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Dislocation structures at CuMgO and PdMgO interfaces
Vol. 40, Suppl.,pp. $259-$266, 1992 Printed in Great Britain.All fights reserved
0956-7151/92 $5.00+ 0.00 Copyright © 1992Pergamon Press Lid
Acta metall, mater.
DISLOCATION STRUCTURES AT Cu-MgO AND Pd-MgO INTERFACES P. LU and F. COSANDEY Department of Mechanics and Materials Science, Rutgers University, Piscataway, NJ 08855, U.S.A. Al~raet--The dislocation structures at Cu and Pd-MgO interfaces have been studied by high-resolution and weak beam electron microscopy. The metal-oxide interfaces were formed by internal oxidation of Cu-lwt%Mg and Pd-lwt%Mg alloys. The observations have been made at (111), (100) cube-on-cube and (111) twin interfaces. All interfaces have been found to be partially coherent despite the large misfit of 14.2 and 7.6% for Cu- and Pd-MgO systems, respectively. The dislocation configuration, network periodicity and dislocation type are presented and discussed in terms of the geometrical DSC-CSL lattice model. On 6tudie les structures de dislocations aux interfaces Cu/ et Pd/MgO par microscopic 61ectrenique en haute rtsolution et par microscopie 61ectronique en faisceau faible. Les interfaces m~tal-oxyde sont form~es par oxydation interne d'alliagesCu-Mg ~ 1% en poids et Pd-Mg fi 1% en poids. Les observations ont 6t~ faites sur des interfaces (111), cube-cube (100) et des interfaces maclbys (111). Toutes les interfaces sont trouvb~s partiellement coh~rentes malgr~ le grand d~saccord de 14,2 et 7,6%, respectivement pour les syst~es Cu/et Pd/MgO. La configuration de dislocations, la pbiodicit~ du r~seau et le type de dislocations sont presentts et discutts d'apr~s le module gtomttrique du rtseau DSC/CSL. Zummmeafumag---Die Versetzungsstrukturen tier Grenzflichen Cu/MgO und Pd/MgO werden elektronenmikroskopisch mit hochaufl6sender und weak-beam-Abbildung studiert. Die Grenzfldchen werden mit innerer Oxidation tier Legierungen Cu-lGew.%Mg und Pd-lC-ew.%Mg hergestellt. Beobachtungen werden an (111)-, (100)-kubisch/kubischen und (lll)-Zwilfings-Grenzfl~hen durchgeffthrt. S~mtliche Grenzt~chen sind trotz tier groBen Fehipassung (12,4% bei Cu, 7,6% bei Pd) teilkoh~irent. Versetzungsanordnung, Periodizitit des Netzwerkes and Versetzungstypen werden erl~utert und diskutiert anhand des geometrischen DCS/CSL-Gitter-Modells.
1. INTRODUCTION In view of the complex nature of atomic interactions between metals and oxides, our understanding of their interracial structures is still poorly understood. In recent years, there has been considerable interest from both theoretical and experimental points of view [I]. High-resolution electron microscopy (HREM) has played a major role in these new developments as it is now possible to determine the structure down to the atomic level. Under favorable experimental conditions both the atomic structure and interfacial chemistry can be obtained by H R E M [2]. A notable example is the determination in A g - C d O system of O termination at the polar (111) CdO interface [3]. In addition to chemistry and atomic structure, interracial coherency is of great interest since the presence of misfit dislocations might be indicative of the relative bond strength at the interface. For metal-oxide systems, it is also often found that the dislocations are located in the metal side a few atomic spacings away from the interface [4]. In comparison to metal or oxide grain boundaries there has been relatively few observations on the dislocation structure at metal--oxide interfaces. At the present time the
only systematic study was done for the Pt-NiO system [5]. In a recent study [6], we presented preliminary observations on the structure of Cu and Pd-MgO interfaces produced by internal oxidation. These two metal systems Cu and Pd were selected because of their large misfit of 14.2 and 7.6% with respect to MgO respectively. For the Cu-MgO system, the MgO particles were found to possess primarily (111) facets while both (100) and (111) facets have been observed for Pd-MgO system. In addition, platefike shaped MgO particles have been observed in Pd with a twin orientation relationship with respect to the Pd matrix and with their two broad faces parallel to (111) planes. All interfaces were found to be partially coherent but a detailed analysis of the misfit dislocation configurations was not presented. In this paper we present an analysis of the dislocation structures observed at (111) Cu-MgO, (111), (100) and (111) twin Pd-MgO interfaces. The dislocation configurations are analyzed in terms of the CSL-DSC formalism [7-10] which is presented first in Section 3. In Section 4 we present experimental observations by combined H R E M and weak beam imaging techniques, which is followed in Section 5 by a general discussion.
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LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES 2. EXPERIMENTAL
Alloys of Pd-lwt%Mg and C u - l w t % M g were prepared at AMES Lab Materials Preparation Center in Iowa, in a non-consumable arc melting furnace under an ultra high purity argon atmosphere, and subsequently cold rolled into a ~ 1 mm thick sheet. The Pd-Mg alloy was then oxidized in air at a temperature of 1025°C for ~ 8 days. After oxidation the sample was subsequently annealed in a vacuum pressure of ~10-Ttorr at temperature of ~800, ~600 and ~400°C for 30, 60 and 120h respectively and then slowly cooled down to room temperature. The Cu-Mg alloy was internally oxidized at 1000°C for ~ 3 h in a mixture of Cu20 and Cu powders sealed in an evacuated quartz tube. After oxidation the samples were annealed at ~700°C for 24h in a vacuum of ~10 -7 torr and then slowly cooled down to room temperature. The role of the vacuum annealing was to equilibrate the structure, which was also found to increase interface flatness. Slow cooling was used in order to reduce strain due to differential thermal contraction of the metal and MgO. TEM specimens were prepared by cutting 3 mm discs, followed by grinding, dimpling and ion thinning to perforation. To reduce ion milling damage, the samples were always lightly ion milled in a cold stage using a low current and energy ion beam just prior to observations. The electron microscope used for the observations was an ISI-002B, which has a spherical aberration coefficient (Cs) of 0.4 mm and a point to point resolution of about 0.18 nm when operated at 200keV. All high resolution images were taken along the common (110~ directions using axial illumination. The crystal thickness varied considerably from area to area and between the oxide and metal because of preferential thinning. For high resolution imaging, the optimum thickness was in the range of 4-10nm, defocus values were chosen such that white dots in the images represented the atomic column positions and were often in a range of - 4 0 to - 6 0 nm. Weak beam images were taken using g/3g criteria with Sg > 2 x 10-3(l/nm). 3. GEOMETRICAL DESCRIPTION OF INTERFACIAL DISLOCATIONS In this section we first discuss the expected dislocation structures for the three interfaces based on the general CSL-DSC lattice model [7, 8]. Here only the salient features of the CSL-DSC model pertinent to our interfaces will be presented and we will refer to excellent review articles for further details [10].
3.1. CSL/DSC model The CSL/DSC lattice model [7, 8] is based on the premise that a grain boundary or an interface between dissimilar materials is of low energy
whenever the two adjoining crystal lattices forming the interface are at a misorientation corresponding to a relatively high density of coincidence lattice sites (CSL). When the two crystal deviate from the relatively dense CSL misorientation, a network of the grain boundary dislocations (GBDs) is introduced. The relaxed interface then consists of GBD dislocations separating regions of low energy CSL structure. The Burgers vectors of the GBDs are defined by the vectors of the DSC lattice while the dislocation density and configuration are defined by the O-lattice [8]. For a general boundary the CSL and DSC lattices are constructed according to the following three steps [10]: (1) A pair of cells, Mi and M2, in the strain-free lattice 1 and 2, respectively, are defined which almost match each other in shape and size. (2) The DSC-1 and DSC-2 lattices for lattice 1 and 2 respectively are then defined by first finding a transformation matrix A which relates a vector defining M~ to a vector defining M2 so that XM2ffiAX ~'. Two new lattices 2' and 1' are then defined by X 2"= A - I X 2 and X I' = A X I respectively. The lattice 1 and lattice 2' then form a DSC-1 lattice while lattice 2 and lattice 1' form the DSC-2 lattice. (3) The interface is then produced by cutting a face from lattice 1 and lattice 2 along the desired boundary plane and by joining them together rigidly. If the structure is allowed to relax, a regular array of GBDs is introduced at the interface which possess Burgers vector corresponding to vectors of the average DSC lattice. The configuration and density of these GBDs is defined by the O-lattice produced by the unrelaxed DSC-1 and DSC-2 lattices [8]. The coordinates of the O-lattice points X (°) are defined by the expression X (°) ffi (I - T - 1 ) - l
B
(1)
where B is the matrix of the Burgers vectors of the average DSC lattice and T is the transformation matrix relating DSC-1 and DSC-2 lattices. Atomic relaxation leading to localized dislocations will occur between the O-lattice points. For a given interface plane, the network follows the two dimensional Wigner-Seitz cell drawn around the O-lattice points. 3.1.1. (100) and (11I) interfaces. For the (100) and (111) interfaces the M l and Me cells are simply the crystal lattice cells with each DSC lattice being identical to each crystal lattice. The dislocation content is found by determining the O-lattice formed by lattices 1 and 2. The transformation matrix T between the DSC-I and DSC-2 lattice, is the expansion-contraction matrix E. The DSC Burgers vectors are the lattice vectors for the f.c.c, structure.
LU and COSANDEY:
DISLOCATION STRUCTURES AT INTERFACES
Taking Pd as reference system, the O-lattice points coordinates are given by X (0) = ( I - - E - I ) -
S261
a
~[11o]
IB
~hb- [T10]
I
where 6 is the lattice mismatch between Pd and MgO defined by ---- ( a 2 - - a l ) / a 2
•
~--~
I
(3)
with al and a2 the lattice constants of Pd and MgO respectively. B is the matrix formed by the vectors of the primitive ~nit of the f.c.c, structure. The O-lattice points form a f.c.c, lattice with lattice constant
1
~
b-~[TlO]
The dislocation structures for either (100) or (111) are obtained by the intersection of the boundary plane with the Wigner-Seitz cell walls of the f.c.c. O-lattice. The resulting dislocation structures of the (001) and (111) interfaces are shown in Fig. l(a) and l(b) respectively. The dislocation network of (001) interface is a square array of edge dislocations aligned along (110) directions with Burgers vectors of the type a/2(110). The spacing between dislocation lines is given by
Sd=(~)lbl.
b- ~[110]
oT]
[2~] 1
--
b--~ [121]
1
b-~- [~11]
(5)
The dislocation network of (111) interface has a hexagonal symmetry with edge dislocations aligned along (112) directions and with Burgers vector of the type a/2(l10). The spacing between the dislocation lines can also be calculated using equation (5). £1.2. (111) Twin interface. For the (111) twin interface the M I and M 2 cells, which are chosen as the crystal lattice cells, are related by the transformation matrix A = RE, where R is the 60 ° rotation matrix about the normal to the (111) twin plane. The DSC-I and DSC-2 lattices are now the DSC lattices of the 2;3 misorientation for Pd and MgO respectively. A basic set of three independent DSC Burgers vectors can be written as
[110]
[T01]
Fig. 1. Schematic drawings show dislocation structures of: (a) (001), (b) (111) and (c) (II1) twin interfaces. The O-lattice for this twin orientation has a hexagonal structure with lattice constants of a = (1/~)lbll and c = (1/6)1b3l • For the (111) twin interface the two basic vectors of the O-lattice are (1/6)bl and (1/6)b2 respectively. The resulting dislocation structure shown in Fig. 1(c) is a hexagonal network with b = a / 6 ( 1 1 2 ) edge dislocations laying along the 110) directions. The spacing between the dislocation lines is given by equation (5) with b ffi a/6(112).
B r = (bl, b2, b3) = ~
1 -
(6)
1
where b~, b2 and b3 are the vectors of primitive unit cell of the DSC lattice for 2;3 twin misorientation [7]. The dislocation content is found by determining the O-lattice formed by the DSC-1 and DSC-2 lattices. Since the two DSC lattices are also related by the expansion matrix E, the O-lattice points are now given by X (°) = (I - E - ' ) - I B
r
A property of these DSC dislocations is to shift the origin of the CSL giving rise to steps in the boundary plane [11]. The step height associated with DSC dislocations can be determined by geometrical construction in the frame work of the CSL/DSC lattice [12]. In this formalism the step height is given by S = s~a where n is the boundary normal joining crystal 1 to crystal 2 and s~ the step vector of crystal joining an old coincidence to the new one produced by the translation associated with the interracial dislocation of Burgers vector b. This construction is shown in Fig. 2 which depicts the CSL and DSC lattices for the 2; = 3 interface. The step vector s~ and s: refer to crystal 1 and crystal 2 respectively. The
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LU and COSANDEY:
DISLOCATION STRUCTURES AT INTERFACES
dislocation Burgers vector and step vectors are related by b=st-s2. For the example presented in Fig. 2, the step height associated with b = a/6 [11~] is equal to one (111) lattice spacing. A dislocation of opposite Burgers vectors gives rise to step height corresponding to two (111) interplanar spacings. A similar step height can also be produced by combining a pure CSL step [i.e. 3 (111) spacings] with a dislocation step of opposite direction. In order to accommodate the interfacial dislocations with Burgers vector a/6<112> the interface must be stepped up and down. Considering the hexagonal network depicted in Fig. l(c), the structure shown in Fig. 3(a) is obtained for the interface, in which 0 is the average boundary plane position while at + 1 and - 1 the boundary plane is moved up and down one (111) atomic plane respectively. It can be seen that both the up and down steps are required in order to conserve the average plane of the boundary and the double steps are created at every three dislocations. The energies associated with each dislocation segment are not equivalent and it is expected that the energy associated with the double step is larger than that of the single step. This can be understood if the total dislocation energy is separated into its core, elastic and step energies [12]. Since all the dislocations have the same Burgers vector and therefore the same core and elastic energies, the energy increase can be approximated by the variation in grain boundary energy associated with the difference in step area. With respect to the stability of the dislocation configuration shown in Fig. 3(a) the energy of this interface can be lowered if the dislocation segments containing the double steps are eliminated giving rise to the dislocation network shown in Fig. 3(b). For this configuration the total dislocation line length and interface symmetry remain unchanged. 4. RESULTS
4.1. (111) Interfaces 4.1.1. Pd-MgO. A H R E M image of Pd-MgO (111) interface viewed along the [1"1"0] common direction is shown in Fig. 4(a). The interface is
Lattice
1
I I
I I
'
~
I
I I
I
I
I
'
'
'
I i
I
I
I l
F
I
I I
J,-+ 'l
I
I I
F-,#_
--",-~-,'-',"-,--,'-@",--r'~-,'-2 i , I I I I I I * , * I
Lattice
(3-~.:-t'3
|
I
I
I i
I I
......
I
I
I
i
I
I i
I I
I
I
I
I
I I
I l
- ~ - ' t - - I - "~- . . . . . I !
i I
I
I
I
I
I
I
I
I
I I
I i
I
~ - -I- - i- -J~ - I I
I I
Fig. 2. Schematic drawing ofeSL and DSL lattices for twin interface, showing the step vectors associated with the dislocation Burgers vectors of the type 1/6<112).
a -1
•
b
+ 1"~-
+ 1~--1
1
0 +
X~
o +1~-1
,1~-1 0
+ 1 ~
X
"
<110>
o
T
+ X 1
~
<112>
Fig. 3. Dislocation structures for the (111) twin interface: (a) the average interfacial plane position (0) and the stepping interface up (+1) and down (-1) by one (111) interplanar spacing resulting from the dislocation Burgers vectors of the type 1/6<112>; (b) after the double steps ( - 1 to + 1) in (a) are eliminated due to their relatively higher energies.
atomically fiat and without any interphase layer present between the Pd and MgO. In the image the regions where lattice planes fit perfectly across the interface are arrowed. Misfit dislocations are presumably present between these regions of good fit. The core-fike features of the interfacial misfit dislocation can not be observed directly. However, the periodic contrast variation along the interface is visible. The optical diffractogram obtained with the interface region is shown in Fig. 4(b). Using the lattice parameters of I'd or MgO as an internal reference, the periodicity along [ll~J direction measured from the optical diffractogram is ~ 3.3 nm. Assuming that the (111) interface contains the dislocation network shown in Fig. l(b), the network structure, viewed along the [ll'0] direction, has a periodicity of ~/3/2Sd with Sd given by equation (5). For the Pd-MgO system, this periodicity is 3.1 nm, which is reasonably close to what is obtained experimentally. The structure of the dislocation can not be directly resolved in this projection since the dislocations are not viewed edge-on: one set of dislocations is perpendicular to the electron beam and the other two sets are inclined by 30 ° with respect to the electron beam. The contrast variation along the interface is due to the strain field of the dislocation network. The interfacial dislocation structures have also been investigated by weak beam imaging technique using g={220} or {200} reflection. However, the contrast from the misfit dislocation at the interfaces could not be revealed.
LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
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Fig. 4. (a) High-resolution electron micrograph recorded along the common [11"0]direction and (b) optical diffractogram from the interface region, showing the Pd-MgO (111) interface with a characteristic contrast variation along [1121direction due to misfit dislocations.
4.1.2. Cu-MgO. A HREM of the Cu-MgO (111) interface, recorded along the [1"i-0] direction, is shown in Fig. 5(a). The interface is atomically flat over a large area and does not contain any second phase between Cu and MgO. The periodic contrast variation is clearly visible along the interface. The contrast variation observed here is similar to, but much stronger than the one observed for the Pd-MgO {111} interface. An optical diffractogram from the interface is shown in Fig. 5(b). The periodicity of the contrast along [11~ direction measured from the optical diffractogram is found to be 1.68 nm. However, weak beam imaging with either g = {220} or {200} was also not successful to reveal the interfacial dislocation network. In our previous study [6], high-resolution image simulations were done to determine the origin of the contrast. Simulations using models which did not incorporate the misfit dislocation networks at the interface could not reproduce the observed contrast variation. However, a qualitative match between the experimental and simulated images could be achieved by introducing a simple dislocation network model at the interface similar to the one shown in Fig. l(b). The dislocation network in Fig. l(b),
when projected along (110~ direction, has a periodicity of ~/3/2Sd with Sd given by equation (5). For Cu]MgO system, this value is 1.57nm, very close to 1.68nm measured experimentally. The contrast variation observed in the high-resolution images is therefore due to the strain field o f dislocation network. The strong contrast variation is attributed to the very small spacing of the inclined dislocations.
4.2. Pd-MgO {100} interfaces A HREM image of Pd-MgO (001) interface region taken under axial illumination along the common [110] direction is shown in Fig. 6. As for the {111} interfaces, the image shows an abrupt transition from Pd to MgO lattice with no transition layer. The interface is atomically smooth over a large area of about 30 nm, with only very few atomic steps present near the corners where the {001} interface meets with the {111 } interface. The interfacial misfit dislocations are clearly visible in the image. The core-like feature of the dislocations clearly indicates that the dislocation lines are parallel to the electron beam, e.g. [110] direction. The strain field of the dislocation appears to be largely limited to the metal side of the
Fig. 5. (a) High-resolution electron micrograph recorded along the common [iT0] direction and (b) optical diffractogram from the interface region, showing the Cu-M80 (111) interface with a characteristic contrast variation along [117 direction due to misfit dislocations.
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LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
Fig. 6. High-resolution electron micrograph of the Pd-MgO (001) interface recorded along the common [110] direction, showing a periodic dislocation arrays at the interface. interface. The distance between dislocation core has an average value of Sd = 3.83 nm. Weak beam imaging has been used to observe the dislocation structures of the interfaces. Figure 7 shows the image taken with g = {331} for the Pd-MgO(001) interface, which is obtained by tilting the Pd foil about [3~1] axis out of the [110] projection. A periodic contrast of what could be the misfit dislocations is clearly visible. After taking into account the effect of interface inclination with respect to the electron beam, a square network is found, with the lines along two perpendicular <110) directions. Direct measurement from Fig. 7 gave a value of Sd = 3.75 nm for the spacing between the parallel lines. This result is in agreement with the dislocation line spacing measured from Fig. 6. Assuming the Burgers vector of type b =al/2
Fig. 7. Weak beam image with g = {331} showing the dislocation network of the Pd-MgO (001) interface.
4.3. P d - M g O (111) twin interface
The HREM image of the (111) twin interface taken under axial illumination along the [1T0] direction is shown in Fig. 9. Unlike the {111} and {100} interfaces, the (111) twin interface between Pd and the plate-like MgO particle is more complicated and contains a high density of atomic steps. The interfacial steps can be ciearly visible when viewed along the [ 112"] direction. The interracial dislocations are also visible at the steps. The weak beam image of the interface taken with g = [2~[0]is shown in Fig. 10. The image was obtained by tilting the foil 20 ° about [1T0] axis from an initial [11~] zone axis. After considering the effect of the interface inclination, the network seems to have a hexagonal structure. The network spacing changes slightly from one area to other, with an average value of about ~2.26 nm measured from two parallel lines in the image.
Fig. 8. Highly magnified high-resolution electron micr¢~ graph of the Pd-MgO (001) recorded along the common [110] direction, showing the core structure of the inteffacial misfit dislocations. Note the dislocation cores located o n e (001) Pd lattice spacing away from the interface.
LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
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Fig. 9. High-resolution electron micrograph of the Pd-MgO (111) twin interface recorded along the common [frO] direction. Note the high density atomic steps visible at the interface. A highly magnified image of (111) twin interface taken along [IT0] direction from a very thin area is shown in Fig. l l. The dislocations and atomic steps are clearly visible as indicated in the image. The direct observation of dislocation core indicates that the dislocations are parallel to the (110) direction. Both single and double atomic steps associated with the dislocations are observed. The spacing between the dislocations varies from area to area. The average value measured from the high-resolution image is about 2.28 rim, which is also very close to the 2.1 run, calculated by using Sd=lb[/6 with the Burgers vector b = 1/6(112).
Even for the Cu-MgO system with the largest misfit of 14.2% localized strain has been observed. This is in contrast to results on the structure of Ag-CdO [3] and Cu-Ai203 [13] interface having misfit of 13 and 9.2% respectively, which have been found to be incoherent. At the present time it is not clear what criteria govern inteffacial coherency. From these results it is evident that the presence of misfit dislocations can not be uniquely predicted by geometrical criteria based on the magnitude of the misfit and that other factors associated with interfacial chemistry and atomic bond strength might be important. The measured dislocation spacings for (100) and (111) interfaces was systematically larger by about
5. DISCUSSION The results presented in section 4 indicate that all three interfaces (100), (111) and (111) twin are partially coherent and contain misfit dislocations.
Fig. 10. Weak beam image with g={220} showing the dislocation network of the Pd-MgO (111) twin interface. AMM 40/S--R
Fig. 11. Highly magnified high-resolution electron micrograph of the Pd-MgO (111) twin interface recorded along the common [ITO] direction. Note both single and double atomic steps and dislocations associated with the steps.
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LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
3-5% than the geometrical spacings, indicating that there is some residual strain remaining at the interface. Similar observations have been madeTor Nb-AI203 [4] and the Pt-NiO [5] interface. Another common observation for most metal-oxide interfaces is that the misfit dislocations cores are located in the metal side away from the interface, This "stand off" distance varies from systems to systems ranging from 1 to 3 interplanar spacings [4, 5, 14]. For the (100) Pd-MgO interface, the observed square dislocation network agrees with the geometrical prediction presented in Section 3. For the (111) Pd-MgO and Cu-MgO interfaces the observed strain contrast agrees with the expected model based on a hexagonal configuration. Since we have not been able to observe the dislocation network directly by weak beam microscopy, we do not know whether interfacial dislocations can interact or dissociate into partials to form extended nodes. Such dissociations have been observed to occur in (111) lattice misfit [15] or low angle (111) twist boundaries [16]. These dissociation reactions do not change the overall network periodicity or interface symmetry but give rise to a more complex dislocation arrangement. Such reactions could explain why we have not been able to observe inteffacial dislocations at (111) interfaces by weak beam microscopy. Another reason for the failure to detect the dislocations could be due to the octahedral shape of the particles which cause an overlap between the {111} interfaces resulting possible reduction in contrast. In any case, the high resolution images clearly reveal the presence of localized strain associated with interracial misfit dislocations. For the (111) twin interface we have clearly observed by weak beam microscopy the dislocation network and by high resolution imaging the single and double steps associated with the misfit dislocations. The direct visualization of the double step indicates that the dislocation structure corresponds to the configuration shown in Fig. 3(a). An interesting point to note here is that both dislocation configuration shown in Fig. 3(a) and 3Co) have been observed previously. The configuration depicted in Fig. 3(b) was observed for a twist grain boundary in Au deviating slightly from a Z - - 3 misorientation. In another study on interface between NiSi 2 and Si in a B orientation [17], which is geometrically similar to the (111) twin interface described in this study, the dislocation structure shown in Fig. 3(a) was observed. These results indicate that although the geometrical description for twist misfit or lattice misfit interfaces is similar, dislocation reactions and arrangements might be dependent on dislocation nucleation, mobility and the atomic structure of the interface.
6. CONCLUSIONS The dislocation structures at Cu and Pd-MgO interfaces have been studied by combined high resolution and weak beam electron microscopy. The metal--oxide interfaces were formed by internal oxidation of Cu--lwt%Mg and P d - l w t % M g alloys. The observations have been made at (ll l), (I00) cube-on-cube and (II!) twin interfaces. All interfaces have been found to be partiallycoherent despite the large misfitof 14.2 and 7.6% for C u - M g O and P d - M g O respectively.The dislocationconfiguration, network periodicity and dislocation type are presented and discussed in terms of the geometrical D S C / C S L lattice model. The dislocations at the (III) and (100) interfacesare of the type a/2000) while the (II I) twin interface contains dislocations of the type a/6(112) which are associatedwith both single and double steps. work is supported by the Materials Research Group Program Division of the National Science Foundation under Grant No. NSF-MRG89-07553. Thanks are due to the Center for Ceramic Research at Rutgers University for the use of the High Resolution Electron Microscope Facility. .4cknowledgements--This
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0956-7151/92 $5.00+ 0.00 Copyright © 1992Pergamon Press Lid
Acta metall, mater.
DISLOCATION STRUCTURES AT Cu-MgO AND Pd-MgO INTERFACES P. LU and F. COSANDEY Department of Mechanics and Materials Science, Rutgers University, Piscataway, NJ 08855, U.S.A. Al~raet--The dislocation structures at Cu and Pd-MgO interfaces have been studied by high-resolution and weak beam electron microscopy. The metal-oxide interfaces were formed by internal oxidation of Cu-lwt%Mg and Pd-lwt%Mg alloys. The observations have been made at (111), (100) cube-on-cube and (111) twin interfaces. All interfaces have been found to be partially coherent despite the large misfit of 14.2 and 7.6% for Cu- and Pd-MgO systems, respectively. The dislocation configuration, network periodicity and dislocation type are presented and discussed in terms of the geometrical DSC-CSL lattice model. On 6tudie les structures de dislocations aux interfaces Cu/ et Pd/MgO par microscopic 61ectrenique en haute rtsolution et par microscopie 61ectronique en faisceau faible. Les interfaces m~tal-oxyde sont form~es par oxydation interne d'alliagesCu-Mg ~ 1% en poids et Pd-Mg fi 1% en poids. Les observations ont 6t~ faites sur des interfaces (111), cube-cube (100) et des interfaces maclbys (111). Toutes les interfaces sont trouvb~s partiellement coh~rentes malgr~ le grand d~saccord de 14,2 et 7,6%, respectivement pour les syst~es Cu/et Pd/MgO. La configuration de dislocations, la pbiodicit~ du r~seau et le type de dislocations sont presentts et discutts d'apr~s le module gtomttrique du rtseau DSC/CSL. Zummmeafumag---Die Versetzungsstrukturen tier Grenzflichen Cu/MgO und Pd/MgO werden elektronenmikroskopisch mit hochaufl6sender und weak-beam-Abbildung studiert. Die Grenzfldchen werden mit innerer Oxidation tier Legierungen Cu-lGew.%Mg und Pd-lC-ew.%Mg hergestellt. Beobachtungen werden an (111)-, (100)-kubisch/kubischen und (lll)-Zwilfings-Grenzfl~hen durchgeffthrt. S~mtliche Grenzt~chen sind trotz tier groBen Fehipassung (12,4% bei Cu, 7,6% bei Pd) teilkoh~irent. Versetzungsanordnung, Periodizitit des Netzwerkes and Versetzungstypen werden erl~utert und diskutiert anhand des geometrischen DCS/CSL-Gitter-Modells.
1. INTRODUCTION In view of the complex nature of atomic interactions between metals and oxides, our understanding of their interracial structures is still poorly understood. In recent years, there has been considerable interest from both theoretical and experimental points of view [I]. High-resolution electron microscopy (HREM) has played a major role in these new developments as it is now possible to determine the structure down to the atomic level. Under favorable experimental conditions both the atomic structure and interfacial chemistry can be obtained by H R E M [2]. A notable example is the determination in A g - C d O system of O termination at the polar (111) CdO interface [3]. In addition to chemistry and atomic structure, interracial coherency is of great interest since the presence of misfit dislocations might be indicative of the relative bond strength at the interface. For metal-oxide systems, it is also often found that the dislocations are located in the metal side a few atomic spacings away from the interface [4]. In comparison to metal or oxide grain boundaries there has been relatively few observations on the dislocation structure at metal--oxide interfaces. At the present time the
only systematic study was done for the Pt-NiO system [5]. In a recent study [6], we presented preliminary observations on the structure of Cu and Pd-MgO interfaces produced by internal oxidation. These two metal systems Cu and Pd were selected because of their large misfit of 14.2 and 7.6% with respect to MgO respectively. For the Cu-MgO system, the MgO particles were found to possess primarily (111) facets while both (100) and (111) facets have been observed for Pd-MgO system. In addition, platefike shaped MgO particles have been observed in Pd with a twin orientation relationship with respect to the Pd matrix and with their two broad faces parallel to (111) planes. All interfaces were found to be partially coherent but a detailed analysis of the misfit dislocation configurations was not presented. In this paper we present an analysis of the dislocation structures observed at (111) Cu-MgO, (111), (100) and (111) twin Pd-MgO interfaces. The dislocation configurations are analyzed in terms of the CSL-DSC formalism [7-10] which is presented first in Section 3. In Section 4 we present experimental observations by combined H R E M and weak beam imaging techniques, which is followed in Section 5 by a general discussion.
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LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES 2. EXPERIMENTAL
Alloys of Pd-lwt%Mg and C u - l w t % M g were prepared at AMES Lab Materials Preparation Center in Iowa, in a non-consumable arc melting furnace under an ultra high purity argon atmosphere, and subsequently cold rolled into a ~ 1 mm thick sheet. The Pd-Mg alloy was then oxidized in air at a temperature of 1025°C for ~ 8 days. After oxidation the sample was subsequently annealed in a vacuum pressure of ~10-Ttorr at temperature of ~800, ~600 and ~400°C for 30, 60 and 120h respectively and then slowly cooled down to room temperature. The Cu-Mg alloy was internally oxidized at 1000°C for ~ 3 h in a mixture of Cu20 and Cu powders sealed in an evacuated quartz tube. After oxidation the samples were annealed at ~700°C for 24h in a vacuum of ~10 -7 torr and then slowly cooled down to room temperature. The role of the vacuum annealing was to equilibrate the structure, which was also found to increase interface flatness. Slow cooling was used in order to reduce strain due to differential thermal contraction of the metal and MgO. TEM specimens were prepared by cutting 3 mm discs, followed by grinding, dimpling and ion thinning to perforation. To reduce ion milling damage, the samples were always lightly ion milled in a cold stage using a low current and energy ion beam just prior to observations. The electron microscope used for the observations was an ISI-002B, which has a spherical aberration coefficient (Cs) of 0.4 mm and a point to point resolution of about 0.18 nm when operated at 200keV. All high resolution images were taken along the common (110~ directions using axial illumination. The crystal thickness varied considerably from area to area and between the oxide and metal because of preferential thinning. For high resolution imaging, the optimum thickness was in the range of 4-10nm, defocus values were chosen such that white dots in the images represented the atomic column positions and were often in a range of - 4 0 to - 6 0 nm. Weak beam images were taken using g/3g criteria with Sg > 2 x 10-3(l/nm). 3. GEOMETRICAL DESCRIPTION OF INTERFACIAL DISLOCATIONS In this section we first discuss the expected dislocation structures for the three interfaces based on the general CSL-DSC lattice model [7, 8]. Here only the salient features of the CSL-DSC model pertinent to our interfaces will be presented and we will refer to excellent review articles for further details [10].
3.1. CSL/DSC model The CSL/DSC lattice model [7, 8] is based on the premise that a grain boundary or an interface between dissimilar materials is of low energy
whenever the two adjoining crystal lattices forming the interface are at a misorientation corresponding to a relatively high density of coincidence lattice sites (CSL). When the two crystal deviate from the relatively dense CSL misorientation, a network of the grain boundary dislocations (GBDs) is introduced. The relaxed interface then consists of GBD dislocations separating regions of low energy CSL structure. The Burgers vectors of the GBDs are defined by the vectors of the DSC lattice while the dislocation density and configuration are defined by the O-lattice [8]. For a general boundary the CSL and DSC lattices are constructed according to the following three steps [10]: (1) A pair of cells, Mi and M2, in the strain-free lattice 1 and 2, respectively, are defined which almost match each other in shape and size. (2) The DSC-1 and DSC-2 lattices for lattice 1 and 2 respectively are then defined by first finding a transformation matrix A which relates a vector defining M~ to a vector defining M2 so that XM2ffiAX ~'. Two new lattices 2' and 1' are then defined by X 2"= A - I X 2 and X I' = A X I respectively. The lattice 1 and lattice 2' then form a DSC-1 lattice while lattice 2 and lattice 1' form the DSC-2 lattice. (3) The interface is then produced by cutting a face from lattice 1 and lattice 2 along the desired boundary plane and by joining them together rigidly. If the structure is allowed to relax, a regular array of GBDs is introduced at the interface which possess Burgers vector corresponding to vectors of the average DSC lattice. The configuration and density of these GBDs is defined by the O-lattice produced by the unrelaxed DSC-1 and DSC-2 lattices [8]. The coordinates of the O-lattice points X (°) are defined by the expression X (°) ffi (I - T - 1 ) - l
B
(1)
where B is the matrix of the Burgers vectors of the average DSC lattice and T is the transformation matrix relating DSC-1 and DSC-2 lattices. Atomic relaxation leading to localized dislocations will occur between the O-lattice points. For a given interface plane, the network follows the two dimensional Wigner-Seitz cell drawn around the O-lattice points. 3.1.1. (100) and (11I) interfaces. For the (100) and (111) interfaces the M l and Me cells are simply the crystal lattice cells with each DSC lattice being identical to each crystal lattice. The dislocation content is found by determining the O-lattice formed by lattices 1 and 2. The transformation matrix T between the DSC-I and DSC-2 lattice, is the expansion-contraction matrix E. The DSC Burgers vectors are the lattice vectors for the f.c.c, structure.
LU and COSANDEY:
DISLOCATION STRUCTURES AT INTERFACES
Taking Pd as reference system, the O-lattice points coordinates are given by X (0) = ( I - - E - I ) -
S261
a
~[11o]
IB
~hb- [T10]
I
where 6 is the lattice mismatch between Pd and MgO defined by ---- ( a 2 - - a l ) / a 2
•
~--~
I
(3)
with al and a2 the lattice constants of Pd and MgO respectively. B is the matrix formed by the vectors of the primitive ~nit of the f.c.c, structure. The O-lattice points form a f.c.c, lattice with lattice constant
1
~
b-~[TlO]
The dislocation structures for either (100) or (111) are obtained by the intersection of the boundary plane with the Wigner-Seitz cell walls of the f.c.c. O-lattice. The resulting dislocation structures of the (001) and (111) interfaces are shown in Fig. l(a) and l(b) respectively. The dislocation network of (001) interface is a square array of edge dislocations aligned along (110) directions with Burgers vectors of the type a/2(110). The spacing between dislocation lines is given by
Sd=(~)lbl.
b- ~[110]
oT]
[2~] 1
--
b--~ [121]
1
b-~- [~11]
(5)
The dislocation network of (111) interface has a hexagonal symmetry with edge dislocations aligned along (112) directions and with Burgers vector of the type a/2(l10). The spacing between the dislocation lines can also be calculated using equation (5). £1.2. (111) Twin interface. For the (111) twin interface the M I and M 2 cells, which are chosen as the crystal lattice cells, are related by the transformation matrix A = RE, where R is the 60 ° rotation matrix about the normal to the (111) twin plane. The DSC-I and DSC-2 lattices are now the DSC lattices of the 2;3 misorientation for Pd and MgO respectively. A basic set of three independent DSC Burgers vectors can be written as
[110]
[T01]
Fig. 1. Schematic drawings show dislocation structures of: (a) (001), (b) (111) and (c) (II1) twin interfaces. The O-lattice for this twin orientation has a hexagonal structure with lattice constants of a = (1/~)lbll and c = (1/6)1b3l • For the (111) twin interface the two basic vectors of the O-lattice are (1/6)bl and (1/6)b2 respectively. The resulting dislocation structure shown in Fig. 1(c) is a hexagonal network with b = a / 6 ( 1 1 2 ) edge dislocations laying along the 110) directions. The spacing between the dislocation lines is given by equation (5) with b ffi a/6(112).
B r = (bl, b2, b3) = ~
1 -
(6)
1
where b~, b2 and b3 are the vectors of primitive unit cell of the DSC lattice for 2;3 twin misorientation [7]. The dislocation content is found by determining the O-lattice formed by the DSC-1 and DSC-2 lattices. Since the two DSC lattices are also related by the expansion matrix E, the O-lattice points are now given by X (°) = (I - E - ' ) - I B
r
A property of these DSC dislocations is to shift the origin of the CSL giving rise to steps in the boundary plane [11]. The step height associated with DSC dislocations can be determined by geometrical construction in the frame work of the CSL/DSC lattice [12]. In this formalism the step height is given by S = s~a where n is the boundary normal joining crystal 1 to crystal 2 and s~ the step vector of crystal joining an old coincidence to the new one produced by the translation associated with the interracial dislocation of Burgers vector b. This construction is shown in Fig. 2 which depicts the CSL and DSC lattices for the 2; = 3 interface. The step vector s~ and s: refer to crystal 1 and crystal 2 respectively. The
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LU and COSANDEY:
DISLOCATION STRUCTURES AT INTERFACES
dislocation Burgers vector and step vectors are related by b=st-s2. For the example presented in Fig. 2, the step height associated with b = a/6 [11~] is equal to one (111) lattice spacing. A dislocation of opposite Burgers vectors gives rise to step height corresponding to two (111) interplanar spacings. A similar step height can also be produced by combining a pure CSL step [i.e. 3 (111) spacings] with a dislocation step of opposite direction. In order to accommodate the interfacial dislocations with Burgers vector a/6<112> the interface must be stepped up and down. Considering the hexagonal network depicted in Fig. l(c), the structure shown in Fig. 3(a) is obtained for the interface, in which 0 is the average boundary plane position while at + 1 and - 1 the boundary plane is moved up and down one (111) atomic plane respectively. It can be seen that both the up and down steps are required in order to conserve the average plane of the boundary and the double steps are created at every three dislocations. The energies associated with each dislocation segment are not equivalent and it is expected that the energy associated with the double step is larger than that of the single step. This can be understood if the total dislocation energy is separated into its core, elastic and step energies [12]. Since all the dislocations have the same Burgers vector and therefore the same core and elastic energies, the energy increase can be approximated by the variation in grain boundary energy associated with the difference in step area. With respect to the stability of the dislocation configuration shown in Fig. 3(a) the energy of this interface can be lowered if the dislocation segments containing the double steps are eliminated giving rise to the dislocation network shown in Fig. 3(b). For this configuration the total dislocation line length and interface symmetry remain unchanged. 4. RESULTS
4.1. (111) Interfaces 4.1.1. Pd-MgO. A H R E M image of Pd-MgO (111) interface viewed along the [1"1"0] common direction is shown in Fig. 4(a). The interface is
Lattice
1
I I
I I
'
~
I
I I
I
I
I
'
'
'
I i
I
I
I l
F
I
I I
J,-+ 'l
I
I I
F-,#_
--",-~-,'-',"-,--,'-@",--r'~-,'-2 i , I I I I I I * , * I
Lattice
(3-~.:-t'3
|
I
I
I i
I I
......
I
I
I
i
I
I i
I I
I
I
I
I
I I
I l
- ~ - ' t - - I - "~- . . . . . I !
i I
I
I
I
I
I
I
I
I
I I
I i
I
~ - -I- - i- -J~ - I I
I I
Fig. 2. Schematic drawing ofeSL and DSL lattices for twin interface, showing the step vectors associated with the dislocation Burgers vectors of the type 1/6<112).
a -1
•
b
+ 1"~-
+ 1~--1
1
0 +
X~
o +1~-1
,1~-1 0
+ 1 ~
X
"
<110>
o
T
+ X 1
~
<112>
Fig. 3. Dislocation structures for the (111) twin interface: (a) the average interfacial plane position (0) and the stepping interface up (+1) and down (-1) by one (111) interplanar spacing resulting from the dislocation Burgers vectors of the type 1/6<112>; (b) after the double steps ( - 1 to + 1) in (a) are eliminated due to their relatively higher energies.
atomically fiat and without any interphase layer present between the Pd and MgO. In the image the regions where lattice planes fit perfectly across the interface are arrowed. Misfit dislocations are presumably present between these regions of good fit. The core-fike features of the interfacial misfit dislocation can not be observed directly. However, the periodic contrast variation along the interface is visible. The optical diffractogram obtained with the interface region is shown in Fig. 4(b). Using the lattice parameters of I'd or MgO as an internal reference, the periodicity along [ll~J direction measured from the optical diffractogram is ~ 3.3 nm. Assuming that the (111) interface contains the dislocation network shown in Fig. l(b), the network structure, viewed along the [ll'0] direction, has a periodicity of ~/3/2Sd with Sd given by equation (5). For the Pd-MgO system, this periodicity is 3.1 nm, which is reasonably close to what is obtained experimentally. The structure of the dislocation can not be directly resolved in this projection since the dislocations are not viewed edge-on: one set of dislocations is perpendicular to the electron beam and the other two sets are inclined by 30 ° with respect to the electron beam. The contrast variation along the interface is due to the strain field of the dislocation network. The interfacial dislocation structures have also been investigated by weak beam imaging technique using g={220} or {200} reflection. However, the contrast from the misfit dislocation at the interfaces could not be revealed.
LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
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Fig. 4. (a) High-resolution electron micrograph recorded along the common [11"0]direction and (b) optical diffractogram from the interface region, showing the Pd-MgO (111) interface with a characteristic contrast variation along [1121direction due to misfit dislocations.
4.1.2. Cu-MgO. A HREM of the Cu-MgO (111) interface, recorded along the [1"i-0] direction, is shown in Fig. 5(a). The interface is atomically flat over a large area and does not contain any second phase between Cu and MgO. The periodic contrast variation is clearly visible along the interface. The contrast variation observed here is similar to, but much stronger than the one observed for the Pd-MgO {111} interface. An optical diffractogram from the interface is shown in Fig. 5(b). The periodicity of the contrast along [11~ direction measured from the optical diffractogram is found to be 1.68 nm. However, weak beam imaging with either g = {220} or {200} was also not successful to reveal the interfacial dislocation network. In our previous study [6], high-resolution image simulations were done to determine the origin of the contrast. Simulations using models which did not incorporate the misfit dislocation networks at the interface could not reproduce the observed contrast variation. However, a qualitative match between the experimental and simulated images could be achieved by introducing a simple dislocation network model at the interface similar to the one shown in Fig. l(b). The dislocation network in Fig. l(b),
when projected along (110~ direction, has a periodicity of ~/3/2Sd with Sd given by equation (5). For Cu]MgO system, this value is 1.57nm, very close to 1.68nm measured experimentally. The contrast variation observed in the high-resolution images is therefore due to the strain field o f dislocation network. The strong contrast variation is attributed to the very small spacing of the inclined dislocations.
4.2. Pd-MgO {100} interfaces A HREM image of Pd-MgO (001) interface region taken under axial illumination along the common [110] direction is shown in Fig. 6. As for the {111} interfaces, the image shows an abrupt transition from Pd to MgO lattice with no transition layer. The interface is atomically smooth over a large area of about 30 nm, with only very few atomic steps present near the corners where the {001} interface meets with the {111 } interface. The interfacial misfit dislocations are clearly visible in the image. The core-like feature of the dislocations clearly indicates that the dislocation lines are parallel to the electron beam, e.g. [110] direction. The strain field of the dislocation appears to be largely limited to the metal side of the
Fig. 5. (a) High-resolution electron micrograph recorded along the common [iT0] direction and (b) optical diffractogram from the interface region, showing the Cu-M80 (111) interface with a characteristic contrast variation along [117 direction due to misfit dislocations.
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LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
Fig. 6. High-resolution electron micrograph of the Pd-MgO (001) interface recorded along the common [110] direction, showing a periodic dislocation arrays at the interface. interface. The distance between dislocation core has an average value of Sd = 3.83 nm. Weak beam imaging has been used to observe the dislocation structures of the interfaces. Figure 7 shows the image taken with g = {331} for the Pd-MgO(001) interface, which is obtained by tilting the Pd foil about [3~1] axis out of the [110] projection. A periodic contrast of what could be the misfit dislocations is clearly visible. After taking into account the effect of interface inclination with respect to the electron beam, a square network is found, with the lines along two perpendicular <110) directions. Direct measurement from Fig. 7 gave a value of Sd = 3.75 nm for the spacing between the parallel lines. This result is in agreement with the dislocation line spacing measured from Fig. 6. Assuming the Burgers vector of type b =al/2
Fig. 7. Weak beam image with g = {331} showing the dislocation network of the Pd-MgO (001) interface.
4.3. P d - M g O (111) twin interface
The HREM image of the (111) twin interface taken under axial illumination along the [1T0] direction is shown in Fig. 9. Unlike the {111} and {100} interfaces, the (111) twin interface between Pd and the plate-like MgO particle is more complicated and contains a high density of atomic steps. The interfacial steps can be ciearly visible when viewed along the [ 112"] direction. The interracial dislocations are also visible at the steps. The weak beam image of the interface taken with g = [2~[0]is shown in Fig. 10. The image was obtained by tilting the foil 20 ° about [1T0] axis from an initial [11~] zone axis. After considering the effect of the interface inclination, the network seems to have a hexagonal structure. The network spacing changes slightly from one area to other, with an average value of about ~2.26 nm measured from two parallel lines in the image.
Fig. 8. Highly magnified high-resolution electron micr¢~ graph of the Pd-MgO (001) recorded along the common [110] direction, showing the core structure of the inteffacial misfit dislocations. Note the dislocation cores located o n e (001) Pd lattice spacing away from the interface.
LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
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Fig. 9. High-resolution electron micrograph of the Pd-MgO (111) twin interface recorded along the common [frO] direction. Note the high density atomic steps visible at the interface. A highly magnified image of (111) twin interface taken along [IT0] direction from a very thin area is shown in Fig. l l. The dislocations and atomic steps are clearly visible as indicated in the image. The direct observation of dislocation core indicates that the dislocations are parallel to the (110) direction. Both single and double atomic steps associated with the dislocations are observed. The spacing between the dislocations varies from area to area. The average value measured from the high-resolution image is about 2.28 rim, which is also very close to the 2.1 run, calculated by using Sd=lb[/6 with the Burgers vector b = 1/6(112).
Even for the Cu-MgO system with the largest misfit of 14.2% localized strain has been observed. This is in contrast to results on the structure of Ag-CdO [3] and Cu-Ai203 [13] interface having misfit of 13 and 9.2% respectively, which have been found to be incoherent. At the present time it is not clear what criteria govern inteffacial coherency. From these results it is evident that the presence of misfit dislocations can not be uniquely predicted by geometrical criteria based on the magnitude of the misfit and that other factors associated with interfacial chemistry and atomic bond strength might be important. The measured dislocation spacings for (100) and (111) interfaces was systematically larger by about
5. DISCUSSION The results presented in section 4 indicate that all three interfaces (100), (111) and (111) twin are partially coherent and contain misfit dislocations.
Fig. 10. Weak beam image with g={220} showing the dislocation network of the Pd-MgO (111) twin interface. AMM 40/S--R
Fig. 11. Highly magnified high-resolution electron micrograph of the Pd-MgO (111) twin interface recorded along the common [ITO] direction. Note both single and double atomic steps and dislocations associated with the steps.
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LU and COSANDEY: DISLOCATION STRUCTURES AT INTERFACES
3-5% than the geometrical spacings, indicating that there is some residual strain remaining at the interface. Similar observations have been madeTor Nb-AI203 [4] and the Pt-NiO [5] interface. Another common observation for most metal-oxide interfaces is that the misfit dislocations cores are located in the metal side away from the interface, This "stand off" distance varies from systems to systems ranging from 1 to 3 interplanar spacings [4, 5, 14]. For the (100) Pd-MgO interface, the observed square dislocation network agrees with the geometrical prediction presented in Section 3. For the (111) Pd-MgO and Cu-MgO interfaces the observed strain contrast agrees with the expected model based on a hexagonal configuration. Since we have not been able to observe the dislocation network directly by weak beam microscopy, we do not know whether interfacial dislocations can interact or dissociate into partials to form extended nodes. Such dissociations have been observed to occur in (111) lattice misfit [15] or low angle (111) twist boundaries [16]. These dissociation reactions do not change the overall network periodicity or interface symmetry but give rise to a more complex dislocation arrangement. Such reactions could explain why we have not been able to observe inteffacial dislocations at (111) interfaces by weak beam microscopy. Another reason for the failure to detect the dislocations could be due to the octahedral shape of the particles which cause an overlap between the {111} interfaces resulting possible reduction in contrast. In any case, the high resolution images clearly reveal the presence of localized strain associated with interracial misfit dislocations. For the (111) twin interface we have clearly observed by weak beam microscopy the dislocation network and by high resolution imaging the single and double steps associated with the misfit dislocations. The direct visualization of the double step indicates that the dislocation structure corresponds to the configuration shown in Fig. 3(a). An interesting point to note here is that both dislocation configuration shown in Fig. 3(a) and 3Co) have been observed previously. The configuration depicted in Fig. 3(b) was observed for a twist grain boundary in Au deviating slightly from a Z - - 3 misorientation. In another study on interface between NiSi 2 and Si in a B orientation [17], which is geometrically similar to the (111) twin interface described in this study, the dislocation structure shown in Fig. 3(a) was observed. These results indicate that although the geometrical description for twist misfit or lattice misfit interfaces is similar, dislocation reactions and arrangements might be dependent on dislocation nucleation, mobility and the atomic structure of the interface.
6. CONCLUSIONS The dislocation structures at Cu and Pd-MgO interfaces have been studied by combined high resolution and weak beam electron microscopy. The metal--oxide interfaces were formed by internal oxidation of Cu--lwt%Mg and P d - l w t % M g alloys. The observations have been made at (ll l), (I00) cube-on-cube and (II!) twin interfaces. All interfaces have been found to be partiallycoherent despite the large misfitof 14.2 and 7.6% for C u - M g O and P d - M g O respectively.The dislocationconfiguration, network periodicity and dislocation type are presented and discussed in terms of the geometrical D S C / C S L lattice model. The dislocations at the (III) and (100) interfacesare of the type a/2000) while the (II I) twin interface contains dislocations of the type a/6(112) which are associatedwith both single and double steps. work is supported by the Materials Research Group Program Division of the National Science Foundation under Grant No. NSF-MRG89-07553. Thanks are due to the Center for Ceramic Research at Rutgers University for the use of the High Resolution Electron Microscope Facility. .4cknowledgements--This
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