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TEM investigations of the superdislocations and their interaction with particles in dispersion strengthened intermetallics
Intermetallics 7 (1999) 423±436
TEM investigations of the superdislocations and their interaction with particles in dispersion strengthened intermetallics R. Behr a, J. Mayer b,*, E. Arzt a,b a
Institut fuÈr Metallkunde, UniversitaÈt Stuttgart, Seestraûe 71, 70174 Stuttgart, Germany b Max-Planck-Institut fuÈr Metallforschung, Seestraûe 92, 70174 Stuttgart, Germany Received 13 May 1998; revised 23 July 1998; accepted 18 September 1998
Abstract The strategy of oxide-dispersion strengthening has recently been applied to intermetallic compounds in order to improve their creep resistance at high temperatures. In this paper, we describe selected results of an extensive transmission electron microscopy (TEM) study of the dislocation structures and the particle/dislocation con®gurations in Oxide-dispersion strengthed (ODS) NiAl, Ni3Al and FeAl. High-resolution TEM was employed to characterise the particle/matrix interfaces, and in situ high-temperature deformation in a high-voltage TEM provided insight into the dynamic processes of dislocation detachment from particles. The dissociation of the lattice dislocations into superpartials in FeAl and Ni3Al has important consequences for the particle/dislocation interactions: the superpartials are observed to surmount, and sometimes detach from, the particles separately, which points to a cooperative eect between the partials. The in situ experiments show, in addition, that the climb step is rapid compared with dislocation detachment from the particle. These observations are discussed in the light of our recent theoretical model of creep strength in ordered ODS materials. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Nickel aluminides; Iron aluminides; Dispersion strengthening; Plastic deformation mechanisms; Electron microscopy; Transmission
1. Introduction Dispersion strengthening is an ecient means of raising the high-temperature strength of metallic alloys [1±4]. In view of the limited creep strength of many monolithic intermetallic compounds, the strategy of dispersion strengthening has recently been applied to several compounds, e.g. NiAl, Ni3Al, and FeAl [5±9]. Substantial improvements in creep strength have been achieved in this way, with Oxide-dispersion strengthed (ODS) NiAl occupying even a leading position among all metallic alloys with inherent oxidation resistance [10]. Whereas the room-temperature strength of ODS systems has been well understood for a long time [11,12], the theoretical understanding of high-temperature and creep strength of such systems has lagged far behind. Conceptually, the most dicult aspect has been the strong retardation of creep by dispersoids, which is found in most dispersion-strengthened alloys. Probably the most successful micromechanistic model is based on the assumption of an attractive particle dislocation * Corresponding author. Tel.: +49 711 2095 312; fax: +49 711 2095 320; e-mail: [email protected]
interaction, as is suggested by TEM observations [13± 15] and by model calculations [16]. We have developed a creep model, in which the detachment of dislocations from dispersoid particles is the time-limiting event [17,18]. The resulting creep equation has been shown to successfully describe the creep behaviour of several dispersion-strengthened alloys [18,19]. More recently, we have extended this model to ordered matrix materials, in which the dislocations may dissociate into superpartials, which then have to overcome the dispersoids separately [9,19,20]. The latest model describing the creep strength in dispersion strengthened intermetallics is being published elsewhere [21]. It was found that the interaction between the partials generally lowers the creep strength, but the model also predicts, for a given dislocation spacing, an optimum particle size. This model, which due to the separation into two detachment processes is substantially more complicated than the detachment model for single dislocations, has also been found to agree in a satisfactory way with the creep behaviour of several ODS intermetallics. The objective of the present paper is to present an experimental basis for the theoretical modelling. We
0966-9795/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0966 -9 795(98)00108 -3
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2. Experimental
Attempts to recrystallize the Fe±Al alloys resulted in the formation of voids and porosity. Hence, no recrystallization treatment was applied in the Fe±Al system. The chemical compositions of the ®nal NiAl and FeAl ODS alloys have been determined by Grahle [6] and GoÈhring [9] and the results are given in Table 1. The oxygen which is introduced as contamination during the milling process leads to a higher density of dispersoids than expected from the 2 vol% of Y2O3 which are added to the starting materials. During the subsequent heat treatment the oxygen reacts with the aluminium to form Al2O3 or Y3Al5O12 [6]. In the case of Ni3Al, chromium was added to the alloy to prevent high-temperature oxygen embrittlement whereas the boron content ensured adequate ductility.
2.1. Preparation of the ODS materials
2.2. Creep experiments
The ODS alloys in the Fe±Al and Ni±Al system were prepared using powder metallurgical techniques. FeAl and NiAl powders were obtained by atomisation of pure alloys with the appropriate stoichiometry. Y2O3 particles were added as dispersoids because of their high thermodynamic stability. Mechanical alloying was performed for 24 h in an attritor with steel balls. Subsequently, the mechanically alloyed powders were compacted by extrusion or hot isostatic pressing. The former leads to elongated grains, the latter to an equiaxed grain structure. Further details on the processing can be found in Refs. [5,6,9]. The preparation of new alloys with high creep resistance requires the formation of a coarse grained microstructure. Grahle [5,6] has shown that for the intermetallic phase NiAl secondary recrystallization occurs only in a very narrow deformation/temperature range. The recrystallization treatment for the Ni3Al and NiAl materials was performed at 1400 C and 1500 C, respectively. Only the recrystallized coarse grained alloy shows the desired ODS hardening eect up to temperatures close to the melting point (1400 C) [10].
The creep resistance of ODS Ni3Al, NiAl and FeAl was the subject of earlier investigations [5,8±10]. Deformed samples of these experiments were analysed by TEM in the present work. In addition, for selected materials further creep experiments were performed. Cylindrical creep specimens (length 17 mm, diameter 8 mm) were cut by spark erosion and deformed in a Zwick testing machine in compression. The extrusion axis, i.e. the long axis of the grains, was parallel to the deformation direction. The experiments were carried out in air at 1000 C and with strain rates ranging from 10ÿ5 to 10ÿ7 sÿ1. At a total plastic strain of about 1.5%, a constant stress level was reached in the experiments. At this point the experiments were stopped by cooling the specimen under applied load to immobilise dislocation con®gurations.
have studied, by transmission electron microscopy (TEM), the dislocations and their interactions with dispersoid particles in dispersion-strengthened NiAl, Ni3Al and FeAl. Conventional TEM was employed to characterise the grain and particle microstructure, as well as dislocation/particle con®gurations. These studies were complemented by high-resolution TEM to gain more insight in the particle/matrix interface. Finally, in situ high-temperature deformation experiments were performed in a high-voltage TEM, with the objective to study the details of dynamic processes occurring during the particle/dislocation interaction.
2.3. TEM specimen preparation TEM specimens were extracted from the creep cylinders by cutting slices with spark erosion parallel to the cylinder axis and polishing the slices to a thickness of
Table 1 Chemical compositions of the ODS alloys [6] [9]. (the particles are generally composed of a mixed oxide) Element
Ni
Al
Fe
Particles
Y2O3/Al2O3
At.%
50
43
2
Vol%
4.8
Sample
Element
Fe
Al
Particles
Y2O3
Al2O3
Fe27Al Fe29Al Fe34Al Fe39Al
At.% At.% At.% At.%
73.4 71.1 66.8 62
26.6 28.9 33.2 38
Vol% Vol% Vol% Vol%
2.7 2.8 2.9 2.7
1.1 1.1 1.0 0.9
Element
Ni
Al
Cr
B
Particles
Y2O3/Al2O3
At.%
76
19
5
0.1
Vol%
3.4
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100±150 mm. From these, 3 mm discs were obtained with a disc punch. The geometry was chosen such that the deformation axis lies ¯at within the TEM discs. The 3 mm discs were electrolytically thinned to perforation using a solution of 7.5% perchloric acid in methanol at a temperature of ÿ55 C and an applied voltage of 25 V. The Fe-rich samples of the Fe±Al system are magnetic and thus interact strongly with the magnetic ®eld of the objective lens. In order to minimise image distortions and stability problems of the specimen, a 1 mm diameter disc was extracted from the central area of the perforated TEM specimen with a special disc punch. This 1 mm disc containing the electron-transparent areas was glued onto a 3 mm copper grid. Specimens for the in situ deformation experiments were prepared with the special platelet geometry shown in Fig. 1. The platelets were cut by spark erosion and ground to a thickness of 150 mm. Two 1 mm holes for the bolts with which the force is applied were introduced with a special disc punch. In the middle part the specimen thickness is reduced by dimpling to a value between 20 and 30 mm in order to obtain the maximum tensile deformation in the central region containing the perforated areas. Finally, these specimens were electrolytically thinned in a modi®ed holder under the conditions mentioned above. 2.4. TEM experiments 2.4.1. Conventional TEM With conventional TEM methods, the microstructure of the specimens including grain and precipitate sizes was investigated. The dislocations were imaged with weak-beam dark-®eld techniques and a Burgers vector
Fig. 1. Sample preparation for in situ TEM experiments. The straining holder requires a rectangular specimen geometry with two holes through which the specimen is ®xed and loaded in tension.
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analysis was carried out using the g . b criterion. In most cases, we have also tried to determine the glide plane of the dislocations and in the case of dissociated superpartials attempts were made to measure the dissociation width. In the case of Ni3Al, where many glide planes are possible but hard to distinguish because of projection eects and uncertainties in the identi®cation of the glide plane, these procedures were dicult to perform. For the dislocations attached to the particles, attempts were made to determine the radius of curvature next to the particle, the stable position where the dislocation detaches from the particle and the angle under which the dislocation detaches from the particle surface. Furthermore, in the case of dissociated dislocations we tried to determine possible changes of the dissociation width near the particles as a function of the particle diameter and the distance from the particle. Again, unambiguous results can only be obtained if the glide plane can be determined and is oriented perpendicular to the viewing direction. To take account of projection eects, we have developed a correction scheme which is based on a measurement of the tilt angle of the glide plane with respect to the incident beam direction. 2.4.2. High resolution TEM (HRTEM) With the help of HRTEM, the interface of the particles and the matrix was characterised in order to reveal the structure of the interface and the presence of mis®t dislocations at the interface. The dislocation cores can be studied if they are imaged ``edge-on'' and if the dislocations possess at least a signi®cant edge component. Therefore, for a known Burgers vector in a given material a low index zone axis, which is parallel to the line direction and perpendicular to the Burgers vector, was chosen for HRTEM imaging. For Ni3Al a 0 1 1 direction was chosen, which satis®es the above imaging conditions for an edge dislocation gliding on a (0 0 1) plane in a [0 1 1] direction. For NiAl, the grains were tilted to a [0 0 1] zone axis. In situ experiments were performed to reveal details of the dynamical processes during the dislocation particle interaction. The experiments were carried out in a high-voltage TEM AEI EM 7 which was operated at an accelerating voltage of 1 MV. The microscope is equipped with a liquid-helium cryopump which provides a vacuum in the UHV range in the objective lens area and reduces contamination and oxidation during the hightemperature experiments. A special double-tilt heating deformation holder, which was constructed and built at the Max-Planck-Institut fuÈr Metallforschung, was used for the experiments. A special rectangular specimen geometry was required (cf. Fig. 1) and the specimens were deformed in tension. During the experiments a constant load up to 100 N and a constant temperature up to 1400 C could be maintained. In the actual experiments with the ODS alloys, the temperature and
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Fig. 2. Overview of the microstructure of the ODS NiAl alloy. The dispersoids are homogeneously distributed in the NiAl matrix.
the load were increased in steps. One of the diculties was to identify the areas in which the deformation started and to image the dislocations with maximum contrast. The former was facilitated by an optimised specimen preparation, the latter required the tilt of the specimen to be corrected continuously during the experiment. The deformation experiments were usually terminated by spontaneous nucleation and propagation of cracks.
3. Experimental results and discussion In the following, the experimental results will be presented in a sequence given by the individual TEM techniques employed. In each section the results will be compared for the dierent alloy systems investigated. For all alloys the general microstructure, including the particle sizes and dislocation arrangement, was characterised with conventional TEM. The Burgers vectors,
Fig. 3. Overview of the microstructure of ODS Fe 34at.% Al. The particles are not as homogenously dispersed in the matrix as in NiAl.
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Table 2 Microstructural parameters of the ODS alloys Parameter
Ni3Al
Fe27Al
Fe29Al
Fe34Al
Fe39Al
NiAl
d [nm] fv [vol%] Lp [nm]
43 3.4 150
34 3.8 180
37 3.9 216
40 3.9 232
55 3.6 340
90 4.8 160
d average particle diameter, fv volume fraction, and Lp mean planar particle distance [6,8,9].
line directions and glide planes were analysed with particular emphasis on the dislocation dissociation and the dislocation/particle interaction. The matrix/particle interface was also studied by HRTEM and the results will be discussed. Finally, the in situ microscopy results will be described. 3.1. Microstructural characterisation All the materials in the Ni±Al system are composed of large, elongated grains. The dimensions of the grains are typically 400 50 mm in Ni3Al and 1 mm 100 mm in NiAl. The alloys in the Fe±Al system consist of elongated grains with typical dimensions of 2±10 mm. The TEM micrographs depicted in Figs. 2±4 show the typical oxide particle arrangement in the NiAl, Fe 34at.% Al, and Ni3Al alloys, respectively. The mean particle diameters, the volume fractions and the mean planar distances of the particles for the alloys investigated are listed in Table 2 [6,8,9]. The distribution of the particles in Ni3Al and NiAl appears to be rather uniform, whereas it is somewhat non-uniform in the Fe±Al alloys and the particles seem to be arranged in stringers.
At low magni®cations, the particles appear to be spherical in shape and there is no indication for any special orientation relationship with the matrix. However, at higher magni®cations, many of the particles can be seen to be faceted with the facets parallel to {1 0 0} and {1 1 0} planes of the matrix. As an example, Fig. 5(a) shows an HRTEM micrograph of an oxide particle in an NiAl grain. In addition to the faceting, the particle is well oriented with respect to the matrix, with lowindexed planes of the particle being parallel to (2 0 0) planes of the NiAl. An HRTEM image of an oxide inclusion in Ni3Al, which shows similar features, is displayed in Fig. 5(b). 3.2. Dislocation analysis As an example for the Burgers vector analysis with the g . b =0 method, Fig. 6 shows the case of a dissociated dislocation in the ODS Ni3Al alloy. In the tilt experiments, three dierent diraction conditions were found under which the dislocation contrast is extinct. The Burgers vector of the partials could be determined as b 1=21 0 1a0 . Hence, the analysis con®rms that in
Fig. 4. Overview of the ODS Ni3Al microstructure. The particles are homogeneously dispersed in the matrix.
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Fig. 5. (a) HRTEM micrograph of a particle in the NiAl matrix along the [0 0 1] zone axis. The particle is facetted and the facets are parallel to {1 0 0} and {1 1 0} planes of the matrix. (b) HRTEM micrograph of a particle in Ni3Al with facets parallel to {1 1 1} planes of the matrix. Table 3 Burgers vectors and slip planes, as determined by TEM, in ODS NiAl, FeAl and Ni3Al after creep deformation at the speci®ed temperatures Parameter
NiAl (T=1000 C)
Fe xat.%Al (T=700 C)
at.%Al Burgers vector Slip plane
43 h1 0 0i {1 1 0}
27 1/2 h1 1 1i {1 1 0}
29 1/2 h1 1 1i {1 1 0>
Ni3Al (T=1000 C) 34 1/2 h1 1 1i {1 1 0>
39 1/2 h1 1 1i {1 1 0>
19 1/2 h1 1 0i {1 1 1}
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Fig. 6. Determination of the Burgers vector in Ni3Al of the dislocation which is shown in the weak-beam dark-®eld image in (a). Three dierent imaging conditions were found in (b), (c) and (d) which gave g . b =0. The resulting Burgers vector is b 1=21 0 1a0 .
Ni3Al the dislocations are of h1 1 0i type and are dissociated into two 1/2 h1 1 0i superpartials with an antiphase boundary between them. In the Burgers vector analysis, the characteristic arrangement of oxide particles is very helpful in relocating a given specimen area in the tilt series. The Burgers vector determination was carried out for all alloys investigated in the present work; the results are listed in Table 3. The line directions of the dislocations could only be determined on an average because all dislocations were bowed out between the particles and hence also showed changes in their character. This also complicated the determination of the glide plane which required tilt experiments in which the distance between the superpartials was maximised.
3.3. Analysis of the dislocation dissociation and determination of the APB energy The dissociation widths in the ODS Ni3Al and Ferich Fe±Al alloys were measured from weak-beam dark®eld images taking projection eects into account. The Fe±Al alloys are of particular interest since the APB energy and hence the dissociation width depend strongly on the Fe content [22]. Fig. 7 shows the decrease in the distance between the two partials for the four alloys ranging from Fe 27at.% Al to Fe 39at.% Al. To correct for the projection eect, the distance measured from the micrographs was multiplied by 1/cos , where is the angle between the glide plane normal and the image plane normal. Fig. 8 shows the measured dissociation
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Fig. 7. TEM micrographs of creep-deformed ODS Fe±Al alloys. The dissociation width decreases with increasing Al content.
width as a function of the alloy composition. The dissociation width shows a strong decrease with increasing Al content of the alloys, in good agreement with results by Crawford and Ray [22]. From the dissociation width w the APB energy was calculated according to
APB
Gb2 ; 4w
1
where G is the shear modulus of the matrix. The results obtained for the average dissociation width after projection correction are shown in Fig. 9. A comparison with the results of Crawford and Ray [22], who investigated unreinforced alloys, shows good agreement for an Al content of 29at.%; the APB energy of Fe 27at.% Al
is somewhat lower in our measurements, and higher for Fe 34at.% Al and Fe 39at.% Al. The standard deviation of the APB energies increases with increasing Al content because of the decrease in the dissociation width and the corresponding increase in the relative error of the measurement. Similar experiments were performed for Ni3Al, for which a mean dissociation width of 20 nm was obtained after projection correction. Ni3Al thus ranges about in the middle of the values measured for the dierent Fe± Al alloys. From the measured dissociation width a value of 51 10 mJ/m2 was determined for the APB energy of Ni3Al, which, because of the Cr content, is a factor of 3 lower than the value given by Douin and VeyssieÁre [23] for the stoichiometric alloy, but coincides well with their values for o-stoichiometric alloys.
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Fig. 8. Dissociation width versus composition in the Fe±Al alloys. The ®lled symbols show the width measured in the TEM micrographs after correction for the projection eect. The line corresponds to the literature data (Crawford and Ray [22]).
3.4. Dispersoid/particle interaction One of the main interests of the present investigations was to get detailed information on the dislocation/particle interaction in alloys in which the dislocations dissociate into superpartials. A typical con®guration with a dissociated dislocation attached to a particle is shown in Fig. 10 for the Fe 29at.% Al alloy. The dislocation is strongly attached to the particle and, as a result of the
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Fig. 9. APB energy versus composition in the Fe xat.% Al alloys. Filled symbols correspond to the measured values after projection correction, hollow symbols are the values determined by Crawford and Ray [22].
applied stress, bows out with a characteristic radius of curvature. The leading partial is in a stable position at the backside of the particle and the trailing partial is at a position which corresponds to about the middle of the particle. In the case shown in Fig. 10, the dislocation on both sides of the particle reaches the surface of the TEM specimen and ends there. In this case the stress components which lead to a continuous bowing-out of the dislocation line are relieved and the dislocation segments near the surface become more or less straight. The contrast of the leading superpartial dislocation in the particle/matrix interface is not clearly visible.
Fig. 10. Bright-®eld image showing a typical dislocation/particle con®guration in the Fe 29at.% Al alloy.
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Nevertheless, in keeping with earlier results on other ODS alloys [13,14], the particular con®guration visible in Fig. 10 suggests strongly that the leading partial has overcome the particle by climb (and not by an Orowan process) and is now captured by an attractive force exerted by the particle. This micrograph is thus convincing support for the theoretical modelling of dispersion strengthening in intermetallics, as reported elsewhere [9,20,21]. A particularly instructive example of the dislocation/ particle con®guration in the Ni3Al alloy is depicted in Fig. 11. The dislocation is attached to three particles giving rise to three dierent con®gurations. At particle ``a'' the dislocation is strongly attached, which can be inferred from the small radius of curvature in the matrix. It should be noted that both partials are located close to the centre of the particle and the dissociation width there is somewhat smaller than the equilibrium distance in the matrix. We attribute these observations to the fact that the intersection of the glide plane of the dislocation with the particle is not an equatorial plane, which is a situation frequently observed. The second particle (``b'' in Fig. 11) has a very small diameter of about 15 nm, which is below the dissociation width of the dislocations in the system. It can be clearly seen that
this leads to a substantial local reduction in dissociation width. The trailing partial seems to exert a considerable force on the leading partial, which must be close to detachment from the backside of the particle. At the third particle, the leading partial has already detached from the particle and forms a straight segment. This is an interesting dislocation con®guration, as it shows that the leading superpartial may detach individually from the particle, even at the expense of a considerable increase in APB area. Such a situation is also in agreement with the present state of theoretical modelling [21], which explicitly treats separate detachment events for the two superpartial dislocations. 3.5. In situ TEM The deformation in the in situ experiments started at a temperature of about 900 C under applied load. The onset of deformation led to rapid changes in diraction contrast across the transparent specimen region, but it was sometimes rather dicult to locate the specimen areas with high dislocation activity. In most cases the dislocations originated from thin areas close to the specimen hole. The nucleation of the dislocations usually took place at grain boundaries or large particles
Fig. 11. Weak-beam dark-®eld image of a dislocation/particle con®guration in Ni3Al involving several dierent particles. Both partials are attached to particles ``a'' and ``b'', which is the typical con®guration in this alloy. However, occasionally the leading partial has already detached individually from the particle, as is the case for the particle below.
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Fig. 12. Images taken from a TV sequence recorded during the in situ deformation. The images and the schematic drawings illustrating the experimental situation show two dierent dissociated dislocations which are attached to the particle at the same time. In the last two images the leading partial of the ®rst dislocation detaches from the particle and increases the area of the APB defect but reduces its line length.
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Fig. 13. Distance-time pro®les extracted from the video sequence for the two partials P1 and P2 for two dierent segments on the dislocation line, one in contact with the particle and the other located in the matrix at some distance to the particle. It can clearly be seen that, for the segment getting in contact with the particle, both partials are attached to the particles for several seconds and that the dissociation width varies as the dislocation interacts with the particle.
in the matrix. The dislocations propagated along wellde®ned slip bands to the edge of the specimen or into thicker areas where they could not be traced any further. Usually the experiments were terminated by crack nucleation in a thick area of the specimen which led to failure of the complete TEM specimen. An important observation in the in situ experiments was that the dynamical processes occurring during the dislocation/particle interaction can actually be studied in detail with the time resolution of a TV rate camera. As a complete time-resolved series of such a process cannot be reproduced in the present paper, we will restrict ourselves to the analysis of four individual frames which were extracted from a typical video sequence. This is problematic because individual frames taken out of a video sequence are always rather noisy and have a very limited resolution. Therefore it is dicult to reproduce the information which can be gathered from viewing the whole sequence, which we will describe qualitatively in the following. Typically, in the in situ experiments, the dislocations are inclined steeply in the thin TEM specimen because of the strong interaction with the surfaces. The dislocations approach the particles from the right side and seem to only touch the larger particle, which does not appear to exert a strong retractive force on the dislocations. In contrast, the dislocations seem to be attached rather strongly to the smaller particle and the ®rst pair of partial dislocations does not start to detach even
upon the arrival of a second pair of dislocations. In the real-time sequence, it can be seen that dislocations are not markedly slowed down while climbing across the particle, which happens in a time interval shorter than the time between two video frames. Hence, the rate limiting step is the detachment of the dislocation at the departure side of the particle and in Fig. 12 it is shown that this may take several seconds under the given conditions. During the whole time a strong driving force acts on the dislocations, which can be seen from the elongation of the dislocation line and the large curvature. After about 3 s in real time, the leading partial detaches from the particle and almost instantly reduces its radius of curvature and line length. This increases the area covered by the APB between the two partials. The arrival of further dislocations in the glide band ®nally leads to the detachment of the second partial of the ®rst superdislocation. Surprisingly, under the given conditions, the whole process of the dislocation/particle interaction extends over several seconds and can thus be observed in real time. It appears that the sluggish motion of the dislocations in the in situ experiments is also caused by surface roughness of the thin TEM specimens leading to what appears to be frictional sliding because of the alternating increase and reduction of line length. 3.5.1. Quantitative evaluation of the in situ experiments In order to retrieve the time-resolved information in the video sequence in a quantitative way, we tried to
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quantify the dislocation motion in terms of a distance versus time pro®le. From digitised images of the whole video sequence, the positions are measured as distances between a point on the dislocation line and the centre of the particle for a dislocation segment close to the particle and for a segment which propagates through the matrix at some distance to the particle. The results are given in Fig. 13 as a function of the elapsed time. Whereas the dislocation segment in the matrix is only slightly slowed down after passing the particle, it can be seen that the segment which actually meets the particle is attached to it for almost 4 s. In the distance±time pro®le this interaction time appears as a horizontal plateau at the position of the particle. A detailed analysis shows that the leading partial comes to rest only at the departure side of the particle, whereas the trailing partial stays at a centre position during that period of time and advances to the departure side once the leading partial detaches from the particle. Furthermore, information on the dissociation width can be inferred from the curves given in Fig. 13. Whereas the two partials travel through the matrix at an almost constant separation distance, it is evident that the dissociation width decreases while the two partials are attached to the particle. This observation can be explained by the fact that the particle diameter is rather small, i.e. less than twice the dissociation width. In summary, the in situ experiments provided very useful support for the observations and conclusions which were obtained by conventional TEM. In particular, in situ observations do not suer from possible relaxations of the dislocation/particle con®guration during cooling down from creep temperatures and they show the complete sequence of con®gurations in the interaction process. Furthermore, we have shown that, with the modern means of digitisation, quantitative information can be extracted from in situ observations. However, the main problem of in situ studies of deformation processes certainly is the thin foil geometry which gives rise to substantial interaction of the dislocations with the two surfaces. In the experiments, this can be seen from the fact that only very short dislocation segments can be observed and that the dislocation motion is markedly slowed down by what appears to be a frictional force exerted by the rough surfaces. Therefore, the most complete model for the underlying process can only be obtained by combining input from both sides, careful ex situ analysis with conventional TEM and direct, time-resolved in situ observation. 4. Concluding remarks In the present paper, we have described selected results of an extensive TEM study on the dislocation con®gurations and the dislocation/particle interaction in
435
ODS NiAl, Ni3Al and Fe-rich Fe±Al alloys. Particular emphasis was placed on the details of the interaction of the dislocations with the particles and the information extracted serves as a basis for further theoretical modelling of the hardening eect of the dispersed particles. In all cases, the particles exert a strong retractive force on the dislocations, as is evident from the bowing out of the dislocations between the particles both in specimens cooled down under load and in the in situ experiments. We were able to prove, that the rate limiting step in all cases is the detachment from the back side of the particles and not the climb step across the particles. The main emphasis of the present study was placed on the eect of the dissociation of lattice dislocations, and we could show that the superpartials surmount, and sometimes detach from the particle separately, but that there are also cooperative eects between the partials. The leading partial is always attached to the departure side of the particle and contact angles close to 90 can frequently be observed. In an atomistic model, this can be explained by the fact that the delocalisation of the dislocation core in the particle/matrix interface (which results in an attractive interaction) has to be reversed prior to detachment. The in situ experiments provide further evidence that the climb step is rapid compared with the detachment from the particle, as is assumed in theoretical modelling. The eect of the particles on the dissociation width in the vicinity of the particles strongly depends on the particle diameter. Small particles reduce the dissociation width, which increases the repulsive force between the two partials. An optimum retractive eect seems to be reached for a particle diameter which corresponds to twice the dissociation width, in accordance with theoretical modelling [21]. Our observations show that in this case the leading partial is strongly attached to the departure side of the particle whereas the trailing partial is captured at the maximum of the climb threshold. For larger particles, both partials are able to surmount the particle almost instantly and the trailing partial then exerts a repulsive force on the leading partial driving it closer to the detachment threshold. Overall, the TEM studies lend support to the assumptions made in theoretical modelling of dispersion strengthening in ordered matrices, as is described in detail elsewhere [21]. Acknowledgements We thank B. Inkson, H.J. Schedler, P. Grahle, and E. GoÈhring for their help in the experiments and enlightening discussions. Support by the Deutsche Forschungsgemeinschaft (Project Ar 201, SPP ``Verformung und Bruch geordneter Mischkristalle'') is gratefully acknowledged.
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References [1] Ansell, GS. In: Ansell GS, Cooper TD, Lenel FV, editors. Oxide dispersion strengthening. New York: Gordon and Breach, 1968:61. [2] Lund RW, Nix WD. Acta Metall 1976;24:469. [3] Singer RF, Arzt E. In: Betz W. et al, editors. High Temperature Alloys for Gas Turbines and Other Applications, Dordrecht, 1986:97. [4] Arzt E. Res Mechanica 1991;31:399. [5] Grahle P, Arzt E. Acta Mat 1997;45:201. [6] Grahle P. Ph.D. Dissertation. Institut fuÈr Metallkunde, University of Stuttgart, 1995. [7] Mason RP, Grant NJ. Mat Sci Eng A 1995;192/193:741. [8] Klotz UE, Mason RP, GoÈhring E, Arzt E. Mat Sci Eng A 1998;231:198. [9] GoÈhring E. Ph.D. Dissertation. Institut fuÈr Metallkunde, University of Stuttgart, 1997.
[10] Arzt E, Grahle P. Acta Mat 1998;46:2717. [11] Orowan E. In: Symposium on Internal Stresses. Institute of Metals, London, 1947:451. [12] Ashby MF. In: Proc Second Int Conf on Strength of Metals and Alloys, ASM, Metals Park, Ohio, 1970:507. [13] Nardone VC, Tien JK. Scripta Metall 1983;17:467. [14] SchroÈder J, Arzt E. Scripta Metall 1985;19:1129. [15] Behr R, Mayer J, Arzt E. Scripta Mat 1997;36:341. [16] Srolovitz DJ, Luton MJ, Petkovic-Luton R, Barnett DM, Nix WD. Acta Metall 1984;32:1079. [17] Arzt E, Wilkinson DS. Acta Metall 1986;34:1893. [18] RoÈsler J, Arzt E. Acta Metall 1990;38:671. [19] Arzt E, Grahle P. Z Metallkd 1996;87:874. [20] Arzt E, GoÈhring E. Scripta Metall. 1993;28:843. [21] Arzt E, GoÈhring E. Acta Mat (to be published). [22] Crawford RC, Ray ILF. Philos Mag 1977;35:549. [23] Douin J, VeyssieÁre P. Philos Mag A 1991;64:807.
TEM investigations of the superdislocations and their interaction with particles in dispersion strengthened intermetallics R. Behr a, J. Mayer b,*, E. Arzt a,b a
Institut fuÈr Metallkunde, UniversitaÈt Stuttgart, Seestraûe 71, 70174 Stuttgart, Germany b Max-Planck-Institut fuÈr Metallforschung, Seestraûe 92, 70174 Stuttgart, Germany Received 13 May 1998; revised 23 July 1998; accepted 18 September 1998
Abstract The strategy of oxide-dispersion strengthening has recently been applied to intermetallic compounds in order to improve their creep resistance at high temperatures. In this paper, we describe selected results of an extensive transmission electron microscopy (TEM) study of the dislocation structures and the particle/dislocation con®gurations in Oxide-dispersion strengthed (ODS) NiAl, Ni3Al and FeAl. High-resolution TEM was employed to characterise the particle/matrix interfaces, and in situ high-temperature deformation in a high-voltage TEM provided insight into the dynamic processes of dislocation detachment from particles. The dissociation of the lattice dislocations into superpartials in FeAl and Ni3Al has important consequences for the particle/dislocation interactions: the superpartials are observed to surmount, and sometimes detach from, the particles separately, which points to a cooperative eect between the partials. The in situ experiments show, in addition, that the climb step is rapid compared with dislocation detachment from the particle. These observations are discussed in the light of our recent theoretical model of creep strength in ordered ODS materials. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Nickel aluminides; Iron aluminides; Dispersion strengthening; Plastic deformation mechanisms; Electron microscopy; Transmission
1. Introduction Dispersion strengthening is an ecient means of raising the high-temperature strength of metallic alloys [1±4]. In view of the limited creep strength of many monolithic intermetallic compounds, the strategy of dispersion strengthening has recently been applied to several compounds, e.g. NiAl, Ni3Al, and FeAl [5±9]. Substantial improvements in creep strength have been achieved in this way, with Oxide-dispersion strengthed (ODS) NiAl occupying even a leading position among all metallic alloys with inherent oxidation resistance [10]. Whereas the room-temperature strength of ODS systems has been well understood for a long time [11,12], the theoretical understanding of high-temperature and creep strength of such systems has lagged far behind. Conceptually, the most dicult aspect has been the strong retardation of creep by dispersoids, which is found in most dispersion-strengthened alloys. Probably the most successful micromechanistic model is based on the assumption of an attractive particle dislocation * Corresponding author. Tel.: +49 711 2095 312; fax: +49 711 2095 320; e-mail: [email protected]
interaction, as is suggested by TEM observations [13± 15] and by model calculations [16]. We have developed a creep model, in which the detachment of dislocations from dispersoid particles is the time-limiting event [17,18]. The resulting creep equation has been shown to successfully describe the creep behaviour of several dispersion-strengthened alloys [18,19]. More recently, we have extended this model to ordered matrix materials, in which the dislocations may dissociate into superpartials, which then have to overcome the dispersoids separately [9,19,20]. The latest model describing the creep strength in dispersion strengthened intermetallics is being published elsewhere [21]. It was found that the interaction between the partials generally lowers the creep strength, but the model also predicts, for a given dislocation spacing, an optimum particle size. This model, which due to the separation into two detachment processes is substantially more complicated than the detachment model for single dislocations, has also been found to agree in a satisfactory way with the creep behaviour of several ODS intermetallics. The objective of the present paper is to present an experimental basis for the theoretical modelling. We
0966-9795/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0966 -9 795(98)00108 -3
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2. Experimental
Attempts to recrystallize the Fe±Al alloys resulted in the formation of voids and porosity. Hence, no recrystallization treatment was applied in the Fe±Al system. The chemical compositions of the ®nal NiAl and FeAl ODS alloys have been determined by Grahle [6] and GoÈhring [9] and the results are given in Table 1. The oxygen which is introduced as contamination during the milling process leads to a higher density of dispersoids than expected from the 2 vol% of Y2O3 which are added to the starting materials. During the subsequent heat treatment the oxygen reacts with the aluminium to form Al2O3 or Y3Al5O12 [6]. In the case of Ni3Al, chromium was added to the alloy to prevent high-temperature oxygen embrittlement whereas the boron content ensured adequate ductility.
2.1. Preparation of the ODS materials
2.2. Creep experiments
The ODS alloys in the Fe±Al and Ni±Al system were prepared using powder metallurgical techniques. FeAl and NiAl powders were obtained by atomisation of pure alloys with the appropriate stoichiometry. Y2O3 particles were added as dispersoids because of their high thermodynamic stability. Mechanical alloying was performed for 24 h in an attritor with steel balls. Subsequently, the mechanically alloyed powders were compacted by extrusion or hot isostatic pressing. The former leads to elongated grains, the latter to an equiaxed grain structure. Further details on the processing can be found in Refs. [5,6,9]. The preparation of new alloys with high creep resistance requires the formation of a coarse grained microstructure. Grahle [5,6] has shown that for the intermetallic phase NiAl secondary recrystallization occurs only in a very narrow deformation/temperature range. The recrystallization treatment for the Ni3Al and NiAl materials was performed at 1400 C and 1500 C, respectively. Only the recrystallized coarse grained alloy shows the desired ODS hardening eect up to temperatures close to the melting point (1400 C) [10].
The creep resistance of ODS Ni3Al, NiAl and FeAl was the subject of earlier investigations [5,8±10]. Deformed samples of these experiments were analysed by TEM in the present work. In addition, for selected materials further creep experiments were performed. Cylindrical creep specimens (length 17 mm, diameter 8 mm) were cut by spark erosion and deformed in a Zwick testing machine in compression. The extrusion axis, i.e. the long axis of the grains, was parallel to the deformation direction. The experiments were carried out in air at 1000 C and with strain rates ranging from 10ÿ5 to 10ÿ7 sÿ1. At a total plastic strain of about 1.5%, a constant stress level was reached in the experiments. At this point the experiments were stopped by cooling the specimen under applied load to immobilise dislocation con®gurations.
have studied, by transmission electron microscopy (TEM), the dislocations and their interactions with dispersoid particles in dispersion-strengthened NiAl, Ni3Al and FeAl. Conventional TEM was employed to characterise the grain and particle microstructure, as well as dislocation/particle con®gurations. These studies were complemented by high-resolution TEM to gain more insight in the particle/matrix interface. Finally, in situ high-temperature deformation experiments were performed in a high-voltage TEM, with the objective to study the details of dynamic processes occurring during the particle/dislocation interaction.
2.3. TEM specimen preparation TEM specimens were extracted from the creep cylinders by cutting slices with spark erosion parallel to the cylinder axis and polishing the slices to a thickness of
Table 1 Chemical compositions of the ODS alloys [6] [9]. (the particles are generally composed of a mixed oxide) Element
Ni
Al
Fe
Particles
Y2O3/Al2O3
At.%
50
43
2
Vol%
4.8
Sample
Element
Fe
Al
Particles
Y2O3
Al2O3
Fe27Al Fe29Al Fe34Al Fe39Al
At.% At.% At.% At.%
73.4 71.1 66.8 62
26.6 28.9 33.2 38
Vol% Vol% Vol% Vol%
2.7 2.8 2.9 2.7
1.1 1.1 1.0 0.9
Element
Ni
Al
Cr
B
Particles
Y2O3/Al2O3
At.%
76
19
5
0.1
Vol%
3.4
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100±150 mm. From these, 3 mm discs were obtained with a disc punch. The geometry was chosen such that the deformation axis lies ¯at within the TEM discs. The 3 mm discs were electrolytically thinned to perforation using a solution of 7.5% perchloric acid in methanol at a temperature of ÿ55 C and an applied voltage of 25 V. The Fe-rich samples of the Fe±Al system are magnetic and thus interact strongly with the magnetic ®eld of the objective lens. In order to minimise image distortions and stability problems of the specimen, a 1 mm diameter disc was extracted from the central area of the perforated TEM specimen with a special disc punch. This 1 mm disc containing the electron-transparent areas was glued onto a 3 mm copper grid. Specimens for the in situ deformation experiments were prepared with the special platelet geometry shown in Fig. 1. The platelets were cut by spark erosion and ground to a thickness of 150 mm. Two 1 mm holes for the bolts with which the force is applied were introduced with a special disc punch. In the middle part the specimen thickness is reduced by dimpling to a value between 20 and 30 mm in order to obtain the maximum tensile deformation in the central region containing the perforated areas. Finally, these specimens were electrolytically thinned in a modi®ed holder under the conditions mentioned above. 2.4. TEM experiments 2.4.1. Conventional TEM With conventional TEM methods, the microstructure of the specimens including grain and precipitate sizes was investigated. The dislocations were imaged with weak-beam dark-®eld techniques and a Burgers vector
Fig. 1. Sample preparation for in situ TEM experiments. The straining holder requires a rectangular specimen geometry with two holes through which the specimen is ®xed and loaded in tension.
425
analysis was carried out using the g . b criterion. In most cases, we have also tried to determine the glide plane of the dislocations and in the case of dissociated superpartials attempts were made to measure the dissociation width. In the case of Ni3Al, where many glide planes are possible but hard to distinguish because of projection eects and uncertainties in the identi®cation of the glide plane, these procedures were dicult to perform. For the dislocations attached to the particles, attempts were made to determine the radius of curvature next to the particle, the stable position where the dislocation detaches from the particle and the angle under which the dislocation detaches from the particle surface. Furthermore, in the case of dissociated dislocations we tried to determine possible changes of the dissociation width near the particles as a function of the particle diameter and the distance from the particle. Again, unambiguous results can only be obtained if the glide plane can be determined and is oriented perpendicular to the viewing direction. To take account of projection eects, we have developed a correction scheme which is based on a measurement of the tilt angle of the glide plane with respect to the incident beam direction. 2.4.2. High resolution TEM (HRTEM) With the help of HRTEM, the interface of the particles and the matrix was characterised in order to reveal the structure of the interface and the presence of mis®t dislocations at the interface. The dislocation cores can be studied if they are imaged ``edge-on'' and if the dislocations possess at least a signi®cant edge component. Therefore, for a known Burgers vector in a given material a low index zone axis, which is parallel to the line direction and perpendicular to the Burgers vector, was chosen for HRTEM imaging. For Ni3Al a 0 1 1 direction was chosen, which satis®es the above imaging conditions for an edge dislocation gliding on a (0 0 1) plane in a [0 1 1] direction. For NiAl, the grains were tilted to a [0 0 1] zone axis. In situ experiments were performed to reveal details of the dynamical processes during the dislocation particle interaction. The experiments were carried out in a high-voltage TEM AEI EM 7 which was operated at an accelerating voltage of 1 MV. The microscope is equipped with a liquid-helium cryopump which provides a vacuum in the UHV range in the objective lens area and reduces contamination and oxidation during the hightemperature experiments. A special double-tilt heating deformation holder, which was constructed and built at the Max-Planck-Institut fuÈr Metallforschung, was used for the experiments. A special rectangular specimen geometry was required (cf. Fig. 1) and the specimens were deformed in tension. During the experiments a constant load up to 100 N and a constant temperature up to 1400 C could be maintained. In the actual experiments with the ODS alloys, the temperature and
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Fig. 2. Overview of the microstructure of the ODS NiAl alloy. The dispersoids are homogeneously distributed in the NiAl matrix.
the load were increased in steps. One of the diculties was to identify the areas in which the deformation started and to image the dislocations with maximum contrast. The former was facilitated by an optimised specimen preparation, the latter required the tilt of the specimen to be corrected continuously during the experiment. The deformation experiments were usually terminated by spontaneous nucleation and propagation of cracks.
3. Experimental results and discussion In the following, the experimental results will be presented in a sequence given by the individual TEM techniques employed. In each section the results will be compared for the dierent alloy systems investigated. For all alloys the general microstructure, including the particle sizes and dislocation arrangement, was characterised with conventional TEM. The Burgers vectors,
Fig. 3. Overview of the microstructure of ODS Fe 34at.% Al. The particles are not as homogenously dispersed in the matrix as in NiAl.
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427
Table 2 Microstructural parameters of the ODS alloys Parameter
Ni3Al
Fe27Al
Fe29Al
Fe34Al
Fe39Al
NiAl
d [nm] fv [vol%] Lp [nm]
43 3.4 150
34 3.8 180
37 3.9 216
40 3.9 232
55 3.6 340
90 4.8 160
d average particle diameter, fv volume fraction, and Lp mean planar particle distance [6,8,9].
line directions and glide planes were analysed with particular emphasis on the dislocation dissociation and the dislocation/particle interaction. The matrix/particle interface was also studied by HRTEM and the results will be discussed. Finally, the in situ microscopy results will be described. 3.1. Microstructural characterisation All the materials in the Ni±Al system are composed of large, elongated grains. The dimensions of the grains are typically 400 50 mm in Ni3Al and 1 mm 100 mm in NiAl. The alloys in the Fe±Al system consist of elongated grains with typical dimensions of 2±10 mm. The TEM micrographs depicted in Figs. 2±4 show the typical oxide particle arrangement in the NiAl, Fe 34at.% Al, and Ni3Al alloys, respectively. The mean particle diameters, the volume fractions and the mean planar distances of the particles for the alloys investigated are listed in Table 2 [6,8,9]. The distribution of the particles in Ni3Al and NiAl appears to be rather uniform, whereas it is somewhat non-uniform in the Fe±Al alloys and the particles seem to be arranged in stringers.
At low magni®cations, the particles appear to be spherical in shape and there is no indication for any special orientation relationship with the matrix. However, at higher magni®cations, many of the particles can be seen to be faceted with the facets parallel to {1 0 0} and {1 1 0} planes of the matrix. As an example, Fig. 5(a) shows an HRTEM micrograph of an oxide particle in an NiAl grain. In addition to the faceting, the particle is well oriented with respect to the matrix, with lowindexed planes of the particle being parallel to (2 0 0) planes of the NiAl. An HRTEM image of an oxide inclusion in Ni3Al, which shows similar features, is displayed in Fig. 5(b). 3.2. Dislocation analysis As an example for the Burgers vector analysis with the g . b =0 method, Fig. 6 shows the case of a dissociated dislocation in the ODS Ni3Al alloy. In the tilt experiments, three dierent diraction conditions were found under which the dislocation contrast is extinct. The Burgers vector of the partials could be determined as b 1=21 0 1a0 . Hence, the analysis con®rms that in
Fig. 4. Overview of the ODS Ni3Al microstructure. The particles are homogeneously dispersed in the matrix.
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Fig. 5. (a) HRTEM micrograph of a particle in the NiAl matrix along the [0 0 1] zone axis. The particle is facetted and the facets are parallel to {1 0 0} and {1 1 0} planes of the matrix. (b) HRTEM micrograph of a particle in Ni3Al with facets parallel to {1 1 1} planes of the matrix. Table 3 Burgers vectors and slip planes, as determined by TEM, in ODS NiAl, FeAl and Ni3Al after creep deformation at the speci®ed temperatures Parameter
NiAl (T=1000 C)
Fe xat.%Al (T=700 C)
at.%Al Burgers vector Slip plane
43 h1 0 0i {1 1 0}
27 1/2 h1 1 1i {1 1 0}
29 1/2 h1 1 1i {1 1 0>
Ni3Al (T=1000 C) 34 1/2 h1 1 1i {1 1 0>
39 1/2 h1 1 1i {1 1 0>
19 1/2 h1 1 0i {1 1 1}
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429
Fig. 6. Determination of the Burgers vector in Ni3Al of the dislocation which is shown in the weak-beam dark-®eld image in (a). Three dierent imaging conditions were found in (b), (c) and (d) which gave g . b =0. The resulting Burgers vector is b 1=21 0 1a0 .
Ni3Al the dislocations are of h1 1 0i type and are dissociated into two 1/2 h1 1 0i superpartials with an antiphase boundary between them. In the Burgers vector analysis, the characteristic arrangement of oxide particles is very helpful in relocating a given specimen area in the tilt series. The Burgers vector determination was carried out for all alloys investigated in the present work; the results are listed in Table 3. The line directions of the dislocations could only be determined on an average because all dislocations were bowed out between the particles and hence also showed changes in their character. This also complicated the determination of the glide plane which required tilt experiments in which the distance between the superpartials was maximised.
3.3. Analysis of the dislocation dissociation and determination of the APB energy The dissociation widths in the ODS Ni3Al and Ferich Fe±Al alloys were measured from weak-beam dark®eld images taking projection eects into account. The Fe±Al alloys are of particular interest since the APB energy and hence the dissociation width depend strongly on the Fe content [22]. Fig. 7 shows the decrease in the distance between the two partials for the four alloys ranging from Fe 27at.% Al to Fe 39at.% Al. To correct for the projection eect, the distance measured from the micrographs was multiplied by 1/cos , where is the angle between the glide plane normal and the image plane normal. Fig. 8 shows the measured dissociation
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Fig. 7. TEM micrographs of creep-deformed ODS Fe±Al alloys. The dissociation width decreases with increasing Al content.
width as a function of the alloy composition. The dissociation width shows a strong decrease with increasing Al content of the alloys, in good agreement with results by Crawford and Ray [22]. From the dissociation width w the APB energy was calculated according to
APB
Gb2 ; 4w
1
where G is the shear modulus of the matrix. The results obtained for the average dissociation width after projection correction are shown in Fig. 9. A comparison with the results of Crawford and Ray [22], who investigated unreinforced alloys, shows good agreement for an Al content of 29at.%; the APB energy of Fe 27at.% Al
is somewhat lower in our measurements, and higher for Fe 34at.% Al and Fe 39at.% Al. The standard deviation of the APB energies increases with increasing Al content because of the decrease in the dissociation width and the corresponding increase in the relative error of the measurement. Similar experiments were performed for Ni3Al, for which a mean dissociation width of 20 nm was obtained after projection correction. Ni3Al thus ranges about in the middle of the values measured for the dierent Fe± Al alloys. From the measured dissociation width a value of 51 10 mJ/m2 was determined for the APB energy of Ni3Al, which, because of the Cr content, is a factor of 3 lower than the value given by Douin and VeyssieÁre [23] for the stoichiometric alloy, but coincides well with their values for o-stoichiometric alloys.
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Fig. 8. Dissociation width versus composition in the Fe±Al alloys. The ®lled symbols show the width measured in the TEM micrographs after correction for the projection eect. The line corresponds to the literature data (Crawford and Ray [22]).
3.4. Dispersoid/particle interaction One of the main interests of the present investigations was to get detailed information on the dislocation/particle interaction in alloys in which the dislocations dissociate into superpartials. A typical con®guration with a dissociated dislocation attached to a particle is shown in Fig. 10 for the Fe 29at.% Al alloy. The dislocation is strongly attached to the particle and, as a result of the
431
Fig. 9. APB energy versus composition in the Fe xat.% Al alloys. Filled symbols correspond to the measured values after projection correction, hollow symbols are the values determined by Crawford and Ray [22].
applied stress, bows out with a characteristic radius of curvature. The leading partial is in a stable position at the backside of the particle and the trailing partial is at a position which corresponds to about the middle of the particle. In the case shown in Fig. 10, the dislocation on both sides of the particle reaches the surface of the TEM specimen and ends there. In this case the stress components which lead to a continuous bowing-out of the dislocation line are relieved and the dislocation segments near the surface become more or less straight. The contrast of the leading superpartial dislocation in the particle/matrix interface is not clearly visible.
Fig. 10. Bright-®eld image showing a typical dislocation/particle con®guration in the Fe 29at.% Al alloy.
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Nevertheless, in keeping with earlier results on other ODS alloys [13,14], the particular con®guration visible in Fig. 10 suggests strongly that the leading partial has overcome the particle by climb (and not by an Orowan process) and is now captured by an attractive force exerted by the particle. This micrograph is thus convincing support for the theoretical modelling of dispersion strengthening in intermetallics, as reported elsewhere [9,20,21]. A particularly instructive example of the dislocation/ particle con®guration in the Ni3Al alloy is depicted in Fig. 11. The dislocation is attached to three particles giving rise to three dierent con®gurations. At particle ``a'' the dislocation is strongly attached, which can be inferred from the small radius of curvature in the matrix. It should be noted that both partials are located close to the centre of the particle and the dissociation width there is somewhat smaller than the equilibrium distance in the matrix. We attribute these observations to the fact that the intersection of the glide plane of the dislocation with the particle is not an equatorial plane, which is a situation frequently observed. The second particle (``b'' in Fig. 11) has a very small diameter of about 15 nm, which is below the dissociation width of the dislocations in the system. It can be clearly seen that
this leads to a substantial local reduction in dissociation width. The trailing partial seems to exert a considerable force on the leading partial, which must be close to detachment from the backside of the particle. At the third particle, the leading partial has already detached from the particle and forms a straight segment. This is an interesting dislocation con®guration, as it shows that the leading superpartial may detach individually from the particle, even at the expense of a considerable increase in APB area. Such a situation is also in agreement with the present state of theoretical modelling [21], which explicitly treats separate detachment events for the two superpartial dislocations. 3.5. In situ TEM The deformation in the in situ experiments started at a temperature of about 900 C under applied load. The onset of deformation led to rapid changes in diraction contrast across the transparent specimen region, but it was sometimes rather dicult to locate the specimen areas with high dislocation activity. In most cases the dislocations originated from thin areas close to the specimen hole. The nucleation of the dislocations usually took place at grain boundaries or large particles
Fig. 11. Weak-beam dark-®eld image of a dislocation/particle con®guration in Ni3Al involving several dierent particles. Both partials are attached to particles ``a'' and ``b'', which is the typical con®guration in this alloy. However, occasionally the leading partial has already detached individually from the particle, as is the case for the particle below.
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433
Fig. 12. Images taken from a TV sequence recorded during the in situ deformation. The images and the schematic drawings illustrating the experimental situation show two dierent dissociated dislocations which are attached to the particle at the same time. In the last two images the leading partial of the ®rst dislocation detaches from the particle and increases the area of the APB defect but reduces its line length.
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Fig. 13. Distance-time pro®les extracted from the video sequence for the two partials P1 and P2 for two dierent segments on the dislocation line, one in contact with the particle and the other located in the matrix at some distance to the particle. It can clearly be seen that, for the segment getting in contact with the particle, both partials are attached to the particles for several seconds and that the dissociation width varies as the dislocation interacts with the particle.
in the matrix. The dislocations propagated along wellde®ned slip bands to the edge of the specimen or into thicker areas where they could not be traced any further. Usually the experiments were terminated by crack nucleation in a thick area of the specimen which led to failure of the complete TEM specimen. An important observation in the in situ experiments was that the dynamical processes occurring during the dislocation/particle interaction can actually be studied in detail with the time resolution of a TV rate camera. As a complete time-resolved series of such a process cannot be reproduced in the present paper, we will restrict ourselves to the analysis of four individual frames which were extracted from a typical video sequence. This is problematic because individual frames taken out of a video sequence are always rather noisy and have a very limited resolution. Therefore it is dicult to reproduce the information which can be gathered from viewing the whole sequence, which we will describe qualitatively in the following. Typically, in the in situ experiments, the dislocations are inclined steeply in the thin TEM specimen because of the strong interaction with the surfaces. The dislocations approach the particles from the right side and seem to only touch the larger particle, which does not appear to exert a strong retractive force on the dislocations. In contrast, the dislocations seem to be attached rather strongly to the smaller particle and the ®rst pair of partial dislocations does not start to detach even
upon the arrival of a second pair of dislocations. In the real-time sequence, it can be seen that dislocations are not markedly slowed down while climbing across the particle, which happens in a time interval shorter than the time between two video frames. Hence, the rate limiting step is the detachment of the dislocation at the departure side of the particle and in Fig. 12 it is shown that this may take several seconds under the given conditions. During the whole time a strong driving force acts on the dislocations, which can be seen from the elongation of the dislocation line and the large curvature. After about 3 s in real time, the leading partial detaches from the particle and almost instantly reduces its radius of curvature and line length. This increases the area covered by the APB between the two partials. The arrival of further dislocations in the glide band ®nally leads to the detachment of the second partial of the ®rst superdislocation. Surprisingly, under the given conditions, the whole process of the dislocation/particle interaction extends over several seconds and can thus be observed in real time. It appears that the sluggish motion of the dislocations in the in situ experiments is also caused by surface roughness of the thin TEM specimens leading to what appears to be frictional sliding because of the alternating increase and reduction of line length. 3.5.1. Quantitative evaluation of the in situ experiments In order to retrieve the time-resolved information in the video sequence in a quantitative way, we tried to
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quantify the dislocation motion in terms of a distance versus time pro®le. From digitised images of the whole video sequence, the positions are measured as distances between a point on the dislocation line and the centre of the particle for a dislocation segment close to the particle and for a segment which propagates through the matrix at some distance to the particle. The results are given in Fig. 13 as a function of the elapsed time. Whereas the dislocation segment in the matrix is only slightly slowed down after passing the particle, it can be seen that the segment which actually meets the particle is attached to it for almost 4 s. In the distance±time pro®le this interaction time appears as a horizontal plateau at the position of the particle. A detailed analysis shows that the leading partial comes to rest only at the departure side of the particle, whereas the trailing partial stays at a centre position during that period of time and advances to the departure side once the leading partial detaches from the particle. Furthermore, information on the dissociation width can be inferred from the curves given in Fig. 13. Whereas the two partials travel through the matrix at an almost constant separation distance, it is evident that the dissociation width decreases while the two partials are attached to the particle. This observation can be explained by the fact that the particle diameter is rather small, i.e. less than twice the dissociation width. In summary, the in situ experiments provided very useful support for the observations and conclusions which were obtained by conventional TEM. In particular, in situ observations do not suer from possible relaxations of the dislocation/particle con®guration during cooling down from creep temperatures and they show the complete sequence of con®gurations in the interaction process. Furthermore, we have shown that, with the modern means of digitisation, quantitative information can be extracted from in situ observations. However, the main problem of in situ studies of deformation processes certainly is the thin foil geometry which gives rise to substantial interaction of the dislocations with the two surfaces. In the experiments, this can be seen from the fact that only very short dislocation segments can be observed and that the dislocation motion is markedly slowed down by what appears to be a frictional force exerted by the rough surfaces. Therefore, the most complete model for the underlying process can only be obtained by combining input from both sides, careful ex situ analysis with conventional TEM and direct, time-resolved in situ observation. 4. Concluding remarks In the present paper, we have described selected results of an extensive TEM study on the dislocation con®gurations and the dislocation/particle interaction in
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ODS NiAl, Ni3Al and Fe-rich Fe±Al alloys. Particular emphasis was placed on the details of the interaction of the dislocations with the particles and the information extracted serves as a basis for further theoretical modelling of the hardening eect of the dispersed particles. In all cases, the particles exert a strong retractive force on the dislocations, as is evident from the bowing out of the dislocations between the particles both in specimens cooled down under load and in the in situ experiments. We were able to prove, that the rate limiting step in all cases is the detachment from the back side of the particles and not the climb step across the particles. The main emphasis of the present study was placed on the eect of the dissociation of lattice dislocations, and we could show that the superpartials surmount, and sometimes detach from the particle separately, but that there are also cooperative eects between the partials. The leading partial is always attached to the departure side of the particle and contact angles close to 90 can frequently be observed. In an atomistic model, this can be explained by the fact that the delocalisation of the dislocation core in the particle/matrix interface (which results in an attractive interaction) has to be reversed prior to detachment. The in situ experiments provide further evidence that the climb step is rapid compared with the detachment from the particle, as is assumed in theoretical modelling. The eect of the particles on the dissociation width in the vicinity of the particles strongly depends on the particle diameter. Small particles reduce the dissociation width, which increases the repulsive force between the two partials. An optimum retractive eect seems to be reached for a particle diameter which corresponds to twice the dissociation width, in accordance with theoretical modelling [21]. Our observations show that in this case the leading partial is strongly attached to the departure side of the particle whereas the trailing partial is captured at the maximum of the climb threshold. For larger particles, both partials are able to surmount the particle almost instantly and the trailing partial then exerts a repulsive force on the leading partial driving it closer to the detachment threshold. Overall, the TEM studies lend support to the assumptions made in theoretical modelling of dispersion strengthening in ordered matrices, as is described in detail elsewhere [21]. Acknowledgements We thank B. Inkson, H.J. Schedler, P. Grahle, and E. GoÈhring for their help in the experiments and enlightening discussions. Support by the Deutsche Forschungsgemeinschaft (Project Ar 201, SPP ``Verformung und Bruch geordneter Mischkristalle'') is gratefully acknowledged.
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