TEM characterization of Ge precipitates in an Al–1.6 at% Ge alloy

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Ultramicroscopy 108 (2008) 210–220 www.elsevier.com/locate/ultramic

TEM characterization of Ge precipitates in an Al–1.6 at% Ge alloy K. Kanekoa,, K. Inokeb, K. Satoa, K. Kitawakia, H. Higashidaa, I. Arslanc,1, P.A. Midgleyc a

Department of Material Science and Engineering, Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan b FEI Company Japan Ltd., 13–34 Kohnan 2, Minato, Tokyo 108-0075, Japan c Department of Material Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK

Abstract The growth mechanism and morphology of Ge precipitates in an Al–Ge alloy was characterized by a combination of in-situ transmission electron microscopy, high-resolution transmission electron microscopy and three-dimensional electron tomography. Anisotropic growth of rod-shaped Ge precipitates was observed by in-situ transmission electron microscopy over different time periods, and faceting of the precipitates was clearly seen using high-resolution transmission electron microscopy and three-dimensional electron tomography. This anisotropic growth of rod-shaped Ge precipitates was enhanced by vacancy concentration as proposed previously, but also by surface diffusion as observed during the in-situ experiment. Furthermore, a variety of precipitate morphologies was identified by three-dimensional electron tomography. r 2007 Elsevier B.V. All rights reserved. PACS: 61.66Dk; 68.73Lp; 81.70Tx Keywords: In-situ TEM; High-resolution TEM; Electron tomography; Aluminum alloy

1. Introduction The shape, size, and distribution of precipitates play important roles in the properties of dispersion-hardening alloys, and controlling these features is of great importance in alloy design [1]. Al–Ge alloys have attracted considerable attention including fundamental studies on nucleation in solids [2] and principles of precipitation reaction [3,4]. The equilibrium phase diagram shows the system to be a simple binary eutectic with a limited solubility of Ge in Al [5]. The solid solubility of Al in Ge is negligible, whereas Ge has a maximum solid solubility in Al of 2.0 at% at the eutectic temperature (693 K), and decreases rapidly with decreasing temperature, features typical of age–hardening systems [5]. Although the matrix and precipitate phases have a cubic (face-centered cubic)–cubic (diamond cubic) relationship, after ageing of the supersaturated Al–Ge Corresponding author. Tel./fax: +81 92 802 2959.

E-mail address: [email protected] (K. Kaneko). Now at Sandia National Laboratories, California, Livermore, CA 94551-0969, USA. 1

0304-3991/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2007.04.020

alloy, a variety of pure Ge precipitate morphologies and orientation relationships are formed without formation of any metastable intermediate phase, as shown in Table 1 [2,3,6–17]. In particular, a rod-shaped morphology of Ge precipitates lying along the /1 0 0SAl directions in an Al–Ge alloy was firstly reported by Lorimer and Nicholson in 1969 [7] and Ko¨ster in 1970 [8], as one of the three different shapes in an Al–1.3 at% Ge alloy aged at 523 K. Hugo and Muddle also observed the presence of rod-shaped precipitates in an Al–1.5 at% Ge alloy aged at 473 K, as one of five distinguished precipitate forms [14,15]. Dahmen and Westmacott have examined the rod-shaped Ge precipitates in an Al–1.0 at% Ge alloy using high-resolution transmission electron microscopy (TEM) [13] and reported that the shapes are critically dependent on internal twinning. Recently, Deaf also observed rod-shaped Ge precipitates in an Al–1.0 at% Ge alloy aged at 523 K [2]. The large lattice misfit between cubic Al and cubic Ge (aAl ¼ 0.4050 nm and aGe ¼ 0.5658 nm) ensures that the quenched-in vacancies play a vital role in the precipitation [11,12], and cause the diffusion of solute atoms during Ge

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Table 1 Summary of Ge precipitates in an Al matrix found in the literature. The observed morphologies are indicated Year

Ref.

Authors

Composition

Aging condition

Precipitate types

1968

[6]

Al–1.5 at% Ge

523 K

Triangular plates on {1 1 1}Al

1969

[7]

Sorokin and Mosina Lorimer and Nicholson

Al–1.7 at% Ge

413 K

Triangular plates on {1 1 1}Al

1970

[8]

Ko¨ster

Al–1.3 at% Ge

4473 K o423 K 523 K

1971

[9]

Ceresara and Fiorini

Al–0.18 at% Ge

443 K

Rods parallel to /1 0 0SAl Triangular plates on {1 1 1}Al Rods along /1 0 0SAl Rectangular plates on {1 0 0}Al Rods

[10] [11]

463 K

Rods, incoherent Ge clusters with a diamond structure Rods

1976 1986

[12] [13]

Al–1.5 at% Ge Al–1.0 at% Ge

433 K Less than 693 K

Rods Rods// /1 0 0SAl with twinning

1990a 1990b

[14] [15]

Beller Ka¨hko¨nen and Suhonen Ka¨hko¨nen et al. Dahmen and Westmacott Hugo and Muddle

Al–0.75 at% Ge Al–1.5 at% Ge Al–1.5 at% Ge

413 418, 433 K

1972 1975

Al–1.5 at% Ge

Between 423 and 473 K for 3 h

1991

[16]

Douin et al.

Al–1.0 at% Ge

Between 473 and 533 K for 4 h

1996

[3]

Hinderberger et al.

Al–1.8 at% Ge

523 and 573 K

2000

[17]

Hinderberger et al.

Al–0.68 at% Ge

Thermal cycle, between 523 and 593 K

Triangular plates on {1 1 1}Al Lath parallel to /1 0 0SAl Hexagonal plates on {1 1 1}Al Rods parallel to /1 1 0SAl Tetrahedral with {1 1 1}Al Rods parallel to /1 0 0SAl with twinning Rods along /1 1 0SAl Tetrahedral with {1 1 1}Al Octahedral with {1 1 1}Al Triangular plates on {1 1 1}Al Laths parallel to /1 0 0SAl Rods parallel to /1 1 0SAl Large plates on {1 0 0}Al Triangular plates on {1 1 1}Al

2004

[2]

Deaf

Al–1.5 at% Ge

348, 423, 523 K

nucleation and subsequent growth of precipitates. Many researchers agree that vacancies play an important role in the transformation from coherent clusters to non-coherent particles [18]. Ko¨ster assumed that there was a strong relationship between vacancy concentration and precipitation behavior and that the rod-shaped Ge precipitates were favored at high annealing temperatures (523 K) with a small vacancy concentration [8]. Beller and co-workers inferred by small-angle X-ray scattering that nuclei are constituted of vacancies and Ge atoms, and that these have a diamond structure [19]. They considered that vacancies aggregate to Ge precipitates to relax their strain since the precipitates expand the lattice constant of the Al matrix. Ceresara and Fiorini concluded that Ge atoms aggregate

Tetrahedral with {1 1 1}Al Octahedral with {1 1 1}Al Laths parallel to /1 0 0SAl Irregular particles Spheres Hexagonal plates on {1 1 1}Al Rod-shaped// /1 1 0SAl Triangular plates on {1 1 1}Al Laths// /1 0 0SAl Tetrahedral with {1 1 1}Al Rectangular plates Lamellae shape

on dislocation loops [9]. Hugo and Muddle have suggested an explanation for the formation of the different morphologies in an Al–Ge system based on the lattice misfit between Ge precipitates and the Al matrix (lattice misfit 36%), and that this misfit strain can be accommodated by vacancies [14,15]. Moreover, the morphology of these precipitates in a solid matrix is strongly dependent on the conditions of heat treatment, such as the quenching temperature and aging temperature [18]. The point symmetry of the matrix and precipitates, and the orientation relationship that exists between them, is emphasized by Portier and Gratias [20]. The microstructure of the precipitates is one of the key factors that control the physical and mechanical properties

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of the materials and, in particular, the orientation relationships of precipitates with respect to the matrix can play a significant role. Furthermore, the morphology of precipitates can be illustrated in terms of the symmetry and orientation relationship between the matrix and the precipitate [13,14]. In this study, the growth mechanism and morphology of Ge precipitates in a quenched and aged Al–1.6 at% Ge alloy is characterized. In-situ TEM of the precipitation process was undertaken to understand the precipitation behavior of the Al–Ge alloy. High-resolution TEM was carried out to study the atomic arrangements at the interface between the matrix and the rod-shaped Ge precipitates. Three-dimensional electron tomography (3D-ET) was carried out to study the morphology of the Ge precipitates. 2. Experimental methods 2.1. Specimen Alloys of Al–1.6 at% Ge were prepared from a melt of 99.99% purity Al and 99.999% purity Ge starting materials using an electric-arc furnace in an argon atmosphere. The specimen was then homogenized at 698 K for 2 h, and quenched in water to room temperature. Specimens for TEM were prepared by twin-jet electro-polishing with a solution of 40% acetic acid, 30% orthophosphoric acid, 20% nitric acid and 10% water at a temperature of 293 K and 12 V (0.2 A). 2.2. Transmission electron microscopy (TEM) TEM was performed on two different microscopes. The structures and morphologies of Ge precipitates were observed by a high-resolution TEM (JEM-4000EX, JEOL, Japan). In-situ observations were conducted by a computer-controlled fully digitized TEM (TECNAI-20, FEI, Eindhoven, The Netherlands), with a heating holder (Gatan Instruments, USA) at 453 K for up to 180 min. Heating of the specimen was carried out at a heating rate of 10 K/min. 3D-ET observations with a scanning-TEM highangle annular dark-field (STEM-HAADF) detector were conducted by another computer-controlled fully digitized TEM (TECNAI-F20, FEI, Eindhoven, The Netherlands) with a specially designed high-tilt holder (E.A. Fischione Instruments Inc., USA). 2.3. Three-dimensional electron tomography (3D-ET) In the case of 3D-ET, many TEM parameters were controlled during the acquisition of the tilt series of projections: the defocus, the beam shift, the beam tilt, the image shift, the specimen tilt, and the specimen height. Data collection for 3D-ET was carried out by tilting the specimen about a single axis with respect to the electron beam. The resolution and quality of the reconstructed

volume are dependent not only on the 2D image resolution but also on the total angular range and the angular increment. Typically, this consists of collecting images at 1–21 angular intervals over an angular range of 701 to+701 [21–26]. In this case, a series of projections was acquired from 701 to 701, with a STEM-HAADF image recorded every 21 giving a total of 71 images. An HAADF detector collects electrons that undergo high-angle scattering, and the signal is approximately proportional to Z2, where Z is the atomic number. Furthermore, Z-contrast imaging is useful in the study of (poly-) crystalline materials because of the reduction of coherent diffraction contrast [21,22,25–27], which is unwanted for tomographic reconstructions. The exposure time was kept to a minimum (15 s) to reduce the possible effects of irradiation damage on the Al–Ge alloy. In addition, it is necessary to consider the increase of thickness, e.g. the path length of the electron beam through the specimen becomes twice the specimen thickness at 601 and approximately three times at 701. Although energyfiltering TEM tomography (EFTEM-Tomography) using Ge-L edges might have provided 3D reconstructions of Ge precipitates, a 2D investigation using EFTEM at higher tilts revealed weak contrast and long exposure times were required for high-quality images. Once the acquisition of the tilt series was completed, the data were transferred to a PC for alignment and 3D reconstruction. Images were spatially aligned by a crosscorrelation algorithm using Inspect3D software (FEI, Einthoven), and 3D reconstructions were achieved using a weighted back-projection of consecutive 2D slices. Visualization was performed using AMIRA 4.0. 3. Results and discussion 3.1. Conventional TEM imaging Seven different precipitate morphologies were observed in TEM micrographs, as shown in Fig. 1, which had been described in detail previously [2,3,14]. The morphology and distribution of these precipitates was readily identified, such as platelets on {1 1 1}Al planes and rods or laths parallel to the /1 1 0SAl or /1 0 0SAl directions. Equilateral triangular plates, truncated triangular plates and regular hexagonal plates were commonly observed on {1 1 1}Al planes, as shown in Fig. 1(a) and (b). Triangular plates exhibited a range of sizes with the larger plates having a side of typically 70 nm. Small precipitates of tetrahedral form were also seen, as shown in Fig. 1(c), bounded by {1 1 1}Al facets with edges parallel to closepacked /1 1 0SAl directions. The shape of a tetrahedron projected parallel to a /1 1 1SAl zone axis is an equilateral triangle, so that it was difficult to differentiate in projection between tetrahedral and triangular plates. Typically, tetrahedral precipitates had edges about 50 nm, similar to those of the triangular plates. The rod-shaped Ge precipitates were a few hundred nm in length, with a

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Fig. 1. Various types of Ge precipitates observed within the Al–Ge alloy: (a) triangular plate; (b) hexagonal (or truncated triangular) plate; (c) tetrahedron; (d) rod-shaped; (e) rectangular plate; and (f) spherical morphologies.

Al <111> zone axis reflections Ge <111> zone axis reflections Double Diffracted reflections Fig. 2. (a) Bright-field image, (b) selected-area diffraction pattern, and (c) dark-field image including a grain boundary of the Al–Ge alloy. Fig. 2(d) shows a schematic diagram of Fig. 2(b). A PFZ is seen on right hand side of the grain boundary.

projected width of approximately 5 nm, as shown in Fig. 1(d). Rectangular plates were also seen on {1 0 0}Al planes with dimensions typically 50  25 nm2, as shown in Fig. 1(e). A relatively small sized spherical particle with a 5 nm diameter, was also observed, as shown in Fig. 1(f).

Fig. 2(a) shows a typical bright-field TEM image of Ge precipitates in the Al–Ge alloy, in which a large number of triangular-plate-type precipitates are distributed within the field of view. A selected-area diffraction pattern of the same region, Fig. 2(b), indicates the beam direction to be

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parallel to /1 1 1S. A typical dark-field TEM image, Fig. 2(c), was also obtained from the same region as (a) using the diffraction spot indicated by a white arrow in Fig. 2(b) and by a black arrow in Fig. 2(d). Within the selected area diffraction pattern, intense spots correspond to diffracted beams from the Al matrix and weaker spots correspond to those from the diamond structure of the Ge precipitates. The presence of other weaker spots is due to double diffraction, as shown schematically in Fig. 2(d). A precipitate-free zone (PFZ) was also observed parallel to some grain boundaries, with relatively coarse Ge precipitates on one side, as shown in Fig. 2(a). There are a few large irregular Ge particles, perhaps undissolved during the specimen preparation, at the grain boundary. Some of the triangular plates, seen at the top left corner of Fig. 2(a) and (c), each have an apex truncated parallel to the /1 1 0SAl bounding the opposite face. In addition, within the grain on the right-hand side, the average precipitate sizes appear to be smaller than that of the grain on the left. This difference, coupled with the presence of the PFZ, remains to be fully explained.

of precipitates, such as the triangular plates. Quantitative analysis of the time dependence showed that the precipitate sizes coarsened continuously up to 120 min, after which growth appeared to reduce, particularly in the case of rod-shaped Ge precipitates, as shown in Fig. 3(d). This ‘‘saturation’’ is probably caused by the expenditure of Ge clusters near Ge precipitates within the Al matrix. Apparent short rod-like precipitates were in fact edge-on triangular Ge plates seen in projection, and had the same growth rate as other triangular Ge plates. It is worth noting that near some precipitates (e.g., that encircled by thin dotted lines in Fig. 3(a)) strong diffraction contrast appearing after 120 min of annealing is probably due to the precipitates straining the lattice of the Al matrix. In addition, the apparent widths of the rod-shaped Ge precipitate increased, probably again caused by the effect of strain contrast. It is most likely that there are insufficient vacancies to aggregate to the Ge precipitates to relax the matrix strain at this stage.

3.2. In-situ observation

Typical high-resolution TEM images of the Ge precipitates with a clear orientation relationship are shown in Fig. 4, viewed from the /1 1 0SAl directions, comparable to those reported by others [2,14]. The presence of {1 1 1} coherent interfaces enhances the growth of the precipitates in certain directions to maximize the {1 1 1} interfacial area. The presence of defects caused by the lattice mismatch in the matrix is seen at the interface, indicated by a thin black arrow. It was seen that the rod-shaped precipitate has an internal twin boundary (TB) indicated by a thick arrow. Fourier transforms of matrix regions and the rod-shaped Ge precipitate showed that there is an orientation relationship between both parts of the twin and the matrix, and most probably this precipitate was formed as a diversified prism as described by Douin et al. [16]. Some periodical contrast changes within facets due to the Moire´ fringes are also seen. The presence of dislocations caused by the lattice mismatch is seen at the interfaces, as in the case of a rodshaped Ge precipitate. Fourier transforms of the matrix and triangular and hexagonal plate-type precipitates showed that there is an orientation relationship with the matrix, as cube (fcc)–cube (diamond), [0 0 1]Al//[0 0 1]Ge and [1 1 0]Al//[1 1 0]Ge, as shown in Figs. 4(b) and (c). It is worth noting that some of the apices of triangular plates are rounded. Z-contrast images were also taken to study the atomic arrangements at interfaces and precipitates from a similar field of view, as shown in Fig. 5. In particular, crosssectional images of triangular plates were observed as shown in Fig. 5(a) and (b), in which the presence of single and multiple twinning could be seen, respectively. Fig. 5(c) shows the presence of multiple twinning within the rod-shaped Ge precipitate, indicated by white arrows. Other precipitates, such as (d) tetrahedral precipitate,

In-situ hot stage TEM observations were carried out to examine the precipitation behavior of the Al–Ge alloy. In-situ TEM micrographs were recorded at 5 min intervals, parallel to the [1 1 0]Al direction (only a part of the series is shown in Fig. 3(a)). It can be seen that the coarsening rate of the rod-shaped Ge precipitate indicated by white arrows was considerably faster than other types of precipitates, whose length reached almost 650 nm after 180 min of annealing. Triangular plates on {1 1 1}Al planes encircled by thin black circles at 30, 60, 90 and 120 min all grew at a similar growth rate, whose length reached almost 70 nm after 180 min of annealing. A schematic diagram of the precipitate distribution after 60 min of the in-situ experiment is shown in Fig. 3(b). It is thought that the kinetics of coarsening of the rod-shaped Ge precipitates is enhanced by a high vacancy concentration brought about by rapid quenching and the presence of {1 1 1} coherent interfaces. It is also considered that the enhancement may be due to the surface diffusion because the in-situ observation was undertaken using ultra-thin TEM specimen. Furthermore, a round-shaped Ge precipitate encircled by a thick white circle in Fig. 3(a), after 10 min of annealing at 453 K, changed to a truncated triangular Ge plate, and finally became almost an equilateral triangular Ge plate. This change in shape is schematically shown in Fig. 3(c). Schmu¨cker and Ko¨ster explained that the different precipitation behavior could be caused by the different number of Ge clusters in the solid solution, acting as nucleation sites upon aging [4]. In addition, some of the triangular Ge plates maintained their shape from the beginning, as shown by thick dotted black circles in Fig. 3(a). It was clear that the coarsening rate of the rodshaped Ge precipitates was faster than that of other types

3.3. High-resolution TEM and HAADF imaging

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30min

215

700

60min

10min 120min

90min

180min

Maximum length (nm)

600 Rod Edge Edge Plate Plate

500 400 300 200 100 0 0

50

100 Time (minutes)

150

200

Triangular plate

rod

Truncated triangular or hexagonal plate Rod-shaped viewing end-on Irregular shape

200 nm

Fig. 3. (a) Series of in-situ TEM micrographs recorded parallel to the /1 1 0SAl direction, (b) schematic diagram of the in-situ TEM micrograph in Fig. 3(a) after 60 min of observation, (c) a schematic diagram of the transformation from a spherical precipitate to a triangular plate, (d) quantitative analysis of the time-dependence of precipitate size.

(e) octahedral precipitate and (f) spherical precipitate are also observed by Z-contrast imaging. Furthermore, a schematic diagram of triangular plate with multiple twinning is drawn in Fig. 5(g). Apexes of octahedral precipitate, /0 0 1S, are missing as can be seen from Fig. 5(e), which is also schematically drawn in Fig. 5(h). 3.4. 3D-ET Although the conventional TEM method provides information with regard to the 2D distribution and microstructure of the Ge precipitates in the Al–Ge alloy, in-depth information and their 3D morphology is still

unknown. Therefore, 3D-ET was carried out to enable further investigation of the 3D characterization of Ge precipitates. A tilt series of STEM-HAADF images was acquired from 701 to 701 with an image taken every 21 (a part of the series is shown in Fig. 6). Fig. 7 shows a reconstruction of Ge precipitates within the matrix, which shows the three-dimensional distribution of various Ge precipitates within the volume. More than a hundred precipitates can be seen, and were color-coded manually to categorize into five types: blue for plates, green for tetrahedra, orange for octahedra, yellow for rod shape and white for irregular shape. Although it has been suggested by Beller that the variation in precipitate

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TB

Matrix

111 200

111

200 111

111

011

100

011

Matrix

100

111 200

111

200 111

Matrix

111

111

111

200

200 111 111

011 100

Fig. 4. (a) Rod-shaped Ge precipitate parallel to the /1 1 0SAl direction with twin boundary, (b) an HRTEM image of the triangular-plate, parallel to the /1 1 0SAl direction, (c) an HRTEM image of truncated triangular-plate recorded parallel to the /1 1 0SAl direction.

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2 nm

217

5 nm

5 nm

10 nm

5 nm

2 nm [001]

000

[010]

[100] Fig. 5. Z-contrast images of precipitates: (a) triangular plate with single twinning; (b) triangular plate with multiple twinning; (c) edge of rod-shaped Ge precipitate with twinning indicated by white arrows; (d) tetrahedral precipitate; (e) octahedral precipitate; and (f) spherical precipitate. All of these precipitates are seen from /1 1 0SAl direction, except for (d) from /1 1 1SAl direction. Schematically drawn triangular plate with multiple twinning and slightly truncated octahedral plate (g) and (h), seen as (b) and (e), respectively.

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-50°

-40°

-30°

-20°

-10°

50°

10°

20°

30°

40°

Fig. 6. Representative STEM-HAADF images from a 3D-ET tilt series of the Al–Ge alloy.

Fig. 7. A tomographic reconstruction of Ge precipitates showing various morphologies. Precipitates were intentionally colored to classify them into five types: blue for plates, green for tetrahedra, orange for octahedra, yellow for rod-shaped and white for irregular shapes. The truncation of some precipitates (also colored white) occurs at the top and bottom surface of the TEM specimen and has arisen from the sample preparation.

morphology might be associated with differences in the required vacancy concentration for a given form and local variations in vacancy supersaturation in the matrix phase [10], there are many types of Ge precipitates seen within the field of 500 nm width 500 nm height 100 nm thickness. It appears likely that the restricted size of each observed shape can be attributed to the large volume accommodation that must accompany growth. It is straightforward to distinguish between a triangular plate and tetrahedral

precipitates by 3D-ET. Furthermore, some of the triangular plates have thicknesses between 5 and 10 nm. It is difficult to judge from these reconstructions whether these triangular plates have twinning morphologies parallel to the habit planes, as discussed by Douin et al. [16]. Although the cross-section of rod-shaped Ge precipitates was not clear from HRTEM images, the 3D-ET observation provided clear evidence of the presence of facets when the precipitates are viewed end-on; a distorted hexagonal shape

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is indicated by a thick black arrow in Fig. 8. It can be clearly seen from cross-sectional image that the triangular plate indicated by thin black arrows have variable thicknesses between different plates. The effect of artifacts is also present within this image, mainly due to the missing wedge. This alignment could be improved using the particles for marker tracking instead of only on cross-correlations. Precipitates with a truncated triangular plate morphology and those with a hexagonal morphology are shown in Fig. 9(a). These precipitates exhibit a range of sizes, depending on the annealing period, as discussed in 3.2. Regular tetrahedra and regular octahedra are also seen, as shown in Fig. 9(b). Tetrahedral and octahedral precipitates were bounded by {1 1 1}Al facets, with edges parallel to close-packed /1 1 0SAl directions. Although it was difficult to distinguish between tetrahedral and triangular precipitates when projected parallel to the /1 1 1SAl directions, 3D-ET was capable of distinguishing these precipitates straightforwardly, as indicated by the white arrow in Fig. 9(b) and as shown in Fig. 9(c).

Fig. 8. Cross-sectional view of the part of Fig. 7 enclosed by a dotted white square. The image is viewed parallel to the /1 1 0SAl direction, so that a rod-shaped Ge precipitate could be viewed end-on at the center of the field of view.

4. Conclusions The present study demonstrated an in-situ observation of precipitates in aged Al–Ge alloys and a fast coarsening

Fig. 9. Magnified images of parts of Fig. 6 for further characterization of the morphologies of precipitates in detail. Tetrahedral, octahedral, triangular and other shaped precipitates are seen: (a) hexagonal plate (white square) and truncated triangular plate (arrow); (b) triangular plate (white arrow); tetrahedron (white square) and octahedron (white ellipse); and (c) triangular plate.

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process of rod-shaped Ge precipitates. This coarsening is unusual because the alloy forms no intermediate phases, and the matrix and regular rod-shaped Ge precipitate have a cube–cube relationship. Investigation of rod-shaped Ge precipitates, triangular plates, and hexagonal plates did not obey Ostwald ripening kinetics during in-situ observation. If it had taken place, then some precipitates should have reduced in size and/or disappeared during the growth of others. It is probably the case that the diffusion of solid–solutioned Ge within the surrounding matrix in the vicinity of the Ge precipitates plays an important role in the coarsening process. A variety of Ge precipitates were seen at different depths by 3D-ET using STEM-HAADF imaging. In particular, the cross-section of a rod-shaped Ge precipitate was confirmed as being a truncated hexagonal shape, and three-dimensional precipitates including tetrahedra and octahedra were easily judged by this method. Acknowledgments This work was supported in part by a ‘Grant-in-Aid for Scientific Research (No. 19360317)’ and by the ‘Global-COE program (Future Molecular System)’, of the Ministry of Education, Culture, Sports, Science and Technology of Japan. The authors thank Mr. Y. Yoshida and Mr. R. Nagayama of Kyushu University for their technical assistance, and Prof. Z. Horita for fruitful discussion. P.A.M. thanks the Isaac Newton Trust for funding and the Royal Academy of Engineering and the Leverhulme Trust for the award of a Senior Research Fellowships. I.A. thanks the Royal Society for a Research Fellowship.

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