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Bulk interfaces in a Ni-rich Ni–Au alloy investigated by high-resolution Z-contrast imaging
Micron 35 (2004) 695–700 www.elsevier.com/locate/micron
Bulk interfaces in a Ni-rich Ni –Au alloy investigated by high-resolution Z-contrast imaging M.J. Portmann, R. Erni1, H. Heinrich2, G. Kostorz* ETH Zu¨rich, Institute of Applied Physics, CH-8093 Zu¨rich, Switzerland Received 27 July 2003; revised 29 November 2003; accepted 7 April 2004
Abstract Interfaces between Au-rich precipitates and the Ni-rich matrix in a decomposed Ni-10 at.% Au alloy were investigated by lowmagnification and high-resolution Z-contrast imaging. During aging at 923 K, the originally single crystalline sample decomposed and recrystallized resulting in a microstructure consisting of subgrains separated by small-angle grain boundaries. These small-angle grain boundaries are decorated by Au-rich precipitates. The interfaces between the Au-rich precipitates and the Ni-rich matrix were characterized with respect to the orientation relationship between precipitates and matrix, misfit dislocations and concentration gradients. Two transformation modes were identified that are involved in the decomposition of bulk Ni-rich Ni – Au alloys. While in the first mode the interface is semi-coherent, in the second mode the interface corresponds to an incoherent twin boundary. It is further shown that strain fields around misfit dislocations can result in systematic errors in the determination of the concentration gradients across interfaces between precipitates and matrix. q 2004 Elsevier Ltd. All rights reserved. PACS: 81.05.Bx; 68.37.Lp; 68.35.Dv; 61.72.Lk Keywords: Ni–Au alloys; Decomposition; Misfit dislocations; High-resolution high-angle annular dark-field scanning transmission electron microscopy
1. Introduction The microstructure of Ni– Au alloys is strongly affected by the large atomic size mismatch of about 15%. At temperatures below the solid-solution regime, a large asymmetric miscibility gap with a critical temperature of 1083 K is found (Okamoto, 1987), i.e. the Ni– Au solid solution with face-centered cubic (fcc) structure decomposes into a Ni-rich and a Au-rich phase with fcc structure. While the microstructure of the solid solution above the miscibility gap was determined for Ni-60 at.% Au (Wu and Cohen, 1983) and Ni-8.4 at.% Au (Portmann et al., 2002) by employing diffuse X-ray and neutron scattering, * Corresponding author. Tel.: þ 41-16333399; fax: þ 41-16331105. E-mail address: [email protected] (G. Kostorz). 1 Present address: Department of Chemical Engineering and Materials Science, University of California-Davis, 1 Shields Ave. Davis, CA 95616; National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 2 Present address: Advanced Materials Processing and Analysis Center (AMPAC), University of Central Florida, Box 162455, Orlando, FL 328162455, USA. 0968-4328/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2004.04.002
phase-separated states were mainly investigated using transmission electron microscopy (TEM). Modulated structures observed for Au-rich bulk alloys attracted particular interest as it remained unclear whether these structures are a result of order or phase-separation (Janghorban et al., 2001; Zhao and Notis, 1999; Bienzle et al., 1995; Hofer and Warbichler, 1985). Bulk properties of Ni-50 at.% Au and Ni-60 at.% Au alloys were investigated by Zhao and Notis (1999) using TEM to characterize the kinetics in TTT diagrams. On the basis of selected area diffraction patterns, a transient long-range ordered phase was proposed for specimens which were first annealed at 473 K (below the coherent spinodal) for 8.3 h or 32 d and subsequently heat treated at 763 K (above the coherent spinodal) in-situ in a transmission electron microscope. The L10 structure of this transient state evolved at interfaces between precipitates and matrix and also at surfaces of specimens. On the basis of this TEM study, it seems likely that the formation of a metastable ordered phase in the bulk of Ni – Au alloys is one possibility to reduce the coherency strain of the lattice.
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For epitaxially grown thin Au/Ni films, similar results were reported. Dynna et al. (1996) found that ordered phases can be stabilized by elastic constraints imposed by the substrate. For Au/Ni multilayers, Bayle et al. (1994) showed that the strain is only relieved via interdiffusion of Au atoms into the Ni layers with less than five subsequent (001) Nilayers. Therefore besides strain relaxation via introduction of misfit dislocations or twinning, for thin films also strain relaxation via ordering of its components was proposed. This idea was corroborated by first-principles calculations of the epitaxial strain energies for Ni – Au thin films (Ozolins et al., 1998). In the present study, high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) was used to characterize chemical composition and structural changes at interfaces between Au-rich precipitates and the Ni-matrix in a phase-separated Ni-10 at.% Au solid solution. In the following, HAADF STEM is termed Z-contrast imaging, as the scattering signal at high scattering angles is dominated by Rutherford scattering which is nearly proportional to the square of the atomic number Z of the elements in the foil (Pennycook and Jesson, 1997). Contrary to conventional high-resolution TEM, imaging and image artifacts caused by image delocalization, contrast oscillations with increasing thickness of the foils and focus-dependent contrast variations are negligible (Pennycook and Jesson, 1997), as Z-contrast imaging is to a good approximation an incoherent imaging technique (Rafferty et al., 2001; Erni et al., 2003). Therefore, an unambiguous relation between a Z-contrast micrograph and the corresponding object function determined by the electrostatic crystal potential is usally assumed. The small electron probe of a field-emission transmission electron microscope provides atomic-column resolution Z-contrast imaging. For Ni-rich Ni – Au, the influence of the lattice mismatch between the two phases on the structure and the symmetry of the interfaces between the phases was investigated. As the atomic-number difference between Ni and Au (ZNi ¼ 28; ZAu ¼ 79) is large, high-resolution Z-contrast imaging is advantageous for a direct identification of the Aurich precipitates, simultaneously providing direct access to concentration gradients and structural relations across the interfaces. Zhao and Notis (1999) indicated a transient ordered phase at the interfaces. If this phase is missing, the lattice mismatch between the Au-rich precipitates and the Nirich matrix may be accommodated by misfit dislocations.
After homogenization for 5 days at 1173 K, k110l-oriented discs (0.3 mm in thickness and 3 mm in diameter) were cut using spark erosion. In order to obtain a decomposed state, these discs were aged for 24 h at 923 K (70 K below the solvus line of the miscibility gap). Finally, the aged discs were mechanically polished, dimple-ground and ion-milled with Ar ions (4 keV). HAADF STEM was performed in a Philips Tecnai F30 ST microscope equipped with a Schottky field-emission source, a scanning unit, a high-angle annular dark-field detector and a post-column electron-energy filter (GIF 2000). The microscope was operated at 300 kV using a condenser aperture of 10.7 mrad (semi-angle). The camera length was chosen to yield inner and outer HAADF detector semi-angles of 48 and 302 mrad (values determined by diffraction shift). Working at Scherzer (incoherent) defocus, these settings yield an electron probe diameter of about ˚ , defining the resolution of the imaging process in the 1.7 A scanning mode and providing atomic column resolution.
3. Low-magnification Z-contrast imaging The low-magnification Z-contrast micrograph of Ni-10 at.% Au (Fig. 1a) shows two phases, one appears bright, the other is darker. To identify the Au-rich and Nirich phases unequivocally, elemental maps shown in Fig. 1b and c were acquired by the three-window technique (Egerton, 1986). The Ni map in Fig. 1b was recorded using the Ni L2,3 absorption edge at an electron energy loss of 855 eV with an energy window of 40 eV centered at 790, 830 eV (pre-edge images) and 875 eV (post-edge image). The Au map in Fig. 1c was recorded using the Au M5,4 absorption edge at an electron energy loss of 2206 eV with an energy window of 100 eV centered at 2046, 2256 eV (pre-edge images) and 2256 eV (post-edge image). As expected, the image intensity of the Z-contrast micrograph in Fig. 1a can be related directly to the chemical
2. Experiment An alloy of nominal composition Ni-10 at.% Au was prepared from 99.9999 þ % nickel (Materials Research GmbH, Mu¨nchen, Germany) and 99.999 þ % gold (Me´taux Pre´cieux SA METALOR, Neuchaˆtel, Switzerland). From the ingot, a single crystal was grown by the Bridgman technique.
Fig. 1. Low-resolution Z-contrast image of a Ni-10 at.% Au alloy. (a) The area outlined by white lines indicates where the elemental maps of (b) Ni (L2,3 absorption edge) and (c) Au (M5,4 absorption edge) were taken. The letters A and B refer to the interfaces described below.
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composition of the foil, i.e. the Z-contrast micrograph shows atomic-number contrast. The Au-rich precipitates appear bright (higher atomic number), for the Ni-rich matrix the image intensity is reduced. A qualitative chemical characterization of the foil on the basis of the Z-contrast micrograph in Fig. 1a is therefore straightforward. Electron diffraction patterns reveal that the crystal orientation varies by about 58 while moving from one Ni-rich region to another, i.e. the individual Ni-rich subgrains are slightly inclined. Hence, small-angle grain boundaries are present. Most of the small-angle grain boundaries are decorated with Au-rich precipitates. The presence of grain boundaries is surprising, as the original sample was single crystalline and undeformed prior to annealing. To confirm this result, a k100l oriented single crystalline sample (3 mm in thickness and 8 mm in diameter) was annealed in situ on a high-resolution twocircle X-ray diffractometer at 923 K while registering the diffuse X-ray scattering around a 400 reflection in v 2 2u mappings using Mo Ka radiation and a position sensitive detector. It was found that the scattering intensities continuously decrease and vanish finally after 1.5 h. The subsequently metallographically etched sample showed grain boundaries proving that the originally single crystalline sample had completely recrystallized. Concentration gradients across interfaces can only be revealed directly by TEM if the interface is exposed edgeone. Inclined interfaces between phases of different lattice parameters lead to Moire´ patterns in low-resolution Z-contrast images. Grey areas in Fig. 1a correspond to such Moire´ patterns (Fig. 2a). The image contrast is affected by the stacking of two crystal lattices with different lattice parameters. The spacing of the Moire pattern in Fig. 2a is in agreement with a lattice mismatch of about 15%. In contrast, interfaces vertically aligned in the thin foil show a sharp change in the image intensity across the interface (Fig. 2b).
Fig. 2. Low-magnification Z-contrast image of two interfaces between Au-rich precipitates and the Ni-rich matrix corresponding to interfaces at (a) (A) and (b) (B) in Fig. 1. (a) A Moire´ pattern at the lower part of the precipitate is clearly visible. (b) In contrast, these interfaces are not tilted and can be viewed edge on.
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4. High-resolution Z-contrast imaging Fig. 3a shows a high-resolution Z-contrast micrograph of the interface between a Au-rich precipitate and the Ni-rich matrix at the position A in Fig. 1a. The micrograph was acquired in a k110l zone-axis orientation. The interface is shown edge-on, but the interfacial plane does not correspond to a low-indexed lattice plane, i.e. the interfacial 1Þ Ni-rich 1Þ Au-rich ==ð11 plane slightly deviates from an exact ð11 relationship. The Fourier-filtered image of Fig. 3a—shown in Fig. 3c—allows the misfit dislocations to be located along the interface via circuit mapping as proposed by Pond (1995). The Z-contrast signal around the direct beam in the Fourier transform (Fig. 3b) of Fig. 3a was also filtered out to separate the structural information from the chemical information as shown in Fig. 3d. The sketched circuit mappings indicate that additional {111} planes are present in the Ni-rich matrix, which compensate the coherency strain. The visible Burgers vector component is ð1=4Þk112l and corresponds to the projected length of a ð1=2Þk101l-type misfit dislocation, as no faults in the stacking sequence can be found. The ratio (e.g. Jesser and Kuhlmann-Wilsdorf, 1967) of the distance between the misfit dislocations (Fig. 3) and the corresponding Burgers vector are in good agreement with the estimated lattice mismatch of about 15%. Assuming that the observed dislocations are pure edge dislocations, strain fields are present in planes perpendicular to the incident beam direction. The effect of these lattice distortions on the image intensity of Z-contrast micrographs is not completely negligible, as close to the dislocation cores the image intensity is slightly reduced. This can be seen best if the positions in the non-filtered image (Fig. 3a) are compared with the indicated dislocation positions in
Fig. 3. (a) High-resolution Z-contrast image of a semi-coherent interface between the Ni-rich matrix and a Au-rich precipitate. (b) shows the Fourier transform of (a). In (c) a Fourier-filtered image is shown where the edge dislocations are indicated. The mask in (d) is used for Fourier filtering.
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Fig. 4. Scattering intensity versus the distance perpendicular to the interfaces for the semi-coherent interface in Fig. 3a (W) and the incoherent twin-boundary interface in Fig. 5a (X). Both interfaces are centered with respect to their half-height values.
the Fourier-filtered image (Fig. 3c). In Fig. 4 an intensity profile of the s-shaped Z-contrast signal across the interface is shown. The atomic-column resolution is clearly visible Au-rich ==ð111Þ Ni-rich relationship. As the owing to the ð111Þ Z-contrast signal directly reflects the chemistry of the foil without suffering from long-range image delocalization, and as the interface is analyzed edge-on, the intensity profile in Fig. 3c directly reveals the concentration gradient across the interface. If the electron scattering cross sections corresponding to the HAADF-detector area are known and if it is assumed that the phase-separated alloy is in thermodynamic equilibrium (i.e. if the concentration of the two phases are known) the concentration gradient can be calibrated. However, such a straightforward evaluation is based on the incoherent imaging model (Erni et al., 2003), which, in case of large lattice strains, may not be fully correct. In Fig. 5a, a high-resolution Z-contrast micrograph of the interface at position B in Fig. 1a is shown. Again, the Au-rich precipitate and the Ni-rich matrix have (111) planes in common. Across the interface, the crystal structure is rotated by 1808 about the normal of these (111) planes and the interface can locally be described by a twin-relation. The (111) planes correspond to the twin planes. As the sizes of the unit cells in the Au-rich precipitate and the Ni-rich matrix differ, the resulting lattice misfit has to be compensated additionally by misfit dislocations. Therefore, the interface is tilted by about 158 with respect to the twin 1Þ planes in the Ni-rich matrix are plane, while the ð11 perpendicular to the interface. In this configuration, the 1Þ planes in the Ni-rich distance between two subsequent ð11 matrix is nearly equivalent to the distance between the intersection lines of the interfacial plane and the (002) planes in the Au-rich precipitate. In this projection, the interface seems to be coherent, as no faults in the stacking sequence can be found on either side of the interface. Circuit mappings across the interface according to Pond (1995)
Fig. 5. High-resolution Z-contrast image of an incoherent twin-boundary interface between the Ni-rich matrix and a Au-rich precipitate. (b) shows the Fourier transform of (a). In (c) the Fourier-filtered image is shown where exemplary circuit mappings according to Pond (1995) were indicated. The mask in (d) is used for Fourier filtering.
were drawn to check whether the interface is coherent or not. These mappings are sketched in Fig. 5c and reveal Burgers vector components of ð1=4Þk112l: These components correspond to the projected Burgers vectors of the ð1=2Þk110l type. To maintain the twin-like orientation 1Þ Ni-rich planes are required relation, three additional ð11 for 10 ð111ÞAu-rich planes. The interface can therefore be described as an incoherent twin-boundary. As seen in Fig. 5a, the Z-contrast signal is reduced near the interface. It is not s-shaped as for the semi-coherent interface, but is asymmetric, slowly increasing inside the Au-rich precipitate. The upper boundary of this region corresponds to two bands in the Fourier-filtered image (Fig. 5c) where the Z-contrast signal is blurred on two subsequent (111) planes. This contrast is attributed to coherency strains near the interface as the (111)Ni-rich planes have to be rotated locally by about 28 in order to provide a proper matching with the (111)Au-rich planes. As along the k111l direction across the interface (twinrelation), on every third (111) plane atomic columns can be found that are not blurred out, the circuit mappings according to Pond (1995) are not affected by the blurred Z-contrast signal. If stacking faults on ð111Þ planes were present, the intensity would be blurred within the ð111Þ planes. In the present case, there are no stacking faults, and the intensity is blurred perpendicular to the ð111Þ planes. As the dislocation network found is located near the upper boundary of the low-intensity region near the interface, the lower intensity can not be related to the strain fields of misfit dislocations. The low intensity is due to a reduction of the lattice parameter within the Au-rich precipitate whereby a better matching at the interface is provided. Thus, the coherency strains in this interface are
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compensated by a combination of tilting, misfit dislocations and a concentration gradient in the Au-rich precipitate.
5. Discussion Z-contrast imaging of a decomposed Ni-rich Ni–Au alloy allows bulk interfaces between Au-rich precipitates and the Ni-rich matrix to be characterized on the atomic scale. The interfaces between the Ni-rich matrix and the Au-rich precipitates are affected by a lattice mismatch of about 15%. Contrary to TEM studies of epitaxially grown Ni–Au layers (Dynna et al., 1996; Bayle et al., 1994), the results presented here are characteristic for interfaces between the Ni-rich matrix and Au-rich precipitates formed during phase separation of a bulk Ni-10 at.% Au alloy. Both, the strain relaxation via misfit dislocations only and twinning combined with misfit dislocations are analyzed in circuit mappings across the interfaces of Fourier filtered high-resolution Z-contrast micrographs. The projections of ð1=2Þk110l Burgers vectors are imaged in these micrographs. Longrange ordered structures as reported for Ni-60 at.% Au (Zhao and Notis, 1999) were not found, indicating that for the annealing conditions used here, the relaxation of the coherency strain via ordering of the components is not favorable. The present study yields clear evidence that at least two different transformation modes are involved in the decomposition of bulk Ni-rich Ni – Au alloys. The first mode observed is a semi-coherent stage, where the coherency strain between matrix and precipitates is reduced by misfit dislocations. The width of the interface is about ^ 1 nm. Similar semi-coherent interfaces were observed for epitaxially grown Cu/Au layers (Hartung and Schmitz, 2001) using conventional high-resolution TEM. In the second mode the coherency strain is reduced via twinning combined with misfit dislocations. The formation of the interfaces in the second mode causes the formation of subgrains which are separated by grain boundaries. The concentration gradient in this second stage is more extended (^ 2 nm) than in the first stage. The lateral resolution of the imaging process, which is solely determined by the diameter ˚ ), is better than 2 nm of the incident electron probe (, 2 A and does therefore not limit the resolution of concentration gradients or defect structures in the present case. However, if long-range strain fields are present (as is likely in the decomposed Ni-rich Ni– Au alloy), the image intensity of the corresponding Z-contrast micrographs may not directly reflect the chemical composition of the thin foil. Liu et al. (2001) analyzed low-magnification Z-contrast micrographs of Ge islands on Si surfaces. They observed contrast features due to strain fields which can not directly be explained within the incoherent imaging model. Strain fields caused by dislocations can similarly affect Z-contrast micrographs (Arslan and Browning, 2002). As the image
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contrast around the ð1=2Þk110l-type dislocations (Fig. 3) is systematically reduced, their study indicates that lattice strain fields close to dislocation cores may affect the image intensity of high-resolution Z-contrast micrographs. As the effect is small, the image intensity can still be directly related to the chemistry across the interface. Contrary to the semicoherent interface for the incoherent twin-boundary, the more gradual increase of HAADF intensity in the Au-rich precipitate can not be attributed to strain fields. It is related to a concentration gradient relaxing the lattice parameter. For inclined interfaces, the overlap of the two fcc lattices with different lattice parameters causes Moire´ patterns. If such Moire´ patterns are formed, the image intensity of the corresponding Z-contrast micrographs can not be directly related to the chemistry of the foil.
Acknowledgements The authors are grateful to E. Fischer for growing the single crystal used in these experiments, and to Dr P. Mu¨llner for his help in interpreting the experimental results. This work has been supported in part by the Swiss National Science Foundation (project no. 2000-056570.99).
References Arslan, I., Browning, N.D., 2002. Intrinsic electronic structure of threading dislocations in GaN. Phys. Rev. B 65(075310), 1–10. Bayle, P., Deutsch, T., Gilles, B., Marty, A., Thibault, J., 1994. Quantitative analysis of the deformation and chemical profiles of strained multilayers. Ultramicroscopy 56, 94–107. Bienzle, M., Oishi, T., Sommer, F., 1995. Thermodynamics and local atomic arrangements of gold–nickel alloys. J. Alloy Compd 220, 182– 188. Dynna, M., Marty, A., Gilles, B., Patrat, G., 1996. Ordering and the relaxation of elastic strain in thin Au– Ni films grown on Au(001). Acta Mater. 44, 4417–4431. Egerton, R.F., 1986. Electron Energy-Loss Spectroscopy in the Electron Microscope, Plenum Press, New York. Erni, R., Heinrich, H., Kostorz, G., 2003. Quantitative characterization of chemical inhomogeneities in Al– Ag using high-resolution Z-contrast STEM. Ultramicroscopy 94, 125–133. Hartung, F., Schmitz, G., 2001. Interdiffusion and reaction of metals: the influence and relaxation of mismatch induced stress. Phys. Rev. B 64(245418), 1–13. Hofer, F., Warbichler, P., 1985. Spinodal decomposition in the gold– nickel-system. Z. Metallkd. 76, 11–15. Janghorban, K., Kirkaldy, J.-S., Weatherly, G.-C., 2001. The HumeRothery size rule and double-well microstructures in gold–nickel. J. Phys.: Condens. Matter. 13, 8661–8676. Jesser, W.A., Kuhlmann-Wilsdorf, D., 1967. On the theory of interfacial energy and elastic strain of epitaxial overgrowth in parallel alignment on single crystal substrates. Phys. Status Solidi. 19, 95– 105. Liu, Ch.-P., Twesten, R.D., Gibson, J.M., 2001. High-angle annular darkfield imaging of self-assembled Ge islands on Si(001). Ultramicroscopy 87, 79–88. Portmann, M.J., Scho¨nfeld, B., Kostorz, G., Altorfer, F., 2002. Short-range order in Ni-8.4 at.% Au above the miscibility gap. Phys. Rev. B 65, 024110–024111.
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Okamoto, H., 1987. The Au–Ni (gold–nickel) system. In: Okamoto, H., Massalski, T.B. (Eds.), Phase Diagrams of Binary Gold Alloys, ASM International, Materials Park, OH, pp. 193 –208. Ozolins, V., Wolverton, C., Zunger, A., 1998. Effects of anharmonic strain on the phase stability of epitaxial films and superlattices: applications to noble metals. Phys. Rev. B 57, 4816–4828. Pennycook, S.J., Jesson, D.E., 1997. Scanning transmission electron microscopy. In: Amelinckx, S., Van Dyck, D., Van Landuyt, J., Van Tendeloo, G. (Eds.), Handbook of Microscopy, vol. 2. VCH, Weinheim, pp. 595–620.
Pond, R.C., 1995. On the characterisation of interfacial defects using high resolution electron microscopy. Interf Sci 2, 299–310. Rafferty, B., Nellist, P.D., Pennycook, S.J., 2001. On the origin of transverse incoherence in Z-contrast STEM. J. Electron Microsc. 50, 227 –233. Wu, T.B., Cohen, J.B., 1983. Clustering in a Au–Ni alloy above the miscibility gap. Acta Metall. 31, 1929–1935. Zhao, J.-C., Notis, A., 1999. Ordering transformation and spinodal decomposition. Metall. Mater. Trans. A 30, 707– 716.
Bulk interfaces in a Ni-rich Ni –Au alloy investigated by high-resolution Z-contrast imaging M.J. Portmann, R. Erni1, H. Heinrich2, G. Kostorz* ETH Zu¨rich, Institute of Applied Physics, CH-8093 Zu¨rich, Switzerland Received 27 July 2003; revised 29 November 2003; accepted 7 April 2004
Abstract Interfaces between Au-rich precipitates and the Ni-rich matrix in a decomposed Ni-10 at.% Au alloy were investigated by lowmagnification and high-resolution Z-contrast imaging. During aging at 923 K, the originally single crystalline sample decomposed and recrystallized resulting in a microstructure consisting of subgrains separated by small-angle grain boundaries. These small-angle grain boundaries are decorated by Au-rich precipitates. The interfaces between the Au-rich precipitates and the Ni-rich matrix were characterized with respect to the orientation relationship between precipitates and matrix, misfit dislocations and concentration gradients. Two transformation modes were identified that are involved in the decomposition of bulk Ni-rich Ni – Au alloys. While in the first mode the interface is semi-coherent, in the second mode the interface corresponds to an incoherent twin boundary. It is further shown that strain fields around misfit dislocations can result in systematic errors in the determination of the concentration gradients across interfaces between precipitates and matrix. q 2004 Elsevier Ltd. All rights reserved. PACS: 81.05.Bx; 68.37.Lp; 68.35.Dv; 61.72.Lk Keywords: Ni–Au alloys; Decomposition; Misfit dislocations; High-resolution high-angle annular dark-field scanning transmission electron microscopy
1. Introduction The microstructure of Ni– Au alloys is strongly affected by the large atomic size mismatch of about 15%. At temperatures below the solid-solution regime, a large asymmetric miscibility gap with a critical temperature of 1083 K is found (Okamoto, 1987), i.e. the Ni– Au solid solution with face-centered cubic (fcc) structure decomposes into a Ni-rich and a Au-rich phase with fcc structure. While the microstructure of the solid solution above the miscibility gap was determined for Ni-60 at.% Au (Wu and Cohen, 1983) and Ni-8.4 at.% Au (Portmann et al., 2002) by employing diffuse X-ray and neutron scattering, * Corresponding author. Tel.: þ 41-16333399; fax: þ 41-16331105. E-mail address: [email protected] (G. Kostorz). 1 Present address: Department of Chemical Engineering and Materials Science, University of California-Davis, 1 Shields Ave. Davis, CA 95616; National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. 2 Present address: Advanced Materials Processing and Analysis Center (AMPAC), University of Central Florida, Box 162455, Orlando, FL 328162455, USA. 0968-4328/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.micron.2004.04.002
phase-separated states were mainly investigated using transmission electron microscopy (TEM). Modulated structures observed for Au-rich bulk alloys attracted particular interest as it remained unclear whether these structures are a result of order or phase-separation (Janghorban et al., 2001; Zhao and Notis, 1999; Bienzle et al., 1995; Hofer and Warbichler, 1985). Bulk properties of Ni-50 at.% Au and Ni-60 at.% Au alloys were investigated by Zhao and Notis (1999) using TEM to characterize the kinetics in TTT diagrams. On the basis of selected area diffraction patterns, a transient long-range ordered phase was proposed for specimens which were first annealed at 473 K (below the coherent spinodal) for 8.3 h or 32 d and subsequently heat treated at 763 K (above the coherent spinodal) in-situ in a transmission electron microscope. The L10 structure of this transient state evolved at interfaces between precipitates and matrix and also at surfaces of specimens. On the basis of this TEM study, it seems likely that the formation of a metastable ordered phase in the bulk of Ni – Au alloys is one possibility to reduce the coherency strain of the lattice.
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For epitaxially grown thin Au/Ni films, similar results were reported. Dynna et al. (1996) found that ordered phases can be stabilized by elastic constraints imposed by the substrate. For Au/Ni multilayers, Bayle et al. (1994) showed that the strain is only relieved via interdiffusion of Au atoms into the Ni layers with less than five subsequent (001) Nilayers. Therefore besides strain relaxation via introduction of misfit dislocations or twinning, for thin films also strain relaxation via ordering of its components was proposed. This idea was corroborated by first-principles calculations of the epitaxial strain energies for Ni – Au thin films (Ozolins et al., 1998). In the present study, high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) was used to characterize chemical composition and structural changes at interfaces between Au-rich precipitates and the Ni-matrix in a phase-separated Ni-10 at.% Au solid solution. In the following, HAADF STEM is termed Z-contrast imaging, as the scattering signal at high scattering angles is dominated by Rutherford scattering which is nearly proportional to the square of the atomic number Z of the elements in the foil (Pennycook and Jesson, 1997). Contrary to conventional high-resolution TEM, imaging and image artifacts caused by image delocalization, contrast oscillations with increasing thickness of the foils and focus-dependent contrast variations are negligible (Pennycook and Jesson, 1997), as Z-contrast imaging is to a good approximation an incoherent imaging technique (Rafferty et al., 2001; Erni et al., 2003). Therefore, an unambiguous relation between a Z-contrast micrograph and the corresponding object function determined by the electrostatic crystal potential is usally assumed. The small electron probe of a field-emission transmission electron microscope provides atomic-column resolution Z-contrast imaging. For Ni-rich Ni – Au, the influence of the lattice mismatch between the two phases on the structure and the symmetry of the interfaces between the phases was investigated. As the atomic-number difference between Ni and Au (ZNi ¼ 28; ZAu ¼ 79) is large, high-resolution Z-contrast imaging is advantageous for a direct identification of the Aurich precipitates, simultaneously providing direct access to concentration gradients and structural relations across the interfaces. Zhao and Notis (1999) indicated a transient ordered phase at the interfaces. If this phase is missing, the lattice mismatch between the Au-rich precipitates and the Nirich matrix may be accommodated by misfit dislocations.
After homogenization for 5 days at 1173 K, k110l-oriented discs (0.3 mm in thickness and 3 mm in diameter) were cut using spark erosion. In order to obtain a decomposed state, these discs were aged for 24 h at 923 K (70 K below the solvus line of the miscibility gap). Finally, the aged discs were mechanically polished, dimple-ground and ion-milled with Ar ions (4 keV). HAADF STEM was performed in a Philips Tecnai F30 ST microscope equipped with a Schottky field-emission source, a scanning unit, a high-angle annular dark-field detector and a post-column electron-energy filter (GIF 2000). The microscope was operated at 300 kV using a condenser aperture of 10.7 mrad (semi-angle). The camera length was chosen to yield inner and outer HAADF detector semi-angles of 48 and 302 mrad (values determined by diffraction shift). Working at Scherzer (incoherent) defocus, these settings yield an electron probe diameter of about ˚ , defining the resolution of the imaging process in the 1.7 A scanning mode and providing atomic column resolution.
3. Low-magnification Z-contrast imaging The low-magnification Z-contrast micrograph of Ni-10 at.% Au (Fig. 1a) shows two phases, one appears bright, the other is darker. To identify the Au-rich and Nirich phases unequivocally, elemental maps shown in Fig. 1b and c were acquired by the three-window technique (Egerton, 1986). The Ni map in Fig. 1b was recorded using the Ni L2,3 absorption edge at an electron energy loss of 855 eV with an energy window of 40 eV centered at 790, 830 eV (pre-edge images) and 875 eV (post-edge image). The Au map in Fig. 1c was recorded using the Au M5,4 absorption edge at an electron energy loss of 2206 eV with an energy window of 100 eV centered at 2046, 2256 eV (pre-edge images) and 2256 eV (post-edge image). As expected, the image intensity of the Z-contrast micrograph in Fig. 1a can be related directly to the chemical
2. Experiment An alloy of nominal composition Ni-10 at.% Au was prepared from 99.9999 þ % nickel (Materials Research GmbH, Mu¨nchen, Germany) and 99.999 þ % gold (Me´taux Pre´cieux SA METALOR, Neuchaˆtel, Switzerland). From the ingot, a single crystal was grown by the Bridgman technique.
Fig. 1. Low-resolution Z-contrast image of a Ni-10 at.% Au alloy. (a) The area outlined by white lines indicates where the elemental maps of (b) Ni (L2,3 absorption edge) and (c) Au (M5,4 absorption edge) were taken. The letters A and B refer to the interfaces described below.
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composition of the foil, i.e. the Z-contrast micrograph shows atomic-number contrast. The Au-rich precipitates appear bright (higher atomic number), for the Ni-rich matrix the image intensity is reduced. A qualitative chemical characterization of the foil on the basis of the Z-contrast micrograph in Fig. 1a is therefore straightforward. Electron diffraction patterns reveal that the crystal orientation varies by about 58 while moving from one Ni-rich region to another, i.e. the individual Ni-rich subgrains are slightly inclined. Hence, small-angle grain boundaries are present. Most of the small-angle grain boundaries are decorated with Au-rich precipitates. The presence of grain boundaries is surprising, as the original sample was single crystalline and undeformed prior to annealing. To confirm this result, a k100l oriented single crystalline sample (3 mm in thickness and 8 mm in diameter) was annealed in situ on a high-resolution twocircle X-ray diffractometer at 923 K while registering the diffuse X-ray scattering around a 400 reflection in v 2 2u mappings using Mo Ka radiation and a position sensitive detector. It was found that the scattering intensities continuously decrease and vanish finally after 1.5 h. The subsequently metallographically etched sample showed grain boundaries proving that the originally single crystalline sample had completely recrystallized. Concentration gradients across interfaces can only be revealed directly by TEM if the interface is exposed edgeone. Inclined interfaces between phases of different lattice parameters lead to Moire´ patterns in low-resolution Z-contrast images. Grey areas in Fig. 1a correspond to such Moire´ patterns (Fig. 2a). The image contrast is affected by the stacking of two crystal lattices with different lattice parameters. The spacing of the Moire pattern in Fig. 2a is in agreement with a lattice mismatch of about 15%. In contrast, interfaces vertically aligned in the thin foil show a sharp change in the image intensity across the interface (Fig. 2b).
Fig. 2. Low-magnification Z-contrast image of two interfaces between Au-rich precipitates and the Ni-rich matrix corresponding to interfaces at (a) (A) and (b) (B) in Fig. 1. (a) A Moire´ pattern at the lower part of the precipitate is clearly visible. (b) In contrast, these interfaces are not tilted and can be viewed edge on.
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4. High-resolution Z-contrast imaging Fig. 3a shows a high-resolution Z-contrast micrograph of the interface between a Au-rich precipitate and the Ni-rich matrix at the position A in Fig. 1a. The micrograph was acquired in a k110l zone-axis orientation. The interface is shown edge-on, but the interfacial plane does not correspond to a low-indexed lattice plane, i.e. the interfacial 1Þ Ni-rich 1Þ Au-rich ==ð11 plane slightly deviates from an exact ð11 relationship. The Fourier-filtered image of Fig. 3a—shown in Fig. 3c—allows the misfit dislocations to be located along the interface via circuit mapping as proposed by Pond (1995). The Z-contrast signal around the direct beam in the Fourier transform (Fig. 3b) of Fig. 3a was also filtered out to separate the structural information from the chemical information as shown in Fig. 3d. The sketched circuit mappings indicate that additional {111} planes are present in the Ni-rich matrix, which compensate the coherency strain. The visible Burgers vector component is ð1=4Þk112l and corresponds to the projected length of a ð1=2Þk101l-type misfit dislocation, as no faults in the stacking sequence can be found. The ratio (e.g. Jesser and Kuhlmann-Wilsdorf, 1967) of the distance between the misfit dislocations (Fig. 3) and the corresponding Burgers vector are in good agreement with the estimated lattice mismatch of about 15%. Assuming that the observed dislocations are pure edge dislocations, strain fields are present in planes perpendicular to the incident beam direction. The effect of these lattice distortions on the image intensity of Z-contrast micrographs is not completely negligible, as close to the dislocation cores the image intensity is slightly reduced. This can be seen best if the positions in the non-filtered image (Fig. 3a) are compared with the indicated dislocation positions in
Fig. 3. (a) High-resolution Z-contrast image of a semi-coherent interface between the Ni-rich matrix and a Au-rich precipitate. (b) shows the Fourier transform of (a). In (c) a Fourier-filtered image is shown where the edge dislocations are indicated. The mask in (d) is used for Fourier filtering.
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Fig. 4. Scattering intensity versus the distance perpendicular to the interfaces for the semi-coherent interface in Fig. 3a (W) and the incoherent twin-boundary interface in Fig. 5a (X). Both interfaces are centered with respect to their half-height values.
the Fourier-filtered image (Fig. 3c). In Fig. 4 an intensity profile of the s-shaped Z-contrast signal across the interface is shown. The atomic-column resolution is clearly visible Au-rich ==ð111Þ Ni-rich relationship. As the owing to the ð111Þ Z-contrast signal directly reflects the chemistry of the foil without suffering from long-range image delocalization, and as the interface is analyzed edge-on, the intensity profile in Fig. 3c directly reveals the concentration gradient across the interface. If the electron scattering cross sections corresponding to the HAADF-detector area are known and if it is assumed that the phase-separated alloy is in thermodynamic equilibrium (i.e. if the concentration of the two phases are known) the concentration gradient can be calibrated. However, such a straightforward evaluation is based on the incoherent imaging model (Erni et al., 2003), which, in case of large lattice strains, may not be fully correct. In Fig. 5a, a high-resolution Z-contrast micrograph of the interface at position B in Fig. 1a is shown. Again, the Au-rich precipitate and the Ni-rich matrix have (111) planes in common. Across the interface, the crystal structure is rotated by 1808 about the normal of these (111) planes and the interface can locally be described by a twin-relation. The (111) planes correspond to the twin planes. As the sizes of the unit cells in the Au-rich precipitate and the Ni-rich matrix differ, the resulting lattice misfit has to be compensated additionally by misfit dislocations. Therefore, the interface is tilted by about 158 with respect to the twin 1Þ planes in the Ni-rich matrix are plane, while the ð11 perpendicular to the interface. In this configuration, the 1Þ planes in the Ni-rich distance between two subsequent ð11 matrix is nearly equivalent to the distance between the intersection lines of the interfacial plane and the (002) planes in the Au-rich precipitate. In this projection, the interface seems to be coherent, as no faults in the stacking sequence can be found on either side of the interface. Circuit mappings across the interface according to Pond (1995)
Fig. 5. High-resolution Z-contrast image of an incoherent twin-boundary interface between the Ni-rich matrix and a Au-rich precipitate. (b) shows the Fourier transform of (a). In (c) the Fourier-filtered image is shown where exemplary circuit mappings according to Pond (1995) were indicated. The mask in (d) is used for Fourier filtering.
were drawn to check whether the interface is coherent or not. These mappings are sketched in Fig. 5c and reveal Burgers vector components of ð1=4Þk112l: These components correspond to the projected Burgers vectors of the ð1=2Þk110l type. To maintain the twin-like orientation 1Þ Ni-rich planes are required relation, three additional ð11 for 10 ð111ÞAu-rich planes. The interface can therefore be described as an incoherent twin-boundary. As seen in Fig. 5a, the Z-contrast signal is reduced near the interface. It is not s-shaped as for the semi-coherent interface, but is asymmetric, slowly increasing inside the Au-rich precipitate. The upper boundary of this region corresponds to two bands in the Fourier-filtered image (Fig. 5c) where the Z-contrast signal is blurred on two subsequent (111) planes. This contrast is attributed to coherency strains near the interface as the (111)Ni-rich planes have to be rotated locally by about 28 in order to provide a proper matching with the (111)Au-rich planes. As along the k111l direction across the interface (twinrelation), on every third (111) plane atomic columns can be found that are not blurred out, the circuit mappings according to Pond (1995) are not affected by the blurred Z-contrast signal. If stacking faults on ð111Þ planes were present, the intensity would be blurred within the ð111Þ planes. In the present case, there are no stacking faults, and the intensity is blurred perpendicular to the ð111Þ planes. As the dislocation network found is located near the upper boundary of the low-intensity region near the interface, the lower intensity can not be related to the strain fields of misfit dislocations. The low intensity is due to a reduction of the lattice parameter within the Au-rich precipitate whereby a better matching at the interface is provided. Thus, the coherency strains in this interface are
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compensated by a combination of tilting, misfit dislocations and a concentration gradient in the Au-rich precipitate.
5. Discussion Z-contrast imaging of a decomposed Ni-rich Ni–Au alloy allows bulk interfaces between Au-rich precipitates and the Ni-rich matrix to be characterized on the atomic scale. The interfaces between the Ni-rich matrix and the Au-rich precipitates are affected by a lattice mismatch of about 15%. Contrary to TEM studies of epitaxially grown Ni–Au layers (Dynna et al., 1996; Bayle et al., 1994), the results presented here are characteristic for interfaces between the Ni-rich matrix and Au-rich precipitates formed during phase separation of a bulk Ni-10 at.% Au alloy. Both, the strain relaxation via misfit dislocations only and twinning combined with misfit dislocations are analyzed in circuit mappings across the interfaces of Fourier filtered high-resolution Z-contrast micrographs. The projections of ð1=2Þk110l Burgers vectors are imaged in these micrographs. Longrange ordered structures as reported for Ni-60 at.% Au (Zhao and Notis, 1999) were not found, indicating that for the annealing conditions used here, the relaxation of the coherency strain via ordering of the components is not favorable. The present study yields clear evidence that at least two different transformation modes are involved in the decomposition of bulk Ni-rich Ni – Au alloys. The first mode observed is a semi-coherent stage, where the coherency strain between matrix and precipitates is reduced by misfit dislocations. The width of the interface is about ^ 1 nm. Similar semi-coherent interfaces were observed for epitaxially grown Cu/Au layers (Hartung and Schmitz, 2001) using conventional high-resolution TEM. In the second mode the coherency strain is reduced via twinning combined with misfit dislocations. The formation of the interfaces in the second mode causes the formation of subgrains which are separated by grain boundaries. The concentration gradient in this second stage is more extended (^ 2 nm) than in the first stage. The lateral resolution of the imaging process, which is solely determined by the diameter ˚ ), is better than 2 nm of the incident electron probe (, 2 A and does therefore not limit the resolution of concentration gradients or defect structures in the present case. However, if long-range strain fields are present (as is likely in the decomposed Ni-rich Ni– Au alloy), the image intensity of the corresponding Z-contrast micrographs may not directly reflect the chemical composition of the thin foil. Liu et al. (2001) analyzed low-magnification Z-contrast micrographs of Ge islands on Si surfaces. They observed contrast features due to strain fields which can not directly be explained within the incoherent imaging model. Strain fields caused by dislocations can similarly affect Z-contrast micrographs (Arslan and Browning, 2002). As the image
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contrast around the ð1=2Þk110l-type dislocations (Fig. 3) is systematically reduced, their study indicates that lattice strain fields close to dislocation cores may affect the image intensity of high-resolution Z-contrast micrographs. As the effect is small, the image intensity can still be directly related to the chemistry across the interface. Contrary to the semicoherent interface for the incoherent twin-boundary, the more gradual increase of HAADF intensity in the Au-rich precipitate can not be attributed to strain fields. It is related to a concentration gradient relaxing the lattice parameter. For inclined interfaces, the overlap of the two fcc lattices with different lattice parameters causes Moire´ patterns. If such Moire´ patterns are formed, the image intensity of the corresponding Z-contrast micrographs can not be directly related to the chemistry of the foil.
Acknowledgements The authors are grateful to E. Fischer for growing the single crystal used in these experiments, and to Dr P. Mu¨llner for his help in interpreting the experimental results. This work has been supported in part by the Swiss National Science Foundation (project no. 2000-056570.99).
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