- Email: [email protected]
Theoretical and experimental studies of the dislocation structure at the NiAl–Cr(Mo) interfaces
June 2000
Materials Letters 44 Ž2000. 186–191 www.elsevier.comrlocatermatlet
Theoretical and experimental studies of the dislocation structure at the NiAl–Cr žMo/ interfaces Y.X. Chen a,) , C.Y. Cui b, L.L. He a , J.T. Guo b, D.X. Li a a
b
Laboratory of Atomic Imaging of Solids, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China Received 1 July 1999; received in revised form 17 September 1999; accepted 1 November 1999
Abstract The dislocation structure at the NiAlrCrŽMo. interfaces has been studied by high resolution electron microscopy ŽHREM.. The Ž110. and Ž111. cube-on-cube interfaces were examined. Both of the interfaces have been found to be partially coherent. Theoretical calculation of the expected dislocation structure at the interfaces was made based on the CSLrDSC lattice model. The experimental observations and theoretical prediction were shown to be in generally good agreement, with some differences with respect to the detailed structure. q 2000 Elsevier Science B.V. All rights reserved. Keywords: HREM; Dislocation structure; CSLrDSC lattice model; NiAl–CrŽMo. interface
1. Introduction Directionally solidified NiAl–CrŽMo. eutectic alloy had been studied for many years w1,2x and interest was renewed recently w3x for its much higher fracture toughness than that of polycrystalline NiAl. Its microstructure was characterized by a lamellar CrŽMo. phase embedded within the NiAl matrix. However, their interfacial structure was still poorly understood. For metal y oxide systems, it was found that the dislocations were located on the metal side, a few atomic spacing away from the interface w4x. In comparison to NiAl single crystal, there has been relatively few observations on the dislocation structure at the NiAl–CrŽMo. interfaces. In this paper, the dislocation structure at the interfaces was studied by )
Corresponding author. Fax: q86-24-2389-1320.
HREM and the observation was compared to predictions from an analysis based on the CSLrDSC lattice model.
2. Experimental procedure A vacuum induction melted and drop cast ingot of NiAl–28Cr–5.5Mo–0.5Hf Žat.%. was directionally solidified under Ar atmosphere in the Al 2 O 3 –SiO 2 ceramic mold by the standard Bridgman method. The TEM samples were prepared using conventional procedure, including cutting discs perpendicular to the growth direction with a thickness of 0.2 mm, mechanical polishing them to 50 mm thickness, dimpling to 20 mm and finally ion milling. TEM observations were performed with a JEM2010 high resolution electron microscope.
00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 0 . 0 0 0 2 4 - 0
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
187
3. Theoretical description of dislocation structure at the NiAl r Cr(Mo) interfaces In this section, we discuss the expected dislocation structure for two interfaces based on the CSLrDSC lattice model Žsee more details in the literature w5x.. The CSLrDSC lattice model postulates that the structure of a crystal interface is determined by two sets of parameters. The first set is related to the structure and relative orientation of the two crystals neighboring the interface, which determines the O-lattice that is present. The second set of parameters is given by the path of the boundary, i.e. the boundary plane. The dislocation structure of the interface is then given by the intersection of the boundary plane with the O-lattice cell walls, i.e. the Wigner–Seitz cell, with the translation vector attributed to the respective cell wall being the Burgers vector of the dislocation. The coordinates of the O-lattice points X ŽO . are defined by the expression
X ŽO . s Ž IyAy1 .
y1
B
where A is the transformation matrix relating the DSC-1 and DSC-2 lattices, B is the matrix formed by the vectors of the primitive unit of the crystal lattice and I is the unitary matrix. The first step to obtain the O-lattice is to find the transformation matrix A. The CrŽMo. phase is a solid solution with the bcc structure, the lattice parameter can be determined by the work of Cline et al. w6x, which indicated that when the level of Mo is 5.5 at.%, the lattice parameter of CrŽMo. is 0.2942 nm. NiAl has B 2-ordered crystal structure with lattice parameter 0.2887 nm. Since the CSLrDSC model is a geometrical model and does not account for energetic aspects, we take NiAl as the bcc structure. In this simple bccrbcc system, the transformation matrix A is an expansion–contraction matrix, which can be written as:
As
ž
1qd 0 0
0 1qd 0
0 0 1qd
Fig. 1. Schematic drawing shows the dislocation structure at Ža. Ž110. Žb. Ž111..
where d is the fractional lattice parameter mismatch between CrŽMo. and NiAl, defined by
ds
2 Ž a1 y a 2 .
Ž 2.
a1 q a2
with a 1 and a 2 as the lattice constants of NiAl and CrŽMo.. For the bcc structure, the matrix B can be written as Bs
1 1 1 2 1
1 1 1
1 1 1
0
Ž 3.
Taking CrŽMo. as a reference system, the O-lattice point coordinates are given by
/
Ž 1.
X ŽO . s Ž I y Ay1 .
y1
Bs
1qd
d
B
Ž 4.
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
188
the O-lattice points form a bcc lattice with lattice constant
4. Experimental results and discussion 4.1. (110) interface
aŽ o. s
1qd
d
a2 s 15.89 nm
Ž 5.
The dislocation networks for either Ž111. or Ž110. are obtained by the intersection of the boundary plane with the Wigner–Seitz cell walls of the bcc O-lattice. The resulting dislocation structures of the Ž111. and Ž110. interfaces are shown in Fig. 1a and 1b, respectively. The dislocation network of the Ž110. interface is an array of two sets of edge dislocations aligned along the ²111: direction with the Burgers vectors of the type 13 ²112:.The spacing between dislocation lines is given by
SD s
1qd
d
< b < s 12.97 nm
Ž 6.
The dislocation network of Ž111. is composed of three sets of edge dislocation aligned along the ²110: direction with the Burgers vectors of the type 1 ²112:.The spacing between dislocation line can 2 also be calculated using Eq. Ž6. S D s 19.45 nm
A HREM image of the NiAlrCrŽMo. Ž110. interface region viewed along the w111x direction is shown in Fig. 2. The image shows an abrupt transition from NiAl to CrŽMo. lattice with no transition layer. The interface dislocations that array periodically are clearly visible in the image. The average spacing of interface dislocations was measured to be 14.13 nm. As shown in Fig. 3, the core-like feature of the interface dislocations indicated clearly that the halfplane of dislocation is present at the elastically softer NiAl side and the dislocation line is parallel to the electron beam, i.e. the w111x direction. The strain field of the dislocation appears to be largely limited to the NiAl side of the interface. An attempt was made to determine the Burgers vectors of these misfit dislocations. A Burgers circuit was drawn across the interface encircling the dislocation core. From the Burgers circuit, it can be seen that the Burgers vector was 13 ²112:, which is a Burgers vector of partial dislocation. 4.2. (111) interface Fig. 4 shows a Bright Field TEM image taken with a small tilt away from the ²111: direction. An
Fig. 2. HREM image viewed along the w111x common direction, which shows that misfit dislocations array periodically at the interface.
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
189
Fig. 5. HREM image viewed along the w110x common direction, indicating that the line direction of misfit dislocations at Ž111. is w110x. Fig. 3. HREM image showing the core-like feature of the misfit dislocation.
array consisting of three sets of dislocations is present at the Ž111. interface. Fig. 5 is a lattice image of NiAl–CrŽMo. viewed along the w110x common direction. The angle between the interface and the Ž110. plane of NiAl is measured to be 358, which is the angle between Ž111. and Ž110. of NiAl. Therefore, it is reasonable to conclude that the interface plane is the common Ž111. planes of both NiAl and CrŽMo.. The line direction of dislocation in the Ž111. interface is ²110:. Since the point-to-point resolution of
Fig. 4. Bright Field TEM image taken with a small tilt away from the ²111: direction, which shows three sets of misfit dislocations present at the 1114 interface between NiAl and CrŽMo..
JEM2010 high resolution electron microscope is 0.19 nm, it was unable to resolve the 2004 spacing of NiAl and CrŽMo. crystals. An attempt to determine the Burgers vector of the dislocations in the Ž111. interface by HREM had failed. The measured spacing between dislocations has as an average of 18.4 nm. 4.3. Discussion NiAl is a B 2-ordered structure and CrŽMo. is a bcc structure, having high symmetry, respectively. Experimental results indicated that there is a consistent orientation relationship between the NiAl and CrŽMo. phases, which indicated that the Ž111. and Ž110. interfaces between NiAl and CrŽMo. should be of low energy, therefore, it is suitable to apply the CSLrDSC theory to their interfaces. For the Ž110. interface, the expected Burgers vector is of the 13 ²112: type, which is a Burgers vector of partial dislocation. By calculation and observation, no interfacial stacking fault is present in the Ž110. interface. Therefore, 13 ²112: should be a projection of a Burgers vector of complete dislocation, which should be ²001:. The dislocation with the Burgers vector of ²001: was stable in the NiAl crystal. Cline et al. w6x and Chen et al. w7x found that the Burgers vector of the interface dislocation in the NiAl–Cr interface was of the ²001: type. The line
190
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
direction of the interface dislocation, i.e. ²111:, was not perpendicular to ²001:, indicating that the misfit dislocations in the Ž110. interface were of mixed type. The Burger vector of w001x is in the Ž110. plane, so that the slip plane of the interface dislocations is Ž110.. The projection of ²001: to ²112: is 1 ²1 2:, which can accommodate the misfit in the 3 Ž110. interface if the average spacing of the dislocations is 12.97 nm. The measured spacing of dislocations in the Ž110. interface is 14.13 nm, which is systematically larger by about 8.5% than the geometrical spacing, indicating that there is a residual strain remaining at the interface. Similar observations have been made in many metal–ceramic systems w8,9x. For the Ž111. interface, the geometric expectation indicated that the Burgers vector of the dislocations is 12 ²112:. However, there was no interfacial stacking fault observed and expected by the CSLrDSC lattice model, so that it is reasonable to take 1 ²112: as a projection of a Burgers vector of 2 complete dislocation, which should be ²101:; in this case, interface dislocations in Ž111. are 608 mixed dislocations with slip plane Ž111.. The projection of the Burgers vectors ²101: to the ²112: direction is 1 ²112:, which can compensate the misfit in the 2 1114 interface. The measured spacing between dislocations is 18.4 nm, which is shorter by about 5.7% than the geometric spacing. This discrepancy was due to the small tilt away from the ²111: direction when the BF image was taken. The actual spacing of dislocations should be at least the same as the geometric result, i.e. 19.45 nm. A lot of experimental studies w10–12x have been conducted on misfit dislocations in low-indexed interfaces between metal and oxides with mutually parallel f.c.c lattices. Most of these studies concern the 1004 and 1114 interfaces. The experimental observations on the 1004 interface often conform to the prediction of the O-lattice theory. However, observations on the 1114 interface differed from system to system. The formation of partial rather than complete dislocations in the 1114 interface was observed in Cu–MnO by HREM w13x viewed along the w011x direction and stacking fault was present between partial dislocations. Mixed dislocations were also observed on the Ž0110.Al 2 O 3 5 Ž112. Nb interface in Al 2 O 3 –Nb w14x. An array consisting of two types of mixed dislocations with Burgers vectors 12 w111x, 12
w11 1x and line direction w111x was present, which, to some extent, was similar to our experimental results. The observed configuration, line direction and spacing of dislocations at the Ž110. and Ž111. interfaces in NiAl–CrŽMo. was in generally good agreement with the theoretical prediction by the CSLrDSC lattice model, with some differences with respect to the detailed structure. The CSLrDSC lattice model has some relevance for the misfit dislocation network forming in the highly symmetric NiAl–CrŽMo. interfaces.
5. Conclusion The dislocation structure at the NiAl–CrŽMo. interfaces has been studied by HREM and theoretical calculation based on the CSLrDSC lattice model. The observations have been made at the Ž110. and Ž111. cube-on-cube interfaces, both of which were partially coherent. The dislocation configuration, line direction and dislocation type were presented and discussed in terms of the CSLrDSC lattice model. The dislocation at the Ž110. interface is of type ²101: mixed dislocation, while the Ž111. interface contains dislocations of 608 mixed type.
Acknowledgements This work was supported by the National Natural Science Foundation of China on Grant Nos. 59831020, 59871055, 59895156 and 59895152.
References w1x E.C. Harvey, J.L. Walter, Metall. Trans. 1 Ž1970. 2907. w2x H.E. Cline, J.L. Walter, E. Lifshin, R.R. Russell, Metall. Trans. 2 Ž1971. 189. w3x J.M. Yang, S.M. Jeng, K. Bain, R.A. Amato, Acta Metall. Mater. 45 Ž1997. 295. w4x W. Mader, Mater. Res. Soc. Symp. Proc. 82 Ž1987. 404. w5x R.W. Balluffi, A. Brokman, A.H. King, Acta Metall. Mater. 30 Ž1982. 1453. w6x H.E. Cline, J.L. Walter, E.F. Koch, L.M. Osika, Acta Metall. Mater. 19 Ž1971. 405.
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191 w7x X.F. Chen, D.R. Johnson, B.F. Oliver, Scripta Metall. 30 Ž1994. 975. w8x D.X. Li, P. Pirouz, A.H. Heuer, Philos. Mag. A 65 Ž1992. 403. w9x P. Lu, F. Cosandey, Acta Metall. Mater. 40 Ž1992. S259. w10x D.X. Li, P. Pirouz, A.H. Heuer, Acta Metall. Mater. 40 Ž1992. S237.
w11x w12x w13x w14x
191
F.S. Shieu, S.L. Sass, Acta Metall. Mater. 38 Ž1990. 1653. W. Mader, M. Ruhle, Acta Metall. Mater. 37 Ž1989. 853. F. Ernst, Mater. Res. Soc. Symp. Proc. 183 Ž1990. 49. V. Vitek, G. Gutekunst, J. Mayer, M. Ruhle, Philos. Mag. A 71 Ž1995. 1219.
Materials Letters 44 Ž2000. 186–191 www.elsevier.comrlocatermatlet
Theoretical and experimental studies of the dislocation structure at the NiAl–Cr žMo/ interfaces Y.X. Chen a,) , C.Y. Cui b, L.L. He a , J.T. Guo b, D.X. Li a a
b
Laboratory of Atomic Imaging of Solids, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China Received 1 July 1999; received in revised form 17 September 1999; accepted 1 November 1999
Abstract The dislocation structure at the NiAlrCrŽMo. interfaces has been studied by high resolution electron microscopy ŽHREM.. The Ž110. and Ž111. cube-on-cube interfaces were examined. Both of the interfaces have been found to be partially coherent. Theoretical calculation of the expected dislocation structure at the interfaces was made based on the CSLrDSC lattice model. The experimental observations and theoretical prediction were shown to be in generally good agreement, with some differences with respect to the detailed structure. q 2000 Elsevier Science B.V. All rights reserved. Keywords: HREM; Dislocation structure; CSLrDSC lattice model; NiAl–CrŽMo. interface
1. Introduction Directionally solidified NiAl–CrŽMo. eutectic alloy had been studied for many years w1,2x and interest was renewed recently w3x for its much higher fracture toughness than that of polycrystalline NiAl. Its microstructure was characterized by a lamellar CrŽMo. phase embedded within the NiAl matrix. However, their interfacial structure was still poorly understood. For metal y oxide systems, it was found that the dislocations were located on the metal side, a few atomic spacing away from the interface w4x. In comparison to NiAl single crystal, there has been relatively few observations on the dislocation structure at the NiAl–CrŽMo. interfaces. In this paper, the dislocation structure at the interfaces was studied by )
Corresponding author. Fax: q86-24-2389-1320.
HREM and the observation was compared to predictions from an analysis based on the CSLrDSC lattice model.
2. Experimental procedure A vacuum induction melted and drop cast ingot of NiAl–28Cr–5.5Mo–0.5Hf Žat.%. was directionally solidified under Ar atmosphere in the Al 2 O 3 –SiO 2 ceramic mold by the standard Bridgman method. The TEM samples were prepared using conventional procedure, including cutting discs perpendicular to the growth direction with a thickness of 0.2 mm, mechanical polishing them to 50 mm thickness, dimpling to 20 mm and finally ion milling. TEM observations were performed with a JEM2010 high resolution electron microscope.
00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 0 . 0 0 0 2 4 - 0
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
187
3. Theoretical description of dislocation structure at the NiAl r Cr(Mo) interfaces In this section, we discuss the expected dislocation structure for two interfaces based on the CSLrDSC lattice model Žsee more details in the literature w5x.. The CSLrDSC lattice model postulates that the structure of a crystal interface is determined by two sets of parameters. The first set is related to the structure and relative orientation of the two crystals neighboring the interface, which determines the O-lattice that is present. The second set of parameters is given by the path of the boundary, i.e. the boundary plane. The dislocation structure of the interface is then given by the intersection of the boundary plane with the O-lattice cell walls, i.e. the Wigner–Seitz cell, with the translation vector attributed to the respective cell wall being the Burgers vector of the dislocation. The coordinates of the O-lattice points X ŽO . are defined by the expression
X ŽO . s Ž IyAy1 .
y1
B
where A is the transformation matrix relating the DSC-1 and DSC-2 lattices, B is the matrix formed by the vectors of the primitive unit of the crystal lattice and I is the unitary matrix. The first step to obtain the O-lattice is to find the transformation matrix A. The CrŽMo. phase is a solid solution with the bcc structure, the lattice parameter can be determined by the work of Cline et al. w6x, which indicated that when the level of Mo is 5.5 at.%, the lattice parameter of CrŽMo. is 0.2942 nm. NiAl has B 2-ordered crystal structure with lattice parameter 0.2887 nm. Since the CSLrDSC model is a geometrical model and does not account for energetic aspects, we take NiAl as the bcc structure. In this simple bccrbcc system, the transformation matrix A is an expansion–contraction matrix, which can be written as:
As
ž
1qd 0 0
0 1qd 0
0 0 1qd
Fig. 1. Schematic drawing shows the dislocation structure at Ža. Ž110. Žb. Ž111..
where d is the fractional lattice parameter mismatch between CrŽMo. and NiAl, defined by
ds
2 Ž a1 y a 2 .
Ž 2.
a1 q a2
with a 1 and a 2 as the lattice constants of NiAl and CrŽMo.. For the bcc structure, the matrix B can be written as Bs
1 1 1 2 1
1 1 1
1 1 1
0
Ž 3.
Taking CrŽMo. as a reference system, the O-lattice point coordinates are given by
/
Ž 1.
X ŽO . s Ž I y Ay1 .
y1
Bs
1qd
d
B
Ž 4.
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
188
the O-lattice points form a bcc lattice with lattice constant
4. Experimental results and discussion 4.1. (110) interface
aŽ o. s
1qd
d
a2 s 15.89 nm
Ž 5.
The dislocation networks for either Ž111. or Ž110. are obtained by the intersection of the boundary plane with the Wigner–Seitz cell walls of the bcc O-lattice. The resulting dislocation structures of the Ž111. and Ž110. interfaces are shown in Fig. 1a and 1b, respectively. The dislocation network of the Ž110. interface is an array of two sets of edge dislocations aligned along the ²111: direction with the Burgers vectors of the type 13 ²112:.The spacing between dislocation lines is given by
SD s
1qd
d
< b < s 12.97 nm
Ž 6.
The dislocation network of Ž111. is composed of three sets of edge dislocation aligned along the ²110: direction with the Burgers vectors of the type 1 ²112:.The spacing between dislocation line can 2 also be calculated using Eq. Ž6. S D s 19.45 nm
A HREM image of the NiAlrCrŽMo. Ž110. interface region viewed along the w111x direction is shown in Fig. 2. The image shows an abrupt transition from NiAl to CrŽMo. lattice with no transition layer. The interface dislocations that array periodically are clearly visible in the image. The average spacing of interface dislocations was measured to be 14.13 nm. As shown in Fig. 3, the core-like feature of the interface dislocations indicated clearly that the halfplane of dislocation is present at the elastically softer NiAl side and the dislocation line is parallel to the electron beam, i.e. the w111x direction. The strain field of the dislocation appears to be largely limited to the NiAl side of the interface. An attempt was made to determine the Burgers vectors of these misfit dislocations. A Burgers circuit was drawn across the interface encircling the dislocation core. From the Burgers circuit, it can be seen that the Burgers vector was 13 ²112:, which is a Burgers vector of partial dislocation. 4.2. (111) interface Fig. 4 shows a Bright Field TEM image taken with a small tilt away from the ²111: direction. An
Fig. 2. HREM image viewed along the w111x common direction, which shows that misfit dislocations array periodically at the interface.
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
189
Fig. 5. HREM image viewed along the w110x common direction, indicating that the line direction of misfit dislocations at Ž111. is w110x. Fig. 3. HREM image showing the core-like feature of the misfit dislocation.
array consisting of three sets of dislocations is present at the Ž111. interface. Fig. 5 is a lattice image of NiAl–CrŽMo. viewed along the w110x common direction. The angle between the interface and the Ž110. plane of NiAl is measured to be 358, which is the angle between Ž111. and Ž110. of NiAl. Therefore, it is reasonable to conclude that the interface plane is the common Ž111. planes of both NiAl and CrŽMo.. The line direction of dislocation in the Ž111. interface is ²110:. Since the point-to-point resolution of
Fig. 4. Bright Field TEM image taken with a small tilt away from the ²111: direction, which shows three sets of misfit dislocations present at the 1114 interface between NiAl and CrŽMo..
JEM2010 high resolution electron microscope is 0.19 nm, it was unable to resolve the 2004 spacing of NiAl and CrŽMo. crystals. An attempt to determine the Burgers vector of the dislocations in the Ž111. interface by HREM had failed. The measured spacing between dislocations has as an average of 18.4 nm. 4.3. Discussion NiAl is a B 2-ordered structure and CrŽMo. is a bcc structure, having high symmetry, respectively. Experimental results indicated that there is a consistent orientation relationship between the NiAl and CrŽMo. phases, which indicated that the Ž111. and Ž110. interfaces between NiAl and CrŽMo. should be of low energy, therefore, it is suitable to apply the CSLrDSC theory to their interfaces. For the Ž110. interface, the expected Burgers vector is of the 13 ²112: type, which is a Burgers vector of partial dislocation. By calculation and observation, no interfacial stacking fault is present in the Ž110. interface. Therefore, 13 ²112: should be a projection of a Burgers vector of complete dislocation, which should be ²001:. The dislocation with the Burgers vector of ²001: was stable in the NiAl crystal. Cline et al. w6x and Chen et al. w7x found that the Burgers vector of the interface dislocation in the NiAl–Cr interface was of the ²001: type. The line
190
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191
direction of the interface dislocation, i.e. ²111:, was not perpendicular to ²001:, indicating that the misfit dislocations in the Ž110. interface were of mixed type. The Burger vector of w001x is in the Ž110. plane, so that the slip plane of the interface dislocations is Ž110.. The projection of ²001: to ²112: is 1 ²1 2:, which can accommodate the misfit in the 3 Ž110. interface if the average spacing of the dislocations is 12.97 nm. The measured spacing of dislocations in the Ž110. interface is 14.13 nm, which is systematically larger by about 8.5% than the geometrical spacing, indicating that there is a residual strain remaining at the interface. Similar observations have been made in many metal–ceramic systems w8,9x. For the Ž111. interface, the geometric expectation indicated that the Burgers vector of the dislocations is 12 ²112:. However, there was no interfacial stacking fault observed and expected by the CSLrDSC lattice model, so that it is reasonable to take 1 ²112: as a projection of a Burgers vector of 2 complete dislocation, which should be ²101:; in this case, interface dislocations in Ž111. are 608 mixed dislocations with slip plane Ž111.. The projection of the Burgers vectors ²101: to the ²112: direction is 1 ²112:, which can compensate the misfit in the 2 1114 interface. The measured spacing between dislocations is 18.4 nm, which is shorter by about 5.7% than the geometric spacing. This discrepancy was due to the small tilt away from the ²111: direction when the BF image was taken. The actual spacing of dislocations should be at least the same as the geometric result, i.e. 19.45 nm. A lot of experimental studies w10–12x have been conducted on misfit dislocations in low-indexed interfaces between metal and oxides with mutually parallel f.c.c lattices. Most of these studies concern the 1004 and 1114 interfaces. The experimental observations on the 1004 interface often conform to the prediction of the O-lattice theory. However, observations on the 1114 interface differed from system to system. The formation of partial rather than complete dislocations in the 1114 interface was observed in Cu–MnO by HREM w13x viewed along the w011x direction and stacking fault was present between partial dislocations. Mixed dislocations were also observed on the Ž0110.Al 2 O 3 5 Ž112. Nb interface in Al 2 O 3 –Nb w14x. An array consisting of two types of mixed dislocations with Burgers vectors 12 w111x, 12
w11 1x and line direction w111x was present, which, to some extent, was similar to our experimental results. The observed configuration, line direction and spacing of dislocations at the Ž110. and Ž111. interfaces in NiAl–CrŽMo. was in generally good agreement with the theoretical prediction by the CSLrDSC lattice model, with some differences with respect to the detailed structure. The CSLrDSC lattice model has some relevance for the misfit dislocation network forming in the highly symmetric NiAl–CrŽMo. interfaces.
5. Conclusion The dislocation structure at the NiAl–CrŽMo. interfaces has been studied by HREM and theoretical calculation based on the CSLrDSC lattice model. The observations have been made at the Ž110. and Ž111. cube-on-cube interfaces, both of which were partially coherent. The dislocation configuration, line direction and dislocation type were presented and discussed in terms of the CSLrDSC lattice model. The dislocation at the Ž110. interface is of type ²101: mixed dislocation, while the Ž111. interface contains dislocations of 608 mixed type.
Acknowledgements This work was supported by the National Natural Science Foundation of China on Grant Nos. 59831020, 59871055, 59895156 and 59895152.
References w1x E.C. Harvey, J.L. Walter, Metall. Trans. 1 Ž1970. 2907. w2x H.E. Cline, J.L. Walter, E. Lifshin, R.R. Russell, Metall. Trans. 2 Ž1971. 189. w3x J.M. Yang, S.M. Jeng, K. Bain, R.A. Amato, Acta Metall. Mater. 45 Ž1997. 295. w4x W. Mader, Mater. Res. Soc. Symp. Proc. 82 Ž1987. 404. w5x R.W. Balluffi, A. Brokman, A.H. King, Acta Metall. Mater. 30 Ž1982. 1453. w6x H.E. Cline, J.L. Walter, E.F. Koch, L.M. Osika, Acta Metall. Mater. 19 Ž1971. 405.
Y.X. Chen et al.r Materials Letters 44 (2000) 186–191 w7x X.F. Chen, D.R. Johnson, B.F. Oliver, Scripta Metall. 30 Ž1994. 975. w8x D.X. Li, P. Pirouz, A.H. Heuer, Philos. Mag. A 65 Ž1992. 403. w9x P. Lu, F. Cosandey, Acta Metall. Mater. 40 Ž1992. S259. w10x D.X. Li, P. Pirouz, A.H. Heuer, Acta Metall. Mater. 40 Ž1992. S237.
w11x w12x w13x w14x
191
F.S. Shieu, S.L. Sass, Acta Metall. Mater. 38 Ž1990. 1653. W. Mader, M. Ruhle, Acta Metall. Mater. 37 Ž1989. 853. F. Ernst, Mater. Res. Soc. Symp. Proc. 183 Ž1990. 49. V. Vitek, G. Gutekunst, J. Mayer, M. Ruhle, Philos. Mag. A 71 Ž1995. 1219.