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Deformation in nanocrystalline ceramics: A microstructural study of MgAl2O4
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Deformation in nanocrystalline ceramics: A microstructural study of MgAl2 O4 Barak Ratzker , Avital Wagner , Maxim Sokol , Louisa Meshi , Sergey Kalabukhov , Nachum Frage PII: DOI: Reference:
S1359-6454(19)30743-8 https://doi.org/10.1016/j.actamat.2019.11.015 AM 15641
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Please cite this article as: Barak Ratzker , Avital Wagner , Maxim Sokol , Louisa Meshi , Sergey Kalabukhov , Nachum Frage , Deformation in nanocrystalline ceramics: A microstructural study of MgAl2 O4 , Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.11.015
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Deformation in nanocrystalline ceramics: A microstructural study of MgAl2O4 Barak Ratzkera, Avital Wagnera, Maxim Sokolb, Louisa Meshia, Sergey Kalabukhova and Nachum Fragea,* a
Department of Materials Engineering, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel b
Department of Materials Science & Engineering, Drexel University, Philadelphia, PA 19104, USA
*
Corresponding author: [email protected]
Abstract Contrary to the characteristic strengthening of polycrystalline ceramics with a decrease in grain size, extremely fine nanocrystalline ceramics exhibit softening, increased plasticity and an inverse Hall-Petch relation. Despite experimental evidence, questions remain regarding the underlying deformation mechanisms governing this abnormal mechanical behavior. In the present study, an in-depth microstructural examination was performed on nanostructured transparent magnesium aluminate spinel (MgAl2O4) subjected to microhardness tests. Microstructural observations revealed regions strained to various degrees below the point of indentation, containing varying amounts of dislocations and nano-cavities. Furthermore, the residual strain in different areas was estimated by local electron diffraction. These observations and analysis provided evidence for grain boundary (GB) mediated mechanisms (e.g., GB sliding and rotation). Moreover, shear bands formed and were found to be associated with microcracking. By combining the microstructural analysis with suitable models, it was concluded that these mechanisms govern plastic deformation. By elucidating how strain is accommodated within nanocrystalline ceramics, a deeper understanding of their unique mechanical behavior is gained. Keywords: Nanocrystalline ceramics; indentation; dislocations; grain boundary sliding; grain rotation; shear bands.
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1. Introduction Nanostructured polycrystalline materials are of great interest to the scientific community due to their unique mechanical properties and mechanisms of deformation [1]. One of the most basic and simple methods to determine the mechanical behavior of such materials is hardness testing (i.e. microhardness or nano-indentation). The well-known Hall-Petch relationship [2,3] describes the dependence of hardness and strength of polycrystalline materials on grain size, expressing how a decrease in grain size leads to grain boundary (GB) strengthening and elevated mechanical properties [4]. The relationship is generally described by the following expression: (1)
H (d ) H 0
k d
where H(d) is the hardness of the polycrystal, H0 is the average hardness of different crystallographic orientations of a single crystal, k is a constant (which depends on the chemistry and structure of the material) and d is grain size. It is well established that the behavior of polycrystalline materials is governed by this relation, albeit only up to a certain nanometric grain size. For extremely fine nanostructured materials (i.e., <~50 nm), the Hall-Petch relation does not fit experimental results, instead, hardness decreases upon further reduction in grain size [1,5]. This phenomenon is commonly termed as a reverse or inverse Hall-Petch relation. Due to the relative simplicity of fabricating nanostructured bulk metallic materials with extremely fine grain sizes, the inverse Hall-Petch relation has been well documented in numerous experimental [1,6–8] and theoretical [9–12] studies. Since the nature of plastic deformation in nanocrystalline materials is unique, various nanoscale physical mechanisms have been proposed as explaining the Hall-Petch strengthening limit [1]. These include rapid room temperature GB diffusion [5,13], dislocation pile-up breakdown [14], inhibition of dislocation sources [15], transition to a GB sliding (GBS) regime [6,16], grain rotation [17,18], shear band formation [19,20] and the composite-like behavior of grain interior and boundary phases [21]. Even if GB strengthening is just a size effect [22,23], it is still expected that hardness values would fall below the values predicted by the Hall-Petch relation for nanocrystalline materials due to other deformation mechanisms such as GBS [22]. 2
In the case of nanostructured ceramic materials, it is much more problematic to observe and evaluate mechanical properties due to difficulties in sintering fully dense nanocrystalline bodies. Moreover, processing artifacts, such as precipitates and residual porosity, can cause decreased strength and hardness unrelated to reduction in grain size [24–26]. Nevertheless, several studies have described an inverse Hall-Petch relation in various ceramics, such as ZrN coatings [26], TiN thin films [27], TiO2 compacted powder [28] and sintered MgO [29]. In recent years, advanced ceramic fabrication technologies in which high pressures are applied, leading to significantly reduced sintering temperatures, have gained popularity [30–33]. Such advances allow for the fabrication of dense bulk nanocrystalline transparent ceramics and subsequent studies of their mechanical behavior. It should be noted that the transparency of polycrystalline ceramics confirms they are fully dense and contain no precipitates. Hence, even if a limited degree of residual porosity remains, it is too small to affect mechanical properties of the material. Therefore, an inverse Hall-Petch relation in such materials is due to the nanoscale grain size. For instance, a few recent studies have revealed a Hall-Petch breakdown point and inverse behavior in transparent Al2O3-SiO2 nano-composite [34] and MgAl2O4 [35,36]. Ultimately confirming the softening phenomenon in nanocrystalline ceramics. Generally, the inverse Hall-Petch behavior of nanostructured ceramics can be attributed to two different phenomena. First, upon reduction of grain size, there is a significant change in the ratio of disordered weaker grain boundaries, as compared to crystalline grains [29,36,37]. For instance, for a ceramic with a grain size of 20 nm, only ~80% of the material should be crystalline (estimated based on a GB thickness of 1 nm) [37]. This would obviously reduce the strength, hardness and elastic modulus [25,36] of the material. Secondly, a transition occurs to GB mediated deformation mechanisms [38], such as GBS [16,27,39–41] and/or grain rotation [17,18,42–44], leading to higher plasticity. Potentially allowing to improve properties and performance of nanocrystalline materials [45,46]. To further clarify the deformation mechanisms in nanostructured ceramics, one can study the deformed microstructure below hardness test indentations. For instance, grain rotation and sliding of nanostructured TiN [39] and Al2O3-ZrO2MgAl2O4 nano-composite [47] were observed in in situ indentation experiments. Although such studies that provide microstructural evidence are very promising, their number is still limited. In the present work, nanostructured magnesium aluminate spinel (MgAl2O4; MAS) was taken as a case study designed to elucidate microstructural characteristics of the deformation 3
generated below the indenter tip during Vickers microhardness testing of nanocrystalline ceramics.
2. Experimental 2.1 Sample preparation MAS nano-powder with an average particle size of ~12 nm was synthesized by a solution combustion method described in detail elsewhere [35]. Consolidation of bulk nanocrystalline ceramics was carried out by high-pressure spark plasma sintering (HPSPS) using an SPS apparatus (FCT Systeme, Rauenstein, Germany) as shown in [35]. A detailed description of the SPS-tool setup that allows the application of pressures up to 1 GPa was described in our previous contribution [48]. The HPSPS process was conducted at sintering temperatures of 950 and 1050°C under an applied uniaxial pressure of 850 MPa with a dwell time of 30 min. The heating rate was 50°C/min up to 800°C and was then lowered to 5°C/min up to the soaking temperature. 2.2 Microhardness measurements Sintered disk samples (8 mm in diameter) were ground and mirror-polished to a final thickness of ~1 mm. In-line transmittance was measured by a spectrophotometer in the 300–1100 nm wavelength range (JASCO, V-530 UV-VIS, Easton, MD). Microhardness indentations tests were performed on polished surfaces under a 0.1 kg load applied for 10 s using a Buehler Micromet (Lake Bluff, IL) apparatus with a loading rate of 0.06 mm/s, using a certified (UKAS: accredited calibration) Vickers indenter. The hardness tests were performed in accordance with the ASTM standard [49] and the average hardness values were determined by measuring 10 well-formed indentations. 2.3 Microstructural characterization For microstructural investigation at the center of indentations, electron-transparent cross-section lamella specimens were meticulously prepared by a dual-beam focused ion beam microscope (FEI, Verios-460L, Hillsboro, OR). The detailed process is described in the Supplementary Information (SI). A STEM detector in FIB immediately after sample preparation and high4
resolution transmission electron microscopy (HRTEM; JEOL, JEM 2100F, Tokyo, Japan) were used. Analysis of the structure and deformation strain of selective areas in the samples was facilitated by electron diffraction. The selected area electron diffraction (SAED) aperture used was 0.6 µm in diameter. 3. Results and Discussion 3.1 Sintered sample properties Two transparent nanocrystalline MAS samples were investigated in this study. The sintering parameters, average grain size and hardness of the samples are listed in Table 1. Both samples were fully dense and displayed similarly high levels of transparency (i.e., ~80% at a wavelength of 600 nm), although the difference in grain size was quite significant. The XRD patterns used to calculate grain size are given in the SI section (Fig. s1). Samples with average grain sizes of 43 and 22 nm were suitable to represent nanocrystalline MAS before and after the inverse point (~28 nm) reported elsewhere [35]. Table 1. HPSPS processing parameters and sample properties of nanocrystalline MAS
Sintering
Applied
Heating rate,
Dwell
Avg. grain
Hardness,
temperature, °C
pressure, MPa
°C/min
time, min
size, nm
GPa
1050
850
5
30
42.8±0.4
19.04±1.16
950
850
5
30
21.7±0.3
18.79±1.24
3.2 Microstructural characterization The study of cross-sectional specimens allows for the examination of deformation-related microstructural changes that occur after microhardness indentations. Bright field (BF) images taken with a scanning transmission electron microscope (STEM) detector in the focused ion beam (FIB) apparatus (Fig. 1) show a distinct plastic deformation zone directly under the indentation tip. Additionally, jagged vertical and lateral intergranular micro-cracks can be observed outside this plastic zone, where the largest tensile stresses exist [50,51]. More microcracks (especially lateral cracks) are apparent in the specimen with a grain size of 22 nm, as compared to the specimen with a grain size of 43 nm. The fact that more shallow lateral cracks 5
[52] formed within the finer grained ceramic explains why excessive chipping and spallation occur shortly after indentation (see Fig. 1b, inset). It should be noted that similar spallation behavior after nano-indentation was previously reported by others [36]. Furthermore, localized strain in the form of irregularly curved shear bands (some of which are indicated in Fig. 1) was observed. These shear bands propagate outwards from the indentation tip in a manner reminiscent of shear band behavior in metallic glasses [53,54], which is noticeably different from the classic regularly spaced intragranular diagonal shear bands seen in MAS single crystals [55] and micron-sized grains (see SI Fig. s2c). This observation appears to agree with molecular dynamic simulations of hardness tests of materials with nano-sized grains [56]. It seems that the shear bands in the nanocrystalline ceramic span over numerous grains, accommodating some strain during indentation, and forming the basis for a “macro-” non-homogenous deformation mechanism [1,19,57]. Furthermore, the presence of shear bands may be an indication to the softening of the nanocrystalline ceramic [20].
Fig. 1. General view of microstructure under the indentation tip. STEM BF images taken in FIB from MAS specimens with average grain sizes of (a) 43 and (b) 22 nm. An indentation area is clearly observed at the top of each image. Micro-cracks and some shear bands are indicated. Insets show representative indentations observed for each nanocrystalline MAS sample.
A BF TEM image of a specimen with a grain size of 43 nm is shown in Fig. 2. Three different regions beneath the indentation can be observed, namely a severely strained region directly under the indentation (1), a transitional, moderately strained region (2) and a nearly strain-free area far enough from the indentation, with localized shear bands and cracks (3). It should be underlined that “strain-free” refers to the initial state of the material prior to
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indentation. A schematic illustration of the microstructure of the deformed nanocrystalline ceramic under the indentation is depicted in the inset of Fig. 2.
Fig. 2. TEM BF image of the microstructure under the indentation tip, sample with average grain size of 43 nm. In the inset, a schematic illustration of the areas showing different microstructural features (denoted as 1, 2 and 3) is provided.
Closer examination revealed several interesting microstructural features. There are shear bands which separate the strained and unstrained regions (Fig. 3a). In addition, it is apparent that in the strained regions (1) and (2), it is difficult to distinguish between the different grains. The “serrated” contrast of the grains in these areas is indicative of a high level of strain. Nanocavities that formed between the grains (Fig. 3b) were primarily detected in region (2). The formation of such nano-cavities is likely a result of unaccommodated GBS, where atomistic mass-transport mechanisms are unable to fully accommodate the sliding and rotation processes, resulting in grain separation [41,58–63]. Kumar et al. [58] have described in detail how the GBS mechanism in nanocrystalline materials involves the formation of such nano-cavities. The observed nano wedge cracks (Fig. 3b) support this idea. Furthermore, Ovid’ko et al. [61] suggested that formation of nanoscale cavities could be attributed to a relatively slow (diffusioncontrolled) process driven by release of the elastic energy of GB disclination configurations formed due to GBS. 7
In region (3), a practically pristine microstructure, as obtained after sintering, with clear contrast between the grains, can be seen. In this area, some localized deformation led to shear band formation (Fig. 3c,d), especially in the 22 nm grain size sample. In fact, closer examination of areas with cracks (Fig. 3d, inset) revealed that micro-cracking was associated with localized deformation events and, thus, was related to the formation of shear bands. Both nano-cavities and elongated nano-cracks were clearly revealed using a high-angle annular dark field (HAADF) detector (with contrast sensitive to atomic density) in FIB (Fig. 3d). These features likely indicate local GBS events associated with crack propagation in nanocrystalline materials [61,63].
Fig. 3. Images of deformation features taken in FIB, where (a,b) and (c,d) are from the samples with grain size of 43 and 22 nm, respectively. STEM detector images showing (a) the border zone between strained and non-strained regions and (b) a zoomed-in image of the marked square in the strained area showing nano-cavities that formed between the grains. (c) BF STEM and (d) HAADF images taken in FIB of an area outside the strained zone with
8
cracks and localized shear bands. In the inset, a higher magnification of the marked area is provided, illustrating thin shear bands and related nano-cracks.
The “serrated contrast” observed in the highly strained areas of the samples is not easy to discern due to the ambiguous nature of the contrast of the STEM detector in FIB. In-depth examination of the three regions (marked in Fig. 2) by TEM is presented in Fig. 4. Grains in the moderately and severely deformed regions of the sample (Fig. 4b and c) exhibited the same serrated contrast, indicating that this contrast is diffraction-related. SAED patterns taken from the area size 0.6 µm in diameter, selected by SA aperture, provided the opportunity to study each area independently, as shown in Fig. 4d-f. Here, differences between the three areas are clearly seen. However, the basis for these differences is not apparent. Analysis of the SAED images revealed that the “rings” are less full in Fig. 4d, relative to those shown in Fig. 4e and f, likely reflecting less strain and poorer statistics due to differences in the number of different grain orientations in the non-strained area, as compared to those in the strained areas. The latter may point to rotational GB mediated mechanisms and the effect of grain rotation as a function of strain. Moreover, it seems that the rings seen in Fig. 4f are wider than those noted in Fig. 4d. Considering that the FIB lamella has approximately uniform thickness, these observations can be attributed to grain size or/and microstrain effects. The first option was refuted by dark field (DF) TEM analysis, which showed both severely strained and unaffected areas (SI Fig. s4 and Fig 4a) presenting similar grain sizes. On the other hand, dislocations within the grains was observed in the DF and high-resolution images, as shown in the inset of Fig. 4c and Fig. 5, respectively. In order to enhance visibility of the structural defects (such as dislocations), Bragg filter masking implemented in the DigitalMicrographTM (Gatan, Inc., USA) package, was applied. Fast Fourier transform of HRTEM images was Bragg-filtered so that only {111} reflections underwent inverse fast Fourier transform (IFFT) is shown in Fig. 5b. Thus, the extent of microstrain is responsible for the differences noted between the images and the diffraction patterns obtained from the three regions. Furthermore, this provides additional solid evidence that dislocation mechanisms indeed operate in nanocrystalline ceramics [64].
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Fig. 4. TEM data for different strain regions in the sample with a grain size of 43 nm. BF images of (a) unstrained region 3, (b) moderately strained region 2 (c) and severely strained region 1. The indentation direction is the same in all images. In the inset of (c), a DF image of a representative grain in region 1, taken in g= (311), is shown. Corresponding SAED patterns taken from regions (d) 3, (e) 2 and (f) 1 are presented. Indexing is shown in (d).
Fig. 5. (a) HRTEM image of the spinel sample with 43 nm grain size. (b) The corresponding inversed fast Fourier transform (IFFT), constructed from {111} planes only. The image reveals the presence of dislocations; some of them are indicated by arrows as an example.
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In order to analyze the strain distribution and its nature, SAED patterns were digitally scanned and presented as 1D plots integrated from the Debye rings (Fig. 6a). Taking this approach made it possible to observe relative peak broadening for each region. Using general diffraction theory, the Williamson-Hall (WH) method [65,66] was applied to estimate the effect of strain on peak broadening (see SI for additional details). The relative strain in region 1 and 2 was estimated by using region 3 as an internal reference, thus overcoming the need to know the instrumental broadening function. According to the slopes absolute value in the WH plots for the sample with a grain size of 20 nm (Fig. 6b), microstrain in the severely strained region (1) was estimated as 0.139 vs 0.068 in region (2). It should be noted, the negative slope is not characteristic of XRD data WH plots, even though they have been reported before [67–69]. We believe, the negative slope stems from the substantial background in SAED patterns used for this analysis. This residual strain implies that dislocations still operated within these extremely fine nano-grains and more so close to the indentation tip. Furthermore, the SAED of region (3) was closest to the theoretical value (JCPDF 00-021-1152) with respect to both intensity and hierarchy. In the other regions, the intensity distribution changed, pointing to a preferred orientation, which was likely due to grain rotation.
Fig. 6. (a) Intensity plots of SAED rings taken from different regions. (1) - red, (2) - black and (3) - blue in the sample with a grain size of 23 nm. Peak broadening reflects increased residual strain. (b) the derived WH plots for differently strained regions, the slope indicates strain.
In summary, a thorough microstructural analysis allowed to elucidate the response of nanocrystalline ceramics to micro-hardness indentations. Region (1), closest to the indentation 11
tip, was subjected to extreme compressive stresses [50] and exhibited high degree of misorientation of neighboring grains caused by GB mediated plasticity (e.g., GBS and/or grain rotation). In addition, a substantial amount of dislocations was observed. In region (2), further within the material (with respect to the indentation), the stress field was lower, and GB mediated plasticity played a significant role in the deformation, resulting in formation of GB cavities. Additionally, shear bands (with localized strain) formed and were observed in all three regions, even relatively far away from the indentation tip. In region (3), vertical and lateral intergranular micro-cracks developed in vicinity of the shear bands, indicating their relation. The shear bands accommodated non-homogenous localized deformation and served as defected areas for crack nucleation. It is noted that for the ceramic with a smaller nano-grain size (22 nm), more evidence of localized deformation (i.e., shear bands), unaccommodated GBS and lateral cracks were observed. The latter underlines the importance of these mechanisms in the softening of nanograins. 3.3 Modelling deformation of nanocrystalline ceramics The evidence obtained from microstructural observations suggested that the plasticity of the nanocrystalline ceramic was achieved by a combination of various deformation mechanisms. Therefore, to explain the inverse Hall-Petch behavior of nanostructured MAS [35,36], two different models of deformation, conventional dislocation and GBS mechanisms, were considered. According to the model that considers the GB volume fraction (VF) composite model, the hardness (which is proportional to the elastic modulus), is expressed by an algebraic average (Hill’s approach [70]) of classic models of Voigt and Reuss, that determine the upper and lower bounds of any independent and uncoupled property of a composite material as proposed in [29,37]:
(2)
1 Vg Vgb HV 0.5 Vg H g Vgb H gb H H g gb
where HV is the hardness value, V is the volume fraction and Hg and Hgb indicate hardness of grain interior and of GB, respectively. For the sake of modelling, the hardness of the disordered 12
GB regions was chosen as 70% of that of the fully crystalline grain (Hgb = 0.7Hg) [37,71]. Clearly, the GB volume fraction depends on boundary thickness, the value of which is inconclusive, especially in ceramic materials. Therefore, in the calculations below, we considered that the GB thickness as varying between δ = 0.5 and 1.5 nm [37]. By applying this model for MAS (red area in Fig. 6), it is possible to predict that hardness values begin deviating from the Hall-Petch relation at grain sizes below 100 nm and begin to present inverse behavior at grain sizes below ~30 and ~10 nm for GB thickness of 1.5 and 0.5 nm, respectively. According to the model that accounts for transition to a GBS regime, as proposed by Hahn et al. [16], hardness values can be estimated according to:
(3)
HV HV 0
A d B d
where HV0 is an empirical value with no physical definition, A and B are material parameters and d the grain size. Specifically, B is a parameter related to GB thickness (δ) and is equal to [16]: (4)
B 2 6
The empirical parameters for MAS were determined by treating the experimental data and subtracting the VF effect (calculated previously), yielding eq. 5:
(5)
H 37.59
1 d 0.0027 d
An effective GB thickness equal to 0.6 nm was estimated from eq. 4 using B values equal to 0.0027. The GBS (blue area in Fig. 7) predicts a more abrupt transition to inverse behavior with a significantly steeper slope, as compared to the relatively moderate slope predicted by the VF model. The reasonable conclusion from these observations is that the noted behavior reflects a combination of the two effects. It should be noted that some discrepancy exists between hardness values obtained for nanocrystalline MAS by micro-hardness [35] and nano-indentation [36] testing. Although measured hardness values in both cases revealed inverse Hall-Petch behavior, the strengthening 13
limit under nano-indentation was seen at a smaller grain size. The micro-hardness values appeared to be slightly lower, with the critical grain size being larger (~28 nm, as compared to ~18 nm), while the inverse slope was steeper, as compared to the nano-indentation results reported by Ryou et al. [36]. The micro-hardness and nano-indentation inverse behaviors seem to correspond more with the GBS and VF models, respectively. We suggest that these differences may arise from differences in the indentation methods used, as well as in the starting MAS nanopowders (e.g. variability in impurities) and sintering conditions. The Vickers microhardness tests were performed under applied loads 1-2 orders of magnitude greater than employed with the nano-indentation tests. This invokes a higher stress regime, which could affect the deformation mechanisms at play. Moreover, those specimens tested by nano-indentation were fabricated using a different sintering technique at temperatures of 640-850°C under pressure of 2 GPa and with no electric field [36]. These differences may have affected GB structural order and stability, which have significant effects on the plasticity of nanocrystalline materials [72] and inverse Hall-Petch behavior [46].
Fig. 7. Experimental hardness data and inverse behavior models for MAS. Including Vickers microhardness values (squares) of polycrystalline MAS [35], data from the present study are in white and nano-indentation values [36] are depicted by circles. The VF (red area) and GBS (blue area) model ranges that depend on GB thickness are indicated.
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4. Conclusions The microstructural observations made in this study shed light on the plastic behavior of bulk nanocrystalline ceramics and the deformation mechanisms operating during microhardness testing. The deformed microstructure under the indentation tip was analyzed for nanostructured MAS samples with grain sizes of 43 and 22 nm. Three distinct regions with varying levels of strain and dislocation densities, depending on the distance from the indentation tip, were observed. Namely, a severely strained region with many dislocations, a moderately strained region with relatively few dislocations and many GB nano-cavities, and a nearly unstrained region with micro-cracks were noted. Moreover, shear band formation was observed throughout all three regions, with all cracks being associated with shear bands. Additionally, residual strain in the severely and moderately strained regions was analyzed by TEM electron diffraction. It appears that deformation is controlled by a combination of mechanisms, such as conventional dislocation motion and GB mediated plasticity. The plausibility of an inverse Hall-Petch relation based on these observations was theoretically established according to respective grain boundaries VF and GBS regime models. The findings of this microstructural study shed light on the unique deformation mechanisms in nanocrystalline materials in general and ceramics in particular. Supporting Information The supporting information includes details regarding the XRD patterns of MAS powder and sintered samples, a comprehensive description of the FIB sample preparation process, unmarked STEM images of the cross-section lamella under indentations from the nanocrystalline and a micro-structured sample with relatively large grains, TEM analysis of a severely strained area including a DF image with many grains and a detailed descriptions about the methodology and results regarding the strain analysis by SAED patterns. Acknowledgments
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The authors thank Mr. Atzmon Vakahi from the Hebrew University Center for Nanoscience and Nanotechnology for FIB sample preparation and Dr. Vladimir Ezersky from the Ilse Katz Institute for Nanoscale Science & Technology for TEM analysis.
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Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
24
Deformation in nanocrystalline ceramics: A microstructural study of MgAl2 O4 Barak Ratzker , Avital Wagner , Maxim Sokol , Louisa Meshi , Sergey Kalabukhov , Nachum Frage PII: DOI: Reference:
S1359-6454(19)30743-8 https://doi.org/10.1016/j.actamat.2019.11.015 AM 15641
To appear in:
Acta Materialia
Please cite this article as: Barak Ratzker , Avital Wagner , Maxim Sokol , Louisa Meshi , Sergey Kalabukhov , Nachum Frage , Deformation in nanocrystalline ceramics: A microstructural study of MgAl2 O4 , Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.11.015
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Deformation in nanocrystalline ceramics: A microstructural study of MgAl2O4 Barak Ratzkera, Avital Wagnera, Maxim Sokolb, Louisa Meshia, Sergey Kalabukhova and Nachum Fragea,* a
Department of Materials Engineering, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel b
Department of Materials Science & Engineering, Drexel University, Philadelphia, PA 19104, USA
*
Corresponding author: [email protected]
Abstract Contrary to the characteristic strengthening of polycrystalline ceramics with a decrease in grain size, extremely fine nanocrystalline ceramics exhibit softening, increased plasticity and an inverse Hall-Petch relation. Despite experimental evidence, questions remain regarding the underlying deformation mechanisms governing this abnormal mechanical behavior. In the present study, an in-depth microstructural examination was performed on nanostructured transparent magnesium aluminate spinel (MgAl2O4) subjected to microhardness tests. Microstructural observations revealed regions strained to various degrees below the point of indentation, containing varying amounts of dislocations and nano-cavities. Furthermore, the residual strain in different areas was estimated by local electron diffraction. These observations and analysis provided evidence for grain boundary (GB) mediated mechanisms (e.g., GB sliding and rotation). Moreover, shear bands formed and were found to be associated with microcracking. By combining the microstructural analysis with suitable models, it was concluded that these mechanisms govern plastic deformation. By elucidating how strain is accommodated within nanocrystalline ceramics, a deeper understanding of their unique mechanical behavior is gained. Keywords: Nanocrystalline ceramics; indentation; dislocations; grain boundary sliding; grain rotation; shear bands.
1
1. Introduction Nanostructured polycrystalline materials are of great interest to the scientific community due to their unique mechanical properties and mechanisms of deformation [1]. One of the most basic and simple methods to determine the mechanical behavior of such materials is hardness testing (i.e. microhardness or nano-indentation). The well-known Hall-Petch relationship [2,3] describes the dependence of hardness and strength of polycrystalline materials on grain size, expressing how a decrease in grain size leads to grain boundary (GB) strengthening and elevated mechanical properties [4]. The relationship is generally described by the following expression: (1)
H (d ) H 0
k d
where H(d) is the hardness of the polycrystal, H0 is the average hardness of different crystallographic orientations of a single crystal, k is a constant (which depends on the chemistry and structure of the material) and d is grain size. It is well established that the behavior of polycrystalline materials is governed by this relation, albeit only up to a certain nanometric grain size. For extremely fine nanostructured materials (i.e., <~50 nm), the Hall-Petch relation does not fit experimental results, instead, hardness decreases upon further reduction in grain size [1,5]. This phenomenon is commonly termed as a reverse or inverse Hall-Petch relation. Due to the relative simplicity of fabricating nanostructured bulk metallic materials with extremely fine grain sizes, the inverse Hall-Petch relation has been well documented in numerous experimental [1,6–8] and theoretical [9–12] studies. Since the nature of plastic deformation in nanocrystalline materials is unique, various nanoscale physical mechanisms have been proposed as explaining the Hall-Petch strengthening limit [1]. These include rapid room temperature GB diffusion [5,13], dislocation pile-up breakdown [14], inhibition of dislocation sources [15], transition to a GB sliding (GBS) regime [6,16], grain rotation [17,18], shear band formation [19,20] and the composite-like behavior of grain interior and boundary phases [21]. Even if GB strengthening is just a size effect [22,23], it is still expected that hardness values would fall below the values predicted by the Hall-Petch relation for nanocrystalline materials due to other deformation mechanisms such as GBS [22]. 2
In the case of nanostructured ceramic materials, it is much more problematic to observe and evaluate mechanical properties due to difficulties in sintering fully dense nanocrystalline bodies. Moreover, processing artifacts, such as precipitates and residual porosity, can cause decreased strength and hardness unrelated to reduction in grain size [24–26]. Nevertheless, several studies have described an inverse Hall-Petch relation in various ceramics, such as ZrN coatings [26], TiN thin films [27], TiO2 compacted powder [28] and sintered MgO [29]. In recent years, advanced ceramic fabrication technologies in which high pressures are applied, leading to significantly reduced sintering temperatures, have gained popularity [30–33]. Such advances allow for the fabrication of dense bulk nanocrystalline transparent ceramics and subsequent studies of their mechanical behavior. It should be noted that the transparency of polycrystalline ceramics confirms they are fully dense and contain no precipitates. Hence, even if a limited degree of residual porosity remains, it is too small to affect mechanical properties of the material. Therefore, an inverse Hall-Petch relation in such materials is due to the nanoscale grain size. For instance, a few recent studies have revealed a Hall-Petch breakdown point and inverse behavior in transparent Al2O3-SiO2 nano-composite [34] and MgAl2O4 [35,36]. Ultimately confirming the softening phenomenon in nanocrystalline ceramics. Generally, the inverse Hall-Petch behavior of nanostructured ceramics can be attributed to two different phenomena. First, upon reduction of grain size, there is a significant change in the ratio of disordered weaker grain boundaries, as compared to crystalline grains [29,36,37]. For instance, for a ceramic with a grain size of 20 nm, only ~80% of the material should be crystalline (estimated based on a GB thickness of 1 nm) [37]. This would obviously reduce the strength, hardness and elastic modulus [25,36] of the material. Secondly, a transition occurs to GB mediated deformation mechanisms [38], such as GBS [16,27,39–41] and/or grain rotation [17,18,42–44], leading to higher plasticity. Potentially allowing to improve properties and performance of nanocrystalline materials [45,46]. To further clarify the deformation mechanisms in nanostructured ceramics, one can study the deformed microstructure below hardness test indentations. For instance, grain rotation and sliding of nanostructured TiN [39] and Al2O3-ZrO2MgAl2O4 nano-composite [47] were observed in in situ indentation experiments. Although such studies that provide microstructural evidence are very promising, their number is still limited. In the present work, nanostructured magnesium aluminate spinel (MgAl2O4; MAS) was taken as a case study designed to elucidate microstructural characteristics of the deformation 3
generated below the indenter tip during Vickers microhardness testing of nanocrystalline ceramics.
2. Experimental 2.1 Sample preparation MAS nano-powder with an average particle size of ~12 nm was synthesized by a solution combustion method described in detail elsewhere [35]. Consolidation of bulk nanocrystalline ceramics was carried out by high-pressure spark plasma sintering (HPSPS) using an SPS apparatus (FCT Systeme, Rauenstein, Germany) as shown in [35]. A detailed description of the SPS-tool setup that allows the application of pressures up to 1 GPa was described in our previous contribution [48]. The HPSPS process was conducted at sintering temperatures of 950 and 1050°C under an applied uniaxial pressure of 850 MPa with a dwell time of 30 min. The heating rate was 50°C/min up to 800°C and was then lowered to 5°C/min up to the soaking temperature. 2.2 Microhardness measurements Sintered disk samples (8 mm in diameter) were ground and mirror-polished to a final thickness of ~1 mm. In-line transmittance was measured by a spectrophotometer in the 300–1100 nm wavelength range (JASCO, V-530 UV-VIS, Easton, MD). Microhardness indentations tests were performed on polished surfaces under a 0.1 kg load applied for 10 s using a Buehler Micromet (Lake Bluff, IL) apparatus with a loading rate of 0.06 mm/s, using a certified (UKAS: accredited calibration) Vickers indenter. The hardness tests were performed in accordance with the ASTM standard [49] and the average hardness values were determined by measuring 10 well-formed indentations. 2.3 Microstructural characterization For microstructural investigation at the center of indentations, electron-transparent cross-section lamella specimens were meticulously prepared by a dual-beam focused ion beam microscope (FEI, Verios-460L, Hillsboro, OR). The detailed process is described in the Supplementary Information (SI). A STEM detector in FIB immediately after sample preparation and high4
resolution transmission electron microscopy (HRTEM; JEOL, JEM 2100F, Tokyo, Japan) were used. Analysis of the structure and deformation strain of selective areas in the samples was facilitated by electron diffraction. The selected area electron diffraction (SAED) aperture used was 0.6 µm in diameter. 3. Results and Discussion 3.1 Sintered sample properties Two transparent nanocrystalline MAS samples were investigated in this study. The sintering parameters, average grain size and hardness of the samples are listed in Table 1. Both samples were fully dense and displayed similarly high levels of transparency (i.e., ~80% at a wavelength of 600 nm), although the difference in grain size was quite significant. The XRD patterns used to calculate grain size are given in the SI section (Fig. s1). Samples with average grain sizes of 43 and 22 nm were suitable to represent nanocrystalline MAS before and after the inverse point (~28 nm) reported elsewhere [35]. Table 1. HPSPS processing parameters and sample properties of nanocrystalline MAS
Sintering
Applied
Heating rate,
Dwell
Avg. grain
Hardness,
temperature, °C
pressure, MPa
°C/min
time, min
size, nm
GPa
1050
850
5
30
42.8±0.4
19.04±1.16
950
850
5
30
21.7±0.3
18.79±1.24
3.2 Microstructural characterization The study of cross-sectional specimens allows for the examination of deformation-related microstructural changes that occur after microhardness indentations. Bright field (BF) images taken with a scanning transmission electron microscope (STEM) detector in the focused ion beam (FIB) apparatus (Fig. 1) show a distinct plastic deformation zone directly under the indentation tip. Additionally, jagged vertical and lateral intergranular micro-cracks can be observed outside this plastic zone, where the largest tensile stresses exist [50,51]. More microcracks (especially lateral cracks) are apparent in the specimen with a grain size of 22 nm, as compared to the specimen with a grain size of 43 nm. The fact that more shallow lateral cracks 5
[52] formed within the finer grained ceramic explains why excessive chipping and spallation occur shortly after indentation (see Fig. 1b, inset). It should be noted that similar spallation behavior after nano-indentation was previously reported by others [36]. Furthermore, localized strain in the form of irregularly curved shear bands (some of which are indicated in Fig. 1) was observed. These shear bands propagate outwards from the indentation tip in a manner reminiscent of shear band behavior in metallic glasses [53,54], which is noticeably different from the classic regularly spaced intragranular diagonal shear bands seen in MAS single crystals [55] and micron-sized grains (see SI Fig. s2c). This observation appears to agree with molecular dynamic simulations of hardness tests of materials with nano-sized grains [56]. It seems that the shear bands in the nanocrystalline ceramic span over numerous grains, accommodating some strain during indentation, and forming the basis for a “macro-” non-homogenous deformation mechanism [1,19,57]. Furthermore, the presence of shear bands may be an indication to the softening of the nanocrystalline ceramic [20].
Fig. 1. General view of microstructure under the indentation tip. STEM BF images taken in FIB from MAS specimens with average grain sizes of (a) 43 and (b) 22 nm. An indentation area is clearly observed at the top of each image. Micro-cracks and some shear bands are indicated. Insets show representative indentations observed for each nanocrystalline MAS sample.
A BF TEM image of a specimen with a grain size of 43 nm is shown in Fig. 2. Three different regions beneath the indentation can be observed, namely a severely strained region directly under the indentation (1), a transitional, moderately strained region (2) and a nearly strain-free area far enough from the indentation, with localized shear bands and cracks (3). It should be underlined that “strain-free” refers to the initial state of the material prior to
6
indentation. A schematic illustration of the microstructure of the deformed nanocrystalline ceramic under the indentation is depicted in the inset of Fig. 2.
Fig. 2. TEM BF image of the microstructure under the indentation tip, sample with average grain size of 43 nm. In the inset, a schematic illustration of the areas showing different microstructural features (denoted as 1, 2 and 3) is provided.
Closer examination revealed several interesting microstructural features. There are shear bands which separate the strained and unstrained regions (Fig. 3a). In addition, it is apparent that in the strained regions (1) and (2), it is difficult to distinguish between the different grains. The “serrated” contrast of the grains in these areas is indicative of a high level of strain. Nanocavities that formed between the grains (Fig. 3b) were primarily detected in region (2). The formation of such nano-cavities is likely a result of unaccommodated GBS, where atomistic mass-transport mechanisms are unable to fully accommodate the sliding and rotation processes, resulting in grain separation [41,58–63]. Kumar et al. [58] have described in detail how the GBS mechanism in nanocrystalline materials involves the formation of such nano-cavities. The observed nano wedge cracks (Fig. 3b) support this idea. Furthermore, Ovid’ko et al. [61] suggested that formation of nanoscale cavities could be attributed to a relatively slow (diffusioncontrolled) process driven by release of the elastic energy of GB disclination configurations formed due to GBS. 7
In region (3), a practically pristine microstructure, as obtained after sintering, with clear contrast between the grains, can be seen. In this area, some localized deformation led to shear band formation (Fig. 3c,d), especially in the 22 nm grain size sample. In fact, closer examination of areas with cracks (Fig. 3d, inset) revealed that micro-cracking was associated with localized deformation events and, thus, was related to the formation of shear bands. Both nano-cavities and elongated nano-cracks were clearly revealed using a high-angle annular dark field (HAADF) detector (with contrast sensitive to atomic density) in FIB (Fig. 3d). These features likely indicate local GBS events associated with crack propagation in nanocrystalline materials [61,63].
Fig. 3. Images of deformation features taken in FIB, where (a,b) and (c,d) are from the samples with grain size of 43 and 22 nm, respectively. STEM detector images showing (a) the border zone between strained and non-strained regions and (b) a zoomed-in image of the marked square in the strained area showing nano-cavities that formed between the grains. (c) BF STEM and (d) HAADF images taken in FIB of an area outside the strained zone with
8
cracks and localized shear bands. In the inset, a higher magnification of the marked area is provided, illustrating thin shear bands and related nano-cracks.
The “serrated contrast” observed in the highly strained areas of the samples is not easy to discern due to the ambiguous nature of the contrast of the STEM detector in FIB. In-depth examination of the three regions (marked in Fig. 2) by TEM is presented in Fig. 4. Grains in the moderately and severely deformed regions of the sample (Fig. 4b and c) exhibited the same serrated contrast, indicating that this contrast is diffraction-related. SAED patterns taken from the area size 0.6 µm in diameter, selected by SA aperture, provided the opportunity to study each area independently, as shown in Fig. 4d-f. Here, differences between the three areas are clearly seen. However, the basis for these differences is not apparent. Analysis of the SAED images revealed that the “rings” are less full in Fig. 4d, relative to those shown in Fig. 4e and f, likely reflecting less strain and poorer statistics due to differences in the number of different grain orientations in the non-strained area, as compared to those in the strained areas. The latter may point to rotational GB mediated mechanisms and the effect of grain rotation as a function of strain. Moreover, it seems that the rings seen in Fig. 4f are wider than those noted in Fig. 4d. Considering that the FIB lamella has approximately uniform thickness, these observations can be attributed to grain size or/and microstrain effects. The first option was refuted by dark field (DF) TEM analysis, which showed both severely strained and unaffected areas (SI Fig. s4 and Fig 4a) presenting similar grain sizes. On the other hand, dislocations within the grains was observed in the DF and high-resolution images, as shown in the inset of Fig. 4c and Fig. 5, respectively. In order to enhance visibility of the structural defects (such as dislocations), Bragg filter masking implemented in the DigitalMicrographTM (Gatan, Inc., USA) package, was applied. Fast Fourier transform of HRTEM images was Bragg-filtered so that only {111} reflections underwent inverse fast Fourier transform (IFFT) is shown in Fig. 5b. Thus, the extent of microstrain is responsible for the differences noted between the images and the diffraction patterns obtained from the three regions. Furthermore, this provides additional solid evidence that dislocation mechanisms indeed operate in nanocrystalline ceramics [64].
9
Fig. 4. TEM data for different strain regions in the sample with a grain size of 43 nm. BF images of (a) unstrained region 3, (b) moderately strained region 2 (c) and severely strained region 1. The indentation direction is the same in all images. In the inset of (c), a DF image of a representative grain in region 1, taken in g= (311), is shown. Corresponding SAED patterns taken from regions (d) 3, (e) 2 and (f) 1 are presented. Indexing is shown in (d).
Fig. 5. (a) HRTEM image of the spinel sample with 43 nm grain size. (b) The corresponding inversed fast Fourier transform (IFFT), constructed from {111} planes only. The image reveals the presence of dislocations; some of them are indicated by arrows as an example.
10
In order to analyze the strain distribution and its nature, SAED patterns were digitally scanned and presented as 1D plots integrated from the Debye rings (Fig. 6a). Taking this approach made it possible to observe relative peak broadening for each region. Using general diffraction theory, the Williamson-Hall (WH) method [65,66] was applied to estimate the effect of strain on peak broadening (see SI for additional details). The relative strain in region 1 and 2 was estimated by using region 3 as an internal reference, thus overcoming the need to know the instrumental broadening function. According to the slopes absolute value in the WH plots for the sample with a grain size of 20 nm (Fig. 6b), microstrain in the severely strained region (1) was estimated as 0.139 vs 0.068 in region (2). It should be noted, the negative slope is not characteristic of XRD data WH plots, even though they have been reported before [67–69]. We believe, the negative slope stems from the substantial background in SAED patterns used for this analysis. This residual strain implies that dislocations still operated within these extremely fine nano-grains and more so close to the indentation tip. Furthermore, the SAED of region (3) was closest to the theoretical value (JCPDF 00-021-1152) with respect to both intensity and hierarchy. In the other regions, the intensity distribution changed, pointing to a preferred orientation, which was likely due to grain rotation.
Fig. 6. (a) Intensity plots of SAED rings taken from different regions. (1) - red, (2) - black and (3) - blue in the sample with a grain size of 23 nm. Peak broadening reflects increased residual strain. (b) the derived WH plots for differently strained regions, the slope indicates strain.
In summary, a thorough microstructural analysis allowed to elucidate the response of nanocrystalline ceramics to micro-hardness indentations. Region (1), closest to the indentation 11
tip, was subjected to extreme compressive stresses [50] and exhibited high degree of misorientation of neighboring grains caused by GB mediated plasticity (e.g., GBS and/or grain rotation). In addition, a substantial amount of dislocations was observed. In region (2), further within the material (with respect to the indentation), the stress field was lower, and GB mediated plasticity played a significant role in the deformation, resulting in formation of GB cavities. Additionally, shear bands (with localized strain) formed and were observed in all three regions, even relatively far away from the indentation tip. In region (3), vertical and lateral intergranular micro-cracks developed in vicinity of the shear bands, indicating their relation. The shear bands accommodated non-homogenous localized deformation and served as defected areas for crack nucleation. It is noted that for the ceramic with a smaller nano-grain size (22 nm), more evidence of localized deformation (i.e., shear bands), unaccommodated GBS and lateral cracks were observed. The latter underlines the importance of these mechanisms in the softening of nanograins. 3.3 Modelling deformation of nanocrystalline ceramics The evidence obtained from microstructural observations suggested that the plasticity of the nanocrystalline ceramic was achieved by a combination of various deformation mechanisms. Therefore, to explain the inverse Hall-Petch behavior of nanostructured MAS [35,36], two different models of deformation, conventional dislocation and GBS mechanisms, were considered. According to the model that considers the GB volume fraction (VF) composite model, the hardness (which is proportional to the elastic modulus), is expressed by an algebraic average (Hill’s approach [70]) of classic models of Voigt and Reuss, that determine the upper and lower bounds of any independent and uncoupled property of a composite material as proposed in [29,37]:
(2)
1 Vg Vgb HV 0.5 Vg H g Vgb H gb H H g gb
where HV is the hardness value, V is the volume fraction and Hg and Hgb indicate hardness of grain interior and of GB, respectively. For the sake of modelling, the hardness of the disordered 12
GB regions was chosen as 70% of that of the fully crystalline grain (Hgb = 0.7Hg) [37,71]. Clearly, the GB volume fraction depends on boundary thickness, the value of which is inconclusive, especially in ceramic materials. Therefore, in the calculations below, we considered that the GB thickness as varying between δ = 0.5 and 1.5 nm [37]. By applying this model for MAS (red area in Fig. 6), it is possible to predict that hardness values begin deviating from the Hall-Petch relation at grain sizes below 100 nm and begin to present inverse behavior at grain sizes below ~30 and ~10 nm for GB thickness of 1.5 and 0.5 nm, respectively. According to the model that accounts for transition to a GBS regime, as proposed by Hahn et al. [16], hardness values can be estimated according to:
(3)
HV HV 0
A d B d
where HV0 is an empirical value with no physical definition, A and B are material parameters and d the grain size. Specifically, B is a parameter related to GB thickness (δ) and is equal to [16]: (4)
B 2 6
The empirical parameters for MAS were determined by treating the experimental data and subtracting the VF effect (calculated previously), yielding eq. 5:
(5)
H 37.59
1 d 0.0027 d
An effective GB thickness equal to 0.6 nm was estimated from eq. 4 using B values equal to 0.0027. The GBS (blue area in Fig. 7) predicts a more abrupt transition to inverse behavior with a significantly steeper slope, as compared to the relatively moderate slope predicted by the VF model. The reasonable conclusion from these observations is that the noted behavior reflects a combination of the two effects. It should be noted that some discrepancy exists between hardness values obtained for nanocrystalline MAS by micro-hardness [35] and nano-indentation [36] testing. Although measured hardness values in both cases revealed inverse Hall-Petch behavior, the strengthening 13
limit under nano-indentation was seen at a smaller grain size. The micro-hardness values appeared to be slightly lower, with the critical grain size being larger (~28 nm, as compared to ~18 nm), while the inverse slope was steeper, as compared to the nano-indentation results reported by Ryou et al. [36]. The micro-hardness and nano-indentation inverse behaviors seem to correspond more with the GBS and VF models, respectively. We suggest that these differences may arise from differences in the indentation methods used, as well as in the starting MAS nanopowders (e.g. variability in impurities) and sintering conditions. The Vickers microhardness tests were performed under applied loads 1-2 orders of magnitude greater than employed with the nano-indentation tests. This invokes a higher stress regime, which could affect the deformation mechanisms at play. Moreover, those specimens tested by nano-indentation were fabricated using a different sintering technique at temperatures of 640-850°C under pressure of 2 GPa and with no electric field [36]. These differences may have affected GB structural order and stability, which have significant effects on the plasticity of nanocrystalline materials [72] and inverse Hall-Petch behavior [46].
Fig. 7. Experimental hardness data and inverse behavior models for MAS. Including Vickers microhardness values (squares) of polycrystalline MAS [35], data from the present study are in white and nano-indentation values [36] are depicted by circles. The VF (red area) and GBS (blue area) model ranges that depend on GB thickness are indicated.
14
4. Conclusions The microstructural observations made in this study shed light on the plastic behavior of bulk nanocrystalline ceramics and the deformation mechanisms operating during microhardness testing. The deformed microstructure under the indentation tip was analyzed for nanostructured MAS samples with grain sizes of 43 and 22 nm. Three distinct regions with varying levels of strain and dislocation densities, depending on the distance from the indentation tip, were observed. Namely, a severely strained region with many dislocations, a moderately strained region with relatively few dislocations and many GB nano-cavities, and a nearly unstrained region with micro-cracks were noted. Moreover, shear band formation was observed throughout all three regions, with all cracks being associated with shear bands. Additionally, residual strain in the severely and moderately strained regions was analyzed by TEM electron diffraction. It appears that deformation is controlled by a combination of mechanisms, such as conventional dislocation motion and GB mediated plasticity. The plausibility of an inverse Hall-Petch relation based on these observations was theoretically established according to respective grain boundaries VF and GBS regime models. The findings of this microstructural study shed light on the unique deformation mechanisms in nanocrystalline materials in general and ceramics in particular. Supporting Information The supporting information includes details regarding the XRD patterns of MAS powder and sintered samples, a comprehensive description of the FIB sample preparation process, unmarked STEM images of the cross-section lamella under indentations from the nanocrystalline and a micro-structured sample with relatively large grains, TEM analysis of a severely strained area including a DF image with many grains and a detailed descriptions about the methodology and results regarding the strain analysis by SAED patterns. Acknowledgments
15
The authors thank Mr. Atzmon Vakahi from the Hebrew University Center for Nanoscience and Nanotechnology for FIB sample preparation and Dr. Vladimir Ezersky from the Ilse Katz Institute for Nanoscale Science & Technology for TEM analysis.
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Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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