig. 2(c)), the morphology of eutectic Cr (C 1 and C2) appears to be rod shaped with diameter around 1 ~tm and length around 10 ~tm. Fig. 3 shows the secondary electron images of the etched materials after cold rolling up to 89.8% reduction in thickness. Fig. 3(a) was taken along the longitudinal cross-section (LC), while Fig. 3(b) was taken along the transverse cross-section (TC). The rolling direction (R.D.) has also been indicated in both pictures. It can be seen that after heavy cold rolling, the original morphologies of dendritic Cr and equiaxed Cr could not be distinuished. Some of them have been fully deformed into Cr ribbons (A) with homogeneous

3. Experimental results 3.1. S E M

observation

Fig. 1 shows the backscattered electron images (in reverse mode) of the etched materials as the as-cast state. Fig. l(a) was taken in the area close to the edge of the ingots. It can be seen that most secondary phases are fully developed dendritic Cr with secondary arms or even third arms due to high cooling rate. In the centre of ingots, as shown in Fig. l(b) most secondary phases are equiaxed Cr of spherical shape due to low cooling rate. Figs. 1(c) and (d) are enlarged photographs showing the details of dendritic Cr and equiaxed Cr respectively. The dimension of dendritic Cr (including dendritic arms) varies from 20 to 100 pm, while the size

Fig. 2. SEM backscattered electron images of (a) regular mode and (b) reverse mode and (c) SEM secondary electron image of deeply etched samples, showingmorphologyof eutectic Cr in as-cast state.

Y. Jin et al./ Materials Science and Engineering A212 (1996) 149-156

151

The crystal structures of dendritic Cr, equiaxed Cr and eutectic Cr have been examined systematically by the technique of SAD and convergent beam electron diffraction (CBED). All of them were found to have the same b.c.c, crystal structure as that of pure Cr. Figs. 5(a) and 5(b) are their SAD patterns in [001] and [111] orientatations respectively, while Figs. 5(c) and 5(d) are the corresponding CBED Kossel patterns displaying 4 m m and 3 m whole pattern symmetries respectively. As seen in Figs. 5(a) and 5(b), no secondary diffraction effect from the precipitates can be observed, which agrees with the results from bright field and dark field observations (Fig. 4). 3.2.2. Cr in cold-rolled state

Fig. 6a shows the bright field image of Cr ribbon in [133] orientation. In contrast with dendritic Cr and equiaxed Cr in the as-cast state, both dislocations (A) and small precipitates (B) of nanometre size were observed. The corresponding dark field observation of the (-301) reflection, as shown in Fig. 6(b) also proves the existence of dislocations (A) and small precipitates (B).

Fig. 3. SEM secondary electron images of Cr ribbons in cold-rolled state along (a) longitudinal cross-section and (b) transverse cross-section.

thickness as little as 0.5 gm, while others (B) are less homogeneous with maximum thickness as large as 2 gm. In addition, these Cr ribbons stretch much longer along the longitudinal direction than along the transverse direction. Sphere-shaped particles (C) were also observed with diameter less than 0.5 lam. These particles are from eutectic Cr in the as-cast state, since dendritic Cr and equiaxed Cr cannot be deformed into such a small size. However, it is still under investigation why rod-like eutectic Cr spheroidizes during the coldrolling process. 3.2. Analytical T E M observation 3.2.1. Cr in as-cast state

Fig. 4(a) shows the bright field image taken at the dip of a Cr secondary dendritic arm, while Fig. 4(b) shows the corresponding dark field image of the (110) reflection. Dendritic Cr has been tilted at various orientations and the corresponding dark field image has also been taken at various reflections. However, neither precipitates nor dislocations can be found within the range of observation. The inset in Fig. 4 shows the energy-dispersive spectrum of the same area. It can be seen that dendritic Cr contains only a small amount of Cu as secondary element, on average around 1 at.% by quantitative calculation. This agrees with the previous work by Takeuchi et al. [15] who first reported the existence of Cu in dendritic Cr.

Fig. 4. TEM (a) bright field image and (b) dark field image of (110) reflection at tip of Cr secondary dendritic arm in as-cast state. The inset shows the corresponding energy-dispersive X-ray spectrum.

152

Y. Jin et al./ Materials Science and Engineering A212 (1996) 149-156

~28] should be Rcr = 1.2490 A. By substitution of Cr with Cu while keeping the Cr b.c.c, lattice unchanged, there will be a maximum distortion of 2.34%. Therefore the observed small precipitates are most likely Cu-rich clusters. 3.3. H R E M observation

Fig. 5. Selected area diffraction patterns of dendritic Cr in (a) [001] orientation and (b) [111] orientation; (c) and (d) are corresponding large-angle convergent beam electron diffraction patterns.

The inset in Fig. 6 shows the corresponding energy-dispersive X-ray spectrum, which still indicates the existence of Cu. Owing fo the restriction of incident electron beam size, the Cu concentration in the small precipitates cannot be determined. Similar observations have been conducted for various orientations, reflections and areas. The phenomena are similar, though the precipitate density varies over a wide range. The dark field observations in the same area for different orientations suggest that the larger precipitates appear ellipsoid like, while the smaller ones are sphere like. The growth mechanism of these precipitates is still under investigation. The selected area diffraction patterns of Cr ribbon in various orientations are shown in Fig. 7. The crystal was tilted systematically along its reciprocal axes (110), ( - 101) and (200). The angles between zone axes of adjacent SAD patterns are also given in this figure. It was found that these Cr ribbons after heavy deformation still preserve the same b.c.c, single-crystal structure as that of dendritic Cr and equiaxed Cr in the as-cast state. However, no additional diffraction effects can be observed even though small precipitates exist. This suggests that the observed small precipitates in Fig. 6 are neither an intermetastable phase nor an SRO structure [18,19]. They should share the same lattice as CR ribbon but are different in strain field and Cu concentration. In addition, according to the popular hard sphere assumption, the atomic radius of Cu in pure Cu lattice with f.c.c, structure of a = 3.61536 A [27] should be Rcu = 1.2782 A, while the atomic radius of Cr in pure Cr lattice with b.c.c, structure of a = 2.8844 A

Fig. 8 shows the HREM image of Cr ribbon in [111] orientation with a resolution of 2.04 x 2.04 A 2 for (110) directions. The fundamental two-dimensional hexagonal unit cell of the Cr lattice can be observed in area B, while the distinctive change in contrast in area A indicates the existence of Cu-rich clusters which possess the same lattice as b.c.c. Cr. The dimension of these clusters varies in the range 1-2 nm; larger ones appear ellipsoid shaped and smaller ones appear sphere shaped, which is consistent with the results of bright field and dark field observations (Fig. 6). Lattice distortion was also observed around these clusters as expected. However, the extent of this distortion changes from one cluster to another, which suggests that the concentration of Cu in these clusters varies over a wide range.

Fig. 6. TEM (a) bright field image and (b) dark field image o f ( - 3 0 1 ) reflection of Cr ribbon in cold-rolled state. The inset shows the corresponding energy-dispersive X-ray spectrum.

153

Y. Jin et al./ Materials Science and Engineering A212 (1996) 149-156

Fig. 9. HREM image of Cr ribbon in [001] orientation.

,)

rounding Cr lattice, with a slightly shaded interfacial area. Therefore computer-aided image simulation was carried out to interpret the observed phenomena more accurately.

4. Discussion 4. I. T E M f o i l thickness and defocus conditions

Fig. 7. Selected area diffraction patterns of Cr ribbon in various orientations. Similar observations were also performed in other orientations to verify the phenomenon. Fig. 9 shows the H R E M image of Cr ribbon in [001] orientation with a resolution of 2.04 × 2.04 ,~2 ( 1 1 0 ) directions. Cu-rich clusters (A) of various sizes and with various extents of lattice distortion were also observed. However, their H R E M images are different in detail from those observed in [111] orientation (Fig. 8). As indicated in the picture, the images of clusters of larger size (more than 1 nm) are usually composed of a shaded central area (C), a bright surrounding area (D) and a shaded interfacial area (E), while the clusters (F) of smaller size (less than 1 nm) display a brighter contrast than the sur-

Sample thickness and defocus conditions are very important parameters for image simulation. They can

[0011

(11

[loo] netocus (~) Thickness

200

400

600

800

1000

]200

(A) 20

4O

b 80

100

120

Fig. 8. HREM image of Cr ribbon in [111] orientation.

Fig. 10. (a) B.c.c. atomic model of Cr. (b) Corresponding simulated HREM images in [001] orientation under various thickness and defocus conditions.

Y. Jin et al./ Materials Science and Engineering A212 (1996) 149-156

154

[(X)l]cr I

p0Ol¢,

lOa

a

Fig. 11. (a) Schematic illustration of atomic model o f Cu-rich clusters. (b, c) Corresponding simulated H R E M images in [111] and [001] orientations respectively.

be determined by comparing the observed HREM images of the Cr lattice (Figs. 8 or 9) with the simulated ones under various thickness and defocus conditions according to the Cr atomic structure, as illustrated schematically in Fig. 10(a). Fig. 10(b) shows the simulated HREM images of b.c.c. Cr in [001] orientation for a range of thickness from 20 to 120 A and a range of defocus from 200 to 1200 A. It can be seen that when the sample thickness is less than 80 A, and HREM images (e.g. the image with thickness 60 A and defocus 600 A) will display a resolution of 1.81 x 1.81 A 2 for (100) directions. However, when the sample thickness is larger than 80 A, the HREM images (e.g. the image with thickness 100 A and defocus 600 A) will have a resolution of 2.04 × 2.04 A 2 for (110) directions. Since the image observed in Fig. 9 has a resolution of 2.04 x 2.04 A 2 for (110) directions, the corresponding sample thickness must be larger than 80 A. A more detailed analysis of serial photographs taken under various defocus conditions indicates that Fig. 9 was taken at a defocus around 1000 A with a sample thickness around 100 A. Similar analysis has also been carried out for Fig. 8, which suggests that the photograph was taken at a defocus around 800 A with a sample thickness around 100 A.

10 x 10 x 10 Cr b.c.c, unit cells (28.85 x 28.85 x 28.85 A3), only the central area of 4 x 4 x 4 Cr unit cells (11.54 x 11.54 x 11.54 ]k3) is assumed to be rich in Cu, while the surrounding atomic positions are occupied by pure Cr. This assumption should be reasonable, since the total solubility of Cu in Cr is only around 1 at.% and Cu precipitation would lead to purification of Cr solid solution. Although Cu atoms are distributed randomly in the Cu-rich area, for simulation it can be assumed that Cu has an average occupancy on each atomic position and the remaining occupancy belongs to Cr. The maximum occupancy of Cu in the Cu-rich area is 100%, which corresponds to a pure Cu cluster with the same lattice structure as that of Cr ribbon. Although it is well known that Cu is most stable in the f.c.c, structure up to its melting point, when of nanometre size, Cu in the b.c.c, structure has also been observed as tiny precipitates in b.c.c, matrix [29], as an epitaxial layer on b.c.c, iron substrate [30] and even on the asymmetrical Z3 tilt grain bounary of f.c.c. Cu [31]. Defocus (A) Thickness

200

400

600

800

1000

1200

(k) 20

40

a

60

80

100

120

Defocus (A)

200

400

600

800

I000

1200

Thickness

INNN NNNNNNNN NNNNNINNNNNN b NNIn INNN IN n IN 120m /

(A) 7.0

40

60

80

4.2. Cu-rich clusters

:!:!:!:!!i:!:i:

100

4.2.1. Atomic model

Since the spacing, size and Cu concentration of the observed Cu-rich clusters vary over a wide range (Figs. 6, 8 and 9), they need to be studied by a simplified atomic model as illustrated in Fig. 1l(a). In a region of

Fig. 12. Simulated H R E M images of Cu-rich clusters of sizes (a) 11.54 × 11.54 × l 1.54 A 3 and (b) 5.77 x 5.77 x 5.77 A 3.

Y. Jin et al./ Materials Science and Engineering A212 (1996) 149-156 DEFOCUS 0 O

0 O

o0

O

o

0 ~

0 O

0 O

,~ OO

O o

O

¢N

0 O

0 O

O

0 O

o

0 tN

80 100 120 u~

(/) LM

80

z 100 ¢J z

I-

120 80 100

155

Cu occupancy in [001] orientation and with a range of thickness from 20 to 120 A and a range of defocus from 200 and 1200 A. The morphology of these clusters appears most distinctively only when the sample thickness is larger than 80 A. This conforms well with the sample thickness analysis in Section 4.1 based on the HREM images of the b.c.c. Cr lattice. Fig. 12(b) shows the simulated HREM images of Cu-rich clusters of size 5.77 x 5.77 x 5.77 /~k3 with the same ranges of thickness and defocus as those of Fig. 12(a). It can be seen that when the size becomes smaller, the Cu-rich cluster only displays a brighter contrast than the surrounding Cr lattice, with a slightly shaded interface area. This agrees well with the observation in Fig. 9.

120

Fig. 13. Simulated HREM images of Cu-rich clusters with Cu occupancies of (a) 100%, (b) 90%, (c) 80%, (d) 70%, (e) 60%, (f) 50%, (g) 40%, (h) 30% and (i) 20%.

In order to simplify the problem, the Cu-rich cluster in the present model is assumed to be cube like, although that observed is ellipsoid like. The strain field around Cu-rich clusters was also neglected in simulation owing to the difficulties in estimation of the lattice displacement of each atomic position. There are a total of 2000 atomic positions in the complex unit cell in the present model. Although a larger complex unit cell and larger spacing between Cu-rich clusters would be closer to reality, they would lead to many more atoms in the complex unit cell and would greatly increase the difficulties in simulation. Figs. ll(b) and ll(c) show the simulated HREM images of Cu-rich clusters with 100% Cu occupancy according to the above model, where Fig. 1l(b) is in [111] orientation with thickness 100 A and defocus. 800 and Fig. l l(c) is in [001] orientation with thickness 100/k and defocus 1000 A. It can be seen that in [111] orientation the simulated HREM image of these clusters only has a brighter contrast than the surrounding Cr lattice, while in [001] orientation the same clusters appear to have an HREM image consisting of a shaded central area with a bright surrounding area and a shaded interfacial area. These findings match well with the observations in Figs. 8 and 9. 4.2.2. Size effect of Cu-rich cluster As observed in Fig. 9, in [001] orientation the Cu-rich clusters of different sizes have different HREM images. This phenomenon can be clarified by modifying the size of the Cu-rich area in the present model (Fig. 1la), e.g. from 4 × 4 × 4 Cr b.c.c, unit cells (11.54x 11.54× 11.54 A 3) to 2 × 2 × 2 Cr b.c.c, unit cells (5.77 × 5.77 × 5.77 A3), while keeping other conditions unchanged. Fig. 12(a) displays the simulated HREM images of Cu-clusters of size 11.54 x 11.54 x 11.54 A 3 with 100%

4.2.3. Cu concentration in Cu-rich clusters What is aiscussed above is only a specific case of Cu-rich clusters with 100% Cu occupancy. As revealed in Figs. 8 and 9, because the extent of lattice distortion around Cu-rich clusters varies, the Cu concentration in them should also vary over a wide range. This can be studied by modifying the occupancy of Cu in the present model (Fig. l l(a)) while keeping other conditions unchanged. Fig. 13 displays the simulated HREM images of Cu-rich clusters in [001] orientation, in a range of thickness from 80 to 120 A and a range of defocus from 400 to 1000 A, with Cu occupancies of (a) 100%, (b) 90%, (c) 80%, (d) 70%, (e) 60%, (f) 50%, (g) 40%, (h) 30% and (i) 20%. It can be seen that with decreasing Cu occupancy the Cu-rich cluster appears to have a similar HREM image in the same thickness range (around 100 A) but weakening contrast. When the Cu occupancy is lower than 40%, the image of the Cu-rich cluster becomes invisible. This suggests that the Cu concentration in the observed clusters must be in the range 40-100 at.%. This conclusion is consistent with the experimental observation of Setna et al. [32,33] on early-stage precipitation in Cu-2at.%Co alloy. They found that small localized regions rich in Co (15 at.% Co, 0.5 nm in size) appear first. These regions then become Co richer (more than 50 at.% Co, 1.0 nm in size) and finally reach nearly 100 at.% Co with a size around 2-3 nm.

5. Conclusions

(1) Dendritic Cr of dimension 20-100 ~tm and equiaxed Cr of size 10-20 gm in the as-cast state were mostly deformed into Cr ribbons of thickness 0.5-2 gm after cold rolling to a total thickness reduction of 89.8%. (2) All the observed dendritic Cr, equiaxed Cr and Cr ribbons are single crystal with a b.c.c, structure like that of pure Cr.

156

Y. Jin et aL / Materials Science and Engineering A212 (1996) 149-156

(3) There is 1 at.% solubility of Cu on average in dendritic Cr and equiaxed Cr in the as-cast state. (4) Cu-rich dusters of size around 1 nm exist in Cr ribbon after heavy cold rolling. They have the same lattice as b.c.c. Cr but different Cu concentration varying from 40 to I00 at.%. (5) Lattice distortion exists around Cu-rich clusters, though its extent varies depending on the Cu concentration in each cluster.

Acknowledgements The authors would like to express their gratitude to the Science and Technology Agency (Japan) for financial support in the form of both research grants and an STA fellowship (to Y.J.). The technical support from Dr. K. Ogawa, Dr. Y. Tsubokawa and K. Mihara is highly appreciated. Acknowledgement is also given to Dr. M. Kato (Tokyo Institute of Technology, Japan) and Professor M. Tanino (Tohoku University, Japan) for fruitful discussions.

References [1] W.A. Spitzig, A.R. Pelton and F.C. Labbs, Acta Metall. Mater., 35 (1987) 2427. [2] C.L. Trybus and W.A. Spitzig, Acta Metall. Mater., 37 (1989) 1971. [3] W.A. Spitzig, L.S. Chumbley, J.D. Verhoeven, Y.S. Go and H.L. Downing, J. Mater. Sci., 27 (1992) 2005. [4] W.A. Spitzig and S.B. Biner, J. Mater. Sci., 28 (1993) 4623. [5] C. Biselli and D.G. Morris, Acta Metall. Mater., 42 (1994) 163. [6] D. Raabe, Comput. Mater. Sci., 3 (1995) 402. [7] Y. Sakai, K. Inoue and H. Maeda, Acta Metall. Mater., 43 (1995) 1517.

[8] S. Foner, E.J. McNiff Jr., B.B. Schwartz and R. Roberge, ,4ppl. Phys. Lett., 31 (1977) 853. [9] J.P. Harbison and J. Berk, J. Appl. Phys., 48 (1977) 5180. [10] J.D. Verhoeven, D.K. Finnemore, E.D. Gibson, J.E. Ostenser and L.F. Goodrick, Appl. Phys. Lett., 33 (1978) 101. [11] L. Parrini and R. Schaller, Acta Metall. Mater., 43 (1995) 2149. [12] P. Merle, J. Pelletier and J. Merlin, Mem. Sci. Rev. Met., 76 (1979) 209. [13] D. Hull and D.E. Rimmer, Philos. Mag., 4 (1959) 673. [14] D.J. Chakrabarti and D.E. Laughlin, Bull. Alloy Phase Diag., 2 (1982) 4. [15] T. Takeuehi, K. Togano, K. Inoue and H. Maeda, J. Less-Common Met., 157 (1990) 25. [16] K. Adachi, Internal Rep., H8-7-1, 1995 (Division of Mechanical Properties, NRIM). [17] A.K. Mukhopadhyay, Philos. Mag. Lett., 70 (1994) 135. [18] P.L. Martins and J.C. Williams, Acta Metall., 32 (1984) 1081. [19] Y. Jin and M.C. Chaturvedi, Phys. Rev. Lett., 75 (1995) 681. [20] K. Hono, T. Sakurai and I.J. Polymear, Scr. Metall. Mater., 30 (1994) 695. [21] A. Yamamoto and H. Tsubakino, Scr. Metall. Mater., 31 (1994) 787. [22] Y.M. Koo, S.M. Shapiro and L.E. Tanner, Acta Metall. Mater., 36 (1988) 591. [23] Y.M. Koo and J.B. Cohen, Acta Metall. Mater., 37(1989) 1295. [24] K. Binder, Rep. Prog. Phys., 50 (1987) 783. [25] J.M. Liu, Mater. Lett., 23 (1995) 289. [26] J.M. Cowley, Diffraction Physics, Elsevier, Amsterdam, 1990, p. 228. [27] Y.N. Smirnor and V.A. Finkel, Soy. Phys., 20 (1965) 315. [28] M.E. Straumanis and L.S. Yu, Acta Crystallogr. A, 25 (1969) 676. [29] S.R. Goodman, S.S. Brenner and J.R. Low, Metall. Trans., 4 (1974) 2363. [30] Z. Celinski, B. Heinrich, J.F. Cochran, K. Myrtle and A.S. Arrott, in G.C. Hadjipanayis and G.A. Prinz (eds.), Science and Technology of Nanostructured Magnetic Materials, Plenum, New York, 1991, p. 77. [31] C. Schmidt, F. Ernst, M.W. Finnis and V. Vitek, Phys. Rev. Lett., 75 (1995) 2160. [32] R.P. Setna, J.M. Hyde, A. Cerezo, G.D.W. Smith and M.F. Chisholm, Appl. Surf. Sci., 67 (1993) 368. [33] R.P. Setna, J.M. Hyde, A. Cerezo and G.D.W. Smith, Appl. Surf. Sci., 76-77 (1994) 203.