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Evaluation of strain caused by coherent precipitates in an Al alloy using TEM techniques
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
Available online at www.sciencedirect.com
www.elsevier.com/locate/matchar
Evaluation of strain caused by coherent precipitates in an Al alloy using TEM techniques J.L. Hernández-Riveraa, c,⁎, J.J. Cruz Riverab , C.G. Garay-Reyesb , M. Ramos Azpeitiab , I. Zúñiga-Alonsob , R. Martínez-Sáncheza a
Centro de Investigación en Materiales Avanzados (CIMAV), Laboratorio Nacional de Nanotecnología, Miguel de Cervantes 120, Z.C. 31109, Chihuahua, Mexico a b Facultad de Ingeniería-Instituto de Metalurgia, Universidad Autónoma de San Luis Potosí, Sierra Leona 550, Lomas 2 sección, Z.C. 78210, San Luis Potosí, Mexico c Universidad del Valle de México, Robles 600, Fraccionamiento Jacarandas, Z. C. 78220, San Luis Potosí, Mexico
AR TIC LE D ATA
ABSTR ACT
Article history:
Elastic strains, caused by GP zones in an aged Al alloy, were determined quantitatively using
Received 19 April 2012
two techniques: Dark Field In-line Holography (DFH) and High Resolution Transmission
Received in revised form 25 July 2012
Electron Microscopy-Geometric Phase Analysis (HRTEM-GPA). The results obtained by both
Accepted 27 July 2012
techniques showed that the elastic strain was not uniform along the precipitate–matrix interface. In some areas, it was found that strain had negligible value and this was attributed to
Keywords:
the loss of coherence between the lattices. It is suggested that a possible explanation for this
Electron microscopy
fact could be a variation in the “vacancies pump mechanism” kinetics. To obtain a better
Aluminum alloys
interpretation of the experimental deformation maps, a reference GP precipitate–matrix
Age hardening
structure was built using QSTEM software. The main advantages of DFH over HRTEM-GPA were a bigger field of view and low electron dose requirements without spatial resolution loss. Another difference found was that crystalline defects such as dislocations were evidenced by HRTEM-GPA in contrast to the result obtained by DFH. However, strain measurements were affected by mask size effect in the former. © 2012 Elsevier Inc. All rights reserved.
1.
Introduction
The initial interest for evaluating elastic strains in crystalline lattices started in the semiconductor materials industry [1,2] when researchers realized that the electric charge carrier's mobility was enhanced in the presence of those strains. On the other hand, there have been also some attempts to quantify elastic strains which are caused by coherent ordered precipitates and ceramic reinforcements in metallic alloys [3,4]. The elastic strain gradient's importance relies on the possibility of including them in the mechanical properties predictions that some theoretical models have, mainly due to
alteration of aging kinetics as well as dislocations mobility [5,6]. One alloy on which aging produces nanoscale precipitates as well as strain fields (due to the different lattice parameter values) is the 2024 Al alloy used in aeronautic applications [7]. Coherent metastable precipitates called Guinnier Preston zones (GP) are generated during the heat treatment and precede stable precipitates Al2Cu (θ) which are incoherent with the Al matrix [8]. On the other hand, among the different techniques available for strain mapping, those based on electron scattering offer the highest spatial resolution. The classical technique for strain
⁎ Corresponding author at: Centro de Investigación en Materiales Avanzados, Laboratorio Nacional de Nanotecnología, Miguel de Cervantes 120, Complejo Industrial Chihuahua, Z.C. 31109, Chihuahua, Mexico. Tel.: +52 614 4391146; fax: +52 614 4391147. E-mail address: [email protected] (J.L. Hernández-Rivera). 1044-5803/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.matchar.2012.07.017
62
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
mapping by TEM is the convergent-beam electron diffraction (CBED). However, it has been noticed in a previous publication that [9] the presence of strain gradients in the illuminated area may cause splitting and broadening of high-order Laue zone (HOLZ) lines which severely hampers the interpretation of CBED patterns in the vicinity of defects. Dark field in-line (DFH) as well as dark field off-axis holography (DOAH) are very promising techniques for evaluating strain fields across a large field of view while maintaining a high spatial resolution of 1 nm for the in-line configuration [10] and 4 nm for the off-axis configuration [11]. Note that, apart from the potentially higher spatial resolution and the much simpler experimental setup, the in-line configuration also offers better signal-to-noise properties compared to its off-axis counterpart [11]. Finally, there is another recently developed technique that Hytch et al. [12] has applied for strain, the so-called geometric phase analysis (GPA) technique, which is based on processing HRTEM micrographs. By using GPA, the variation in the local lattice constant in the HRTEM micrographs is calculated by taking a strain free area as a reference [12]. Despite its limitation of a relatively small field of view, the method has been used successfully to quantify strain fields around dislocations [13], Ge nanowires [14] and more recently on Al–Pb interfaces [15]. Because elastic strain values, caused by GP precipitates, are still controversial in the literature [16], this work presents a quantitative comparison of the results obtained by the DFH and HRTEM-GP techniques.
2.
Materials and Methods
Al-2024 alloy, with composition adjusted to the range of commercial alloy, was fabricated by mechanical alloying, sintering and hot extrusion. Hot-extruded samples were solution treated at 530 °C and artificially aged at 140 °C for different lengths of time. Microhardness measurements were performed to evaluate this property behavior as a function of aging time. The maximum hardness observed was obtained after 15 h. Due to this, samples with 13 h of aging (i.e. prior to the maximum attainable hardness) were selected to determine elastic strain fields around GP zones. Preparation of samples for electron microscopy was carried out using ultrasonic cutting, mechanical grinding, jet electropolishing and ion milling. HRTEM work was performed in a JEOL 4000FX microscope operated at 400 kV. Dark field holograms were recorded in the Sub-Electron-Volt Sub-Angstrom Microscope (SESAM) (Carl-Zeiss NTS) operated at 200 kV. To avoid commonly observed artifacts in strain maps (caused by aberrations in HRTEM images), the GPA algorithm was applied to the exit face wave function (EWF). The EWF was reconstructed from a series of HRTEM micrographs recorded at different values of the defocus with the sample oriented along the [001] zone axis using an algorithm proposed by Koch [17]. This algorithm reconstructs an exit face wave function from a set of defocused images by solving a non-linear set of equations. The algorithm also aligns the different images and attempts to correct them for the electron optical distortions caused by the different conditions they have been recorded under. For further details on this procedure it is recommended to read reference [17].
A modified version of the original GPA algorithm was applied [12], which allows for extracting the geometric phase from the EWF. A cosine mask of 0.4 nm−1 in size was applied to obtain the (200) and (020) geometric phase maps, perpendicular (x-axis) and parallel (y-axis) to the GP zones, respectively. Dark-field focal series were taken from (002) and (020) reflections using an objective aperture of 10 μm. SESAM's in-column MANDOLINE filter was used to remove the contribution of inelastically scattered electrons to the recorded micrographs. After that, the modified version of GPA [12] was applied to extract the amplitude and phase from the EWF. In addition, a reference atomic model, consisting of a GP precipitate embedded in an Al supercell, was created by using the software QSTEM [18], which is based in the multislice method proposed by Cowley et al. [19]. The GP precipitate model consisted of a tetragonal lattice with two Cu planes separated by three Al planes with lattice parameters of 0.4049 × 0.4049 × 0.768 nm [16]. Additionally, a uniform strain of 2% was introduced in the first five (200) adjacent planes according to the lattice mismatch between the GP structure and the Al matrix which was considered to have a face centered cubic structure and a lattice parameter of 0.4049 nm. The EWF of this model structure was simulated using the software QSTEM [18].
3.
Results
3.1.
High Resolution Transmission Electron Microscopy
Fig. 1A presents an entire crystal view where the analysis was performed, while Fig. 1B shows the morphology of the precipitates observed by TEM at higher magnifications. Due to these precipitates growing only in certain directions of the Al lattice, it was necessary to orientate this grain along the [001] zone axis. An indicator that the crystal was oriented accurately along this zone axis was the electron diffraction pattern shown in Fig. 1B (top right). It was also observed that the separation distances between the precipitates were variable. It has been reported that the general form of GP precipitates is close to a rectangular prism with dimensions of 15× 15 ×1.5 nm [16]. Elastic strain caused by the difference between the precipitate and matrix lattice parameters, was measured in the surroundings of the precipitates specifically in the direction parallel to the dimension of 1.5 nm. Fig. 2A shows the results obtained in the reconstruction of the EWF from HRTEM experimental images. To apply the GPA technique, the experimental EWF image had to be rotated so that the precipitate stayed aligned with the vertical direction. A certain discontinuity was observed in the crystalline lattice periodicity of experimental EWF micrograph (indicated by a dark ellipse). Therefore, only the region localized to the right of the precipitate was taken into account for application of GPA. In the case of the EWF of the simulated reference lattice shown in Fig. 2B, which was constructed considering idealized conditions. As expected there were no defects during reconstruction. Consequently, both sides of the precipitate were considered for the application of GPA. Fig. 3 shows the strain maps obtained by HRTEM-GPA. The experimental results are presented on the left side while those
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
63
Fig. 2 – Micrographs showing the reconstruction of EWF: A) experimental and B) simulated.
Fig. 1 – TEM images showing: A) the crystal in which the elastic strains were evaluated and B) the precipitates inside the crystal (higher magnifications) together with the typical [001] zone-axis diffraction pattern (top right).
corresponding to the simulated reference lattice are on the right. Additionally, the zones where strain profiles were measured (linescans 1 and 2) and the regions of reference (Aref) are
identified in this figure. The strain component tensor εxx was measured in the x axis (indicated on the simulated reference map in the bottom left corner). In addition, the y axis was considered to be perpendicular to the x axis. In the case of evaluation of εxx in the simulated reference model, it can be seen that certain zones near the precipitate are subjected to tension (red color in Fig. 3), while the rest of the lattice is free of strain in a congruent manner as it was originated. The input 2%-strain value used in the model in a length of 1 nm, was verified and it was found to be 2.4 ± 0.2% on average. At this point, it is noteworthy that fluctuations in the results of this technique are generated mainly due to the mask (aperture) size effect used to select the crystalline reflections (g) in the Fourier's space and in a lower scale because of the noise level that exists in the zone taken as reference [12]. These fluctuations will be described in following paragraphs. The results of experimental εxx show different characteristics. It is observed that the strain distribution is not uniform along GP zone–matrix interface, and it seems to be concentrated close to bottom-right part of the GP zone (indicated with letter A in Fig. 3). The maximum strain was obtained in linescan 2 and its value was about 3.9± 0.4%. In the same map, a strain field can
64
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
Fig. 3 – Strain maps obtained by GPA: (left) experimental and (right) simulated by QSTEM. Graphics of these estimations are presented in the middle. Dotted-line rectangles show areas where the strain profiles were obtained and dashed-line rectangles indicate zones of reference. The black rectangle indicates the position of the precipitate.
be observed, and it was caused by a dislocation which is pointed out with a dark circle. It is suggested that this dislocation corresponds to the discontinuity in the crystalline lattice periodicity, which was commented previously (indicated with an ellipse in Fig. 2B). On the other hand, in experimental and reference profiles there are negative strain values which were measured in areas that were supposed to be strain-free. It is important to point out that the average of these values was lower in the reference profile (approximately −0.3%) compared with those from experimental maps (about −1.2%). Such kinds of fluctuations on strain maps have been reported previously [12,20]. On these reports it is suggested that a variation in the mask size leads to important strain value fluctuations. We believe that the mask size effect is present in both, positive and negative values in our strain profiles. As a similar mask size was used in experimental and reference cases, the mask size effect should have the same value in the strain profiles. Furthermore, we can suggest that it corresponds to the value that was measured in the reference model (−0.3%) because only this effect can be present. Therefore, if the mask size effect of − 0.3% is subtracted from the − 1.2% (for the experimental profile), we obtain a value of − 0.9%. It is believed that this strain difference has been caused by other factors such as marginal changes in the crystal orientation or composition changes in the zone near to matrix– precipitate interface, which can occur locally or through the sample thickness. Unfortunately up to now, the GPA algorithm is not able to take into account such crystalline imperfections to include their effects in the deformation quantification. As has been already mentioned, we believe that total negative strain value (either from mask size effect or crystalline imperfections), is included in the positive part of the experimental profile. For this reason, we propose that total negative strain should be subtracted from the positive value in order to obtain the true strain caused in the matrix due to the GP zone. If we reason this way and we subtract the value of −0.3% (caused by the mask size effect) from the average strain value of
2.4% (for the reference profile), then the resulting strain is 2.1 ± 0.2%, which is similar to the value intentionally introduced in the atomic model. For the experimental case, if we subtract the value of −1.2% from the average strain value of 2.3%, we obtain a strain average value of approximately 1.1 ± 0.4% in the matrix. Finally, the considerations of this section can only be further validated by using a second quantifying method which is presented in the following section.
3.2.
In Line Dark Holography
Fig. 4A and D present the dark field holograms obtained by the DFH technique using the algorithm developed by Koch [10] for reflections [002] and [020], respectively. These holograms illustrate the regions in which the diffraction of the selected vector g was more approximated to the Bragg's condition (white rectangles). It is important to clarify that only one crystallographic variant of the precipitates could be reconstructed for each vector g selected due to the crystalline symmetry. The strain maps obtained for each variant are presented in Fig. 4C and F. In the first image the strain was evaluated in the direction that the dark arrow indicates and in a perpendicular direction in the second map. From these results, it is evident that by using this technique, the field of view evaluated increased significantly. This meant that a larger number of strain fields could be determined in the same reconstruction in comparison with the HRTEM method. The areas where strain by tension was observed are colored in red and are visible in both sides of the precipitates. In addition, the colored-blue precipitates indicate that GP zones are in compression. The rest of the map, colored in green, shows strain-free areas. Worthy of mention is that the free-precipitate zone near to the crystal edge, has been reconstructed properly and is a strain-free zone. Fig. 4B and E illustrate two strain profiles, measured in the precipitates that are indicated with a black ellipse in Fig. 4C and D. Based on these observations it can be stated that, in most of the cases, strain is not homogeneous on both sides of the GP
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
65
Fig. 4 – A) and D) Micrographs of the dark field holograms obtained from reflections [002] and [020], respectively; C) and D) strain maps obtained in two crystalline directions, the black ellipses indicate the areas where the strain profiles, showed in panels B and E, respectively, were evaluated.
zones. Moreover, there exist fluctuations from one region to other. For instance, in the profile shown in Fig. 4B, the maximum strain registered in one side of the precipitate reaches an average
value of 1.45±0.2% and 0.45 ±0.2% on the other side. In the case of the profile presented in Fig. 4E, average strains of 0.9 and 0.5 ± 0.2% are observed on both sides of the precipitate.
66
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
It is important to point it out that in this method the mask size effect does not exist as discussed in the previous section, so that fluctuations observed in the results were considered inherent to the technique without having any important contribution. Finally, the surrounding regions of the crystal studied had different crystalline orientations than the one of the zone axis, and the reconstruction in those areas was not adequate.
4.
Discussion
The complex distribution of the strain fields found by the two techniques, leads to some important conclusions. One of them is that the non-uniformity of the strain distribution can be attributed to microstructural factors that possibly occur at different rates near the precipitate–matrix interface, such as variations in the stoichiometry of the precipitate [16]. The explanation for this refers to the mode through which the elastic strains are “relieved” through the aging treatment. It has been established that the strain-relief around the precipitate can occur due to the so-called “vacancy pump” mechanism, which consists of the migration of vacancies and alloying atoms (Cu in this case) to the strain fields around the precipitate, promoting its growth [21]. When precipitates reach certain dimensions during this step, the coherence strain reaches a limiting value and then the process of loss of coherence begins. Now, the vacancies are aggregated and form dislocation loops that migrate to the precipitate–matrix interface decreasing gradually the strain caused in the matrix. The different kinetics by which this process occurs depends directly on the amount of vacancies present in the precipitate surroundings, which is not uniform. On the other hand, it has been found by a combination of studies of tomographic atom probe (TAP) and HRTEM that the layers of Cu present in GP zones, previously thought to have 100% of this element, have less content [16,24]. Karlik et al. [16] has proposed that concentration of this element varies from 40 to 100%. Bigot et al. [22] reported a Cu content of approximately 50%. These works that have demonstrated the non-uniformity in the GP zones' stoichiometry set the trend to suppose that this is another important factor that affected the strain distribution heterogeneously. Another factor that can explain the difference in the strain level between the experimental and simulated reference maps is that it may be a variation in the number of Cu or Al layers that form the precipitate. If a variation of this type exists as reported in reference [23], the values of the strain will change. Unfortunately, the focal series of HRTEM images obtained in this work did not allow for distinguishing effectively which layers correspond to Cu or Al atoms. The reason is that the contrast on these images is influenced by several factors either from the sample or the microscope. Some examples include thickness changes, amorphous layers and composition gradients in the first case and in the second one, objective lens aberrations and defocus and beam tilt. From the above, it is assumed that the precipitates studied as well as the one considered as reference do not differ in this last point.
A second conclusion that has been reached refers to the advantage of using each technique in the study of GP zones. For example, it was observed that the GPA-HRTEM technique offers the advantage of exhibiting clearly the lattice defects such as the dislocation observed. However, this method is more likely to have variations in the results caused by the size of the mask used during processing. Also, the field of view is much more reduced and the requirements of the electron dose during acquisition of micrographs are greater. By using DFH, it was possible to reconstruct the strain fields with a spatial resolution comparable to GPA-HRTEM. Besides, the requirements of electron dose were much lower (as a result the damage to the specimen is less), a mask to work in the Fourier's space is not used (therefore, the spurious fluctuations are minimized) and finally the field of view increases considerably, which allows for a reconstruction of a larger number of GP zones.
5.
Conclusions
It was demonstrated that the two TEM techniques used in this work were able to show the strain fields caused in the Al matrix by GP zones. Besides, it can be mentioned that the results obtained by these techniques were consistent, in the sense that elastic strain was not homogeneous in the surroundings of the precipitates. This fact was explained based on kinetic differences with which the microstructural events decrease and relieve this type of strain. It can be affirmed that the DFH technique showed important advantages over the GPA-HRTEM. For example, the field of view was larger in the former, maintaining a spatial resolution very similar to that of the latter. In addition, the requirements of electron dose to obtain the micrographs are much less for DFH than for HRTEM by which sample damages are avoided when observed. However, the GPA-HRTEM technique was able to exhibit crystalline defects such as dislocations, which did not occur with DFH. Finally, it can be established that the discrepancy between the results obtained by the two techniques was caused mainly because in DFH there was not a contribution of the mask size effect. However, in the GPA-HRTEM this effect caused important variations.
Acknowledgments This research constitutes a portion of the thesis to be submitted by JLHR to CIMAV in partial fulfillment of the requirements for the Ph.D. degree. It was supported by a scholarship provided to the author by CONACYT (no. 27519). A special acknowledgment is extended to the workers at Stuttgart Center for Electron Microscopy at Max Planck Institute of Intelligent Systems for the kind support received during the performance of the experimental work and simulation. Thanks go especially to Dr. Peter van Aken, Eric Detemple, Burak Özdöl and Cigdem Özöy. Thanks also to Dr. C. T. Koch for his teachings, patience and gentleness and to Marion Kelsch, Peter Kopold and Kestern Hann for their technical assistance and teachings.
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
REFERENCES [1] Zhao W. Ph.D. Thesis. Reliable local strain characterization in Si/SiGe based electronic materials system. North Carolina State University, 2006. [2] Huang J. Ph.D. Thesis. Characterization of nanoscale local lattice strains in Si CMOS devices by TEM/CBED. University of Texas at Dallas, 2006. [3] Wittmann R, Kruse P, Frauenkron M, Gerthsen D. An investigation of strain fields in dispersion strengthened aluminium by convergent beam electron diffraction. Philos Mag A 2000;80:2215-32. [4] Chen W, Liu QKK, Schumacher G, Wanderka N, Neumann W, Chen W, et al. Elastic strain energy study of directional coarsening of γ′ precipitates in single crystal superalloys: a 3D finite element analysis. In: Hazotte A, editor. Solid state transformation and heat treatment. Weinheim: Wiley-VCH Verlag; 2005. p. 69-76. [5] Neumann MX. Modeling the hardness and yield strength evolutions of aluminum alloy with rod/needle-shaped precipitates. Mater Sci Eng A 2007;443:172-5. [6] Song M, Li X, Chen KH. Modeling the age-hardening behavior of SiC/Al metal matrix composites. Metall Mater Trans A 2007;38:638-48. [7] Rendigs KH. Aluminum structures used in aerospace status and prospects. Mater Sci Forum 1997;242:11-24. [8] Martin JW. Precipitate hardening. 2nd ed. Oxford: Butterworh Heinemann; 1998. [9] Jones PM, Rackham GM, Steeds JW. Higher order laue zone effects in electron diffraction and their use in lattice parameter determination. Proc R Soc A 1977;354:197-215. [10] Koch CT, Özdöl VB, van Aken PA. An efficient, simple, and precise way to map strain with nanometer resolution in semiconductor devices. Appl Phys Lett 2010;96:091901-9. [11] Hÿtch M, Houdellier MJ, Hüe F, Snoeck E. Nanoscale holographic interferometry for strain measurements in electronic devices. Nature 2008;453:1086-9. [12] Hÿtch MJ, Snoeck E, Kilaas R. Quantitative measurement of displacement and strain from HREM micrographs. Ultramicroscopy 1998;74:131-46.
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[13] Hÿtch MJ, Putaux JL, Thibault J. Stress and strain around grain boundary dislocations measured by HREM. Philos Mag A 2006;86:4641-56. [14] Taraci JL, Hytch MJ, Clement T, Peralta P, McCartney MR, Drucker J, et al. Strain mapping in nanowires. Nanotechnology 2005;16:2365-71. [15] Rösner H, Koch CT, Wilde G. Strain mapping in a deformation-twinned nanocrystalline Pd grain. Acta Mater 2010;58:162-72. [16] Karlik M, Bigot A, Jouffrey B, Auger PS. HREM, FIM and tomographic atom probe investigation of Guinier–Preston zones in an Al–1.54 at% Cu alloy. Ultramicroscopy 2004;98: 219-30. [17] Koch CT. A flux-preserving non-linear inline holography reconstruction algorithm for partially coherent electrons. Ultramicroscopy 2008;108:141-50. [18] Koch CT. PhD. Thesis. Determination of core structure periodicity and point defect density along dislocations. Arizona State University, 2002. [19] Cowley JM, Moodie AF. The scattering of electrons by atoms and crystals: a new theoretical approach. Acta Crystallogr A 1957;10:609-19. [20] Guerrero E, Galindo P, Yañez A, Ben T, Molina SI. Error quantification in strain mapping methods. Microsc Microanal 2007;13:320-8. [21] Ipohorski M, Bonfiglioli F. Kinetics of growth of spherical GP zones: experimental verification of the vacancy pump model. Acta Metall Mater 1970;18:281-5. [22] Bigot A, Danoix F, Auger P, Blavette D, Menand A. 3D reconstruction and analysis of GP zones in Al–1.7Cu (at%): a tomographic atom probe investigation. Appl Surf Sci 1996;94–95:261-6. [23] Konno TJ, Kawasaki M, Hiraga K. Guinier–Preston observed by high-angle annular detector dark-field scanning transmission electron microscopy. Philos Mag B 2001;81:1713-24. [24] Kret S, Ruterana P, Rosenauer A, Gerthsen D. Extracting quantitative information from high resolution electron microscopy. Phys Status Solidi 2001;227:247-95.
Available online at www.sciencedirect.com
www.elsevier.com/locate/matchar
Evaluation of strain caused by coherent precipitates in an Al alloy using TEM techniques J.L. Hernández-Riveraa, c,⁎, J.J. Cruz Riverab , C.G. Garay-Reyesb , M. Ramos Azpeitiab , I. Zúñiga-Alonsob , R. Martínez-Sáncheza a
Centro de Investigación en Materiales Avanzados (CIMAV), Laboratorio Nacional de Nanotecnología, Miguel de Cervantes 120, Z.C. 31109, Chihuahua, Mexico a b Facultad de Ingeniería-Instituto de Metalurgia, Universidad Autónoma de San Luis Potosí, Sierra Leona 550, Lomas 2 sección, Z.C. 78210, San Luis Potosí, Mexico c Universidad del Valle de México, Robles 600, Fraccionamiento Jacarandas, Z. C. 78220, San Luis Potosí, Mexico
AR TIC LE D ATA
ABSTR ACT
Article history:
Elastic strains, caused by GP zones in an aged Al alloy, were determined quantitatively using
Received 19 April 2012
two techniques: Dark Field In-line Holography (DFH) and High Resolution Transmission
Received in revised form 25 July 2012
Electron Microscopy-Geometric Phase Analysis (HRTEM-GPA). The results obtained by both
Accepted 27 July 2012
techniques showed that the elastic strain was not uniform along the precipitate–matrix interface. In some areas, it was found that strain had negligible value and this was attributed to
Keywords:
the loss of coherence between the lattices. It is suggested that a possible explanation for this
Electron microscopy
fact could be a variation in the “vacancies pump mechanism” kinetics. To obtain a better
Aluminum alloys
interpretation of the experimental deformation maps, a reference GP precipitate–matrix
Age hardening
structure was built using QSTEM software. The main advantages of DFH over HRTEM-GPA were a bigger field of view and low electron dose requirements without spatial resolution loss. Another difference found was that crystalline defects such as dislocations were evidenced by HRTEM-GPA in contrast to the result obtained by DFH. However, strain measurements were affected by mask size effect in the former. © 2012 Elsevier Inc. All rights reserved.
1.
Introduction
The initial interest for evaluating elastic strains in crystalline lattices started in the semiconductor materials industry [1,2] when researchers realized that the electric charge carrier's mobility was enhanced in the presence of those strains. On the other hand, there have been also some attempts to quantify elastic strains which are caused by coherent ordered precipitates and ceramic reinforcements in metallic alloys [3,4]. The elastic strain gradient's importance relies on the possibility of including them in the mechanical properties predictions that some theoretical models have, mainly due to
alteration of aging kinetics as well as dislocations mobility [5,6]. One alloy on which aging produces nanoscale precipitates as well as strain fields (due to the different lattice parameter values) is the 2024 Al alloy used in aeronautic applications [7]. Coherent metastable precipitates called Guinnier Preston zones (GP) are generated during the heat treatment and precede stable precipitates Al2Cu (θ) which are incoherent with the Al matrix [8]. On the other hand, among the different techniques available for strain mapping, those based on electron scattering offer the highest spatial resolution. The classical technique for strain
⁎ Corresponding author at: Centro de Investigación en Materiales Avanzados, Laboratorio Nacional de Nanotecnología, Miguel de Cervantes 120, Complejo Industrial Chihuahua, Z.C. 31109, Chihuahua, Mexico. Tel.: +52 614 4391146; fax: +52 614 4391147. E-mail address: [email protected] (J.L. Hernández-Rivera). 1044-5803/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.matchar.2012.07.017
62
MA TE RI A L S CH A R A CT ER IZ A TI O N 7 3 (2 0 1 2) 6 1–6 7
mapping by TEM is the convergent-beam electron diffraction (CBED). However, it has been noticed in a previous publication that [9] the presence of strain gradients in the illuminated area may cause splitting and broadening of high-order Laue zone (HOLZ) lines which severely hampers the interpretation of CBED patterns in the vicinity of defects. Dark field in-line (DFH) as well as dark field off-axis holography (DOAH) are very promising techniques for evaluating strain fields across a large field of view while maintaining a high spatial resolution of 1 nm for the in-line configuration [10] and 4 nm for the off-axis configuration [11]. Note that, apart from the potentially higher spatial resolution and the much simpler experimental setup, the in-line configuration also offers better signal-to-noise properties compared to its off-axis counterpart [11]. Finally, there is another recently developed technique that Hytch et al. [12] has applied for strain, the so-called geometric phase analysis (GPA) technique, which is based on processing HRTEM micrographs. By using GPA, the variation in the local lattice constant in the HRTEM micrographs is calculated by taking a strain free area as a reference [12]. Despite its limitation of a relatively small field of view, the method has been used successfully to quantify strain fields around dislocations [13], Ge nanowires [14] and more recently on Al–Pb interfaces [15]. Because elastic strain values, caused by GP precipitates, are still controversial in the literature [16], this work presents a quantitative comparison of the results obtained by the DFH and HRTEM-GP techniques.
2.
Materials and Methods
Al-2024 alloy, with composition adjusted to the range of commercial alloy, was fabricated by mechanical alloying, sintering and hot extrusion. Hot-extruded samples were solution treated at 530 °C and artificially aged at 140 °C for different lengths of time. Microhardness measurements were performed to evaluate this property behavior as a function of aging time. The maximum hardness observed was obtained after 15 h. Due to this, samples with 13 h of aging (i.e. prior to the maximum attainable hardness) were selected to determine elastic strain fields around GP zones. Preparation of samples for electron microscopy was carried out using ultrasonic cutting, mechanical grinding, jet electropolishing and ion milling. HRTEM work was performed in a JEOL 4000FX microscope operated at 400 kV. Dark field holograms were recorded in the Sub-Electron-Volt Sub-Angstrom Microscope (SESAM) (Carl-Zeiss NTS) operated at 200 kV. To avoid commonly observed artifacts in strain maps (caused by aberrations in HRTEM images), the GPA algorithm was applied to the exit face wave function (EWF). The EWF was reconstructed from a series of HRTEM micrographs recorded at different values of the defocus with the sample oriented along the [001] zone axis using an algorithm proposed by Koch [17]. This algorithm reconstructs an exit face wave function from a set of defocused images by solving a non-linear set of equations. The algorithm also aligns the different images and attempts to correct them for the electron optical distortions caused by the different conditions they have been recorded under. For further details on this procedure it is recommended to read reference [17].
A modified version of the original GPA algorithm was applied [12], which allows for extracting the geometric phase from the EWF. A cosine mask of 0.4 nm−1 in size was applied to obtain the (200) and (020) geometric phase maps, perpendicular (x-axis) and parallel (y-axis) to the GP zones, respectively. Dark-field focal series were taken from (002) and (020) reflections using an objective aperture of 10 μm. SESAM's in-column MANDOLINE filter was used to remove the contribution of inelastically scattered electrons to the recorded micrographs. After that, the modified version of GPA [12] was applied to extract the amplitude and phase from the EWF. In addition, a reference atomic model, consisting of a GP precipitate embedded in an Al supercell, was created by using the software QSTEM [18], which is based in the multislice method proposed by Cowley et al. [19]. The GP precipitate model consisted of a tetragonal lattice with two Cu planes separated by three Al planes with lattice parameters of 0.4049 × 0.4049 × 0.768 nm [16]. Additionally, a uniform strain of 2% was introduced in the first five (200) adjacent planes according to the lattice mismatch between the GP structure and the Al matrix which was considered to have a face centered cubic structure and a lattice parameter of 0.4049 nm. The EWF of this model structure was simulated using the software QSTEM [18].
3.
Results
3.1.
High Resolution Transmission Electron Microscopy
Fig. 1A presents an entire crystal view where the analysis was performed, while Fig. 1B shows the morphology of the precipitates observed by TEM at higher magnifications. Due to these precipitates growing only in certain directions of the Al lattice, it was necessary to orientate this grain along the [001] zone axis. An indicator that the crystal was oriented accurately along this zone axis was the electron diffraction pattern shown in Fig. 1B (top right). It was also observed that the separation distances between the precipitates were variable. It has been reported that the general form of GP precipitates is close to a rectangular prism with dimensions of 15× 15 ×1.5 nm [16]. Elastic strain caused by the difference between the precipitate and matrix lattice parameters, was measured in the surroundings of the precipitates specifically in the direction parallel to the dimension of 1.5 nm. Fig. 2A shows the results obtained in the reconstruction of the EWF from HRTEM experimental images. To apply the GPA technique, the experimental EWF image had to be rotated so that the precipitate stayed aligned with the vertical direction. A certain discontinuity was observed in the crystalline lattice periodicity of experimental EWF micrograph (indicated by a dark ellipse). Therefore, only the region localized to the right of the precipitate was taken into account for application of GPA. In the case of the EWF of the simulated reference lattice shown in Fig. 2B, which was constructed considering idealized conditions. As expected there were no defects during reconstruction. Consequently, both sides of the precipitate were considered for the application of GPA. Fig. 3 shows the strain maps obtained by HRTEM-GPA. The experimental results are presented on the left side while those
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Fig. 2 – Micrographs showing the reconstruction of EWF: A) experimental and B) simulated.
Fig. 1 – TEM images showing: A) the crystal in which the elastic strains were evaluated and B) the precipitates inside the crystal (higher magnifications) together with the typical [001] zone-axis diffraction pattern (top right).
corresponding to the simulated reference lattice are on the right. Additionally, the zones where strain profiles were measured (linescans 1 and 2) and the regions of reference (Aref) are
identified in this figure. The strain component tensor εxx was measured in the x axis (indicated on the simulated reference map in the bottom left corner). In addition, the y axis was considered to be perpendicular to the x axis. In the case of evaluation of εxx in the simulated reference model, it can be seen that certain zones near the precipitate are subjected to tension (red color in Fig. 3), while the rest of the lattice is free of strain in a congruent manner as it was originated. The input 2%-strain value used in the model in a length of 1 nm, was verified and it was found to be 2.4 ± 0.2% on average. At this point, it is noteworthy that fluctuations in the results of this technique are generated mainly due to the mask (aperture) size effect used to select the crystalline reflections (g) in the Fourier's space and in a lower scale because of the noise level that exists in the zone taken as reference [12]. These fluctuations will be described in following paragraphs. The results of experimental εxx show different characteristics. It is observed that the strain distribution is not uniform along GP zone–matrix interface, and it seems to be concentrated close to bottom-right part of the GP zone (indicated with letter A in Fig. 3). The maximum strain was obtained in linescan 2 and its value was about 3.9± 0.4%. In the same map, a strain field can
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Fig. 3 – Strain maps obtained by GPA: (left) experimental and (right) simulated by QSTEM. Graphics of these estimations are presented in the middle. Dotted-line rectangles show areas where the strain profiles were obtained and dashed-line rectangles indicate zones of reference. The black rectangle indicates the position of the precipitate.
be observed, and it was caused by a dislocation which is pointed out with a dark circle. It is suggested that this dislocation corresponds to the discontinuity in the crystalline lattice periodicity, which was commented previously (indicated with an ellipse in Fig. 2B). On the other hand, in experimental and reference profiles there are negative strain values which were measured in areas that were supposed to be strain-free. It is important to point out that the average of these values was lower in the reference profile (approximately −0.3%) compared with those from experimental maps (about −1.2%). Such kinds of fluctuations on strain maps have been reported previously [12,20]. On these reports it is suggested that a variation in the mask size leads to important strain value fluctuations. We believe that the mask size effect is present in both, positive and negative values in our strain profiles. As a similar mask size was used in experimental and reference cases, the mask size effect should have the same value in the strain profiles. Furthermore, we can suggest that it corresponds to the value that was measured in the reference model (−0.3%) because only this effect can be present. Therefore, if the mask size effect of − 0.3% is subtracted from the − 1.2% (for the experimental profile), we obtain a value of − 0.9%. It is believed that this strain difference has been caused by other factors such as marginal changes in the crystal orientation or composition changes in the zone near to matrix– precipitate interface, which can occur locally or through the sample thickness. Unfortunately up to now, the GPA algorithm is not able to take into account such crystalline imperfections to include their effects in the deformation quantification. As has been already mentioned, we believe that total negative strain value (either from mask size effect or crystalline imperfections), is included in the positive part of the experimental profile. For this reason, we propose that total negative strain should be subtracted from the positive value in order to obtain the true strain caused in the matrix due to the GP zone. If we reason this way and we subtract the value of −0.3% (caused by the mask size effect) from the average strain value of
2.4% (for the reference profile), then the resulting strain is 2.1 ± 0.2%, which is similar to the value intentionally introduced in the atomic model. For the experimental case, if we subtract the value of −1.2% from the average strain value of 2.3%, we obtain a strain average value of approximately 1.1 ± 0.4% in the matrix. Finally, the considerations of this section can only be further validated by using a second quantifying method which is presented in the following section.
3.2.
In Line Dark Holography
Fig. 4A and D present the dark field holograms obtained by the DFH technique using the algorithm developed by Koch [10] for reflections [002] and [020], respectively. These holograms illustrate the regions in which the diffraction of the selected vector g was more approximated to the Bragg's condition (white rectangles). It is important to clarify that only one crystallographic variant of the precipitates could be reconstructed for each vector g selected due to the crystalline symmetry. The strain maps obtained for each variant are presented in Fig. 4C and F. In the first image the strain was evaluated in the direction that the dark arrow indicates and in a perpendicular direction in the second map. From these results, it is evident that by using this technique, the field of view evaluated increased significantly. This meant that a larger number of strain fields could be determined in the same reconstruction in comparison with the HRTEM method. The areas where strain by tension was observed are colored in red and are visible in both sides of the precipitates. In addition, the colored-blue precipitates indicate that GP zones are in compression. The rest of the map, colored in green, shows strain-free areas. Worthy of mention is that the free-precipitate zone near to the crystal edge, has been reconstructed properly and is a strain-free zone. Fig. 4B and E illustrate two strain profiles, measured in the precipitates that are indicated with a black ellipse in Fig. 4C and D. Based on these observations it can be stated that, in most of the cases, strain is not homogeneous on both sides of the GP
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Fig. 4 – A) and D) Micrographs of the dark field holograms obtained from reflections [002] and [020], respectively; C) and D) strain maps obtained in two crystalline directions, the black ellipses indicate the areas where the strain profiles, showed in panels B and E, respectively, were evaluated.
zones. Moreover, there exist fluctuations from one region to other. For instance, in the profile shown in Fig. 4B, the maximum strain registered in one side of the precipitate reaches an average
value of 1.45±0.2% and 0.45 ±0.2% on the other side. In the case of the profile presented in Fig. 4E, average strains of 0.9 and 0.5 ± 0.2% are observed on both sides of the precipitate.
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It is important to point it out that in this method the mask size effect does not exist as discussed in the previous section, so that fluctuations observed in the results were considered inherent to the technique without having any important contribution. Finally, the surrounding regions of the crystal studied had different crystalline orientations than the one of the zone axis, and the reconstruction in those areas was not adequate.
4.
Discussion
The complex distribution of the strain fields found by the two techniques, leads to some important conclusions. One of them is that the non-uniformity of the strain distribution can be attributed to microstructural factors that possibly occur at different rates near the precipitate–matrix interface, such as variations in the stoichiometry of the precipitate [16]. The explanation for this refers to the mode through which the elastic strains are “relieved” through the aging treatment. It has been established that the strain-relief around the precipitate can occur due to the so-called “vacancy pump” mechanism, which consists of the migration of vacancies and alloying atoms (Cu in this case) to the strain fields around the precipitate, promoting its growth [21]. When precipitates reach certain dimensions during this step, the coherence strain reaches a limiting value and then the process of loss of coherence begins. Now, the vacancies are aggregated and form dislocation loops that migrate to the precipitate–matrix interface decreasing gradually the strain caused in the matrix. The different kinetics by which this process occurs depends directly on the amount of vacancies present in the precipitate surroundings, which is not uniform. On the other hand, it has been found by a combination of studies of tomographic atom probe (TAP) and HRTEM that the layers of Cu present in GP zones, previously thought to have 100% of this element, have less content [16,24]. Karlik et al. [16] has proposed that concentration of this element varies from 40 to 100%. Bigot et al. [22] reported a Cu content of approximately 50%. These works that have demonstrated the non-uniformity in the GP zones' stoichiometry set the trend to suppose that this is another important factor that affected the strain distribution heterogeneously. Another factor that can explain the difference in the strain level between the experimental and simulated reference maps is that it may be a variation in the number of Cu or Al layers that form the precipitate. If a variation of this type exists as reported in reference [23], the values of the strain will change. Unfortunately, the focal series of HRTEM images obtained in this work did not allow for distinguishing effectively which layers correspond to Cu or Al atoms. The reason is that the contrast on these images is influenced by several factors either from the sample or the microscope. Some examples include thickness changes, amorphous layers and composition gradients in the first case and in the second one, objective lens aberrations and defocus and beam tilt. From the above, it is assumed that the precipitates studied as well as the one considered as reference do not differ in this last point.
A second conclusion that has been reached refers to the advantage of using each technique in the study of GP zones. For example, it was observed that the GPA-HRTEM technique offers the advantage of exhibiting clearly the lattice defects such as the dislocation observed. However, this method is more likely to have variations in the results caused by the size of the mask used during processing. Also, the field of view is much more reduced and the requirements of the electron dose during acquisition of micrographs are greater. By using DFH, it was possible to reconstruct the strain fields with a spatial resolution comparable to GPA-HRTEM. Besides, the requirements of electron dose were much lower (as a result the damage to the specimen is less), a mask to work in the Fourier's space is not used (therefore, the spurious fluctuations are minimized) and finally the field of view increases considerably, which allows for a reconstruction of a larger number of GP zones.
5.
Conclusions
It was demonstrated that the two TEM techniques used in this work were able to show the strain fields caused in the Al matrix by GP zones. Besides, it can be mentioned that the results obtained by these techniques were consistent, in the sense that elastic strain was not homogeneous in the surroundings of the precipitates. This fact was explained based on kinetic differences with which the microstructural events decrease and relieve this type of strain. It can be affirmed that the DFH technique showed important advantages over the GPA-HRTEM. For example, the field of view was larger in the former, maintaining a spatial resolution very similar to that of the latter. In addition, the requirements of electron dose to obtain the micrographs are much less for DFH than for HRTEM by which sample damages are avoided when observed. However, the GPA-HRTEM technique was able to exhibit crystalline defects such as dislocations, which did not occur with DFH. Finally, it can be established that the discrepancy between the results obtained by the two techniques was caused mainly because in DFH there was not a contribution of the mask size effect. However, in the GPA-HRTEM this effect caused important variations.
Acknowledgments This research constitutes a portion of the thesis to be submitted by JLHR to CIMAV in partial fulfillment of the requirements for the Ph.D. degree. It was supported by a scholarship provided to the author by CONACYT (no. 27519). A special acknowledgment is extended to the workers at Stuttgart Center for Electron Microscopy at Max Planck Institute of Intelligent Systems for the kind support received during the performance of the experimental work and simulation. Thanks go especially to Dr. Peter van Aken, Eric Detemple, Burak Özdöl and Cigdem Özöy. Thanks also to Dr. C. T. Koch for his teachings, patience and gentleness and to Marion Kelsch, Peter Kopold and Kestern Hann for their technical assistance and teachings.
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