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Mechanical properties and dislocation character of YB4 and YB6
Intermetallics 89 (2017) 86–91
Contents lists available at ScienceDirect
Intermetallics journal homepage: www.elsevier.com/locate/intermet
Mechanical properties and dislocation character of YB4 and YB6 Nobuaki Sekido a b c
a,b,∗
b
MARK
c
, Takahito Ohmura , John H. Perepezko
Department of Materials Science and Engineering, Tohoku University, 6-6-02 Aobayama, Sendai 980-8579, Japan National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan Department of Materials Science and Engineering, University of Wisconsin-Madison, 1509 University Avenue, Madison, WI 53706, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Transmission electron microscopy Dislocation Burgers vector Slip system Yttrium borides
YB4/YB6 two-phase alloys were prepared by arc-melting of high purity elemental materials. The Young's moduli of YB4 and YB6 were evaluated by nanoindentation technique. During loading of nanoindentation, pop-in events were clearly observed for YB4 and YB6, suggesting that both have some capability of dislocation emission at room temperature. TEM observation depicts that dislocations have formed in YB4 and YB6 due to the thermal stress that developed during cooling following arc-melting. The Burgers vectors of these dislocations were identified to be [001] for YB4, and 〈100〉 for YB6. Potential slip systems that are indicated to operate were (100) [001] for YB4 and {100}〈001〉 for YB6.
1. Introduction Among the different classes of intermetallics, boride phases often display the highest values of elastic modulus and hardness. Indeed, many of the uses of boride phases are designed based upon their high hardness. At the same time, the borides are not notable for demonstrating a capability for extensive plastic deformation at low temperature. Moreover, many of the characteristic structures for the boride phases are non-cubic and yield anisotropic behavior in thermal expansion which can lead to cracking and a thermal shock sensitivity. Aside from applications where high hardness and wear resistance are necessary there is an important application based upon the high electron emissivity of the rare earth borides such as LaB6. During this application electron gun filaments are subjected to fairly rapid changes in temperature and thermal gradients without cracking. This apparent resistance to thermal shock suggests that some of the rare earth borides may be able to exhibit plastic flow and dislocation motion. However, there seems to be little known about the character and behavior of dislocations in the rare earth borides. In the Y-B binary system, at least five types of borides, YB2, YB4, YB6, YB12, and YB66, are stable [1]. Among them, YB4 has the highest melting temperature (2800 °C) at the congruent point. The YB4 crystal possess a primitive tetragonal structure (tP20: P4/mbm, B4Th type) [2]. This structure consists of Y-layers and B-layers stacking along the [001] direction, and can be described in terms of connecting YB2 and YB6 units [3,4]. On the other hand, the YB6 crystal possess a primitive cubic structure (cP7: Pm3m, B6Ca type) [2], where the cube corners are occupied by Y atoms and a regular octahedron consisting of six boron ∗
atoms is set at the center of the cube. The nearest distance between boron atoms within an octahedron is approximately the same as the distance between boron atoms on neighbouring octahedron. The structures of these borides are schematically illustrated in Fig. 1. Some of the physical and chemical properties of YB4 and YB6 have been investigated previously, including electron resistivity [5,6], thermal conductivity [6], and thermal expansion coefficients [7]. However, limited information is available for mechanical properties except for some hardness measurement results [8–11]. In the present study, dislocations were identified to develop in YB4 and YB6, and were characterized by means of transmission electron microscopy. The slip systems that operate in YB4 and YB6 were deduced from the Burgers vectors and the line vectors of dislocations. 2. Experimental procedures A YB4/YB6 two-phase alloy with the nominal composition of Y-80at. %B was prepared by a conventional arc-melting method. High purity raw materials were melted on a water-cooled Cu plate under an Ar atmosphere with minimal weight change (about 0.1%). Phase identification and lattice parameter measurement were done by X-ray diffractometry. Powdered specimens were examined in a diffractometer operating in Bragg-Brentano geometry with Cu-Kα radiation. Data was corrected by the step-scan method with a fixed time of 2 s per 0.02°. The tube voltage and current were 40 kV and 200 mA, respectively. The divergence slit open angle was 1°, and the receiving slit width was 0.15 mm. The Rietveld analysis on XRD profiles was done with RIETAN2000 software [12]. Microstructures of the alloys were characterized by
Corresponding author. Department of Materials Science and Engineering, Tohoku University, 6-6-02 Aobayama, Sendai 980-8579, Japan. E-mail address: [email protected] (N. Sekido).
http://dx.doi.org/10.1016/j.intermet.2017.05.024 Received 17 February 2017; Received in revised form 16 April 2017; Accepted 30 May 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
Intermetallics 89 (2017) 86–91
N. Sekido et al.
Fig. 1. Crystal views of YB4 from (a) diagonal and (b) [001] directions, and those of YB6 from (c) diagonal and (d) [001] directions.
a = 0.71104(2) (nm) and c = 0.40209(1) (nm) for YB4 with a tetragonal structure, and a = 0.41028(1) (nm) for YB6 with a cubic structure. These lattice parameters agree with those previously reported [16,17].
scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The foils for TEM observation were mechanically thinned and perforated by ion-milling with an accelerating voltage of 4 kV. The Burgers vectors of dislocations formed in the borides were determined by the thickness fringe method [13], and by the conventional contrast analysis based on the invisibility criteria. The line vectors of dislocations were determined by the trace analysis method [14] on images taken from two zone axes. Nanoindentation measurement was done by a Hysitron Triboindenter under a load-controlled condition with the maximum load of 3000 μN. A Berkovich indenter was employed, and the tip truncation was calibrated by using a reference specimen of fused silica. The Oliver-Pharr method [15] was employed for analyzing the hardness and elastic modulus of the YB4 and YB6 phases.
3.2. Elastic constant and nano-hardness of YB4 and YB6 The Young's modulus and nano-hardness of YB4 and YB6 were determined by nanoindentation tests on the arc-melted alloys. Table 1 summarizes the results of the moduli and hardness of YB4 and YB6. The Young's modulus was calculated from the reduced modulus (Er), which was experimentally determined from the slope of the curve upon unloading by
1 − νi2 1 − νs2 1 = + . Er Ei Es
3. Results
(1)
Here, Ei and νi are the Young's modulus and Poisson ratio of the indenter, and Es and νs are those of the specimen. The Young's modulus and the Poisson ratio of the diamond indenter are Ei = 1140 GPa and νi = 0.07. To our best knowledge, no experimental data is available for the Poisson ratios of YB4 and YB6. Thus we used the values predicted by ab-initio calculations: νs = 0.18 for YB4 [18] and νs = 0.348 for YB6 [19]. The Young's moduli of YB4 and YB6 determined in this study are 432 ± 11 GPa and 241 ± 7 GPa, respectively. These are higher than those by the ab-initio calculations: 342 GPa for YB4 [18] and 156 GPa for YB6 [19]. YB4 and YB6 are found to show quite high nano-hardness: 31.6 GPa for YB4, and 24.6 GPa for YB6. Due to the indentation size effect, a hardness value tested by nanoindentation technique is not necessarily comparable to that by micro-hardness [20]. Nonetheless, the tendency, where YB4 shows a higher hardness than YB6, is consistent with a previous report [10]. Another notable result of the nanoindentation measurement is an occurrence of a “pop-in”, which is a discontinuous jump in displacement that appears in load-displacement curves during loading. Fig. 4 shows typical load-displacement curves by nanoindentation of (a) YB4 and (b) YB6, in which pop-ins are indicated by arrows. The average values of the critical load for pop-in, Pc, are 1833 ± 203 μN for YB4, and 1082 ± 114 μN for YB6. The dashed curves in Fig. 4 are calculated by the Hertz elastic contact theory, which is given by Ref. [21].
3.1. Alloy synthesis Fig. 2 shows a microstructure of an as-cast YB4/YB6 two-phase alloy. The YB4 phase crystallises from the liquid as the primary solidification phase, followed by the formation of the YB6 phase through a peritectic reaction. No microcracks were observed in YB4 and YB6 grains, as shown in Fig. 2. Some interfaces between YB4 and YB6 are faceted (representative facets are indicated by arrows), which suggests that the growth of YB4 from liquid is accompanied by the formation of faceted interfaces as expected for intermetallic phases. Fig. 3 shows an XRD profile of an as-cast YB4/YB6 two-phase alloy, together with a result of the Rietveld analysis. Upon analysis, no antisite defects were presumed to occur in both YB4 and YB6, and the atom positions of the both phases were fixed to those previously reported [16,17]. All the peaks in Fig. 3 were assigned to YB4 and YB6 with a reasonable goodness of fitting. The lattice parameters evaluated are:
P=
1 3 4 Er Ri2 h 2 . 3
(2)
Here, P is the indentation load, h is the penetration depth, and Ri is the curvature of the indenter tip. The curvature of the indenter tip has been calibrated to be 290 nm by preliminary measurements on the standard fused silica, and the reduced Young's modulus, Er, used was determined from the slope of an unloading curve. As can be seen in Fig. 4, the experimentally obtained P-h curves coincide with those calculated by Eq. (2), suggesting that deformation underneath the indenter is elastic before the onset of the pop-in event. Since the “pop-in”
Fig. 2. A back-scattered scanning electron micrograph of an as-cast YB4/YB6 two-phase alloy.
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Fig. 3. A Rietveld-refined XRD profile of an YB4/ YB6 two-phase alloy.
the present study. Contrast analysis revealed that these dislocations can be divided into three groups with respect to the Burgers vectors of the dislocations, as shown in Fig. 5(f). Group A is the dislocations that have been developed in the interior of a YB6 grain, and Group B and C are ones that form a sub-grain boundary. Group-A dislocations are out of contrast under the reflection vectors of g = 110 , 100 , and 010, which indicates that the Burgers vector of the dislocations is b = [001]. Group-B dislocations are out of contrast under g = 011 and 010, which indicates that the Burgers vector of these dislocations is b = [100]. Due to the limitation in sample tilting capability of TEM, only a single invisibility condition was identified for Group-C dislocations. Thus, the Burgers vector of Group-C dislocations was not uniquely determined in the present study, while was speculated to be b = [010] since the lattice symmetry of YB6 is primitive and the dislocations were out of contrast only when g = 100 . The line vectors of Group-A dislocations were analyzed by trace analysis. Five dislocations were examined, which are labelled from (A) to (E) in Fig. 6. These dislocations were taken from two zone axes: (a) [121] and (b) [111], and the trace analysis was conducted from the
Table 1 Elastic moduli and nanohardness experimentally determined in this study.
YB4 YB6
Young's Modulus, E (GPa)
Reduced Modulus, Er (GPa)
Poisson ratio, ν
Nano-hardness, Hn (GPa)
432 ± 11 241 ± 7
321 ± 6 221 ± 5
0.18[18] 0.348[19]
31.6 ± 2.1 24.6 ± 1.3
corresponds to the elastic strain relief that includes dislocation nucleation and multiplication in a localized area [22–24], it is indicated that YB4 and YB6 have some plastic deformability accompanying dislocation glides at room temperature. 3.3. Dislocations in YB4 and YB6 By TEM examinations, dislocations were found to develop in YB6 grains of an arc-melted alloy as shown in the bright-field images in Fig. 5. No planar faults or dissociation of dislocations were observed in
Fig. 4. Typical load-displacement nanoindentation curves from YB4 (a) and YB6 (b) grains.
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Fig. 5. Contrast analysis of dislocations formed in YB6. The arrows in the micrographs represent the direction of the reflection vectors for imaging. (a) g = 111, (b) g = 011, (c) g = 110 , (d) g = 110 , (e) g = 010, and (f) the designation of the dislocation groups.
cross products between the Burgers vector (b = [001]) and the line vectors are ranging near (100), and the deviations are only within about 3°. Considering that trace analysis may contain some amount of error, the glide plane of these dislocations is expected to be (100). Therefore it is concluded that a slip system that can operate in YB6 is {100}〈001〉. The identical slip system has been reported in LaB6 which has the same crystal structure with YB6 [25]. Similar to YB6, some dislocations were observed in YB4 grains. However, the dislocation density in YB4 grains was much lower than that in YB6. Thus we applied the weak-beam thickness fringe method [13] that can determine the magnitude and sense of the Burgers vectors of dislocations, but is only applicable to a small area near the edge of perforation. The reflection vector, g, the Burgers vector of dislocation, b, and the number of fringes terminated at the dislocation end, n, satisfy the following equation
Fig. 6. The images used for the trace analysis of the line vectors of dislocations formed in YB6. The images are taken from (a) [121] and (b) [111] zone axes. Table 2 Summary of line vector analysis on dislocation formed in YB6.
g⋅b = n.
Dislocation
Line Vector l
b × l (b = [001])
Deviation from (100)
(A) (B) (C) (D) (E)
[1, 18, 13] [0 2 1] [1, 41, 37] [0 9 1] [1, 16, 5]
(18, 1, 0) (1 0 0)
3.1° 0° 1.4° 0° 3.5°
41, 1, 0 (1 0 0) (16, 1, 0)
(3)
Thus the Burgers vector of a dislocation can be identified by counting the excess thickness contours terminating at the end of each dislocation line imaged in weak-beam dark-field mode under, at least, three non-coplanar reflection vectors. Fig. 7 shows the weak-beam dark-field images of the dislocations in YB4 phase imaged under the reflection vectors of 001, 200 , 022 , and 211. The numbers of excess thickness fringes terminated at the ends of the dislocation are −1, 0, +2, and +1, respectively, which indicates that the Burgers vector of the dislocation is b = [001]. By tilting experiments and trace analysis, the line vector of the dislocation is determined to be [41, 1, 1], which is almost parallel to [100] (only 1.6° deviation). Therefore, the glide plane of this dislocation is expected to be (010). Thus, the slip system that operates in YB4 is expressed as (100)[001].
images. Note that, to enhance the reliability for the trace analysis, the images are taken from the exact zone axes (not with two-beam conditions), and the brightness of the images is adjusted by using an image processing software. The results of trace analysis are summarized in Table 2. Generally, for a glide dislocation, the Burgers vector and the line vector of the dislocation lie on the slip plane. Thus the slip plane of a glide dislocation can be deduced from the cross product between the Burgers vector and the line vector of the dislocation. In Table 2 all the
4. Discussion The high melting temperatures for Y-B alloys impose a number of 89
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shear stress at pop-ins to occur in YB4 and YB6 is approximately G/ 8 ∼ G/6, which is close to the ideal strength of the crystals of G/2π [28]. Therefore the formation (nucleation) of dislocations within a dislocation-free region is the major energetic barrier for pop-in events, as is the case for other materials [26,27]. In the present study, dislocations were observed in both YB4 and YB6. These dislocations are believed to develop by the thermal stresses during cooling following arc-melting of the alloys. TEM observations have revealed that the dislocation density is higher in YB6 than in YB4. A rough estimation of dislocation density from TEM micrographs suggests that the dislocation density in the grain interior of YB6 approaches an order of 1013 (m−2), while that in YB4 is in an order of 1012 (m−2) or less. This observation indicates that generation and movement of dislocations are relatively easier in YB6 due to the simpler and smaller unit cell. This is supported by the results of high-temperature hardness measurements [10], where slip bands were not observed in YB4 by indentation at 1200 °C, while some slip bands were developed in YB6 at above 600 °C. The Burgers vectors of dislocations observed in the present study are [001] for YB4, and 〈100〉 for YB6. These Burgers vectors are reasonable since the vectors are the shortest fundamental translation vectors in the YB4 and the YB6 crystals. Combined with the results of dislocation line vector analysis, the slip systems that operate in YB4 and YB6 are determined as (100)[001] and {001}〈100〉 types, respectively. In general, the Peierls stress for a given slip system decreases with increasing the d/ b ratio, where d is the interplanar spacing of the slip plane, and b is the magnitude of the Burgers vector [28]. That is, the slip systems with higher d/b values are favored. The determined slip systems are reasonable since their d/b values are the highest in the potential slip systems for both YB4 and YB6. The observed development of dislocations in both YB4 and YB6 may indicate a useful thermal shock resistance, In fact, a bounding estimate for the thermal shock resistance can be judged from the following equation [29]:
Fig. 7. Weak-beam dark field images of dislocations formed in YB4 under a set of operation reflections; (a) g = 001, (b) g = 200 , (c) g = 022 , and (d) g = 211. The numbers of thickness fringes terminated at the dislocation end are (a) −1, (b) 0, (c) +2, and (d) +1, respectively.
challenges in alloy synthesis, especially for bulk materials, but the present study has shown that a conventional arc-melting method is applicable to synthesize ingots of YB4 and YB6 alloys. The present study revealed that the elastic moduli of YB4 and YB6 experimentally determined by nanoindentation technique are roughly 20–35% higher than those reported by ab-initio calculations [18,19]. Of course, due to crystalline anisotropy and the uncertainty of the Poisson ratios, the range of error for the evaluated moduli could be larger than that indicated in Table 1. However, the validity of the experimental data is supported by the fact that the loading curve coincides with the one calculated from the reduced modulus obtained from unloading curve by the Hertz contact theory. Due to the complex crystal structures and the high melting temperatures of YB4 and YB6, the Peierls barriers of dislocations in these borides are expected to be very high. Nonetheless the occurrence of pop-in events during nanoindentation loading implies that these borides have some capability of dislocation emission and gliding at room temperature. Previous studies have demonstrated, in bcc metals [26] and bulk metallic glasses [27], that a pop-in occurs when the maximum shear stress reaches nearly the ideal strength of specimens. The maximum shear stress, τmax, underneath the indenter tip is given by the following equation [21],
ΔT =
⎜
E 2(1 + ν )
(6)
5. Conclusion YB4/YB6 two-phase alloys have been successfully synthesized by a conventional arc-melting method. The Young's moduli of YB4 and YB6 determined by nanoindentation are 432 ± 11 GPa and 241 ± 7 GPa, respectively. Upon nanoindentation, pop-in events were observed for YB4 and YB6, suggesting that both have some capability of dislocation emission at room temperature. TEM observation reveals that dislocations develop in both YB4 and YB6 presumably due to the thermal stress during cooling following arc-melting. The Burgers vectors of dislocations have been identified as [001] for YB4 and < 100 > for YB6. The dislocation characters indicate that the slip systems that can operate in YB4 is (100)[001] and that in YB6 is {100} < 001 > .
⎟
(4)
where Er is the reduced modulus, Ri is the curvature of the indenter tip, and P is indentation load. The maximum shear stress at the pop-in events is calculated to be 23.3 ± 0.9 GPa for YB4 and 15.2 ± 0.5 GPa for YB6. For isotropic materials, Young's modulus and shear modulus are connected by the following equation.
G=
,
where ΔT is the temperature range for the onset of cracking, σf is the fracture stress and α is the expansion coefficient. Using the τmax values for σf which will underestimate ΔT, the E values from Table 1, and the α values of 7.6 × 10−6 (K−1) for YB4 [30] and 7.45 × 10−6 (K−1) for YB6 [17], the ΔT range for both borides is several times the melting temperature, which indicates a good thermal shock resistance. This is supported by the observation that the arc-cast ingots were observed to be free of cracks.
2
E 3 1 τmax = 0.18 ⎛ r ⎞ P 3 . ⎝ Ri ⎠
σf αE
Acknowledgements
(5)
Here E is the Young's modulus, G is the shear modulus, and ν is the Poisson ratio. Since the Young's moduli of YB4 and YB6 determined are 432 and 241 GPa, respectively, the shear moduli of YB4 and YB6 are evaluated to be 183 and 89 GPa. From this evaluation, the maximum
The support of ONR (N0014-10-1-0913) is gratefully acknowledged. NS acknowledges Ms. C. Hirosawa for her assistance on sample preparation and nanoindentation measurements and the support by JSPS Grant-in-Aid for Scientific Research (C) 26420670. 90
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91
Contents lists available at ScienceDirect
Intermetallics journal homepage: www.elsevier.com/locate/intermet
Mechanical properties and dislocation character of YB4 and YB6 Nobuaki Sekido a b c
a,b,∗
b
MARK
c
, Takahito Ohmura , John H. Perepezko
Department of Materials Science and Engineering, Tohoku University, 6-6-02 Aobayama, Sendai 980-8579, Japan National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan Department of Materials Science and Engineering, University of Wisconsin-Madison, 1509 University Avenue, Madison, WI 53706, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Transmission electron microscopy Dislocation Burgers vector Slip system Yttrium borides
YB4/YB6 two-phase alloys were prepared by arc-melting of high purity elemental materials. The Young's moduli of YB4 and YB6 were evaluated by nanoindentation technique. During loading of nanoindentation, pop-in events were clearly observed for YB4 and YB6, suggesting that both have some capability of dislocation emission at room temperature. TEM observation depicts that dislocations have formed in YB4 and YB6 due to the thermal stress that developed during cooling following arc-melting. The Burgers vectors of these dislocations were identified to be [001] for YB4, and 〈100〉 for YB6. Potential slip systems that are indicated to operate were (100) [001] for YB4 and {100}〈001〉 for YB6.
1. Introduction Among the different classes of intermetallics, boride phases often display the highest values of elastic modulus and hardness. Indeed, many of the uses of boride phases are designed based upon their high hardness. At the same time, the borides are not notable for demonstrating a capability for extensive plastic deformation at low temperature. Moreover, many of the characteristic structures for the boride phases are non-cubic and yield anisotropic behavior in thermal expansion which can lead to cracking and a thermal shock sensitivity. Aside from applications where high hardness and wear resistance are necessary there is an important application based upon the high electron emissivity of the rare earth borides such as LaB6. During this application electron gun filaments are subjected to fairly rapid changes in temperature and thermal gradients without cracking. This apparent resistance to thermal shock suggests that some of the rare earth borides may be able to exhibit plastic flow and dislocation motion. However, there seems to be little known about the character and behavior of dislocations in the rare earth borides. In the Y-B binary system, at least five types of borides, YB2, YB4, YB6, YB12, and YB66, are stable [1]. Among them, YB4 has the highest melting temperature (2800 °C) at the congruent point. The YB4 crystal possess a primitive tetragonal structure (tP20: P4/mbm, B4Th type) [2]. This structure consists of Y-layers and B-layers stacking along the [001] direction, and can be described in terms of connecting YB2 and YB6 units [3,4]. On the other hand, the YB6 crystal possess a primitive cubic structure (cP7: Pm3m, B6Ca type) [2], where the cube corners are occupied by Y atoms and a regular octahedron consisting of six boron ∗
atoms is set at the center of the cube. The nearest distance between boron atoms within an octahedron is approximately the same as the distance between boron atoms on neighbouring octahedron. The structures of these borides are schematically illustrated in Fig. 1. Some of the physical and chemical properties of YB4 and YB6 have been investigated previously, including electron resistivity [5,6], thermal conductivity [6], and thermal expansion coefficients [7]. However, limited information is available for mechanical properties except for some hardness measurement results [8–11]. In the present study, dislocations were identified to develop in YB4 and YB6, and were characterized by means of transmission electron microscopy. The slip systems that operate in YB4 and YB6 were deduced from the Burgers vectors and the line vectors of dislocations. 2. Experimental procedures A YB4/YB6 two-phase alloy with the nominal composition of Y-80at. %B was prepared by a conventional arc-melting method. High purity raw materials were melted on a water-cooled Cu plate under an Ar atmosphere with minimal weight change (about 0.1%). Phase identification and lattice parameter measurement were done by X-ray diffractometry. Powdered specimens were examined in a diffractometer operating in Bragg-Brentano geometry with Cu-Kα radiation. Data was corrected by the step-scan method with a fixed time of 2 s per 0.02°. The tube voltage and current were 40 kV and 200 mA, respectively. The divergence slit open angle was 1°, and the receiving slit width was 0.15 mm. The Rietveld analysis on XRD profiles was done with RIETAN2000 software [12]. Microstructures of the alloys were characterized by
Corresponding author. Department of Materials Science and Engineering, Tohoku University, 6-6-02 Aobayama, Sendai 980-8579, Japan. E-mail address: [email protected] (N. Sekido).
http://dx.doi.org/10.1016/j.intermet.2017.05.024 Received 17 February 2017; Received in revised form 16 April 2017; Accepted 30 May 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
Intermetallics 89 (2017) 86–91
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Fig. 1. Crystal views of YB4 from (a) diagonal and (b) [001] directions, and those of YB6 from (c) diagonal and (d) [001] directions.
a = 0.71104(2) (nm) and c = 0.40209(1) (nm) for YB4 with a tetragonal structure, and a = 0.41028(1) (nm) for YB6 with a cubic structure. These lattice parameters agree with those previously reported [16,17].
scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The foils for TEM observation were mechanically thinned and perforated by ion-milling with an accelerating voltage of 4 kV. The Burgers vectors of dislocations formed in the borides were determined by the thickness fringe method [13], and by the conventional contrast analysis based on the invisibility criteria. The line vectors of dislocations were determined by the trace analysis method [14] on images taken from two zone axes. Nanoindentation measurement was done by a Hysitron Triboindenter under a load-controlled condition with the maximum load of 3000 μN. A Berkovich indenter was employed, and the tip truncation was calibrated by using a reference specimen of fused silica. The Oliver-Pharr method [15] was employed for analyzing the hardness and elastic modulus of the YB4 and YB6 phases.
3.2. Elastic constant and nano-hardness of YB4 and YB6 The Young's modulus and nano-hardness of YB4 and YB6 were determined by nanoindentation tests on the arc-melted alloys. Table 1 summarizes the results of the moduli and hardness of YB4 and YB6. The Young's modulus was calculated from the reduced modulus (Er), which was experimentally determined from the slope of the curve upon unloading by
1 − νi2 1 − νs2 1 = + . Er Ei Es
3. Results
(1)
Here, Ei and νi are the Young's modulus and Poisson ratio of the indenter, and Es and νs are those of the specimen. The Young's modulus and the Poisson ratio of the diamond indenter are Ei = 1140 GPa and νi = 0.07. To our best knowledge, no experimental data is available for the Poisson ratios of YB4 and YB6. Thus we used the values predicted by ab-initio calculations: νs = 0.18 for YB4 [18] and νs = 0.348 for YB6 [19]. The Young's moduli of YB4 and YB6 determined in this study are 432 ± 11 GPa and 241 ± 7 GPa, respectively. These are higher than those by the ab-initio calculations: 342 GPa for YB4 [18] and 156 GPa for YB6 [19]. YB4 and YB6 are found to show quite high nano-hardness: 31.6 GPa for YB4, and 24.6 GPa for YB6. Due to the indentation size effect, a hardness value tested by nanoindentation technique is not necessarily comparable to that by micro-hardness [20]. Nonetheless, the tendency, where YB4 shows a higher hardness than YB6, is consistent with a previous report [10]. Another notable result of the nanoindentation measurement is an occurrence of a “pop-in”, which is a discontinuous jump in displacement that appears in load-displacement curves during loading. Fig. 4 shows typical load-displacement curves by nanoindentation of (a) YB4 and (b) YB6, in which pop-ins are indicated by arrows. The average values of the critical load for pop-in, Pc, are 1833 ± 203 μN for YB4, and 1082 ± 114 μN for YB6. The dashed curves in Fig. 4 are calculated by the Hertz elastic contact theory, which is given by Ref. [21].
3.1. Alloy synthesis Fig. 2 shows a microstructure of an as-cast YB4/YB6 two-phase alloy. The YB4 phase crystallises from the liquid as the primary solidification phase, followed by the formation of the YB6 phase through a peritectic reaction. No microcracks were observed in YB4 and YB6 grains, as shown in Fig. 2. Some interfaces between YB4 and YB6 are faceted (representative facets are indicated by arrows), which suggests that the growth of YB4 from liquid is accompanied by the formation of faceted interfaces as expected for intermetallic phases. Fig. 3 shows an XRD profile of an as-cast YB4/YB6 two-phase alloy, together with a result of the Rietveld analysis. Upon analysis, no antisite defects were presumed to occur in both YB4 and YB6, and the atom positions of the both phases were fixed to those previously reported [16,17]. All the peaks in Fig. 3 were assigned to YB4 and YB6 with a reasonable goodness of fitting. The lattice parameters evaluated are:
P=
1 3 4 Er Ri2 h 2 . 3
(2)
Here, P is the indentation load, h is the penetration depth, and Ri is the curvature of the indenter tip. The curvature of the indenter tip has been calibrated to be 290 nm by preliminary measurements on the standard fused silica, and the reduced Young's modulus, Er, used was determined from the slope of an unloading curve. As can be seen in Fig. 4, the experimentally obtained P-h curves coincide with those calculated by Eq. (2), suggesting that deformation underneath the indenter is elastic before the onset of the pop-in event. Since the “pop-in”
Fig. 2. A back-scattered scanning electron micrograph of an as-cast YB4/YB6 two-phase alloy.
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Fig. 3. A Rietveld-refined XRD profile of an YB4/ YB6 two-phase alloy.
the present study. Contrast analysis revealed that these dislocations can be divided into three groups with respect to the Burgers vectors of the dislocations, as shown in Fig. 5(f). Group A is the dislocations that have been developed in the interior of a YB6 grain, and Group B and C are ones that form a sub-grain boundary. Group-A dislocations are out of contrast under the reflection vectors of g = 110 , 100 , and 010, which indicates that the Burgers vector of the dislocations is b = [001]. Group-B dislocations are out of contrast under g = 011 and 010, which indicates that the Burgers vector of these dislocations is b = [100]. Due to the limitation in sample tilting capability of TEM, only a single invisibility condition was identified for Group-C dislocations. Thus, the Burgers vector of Group-C dislocations was not uniquely determined in the present study, while was speculated to be b = [010] since the lattice symmetry of YB6 is primitive and the dislocations were out of contrast only when g = 100 . The line vectors of Group-A dislocations were analyzed by trace analysis. Five dislocations were examined, which are labelled from (A) to (E) in Fig. 6. These dislocations were taken from two zone axes: (a) [121] and (b) [111], and the trace analysis was conducted from the
Table 1 Elastic moduli and nanohardness experimentally determined in this study.
YB4 YB6
Young's Modulus, E (GPa)
Reduced Modulus, Er (GPa)
Poisson ratio, ν
Nano-hardness, Hn (GPa)
432 ± 11 241 ± 7
321 ± 6 221 ± 5
0.18[18] 0.348[19]
31.6 ± 2.1 24.6 ± 1.3
corresponds to the elastic strain relief that includes dislocation nucleation and multiplication in a localized area [22–24], it is indicated that YB4 and YB6 have some plastic deformability accompanying dislocation glides at room temperature. 3.3. Dislocations in YB4 and YB6 By TEM examinations, dislocations were found to develop in YB6 grains of an arc-melted alloy as shown in the bright-field images in Fig. 5. No planar faults or dissociation of dislocations were observed in
Fig. 4. Typical load-displacement nanoindentation curves from YB4 (a) and YB6 (b) grains.
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Fig. 5. Contrast analysis of dislocations formed in YB6. The arrows in the micrographs represent the direction of the reflection vectors for imaging. (a) g = 111, (b) g = 011, (c) g = 110 , (d) g = 110 , (e) g = 010, and (f) the designation of the dislocation groups.
cross products between the Burgers vector (b = [001]) and the line vectors are ranging near (100), and the deviations are only within about 3°. Considering that trace analysis may contain some amount of error, the glide plane of these dislocations is expected to be (100). Therefore it is concluded that a slip system that can operate in YB6 is {100}〈001〉. The identical slip system has been reported in LaB6 which has the same crystal structure with YB6 [25]. Similar to YB6, some dislocations were observed in YB4 grains. However, the dislocation density in YB4 grains was much lower than that in YB6. Thus we applied the weak-beam thickness fringe method [13] that can determine the magnitude and sense of the Burgers vectors of dislocations, but is only applicable to a small area near the edge of perforation. The reflection vector, g, the Burgers vector of dislocation, b, and the number of fringes terminated at the dislocation end, n, satisfy the following equation
Fig. 6. The images used for the trace analysis of the line vectors of dislocations formed in YB6. The images are taken from (a) [121] and (b) [111] zone axes. Table 2 Summary of line vector analysis on dislocation formed in YB6.
g⋅b = n.
Dislocation
Line Vector l
b × l (b = [001])
Deviation from (100)
(A) (B) (C) (D) (E)
[1, 18, 13] [0 2 1] [1, 41, 37] [0 9 1] [1, 16, 5]
(18, 1, 0) (1 0 0)
3.1° 0° 1.4° 0° 3.5°
41, 1, 0 (1 0 0) (16, 1, 0)
(3)
Thus the Burgers vector of a dislocation can be identified by counting the excess thickness contours terminating at the end of each dislocation line imaged in weak-beam dark-field mode under, at least, three non-coplanar reflection vectors. Fig. 7 shows the weak-beam dark-field images of the dislocations in YB4 phase imaged under the reflection vectors of 001, 200 , 022 , and 211. The numbers of excess thickness fringes terminated at the ends of the dislocation are −1, 0, +2, and +1, respectively, which indicates that the Burgers vector of the dislocation is b = [001]. By tilting experiments and trace analysis, the line vector of the dislocation is determined to be [41, 1, 1], which is almost parallel to [100] (only 1.6° deviation). Therefore, the glide plane of this dislocation is expected to be (010). Thus, the slip system that operates in YB4 is expressed as (100)[001].
images. Note that, to enhance the reliability for the trace analysis, the images are taken from the exact zone axes (not with two-beam conditions), and the brightness of the images is adjusted by using an image processing software. The results of trace analysis are summarized in Table 2. Generally, for a glide dislocation, the Burgers vector and the line vector of the dislocation lie on the slip plane. Thus the slip plane of a glide dislocation can be deduced from the cross product between the Burgers vector and the line vector of the dislocation. In Table 2 all the
4. Discussion The high melting temperatures for Y-B alloys impose a number of 89
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shear stress at pop-ins to occur in YB4 and YB6 is approximately G/ 8 ∼ G/6, which is close to the ideal strength of the crystals of G/2π [28]. Therefore the formation (nucleation) of dislocations within a dislocation-free region is the major energetic barrier for pop-in events, as is the case for other materials [26,27]. In the present study, dislocations were observed in both YB4 and YB6. These dislocations are believed to develop by the thermal stresses during cooling following arc-melting of the alloys. TEM observations have revealed that the dislocation density is higher in YB6 than in YB4. A rough estimation of dislocation density from TEM micrographs suggests that the dislocation density in the grain interior of YB6 approaches an order of 1013 (m−2), while that in YB4 is in an order of 1012 (m−2) or less. This observation indicates that generation and movement of dislocations are relatively easier in YB6 due to the simpler and smaller unit cell. This is supported by the results of high-temperature hardness measurements [10], where slip bands were not observed in YB4 by indentation at 1200 °C, while some slip bands were developed in YB6 at above 600 °C. The Burgers vectors of dislocations observed in the present study are [001] for YB4, and 〈100〉 for YB6. These Burgers vectors are reasonable since the vectors are the shortest fundamental translation vectors in the YB4 and the YB6 crystals. Combined with the results of dislocation line vector analysis, the slip systems that operate in YB4 and YB6 are determined as (100)[001] and {001}〈100〉 types, respectively. In general, the Peierls stress for a given slip system decreases with increasing the d/ b ratio, where d is the interplanar spacing of the slip plane, and b is the magnitude of the Burgers vector [28]. That is, the slip systems with higher d/b values are favored. The determined slip systems are reasonable since their d/b values are the highest in the potential slip systems for both YB4 and YB6. The observed development of dislocations in both YB4 and YB6 may indicate a useful thermal shock resistance, In fact, a bounding estimate for the thermal shock resistance can be judged from the following equation [29]:
Fig. 7. Weak-beam dark field images of dislocations formed in YB4 under a set of operation reflections; (a) g = 001, (b) g = 200 , (c) g = 022 , and (d) g = 211. The numbers of thickness fringes terminated at the dislocation end are (a) −1, (b) 0, (c) +2, and (d) +1, respectively.
challenges in alloy synthesis, especially for bulk materials, but the present study has shown that a conventional arc-melting method is applicable to synthesize ingots of YB4 and YB6 alloys. The present study revealed that the elastic moduli of YB4 and YB6 experimentally determined by nanoindentation technique are roughly 20–35% higher than those reported by ab-initio calculations [18,19]. Of course, due to crystalline anisotropy and the uncertainty of the Poisson ratios, the range of error for the evaluated moduli could be larger than that indicated in Table 1. However, the validity of the experimental data is supported by the fact that the loading curve coincides with the one calculated from the reduced modulus obtained from unloading curve by the Hertz contact theory. Due to the complex crystal structures and the high melting temperatures of YB4 and YB6, the Peierls barriers of dislocations in these borides are expected to be very high. Nonetheless the occurrence of pop-in events during nanoindentation loading implies that these borides have some capability of dislocation emission and gliding at room temperature. Previous studies have demonstrated, in bcc metals [26] and bulk metallic glasses [27], that a pop-in occurs when the maximum shear stress reaches nearly the ideal strength of specimens. The maximum shear stress, τmax, underneath the indenter tip is given by the following equation [21],
ΔT =
⎜
E 2(1 + ν )
(6)
5. Conclusion YB4/YB6 two-phase alloys have been successfully synthesized by a conventional arc-melting method. The Young's moduli of YB4 and YB6 determined by nanoindentation are 432 ± 11 GPa and 241 ± 7 GPa, respectively. Upon nanoindentation, pop-in events were observed for YB4 and YB6, suggesting that both have some capability of dislocation emission at room temperature. TEM observation reveals that dislocations develop in both YB4 and YB6 presumably due to the thermal stress during cooling following arc-melting. The Burgers vectors of dislocations have been identified as [001] for YB4 and < 100 > for YB6. The dislocation characters indicate that the slip systems that can operate in YB4 is (100)[001] and that in YB6 is {100} < 001 > .
⎟
(4)
where Er is the reduced modulus, Ri is the curvature of the indenter tip, and P is indentation load. The maximum shear stress at the pop-in events is calculated to be 23.3 ± 0.9 GPa for YB4 and 15.2 ± 0.5 GPa for YB6. For isotropic materials, Young's modulus and shear modulus are connected by the following equation.
G=
,
where ΔT is the temperature range for the onset of cracking, σf is the fracture stress and α is the expansion coefficient. Using the τmax values for σf which will underestimate ΔT, the E values from Table 1, and the α values of 7.6 × 10−6 (K−1) for YB4 [30] and 7.45 × 10−6 (K−1) for YB6 [17], the ΔT range for both borides is several times the melting temperature, which indicates a good thermal shock resistance. This is supported by the observation that the arc-cast ingots were observed to be free of cracks.
2
E 3 1 τmax = 0.18 ⎛ r ⎞ P 3 . ⎝ Ri ⎠
σf αE
Acknowledgements
(5)
Here E is the Young's modulus, G is the shear modulus, and ν is the Poisson ratio. Since the Young's moduli of YB4 and YB6 determined are 432 and 241 GPa, respectively, the shear moduli of YB4 and YB6 are evaluated to be 183 and 89 GPa. From this evaluation, the maximum
The support of ONR (N0014-10-1-0913) is gratefully acknowledged. NS acknowledges Ms. C. Hirosawa for her assistance on sample preparation and nanoindentation measurements and the support by JSPS Grant-in-Aid for Scientific Research (C) 26420670. 90
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