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Atomic structure of a ∑ = 5 (310) symmetric tilt boundary in Au
Scripta
METALLURGICA
Vol.
22,
pp.
Printed
1093-1096,
1988
in the U.S.A.
Pergamon Press plc A l l rights reserved
A T O M I C S T R U C T U R E O F A X = 5 (310) S Y M M E T R I C T I L T B O U N D A R Y IN Au F. Cosandey Rutgers, The State University of New Jersey Department of Mechanics and Materials Science Piscataway, NJ 08855-0909, U S A SiuoWai Chan Bell Communications Research Newman Spring Road Red Bank, NJ 07701-9020, U S A P. Stadelmann Swiss Federal Institute of Technology Institut Interdepartemental de Microscopic (I2M) CH-1015 Lausanne, Switzerland (Received April 4, 1988) Introduction Until recently we have been prevented from direct observation of the atomic structure of dislocations and grain boundaries in metals primarily because of the resolution limit of transmission electron microscopes. Consequently, observations at axial illumination were possible only for metals with a large lattice parameter and only for specific crystal orientations. For instance, grain boundary atomic structures in Au have been observed along [110] crystal orientationsfor X = 11 (113) [11, x = 3 (111) and (211) [1,21, and for X = 9 (331) [3] coincidence boundaries where dnl = 0.23 nm. The atomic structure has been reported also in Mo for a X -- 41 (910) tilt boundary viewed aloi~g [001] axis with dll 0 = 012 nm [4]. Since experimental results have been few, most atomic structure determinations have been oS[ained using molecular static and molecular dynamic computational techniques [5]. As a result of recent developments of intermediate voltage electron microscope (300-400 kV), this situation is changing and atomic resolution is now possible for most metals which can be viewed along various crystallographic directions [6]. In this article, we present results on the atomic structure of a X = 5 (310) tilt boundary in Au. This particular coincidence boundary has been selected because results concerning atomic relaxation and displacement field have already been obtained [7,8], and because numerous molecular static simulations have been reported for this boundary [9-15]. Furthermore, simulation results of Vitek et al. [14,15] reveal that this boundary may assume two metastable atomic structures having similar energies. These two structures are shown in Fig. L Also depicted in Fig. 1 are two possible grain boundary unit cells. The unit cell of structure A consists of two atoms located along the boundary plane followed by an atom pair disposed symmetrically, while structure B consists of a row of 3 atoms located along the boundary plane. Structure A is essentially the same as reported by other investigators [10-13] differing slightly by the extent of atomic expansion normal to the boundary plane and by small variations in the atomic positions. Structure B is unique and is obtained from structure A by the removal of two (620) planes from the grain boundary followed by relaxations [14,15]. A t the present time there exists no direct atomic observation of a X = 5 boundary for comparison with computational modeling. Exverimental ProceduTes Thin film Au bicrystals containing X = 5 (310) tilt boundaries were produced by epitaxial growth on NaCl bicrystals using a technique described in detail elsewhere [16]. First, a bicrystal of NaCl with a misorientation 0 = 36.9 about a c o m m o n [001] axis was grown from the melt by the Czochralski technique. A thick Ag (- 05 pro) bicrystal was then produced by epitaxial growth followed by epitaxiai deposition of a t h i n Au film about 20 nm in thickness. T h e NaCI and Ag substrates were then dissolved away, and the thin Au bicrystal mounted on an Au grid. In order to stabilize the structure, the films were given a final air anneal. T h e thickness of these films varied significantly, especially near the boundary region where numerous holes have developed. All high resolution images were taken at the thinnest parts of these films, corresponding to an optimum thickness of 5-10 nm.
1093 0036-9748/88 $3.00 + .00
1094
TILT B O U N D A R Y
IN Au
Vol.
22, No.
7
The high resolution microscopy was performed with a Philips 430 ST (C ! = L1 mm) operated at 300 kV. All images were obtained using axial illumination without objective a p e r t u r e - a n d were recorded at a direct magnification of 700,000 x. The microscope was also equipped with a video camera connected to a frame store with a PDP-11 and array processor. With this set-up, a Fourier transform of the image can be obtained on-line allowing direct optimization of bicrystal alignment and microscope performance. The image simulations were obtained using multislice formalism with EMS programs [17]. All four {200} reflections from each crystal were used for the simulations with the following instrumental parameters: accelerating voltage V = 300 kV, spherical aberration coefficient C s = 1.1 ram, defocus spread/~ = 8 nm and semi-angle beam divergence a = ~ mrad. Results and Discussion Image simulations were performed for the two models A and B of Fig. 1, as a function of specimen thickness and defocus value, in order to determine optimum conditions for observing the atomic structure of these boundaries. As expected the images are strongly dependent on the parameters previously mentioned, but in general, distinct images have been obtained for each of the two models. A n optimum image contrast was obtained near the second broad pass-band of the transfer function corresponding to a defocus value of 86 nm and for thicknesses in the range of 5.6 to 72 rim. Two images simulated for a thickness t = 6.4 nm and for nf = 86 nm are shown in Fig. 2a and 2b for models A and B, respectively. Also marked in these two images are the original atomic columns. For these experimental conditions, the atomic columns appear as white dots. In addition, it can be seen that the atomic positions in the image do not deviate appreciably from the position in the models and that the two models can be clearly identified. A high resolution image taken at an optimum defocus value of about 85 nm is shown in Fig. 3. The grain boundary plane is symmetrically located with respect to the (200) planes of both crystals with 0(200) = 36.5 + 0.5°, corresponding to a • = 5 (310) tilt boundary. A unit cell, which can be repeated along the boundary plane is also drawn in Fig. 3. This unit cell contains the typical pattern of model A with two atomic columns located along the boundary plane and a pair located symmetrically to it. This grain boundary structure has been observed for two other grain boundary areas; a result which indicates that structure A is the most stable grain boundary structure. Molecular static energy calculations using an empirical potential for Cu show that structure A has the lowest energy [15]. This tilt grain boundary Z = 5 (310) can be described by a regular array of primary dislocations which give rise to localized lattice strain detectable by T E M [7]. A Burgers circuit is drawn in Fig. 3 revealing a closure failure corresponding to a Burgers vector b = a [100], as expected for this boundary plane [7]. The measured grain boundary periodicity, or size of the unit cell, of 0.64 + 0:05 nm is also in agreement with theoretical periodicity of 0.65 nm [7]. A common feature of all atomistic calculations, is the rigid body translation of one grain with respect to the other grain. This translation can be expressed in terms of a component Z parallel to the tilt axis, a component X along the boundary plane and the component Y perpendicular to it. Since atomic imaging corresponds to the projected structure along the tilt axis, the Z component cannot be obtained by high resolution TEM. The measured translation along the boundary plane is zero or falls within the experimental error estimated to be 0.12 a ° where a is the lattice parameter. This result agrees with atomistic calculation, using an empirical potential for Cu [13,14a]. The expansion Y normal to the boundary plane was measured as the spacing between eight (620) planes. A value of 1.6 + 0.1 a has been obtained from Fig. 3 which corresponds to a 20% expansion from the unrelaxed configuration. This°value is somewhat larger than the value of L44 a ° estimated from structures calculated using an empirical noble potential for Cu [13,14], but can still be considered to fall within experimental error. Further comparison awaits more detailed analysis of simulated images with computer models.
Acknowledgements Special thanks for G. Peter for technical assistance and for his ski!lfull care of electron microscope and to Donna Foster for typing and editing this manuscript. F. Cosandey would also like to t h a n k Dr. P. Buffat of I2M for provision of laboratory facility. This work is supported in part by the National Science Foundation under G r a n t INT-85-1532L
Vol.
22,
No.
7
TILT BOUNDARY
IN Au
1095
References L 2. 3. 4.
5. 6. 7. g 9. 10. 1L 12. 13. 14. 15. 16. 17.
Y. Ishida, H. Ichinose, M. Mori and M. Hashimoto. Trans. Jap. Inst. Met. 24. 349-359 (1983). H. Ichinose and Y. Ishida. Phil. Mag. A43, 1253-1264 (1981). W. Krakow, J.T. Wetzel and D.A. Smith. Phil. Mag. A53, 739-754 (1986). J.M. Penisson, R. Gronsky and J.B. Brosse. Scripta Met. 16. 1239-1242 (1982). H.F. Fischmeister. J. Physique 46. C4, 3-23 (1985~ A. Bourret and J.M. Penisson. JEOL News 25E, 1-7 (1987). F. Cosandey and C.L. Bauer. Phil. Mag. A44, 391-403 (1981). E.P. Kwam and R.W. Balluffi. Phil. Mag. A56, 137-148 (1987). M.J. Weins, H. Glarer and B. Chalmers. J. Appl. Phys. 42. 2639-2645 (1971). G. Hasson, J.Y. Boos, I. Herbeuval, H. Biscondi and C. Gonx. Surface Sci. 31. 115-137 (1972). D.A. Smith, V. Vitek and R.C. Pond. Acta Met. 25. 475-483 (1977). H. Hashimoto, Y. Ishida, R. Yamamoto and M. Doyama. J. Phys. F: Metal Phys. 10. 1109-1116 (1980). A. Brokman, P.D. Bristowe and R.W. Bailuffi. J. AppL Phys. 52. 6116-6127 (1981). V. Vitek, A.P. Sutton, GJ. Wang and D. Schwartz. Scripta Met. 17. 183-189 (1983). G.I. Wang, A.P. Sutton and V. Vitek. Acta Met~ 32. 1092-1104 (1984). F. Cosandey, Y. Komen and C.L Bauer. Phys. Star. SoL (aM8. 555-563 (1978). P. Stadelmann. Ultramicroscopy 2__L131-146 (1987).
a
b
Fig. 1. Proposed models, (a) A and (b) B, for the atomic structure of a Y. -- 5 (310) tilt boundary. Atomic positions were taken from Ref. [14]. The atomic structure is viewed in projection and no atomic distinction are made for the A B A B sequence along the tilt axis. Also shown are structural units for the two structures.
1096
TILT BOUNDARY
IN Au
Vol.
22, No.
2'
:6
-~) 7.
a
b
Fig. 2 I m a g e simulations f o r model (a) A and (b) B with V ffi 300 kV, A ffi 8 nm, a = 0.8 mrad, C s = 1-1 mm, t = 6.4 n m and Zxf = 86 rim. Also s u p e r i m p o s e d on the images are the atomic positions.
Fig. 3 H i g h resolution image of a ~. = 5 (310) s y m m e t r i c tilt grain b o u n d a r y in Au. A t o m i c c o l u m n s are represented as white dots.
7
METALLURGICA
Vol.
22,
pp.
Printed
1093-1096,
1988
in the U.S.A.
Pergamon Press plc A l l rights reserved
A T O M I C S T R U C T U R E O F A X = 5 (310) S Y M M E T R I C T I L T B O U N D A R Y IN Au F. Cosandey Rutgers, The State University of New Jersey Department of Mechanics and Materials Science Piscataway, NJ 08855-0909, U S A SiuoWai Chan Bell Communications Research Newman Spring Road Red Bank, NJ 07701-9020, U S A P. Stadelmann Swiss Federal Institute of Technology Institut Interdepartemental de Microscopic (I2M) CH-1015 Lausanne, Switzerland (Received April 4, 1988) Introduction Until recently we have been prevented from direct observation of the atomic structure of dislocations and grain boundaries in metals primarily because of the resolution limit of transmission electron microscopes. Consequently, observations at axial illumination were possible only for metals with a large lattice parameter and only for specific crystal orientations. For instance, grain boundary atomic structures in Au have been observed along [110] crystal orientationsfor X = 11 (113) [11, x = 3 (111) and (211) [1,21, and for X = 9 (331) [3] coincidence boundaries where dnl = 0.23 nm. The atomic structure has been reported also in Mo for a X -- 41 (910) tilt boundary viewed aloi~g [001] axis with dll 0 = 012 nm [4]. Since experimental results have been few, most atomic structure determinations have been oS[ained using molecular static and molecular dynamic computational techniques [5]. As a result of recent developments of intermediate voltage electron microscope (300-400 kV), this situation is changing and atomic resolution is now possible for most metals which can be viewed along various crystallographic directions [6]. In this article, we present results on the atomic structure of a X = 5 (310) tilt boundary in Au. This particular coincidence boundary has been selected because results concerning atomic relaxation and displacement field have already been obtained [7,8], and because numerous molecular static simulations have been reported for this boundary [9-15]. Furthermore, simulation results of Vitek et al. [14,15] reveal that this boundary may assume two metastable atomic structures having similar energies. These two structures are shown in Fig. L Also depicted in Fig. 1 are two possible grain boundary unit cells. The unit cell of structure A consists of two atoms located along the boundary plane followed by an atom pair disposed symmetrically, while structure B consists of a row of 3 atoms located along the boundary plane. Structure A is essentially the same as reported by other investigators [10-13] differing slightly by the extent of atomic expansion normal to the boundary plane and by small variations in the atomic positions. Structure B is unique and is obtained from structure A by the removal of two (620) planes from the grain boundary followed by relaxations [14,15]. A t the present time there exists no direct atomic observation of a X = 5 boundary for comparison with computational modeling. Exverimental ProceduTes Thin film Au bicrystals containing X = 5 (310) tilt boundaries were produced by epitaxial growth on NaCl bicrystals using a technique described in detail elsewhere [16]. First, a bicrystal of NaCl with a misorientation 0 = 36.9 about a c o m m o n [001] axis was grown from the melt by the Czochralski technique. A thick Ag (- 05 pro) bicrystal was then produced by epitaxial growth followed by epitaxiai deposition of a t h i n Au film about 20 nm in thickness. T h e NaCI and Ag substrates were then dissolved away, and the thin Au bicrystal mounted on an Au grid. In order to stabilize the structure, the films were given a final air anneal. T h e thickness of these films varied significantly, especially near the boundary region where numerous holes have developed. All high resolution images were taken at the thinnest parts of these films, corresponding to an optimum thickness of 5-10 nm.
1093 0036-9748/88 $3.00 + .00
1094
TILT B O U N D A R Y
IN Au
Vol.
22, No.
7
The high resolution microscopy was performed with a Philips 430 ST (C ! = L1 mm) operated at 300 kV. All images were obtained using axial illumination without objective a p e r t u r e - a n d were recorded at a direct magnification of 700,000 x. The microscope was also equipped with a video camera connected to a frame store with a PDP-11 and array processor. With this set-up, a Fourier transform of the image can be obtained on-line allowing direct optimization of bicrystal alignment and microscope performance. The image simulations were obtained using multislice formalism with EMS programs [17]. All four {200} reflections from each crystal were used for the simulations with the following instrumental parameters: accelerating voltage V = 300 kV, spherical aberration coefficient C s = 1.1 ram, defocus spread/~ = 8 nm and semi-angle beam divergence a = ~ mrad. Results and Discussion Image simulations were performed for the two models A and B of Fig. 1, as a function of specimen thickness and defocus value, in order to determine optimum conditions for observing the atomic structure of these boundaries. As expected the images are strongly dependent on the parameters previously mentioned, but in general, distinct images have been obtained for each of the two models. A n optimum image contrast was obtained near the second broad pass-band of the transfer function corresponding to a defocus value of 86 nm and for thicknesses in the range of 5.6 to 72 rim. Two images simulated for a thickness t = 6.4 nm and for nf = 86 nm are shown in Fig. 2a and 2b for models A and B, respectively. Also marked in these two images are the original atomic columns. For these experimental conditions, the atomic columns appear as white dots. In addition, it can be seen that the atomic positions in the image do not deviate appreciably from the position in the models and that the two models can be clearly identified. A high resolution image taken at an optimum defocus value of about 85 nm is shown in Fig. 3. The grain boundary plane is symmetrically located with respect to the (200) planes of both crystals with 0(200) = 36.5 + 0.5°, corresponding to a • = 5 (310) tilt boundary. A unit cell, which can be repeated along the boundary plane is also drawn in Fig. 3. This unit cell contains the typical pattern of model A with two atomic columns located along the boundary plane and a pair located symmetrically to it. This grain boundary structure has been observed for two other grain boundary areas; a result which indicates that structure A is the most stable grain boundary structure. Molecular static energy calculations using an empirical potential for Cu show that structure A has the lowest energy [15]. This tilt grain boundary Z = 5 (310) can be described by a regular array of primary dislocations which give rise to localized lattice strain detectable by T E M [7]. A Burgers circuit is drawn in Fig. 3 revealing a closure failure corresponding to a Burgers vector b = a [100], as expected for this boundary plane [7]. The measured grain boundary periodicity, or size of the unit cell, of 0.64 + 0:05 nm is also in agreement with theoretical periodicity of 0.65 nm [7]. A common feature of all atomistic calculations, is the rigid body translation of one grain with respect to the other grain. This translation can be expressed in terms of a component Z parallel to the tilt axis, a component X along the boundary plane and the component Y perpendicular to it. Since atomic imaging corresponds to the projected structure along the tilt axis, the Z component cannot be obtained by high resolution TEM. The measured translation along the boundary plane is zero or falls within the experimental error estimated to be 0.12 a ° where a is the lattice parameter. This result agrees with atomistic calculation, using an empirical potential for Cu [13,14a]. The expansion Y normal to the boundary plane was measured as the spacing between eight (620) planes. A value of 1.6 + 0.1 a has been obtained from Fig. 3 which corresponds to a 20% expansion from the unrelaxed configuration. This°value is somewhat larger than the value of L44 a ° estimated from structures calculated using an empirical noble potential for Cu [13,14], but can still be considered to fall within experimental error. Further comparison awaits more detailed analysis of simulated images with computer models.
Acknowledgements Special thanks for G. Peter for technical assistance and for his ski!lfull care of electron microscope and to Donna Foster for typing and editing this manuscript. F. Cosandey would also like to t h a n k Dr. P. Buffat of I2M for provision of laboratory facility. This work is supported in part by the National Science Foundation under G r a n t INT-85-1532L
Vol.
22,
No.
7
TILT BOUNDARY
IN Au
1095
References L 2. 3. 4.
5. 6. 7. g 9. 10. 1L 12. 13. 14. 15. 16. 17.
Y. Ishida, H. Ichinose, M. Mori and M. Hashimoto. Trans. Jap. Inst. Met. 24. 349-359 (1983). H. Ichinose and Y. Ishida. Phil. Mag. A43, 1253-1264 (1981). W. Krakow, J.T. Wetzel and D.A. Smith. Phil. Mag. A53, 739-754 (1986). J.M. Penisson, R. Gronsky and J.B. Brosse. Scripta Met. 16. 1239-1242 (1982). H.F. Fischmeister. J. Physique 46. C4, 3-23 (1985~ A. Bourret and J.M. Penisson. JEOL News 25E, 1-7 (1987). F. Cosandey and C.L. Bauer. Phil. Mag. A44, 391-403 (1981). E.P. Kwam and R.W. Balluffi. Phil. Mag. A56, 137-148 (1987). M.J. Weins, H. Glarer and B. Chalmers. J. Appl. Phys. 42. 2639-2645 (1971). G. Hasson, J.Y. Boos, I. Herbeuval, H. Biscondi and C. Gonx. Surface Sci. 31. 115-137 (1972). D.A. Smith, V. Vitek and R.C. Pond. Acta Met. 25. 475-483 (1977). H. Hashimoto, Y. Ishida, R. Yamamoto and M. Doyama. J. Phys. F: Metal Phys. 10. 1109-1116 (1980). A. Brokman, P.D. Bristowe and R.W. Bailuffi. J. AppL Phys. 52. 6116-6127 (1981). V. Vitek, A.P. Sutton, GJ. Wang and D. Schwartz. Scripta Met. 17. 183-189 (1983). G.I. Wang, A.P. Sutton and V. Vitek. Acta Met~ 32. 1092-1104 (1984). F. Cosandey, Y. Komen and C.L Bauer. Phys. Star. SoL (aM8. 555-563 (1978). P. Stadelmann. Ultramicroscopy 2__L131-146 (1987).
a
b
Fig. 1. Proposed models, (a) A and (b) B, for the atomic structure of a Y. -- 5 (310) tilt boundary. Atomic positions were taken from Ref. [14]. The atomic structure is viewed in projection and no atomic distinction are made for the A B A B sequence along the tilt axis. Also shown are structural units for the two structures.
1096
TILT BOUNDARY
IN Au
Vol.
22, No.
2'
:6
-~) 7.
a
b
Fig. 2 I m a g e simulations f o r model (a) A and (b) B with V ffi 300 kV, A ffi 8 nm, a = 0.8 mrad, C s = 1-1 mm, t = 6.4 n m and Zxf = 86 rim. Also s u p e r i m p o s e d on the images are the atomic positions.
Fig. 3 H i g h resolution image of a ~. = 5 (310) s y m m e t r i c tilt grain b o u n d a r y in Au. A t o m i c c o l u m n s are represented as white dots.
7