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Application of transmission electron microscopy and focused ion beam tomography for microstructure characterization of tungsten based materials
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 Phys. Scr. 2011 014043 (http://iopscience.iop.org/1402-4896/2011/T145/014043) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 23.20.90.102 The article was downloaded on 19/02/2012 at 06:01
Please note that terms and conditions apply.
IOP PUBLISHING
PHYSICA SCRIPTA
Phys. Scr. T145 (2011) 014043 (4pp)
doi:10.1088/0031-8949/2011/T145/014043
Application of transmission electron microscopy and focused ion beam tomography for microstructure characterization of tungsten based materials S Milc1 , A Kruk1 , G Cempura1 , H J Penkalla2 , C Thomser2 and A Czyrska-Filemonowicz1 1
AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science and International Centre of Electron Microscopy for Materials Science, Al A Mickiewicza 30, 30-059 Krakow, Poland 2 Forschungszentrum Jülich EURATOM—Association FZJ, Institute of Energy and Climate Research, 52425 Jülich, Germany E-mail: [email protected]
Received 19 May 2011 Accepted for publication 5 September 2011 Published 16 December 2011 Online at stacks.iop.org/PhysScr/T145/014043 Abstract Tungsten and its alloys are considered as structural materials for plasma-facing applications. The divertor design requires a material with a low ductile–brittle transition temperature and a recrystallization temperature (TR ) of about 1570 K. One of the materials under consideration is W–1.7%TiC. The aim of this work was to perform a detailed microstructural characterization of the two materials, pure W and W–1.7%TiC alloy, by electron microscopy and a new technique, electron tomography. Thin foil preparation for transmission electron microscopy investigation of W-based materials is extremely difficult. After many trials by various techniques, a method for thin foil preparation was successfully elaborated and a transmission electron microscope (TEM) investigation was carried out. A pure tungsten specimen was investigated as a reference material. The application of TEM and focused ion beam–scanning electron microscopy techniques enables the identification of some creep-induced features in pure tungsten and the determination of the size and morphology of three-dimensional pores and particles in W–TiC-based alloy. PACS number: 28.52.Fa
temperature (low border) and increases significantly after recrystallization and neutron irradiation [8]. The upper border of the operating temperature window depends on the tungsten recrystallization temperature (TR ) [5–7]. The requirement for divertor design is a material having a low DBTT and TR of about 1570 K [9]. To improve the high-temperature properties of tungsten, two approaches can be applied. One method involves dispersion strengthening of tungsten by oxides and/or carbides, i.e. Y2 O3 , La2 O3 , Ce2 O, ThO2 , HfC or TiC [9–12]. The effect of dispersion strengthening is almost independent of the type of dispersoids. Addition of particles leads to
1. Introduction Tungsten (W) and its alloys are considered as potential candidates for plasma-facing materials, especially for divertor and first-wall applications in nuclear fusion reactors due to the low sputtering rate, high thermal conductivity, high strength at elevated temperatures and low tritium inventory [1–4]. The operating temperature window for these materials appears to be currently established between 1070 and 1470 K [5–7]. For pure tungsten and tungsten-based materials the ductile–brittle transition temperature (DBTT) is much higher than room 0031-8949/11/014043+04$33.00
1
© 2011 The Royal Swedish Academy of Sciences
Printed in the UK
Phys. Scr. T145 (2011) 014043
S Milc et al
an improvement of creep and tensile strength and to an increase of TR , and enables better component machining. Another way to improve the ductility of tungsten is doping by solution-hardening elements, such as in [6, 13].
2. Material and experimental details Two materials, pure tungsten and W–1.7%TiC alloy, were studied. The investigated pure tungsten material proposed for fusion application was produced by Plansee by sintering, forging and annealing (containing 99.97% tungsten, ASTM grain size 7), whereas the W–1.7%TiC alloy was manufactured by mechanical alloying and hot isostatic pressing. The pure tungsten was creep tested at 1370 K and 80 MPa for 2000 and 5000 h. The head of creep specimens was used as undeformed reference specimens. The microstructural analyses were performed by transmission electron microscopy (TEM) using a JEM-2010 ARP from JEOL and scanning electron microscopy (SEM) accomplished by qualitative energy dispersive x-ray spectroscope (EDS) analyses using an FEG NEON 40EsB CrossBeam from Zeiss. The low ductility of the material was one of the main reasons for difficulty of TEM specimen preparation. It is the reason why no mechanical treatment at the last thinning steps was applicable. Specimens for TEM observation were electrolytically cut in NaOH solution to 3 mm discs. Because of the high electron absorption due to the high atomic weight, very thin specimens of W-based materials for TEM investigations are required. Therefore the 3 mm W discs were subsequently slowly perforated by electro-polishing in TENUPOL 5 (manufactured by Struers) using 10% NaOH solution with a voltage of 5 V at room temperature. Focused ion beam (FIB) tomography was applied for the characterization of the W–1.7%TiC microstructure (shape and size of strengthening particles). Electron tomography images were recorded using a dual-beam workstation (Neon 40EsB CrossBeam of Zeiss) equipped with an FIB column with Ga ions. A series of 314 back-scattered secondary electron (BSE) images was recorded during FIB slicing (the distance between slices was about 5 nm). Due to the configuration of the NEON 40EsB, there was no need for mechanical tilt of the specimen between slicing and imaging during acquisition of tomography series. The recorded micrographs were transformed into a voxel-based data volume. In order to align the images, slightly shifted during the acquisition, FIJI software was used. A three-dimensional (3D) reconstruction was made with the Avizo Fire 6 program.
Figure 1. Ashby map for tungsten [14] with a marker indicating the creep tests conditions performed. Reprint with permission from [14] copyright 1972, with permission from Elsevier.
parameter curves are lines of constant creep rate. The marker indicates the creep test conditions performed (T = 1270 K, TH = 0.37, σ = 80 MPa, G = 161 GPa, σ/G = 5.10–4). Based on the Ashby map, it can be concluded that under given creep conditions, the diffusion creep by the Coble mechanism dominates the creep process and dislocation creep plays only a secondary role. The microstructure of the pure tungsten reference specimen is presented in figure 2. Well-developed sub-grain microstructure was observed after long-term thermal exposure at 1370 K without applied stress (figure 2(a)). The dislocation density within sub-grains was very low which can be caused by the production process (sintering, forging and annealing) (figure 2(b)). After creep deformation for 2000 h at 1370 K and 80 MPa applied stress, a slight increase of dislocation density was visible, but still only a few dislocations were present (figure 3(a)). Due to the small transparent regions of the examined thin foils, the dislocation density could not be estimated. Dislocations were not uniformly distributed. In the tungsten microstructure, sub-grain/low-angle grain boundaries (figure 3(b)) and a small amount of gliding dislocation inside the grains were observed (figure 3(c)). In some areas of the microstructure, very early stages of the formation of creep-induced dislocation meshes were found (figure 3(c)). This fact indicates an early creep state. A longer creep test (5000 h) of the other specimen did not result in pronounced changes in the microstructure of tungsten. A few dislocations inside the grains as well as low-angle grain boundaries were observed (figure 4(a)). The dislocation density was similar to that after 2000 h of creep under the same test conditions. The formation of dislocation meshes was observed as well (figure 4(b)). As the microstructure of tungsten in the gauge length and the head of the creep-deformed specimen were very similar, there were no signs of severe dislocation-controlled creep under these test conditions. Only very early stages of the early primary creep were documented. The findings observed in
3. Results and discussion 3.1. Pure tungsten Figure 1 shows the Ashby map with a marked point, corresponding to the creep test conditions. The Ashby map, with homologous temperature TH (T /TM ) and normalized tensile stress (σ/G) as coordinates, shows the parameter field for different creep mechanisms, mainly the diffusioncontrolled Coble and Nabarro–Herring creep as well as the dislocation movement and climb-controlled creep. The 2
Phys. Scr. T145 (2011) 014043
S Milc et al
Figure 2. Microstructure of pure tungsten (reference specimen): (a) sub-grain boundaries and (b) dislocations inside the grains.
Figure 3. Microstructure of pure tungsten after creep at a temperature of 1370 K and stress of 80 MPa for 2000 h: (a) dislocations inside the grains, (b) sub-grain boundaries and (c) the formation of dislocation meshes.
Figure 4. Microstructure of pure tungsten after creep at a temperature 1370 K and stress of 80 MPa for 5000 h: (a) low-angle grain boundary and (b) the initial formation of dislocation meshes.
the microstructure of tungsten indicate a diffusion-controlled creep and agree with the estimation of the creep behaviour with the help of the Ashby map.
presence of both phases in the investigated alloy was qualitatively confirmed by SEM–EDS mapping. Figure 5(b) shows a 3D visualization of the alloy investigated (volume 4.7 × 2.4 × 1.7 µm3 ), where both pores and particles are included. The relative volume of both features in this volume was estimated to be 5.2 ± 1.4%. The distribution, shape and size of pores and particles are presented in figures 5(c) and (d), respectively. The pores exhibited variable shape and size. The size of pores was larger than that of strengthening particles. The dispersoids, mostly regular in shape, were rather randomly distributed in the matrix. Figure 5(e) shows
3.2. W–1.7%TiC alloy Figure 5(a) presents one of the 314 SEM–BSE images used for the electron tomography investigation of the W1.7%TiC alloy. In this image, the pores and particles (titanium carbides and oxides) are visible. Using only SEM imaging, titanium carbides and oxides cannot be distinguished; however, the 3
Phys. Scr. T145 (2011) 014043
S Milc et al
Figure 5. 3D characterization of W–1.7%TiC alloy microstructure using FIB tomography: (a) microstructure of W–1.7%TiC alloy as seen by SEM–BSE imaging, (b) 3D visualization of pores and particles, (c) 3D visualization of pores, (d) 3D visualization of particles and (e) histogram of particle diameters.
a histogram of the particle diameter. The mean diameter of the particles in that volume was estimated to be 33 ± 19 nm.
fusion energy materials. We acknowledge financial support from the Polish Ministry of Science and Higher Education and the German DAAD. This work, partially supported by the European Communities under the contract of association between EURATOM/Forschungszentrum Jülich, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Finally, we thank Professor Kurishira for his helpful suggestions on the preparation of TEM specimens.
4. Conclusions No pronounced differences in the microstructure of the head and gauge length of the creep deformed pure tungsten specimen were found. The dislocation density was low and sub-grain boundaries, mostly as low-angle grain boundaries, were observed. No significant changes in the microstructure of W specimens were found after creep tests. Only the very early stages of the early primary creep were documented, indicating diffusion-controlled creep. These results agree with the estimation of the creep behaviour with the help of the Ashby map. The microstructure W–1.7%TiC alloy consists of the tungsten matrix as well as carbide and oxide particles, mostly globular in shape with a diameter of 33 ± 19 nm. The W–1.7%TiC alloy exhibited pronounced porosity with irregularly shaped pores of various sizes. The relative volume of both pores and particles was estimated by FIB/SEM tomography to be 5.2 ± 1.4%.
Published under license from EURATOM.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Acknowledgments The study was conducted under cooperation between AGH University of Science and Technology and Forschungszentrum Jülich within the bilateral project on
4
Garcia-Rosales C 1994 J. Nucl. Mater. 211 202 Petti D A et al 1996 J. Nucl. Mater. 233–237 37 Tanabe T et al 1992 J. Nucl. Mater. 196–198 11 Roth J et al 2009 J. Nucl. Mater. 390 1 Norajitra P et al 2004 J. Nucl. Mater. 329 1594 Zinkle S J and Ghoniem N M 2011 J. Nucl. Mater. 417 2 Zinkle S J and Ghoniem N M 2000 Fusion Eng. Des. 51–52 55 Fujitsuka M et al 1996 J. Nucl. Mater. 233–237 638 Chen Y et al 2008 Int. J. Refract. Met. Hard Mater. 26 525 Song G M et al 2003 Int. J. Refract. Met. Hard Mater. 21 1 Mabuchi M et al 1997 Mater. Sci. Eng. A 237 241 Itoh Y et al 1996 JSME Int. J. A 39 42 Wurster H O 2010 Int. J. Refract. Met. Hard Mater. 28 692 Ashby M F 1972 Acta Metall. 20 887
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My IOPscience
Application of transmission electron microscopy and focused ion beam tomography for microstructure characterization of tungsten based materials
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 Phys. Scr. 2011 014043 (http://iopscience.iop.org/1402-4896/2011/T145/014043) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 23.20.90.102 The article was downloaded on 19/02/2012 at 06:01
Please note that terms and conditions apply.
IOP PUBLISHING
PHYSICA SCRIPTA
Phys. Scr. T145 (2011) 014043 (4pp)
doi:10.1088/0031-8949/2011/T145/014043
Application of transmission electron microscopy and focused ion beam tomography for microstructure characterization of tungsten based materials S Milc1 , A Kruk1 , G Cempura1 , H J Penkalla2 , C Thomser2 and A Czyrska-Filemonowicz1 1
AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science and International Centre of Electron Microscopy for Materials Science, Al A Mickiewicza 30, 30-059 Krakow, Poland 2 Forschungszentrum Jülich EURATOM—Association FZJ, Institute of Energy and Climate Research, 52425 Jülich, Germany E-mail: [email protected]
Received 19 May 2011 Accepted for publication 5 September 2011 Published 16 December 2011 Online at stacks.iop.org/PhysScr/T145/014043 Abstract Tungsten and its alloys are considered as structural materials for plasma-facing applications. The divertor design requires a material with a low ductile–brittle transition temperature and a recrystallization temperature (TR ) of about 1570 K. One of the materials under consideration is W–1.7%TiC. The aim of this work was to perform a detailed microstructural characterization of the two materials, pure W and W–1.7%TiC alloy, by electron microscopy and a new technique, electron tomography. Thin foil preparation for transmission electron microscopy investigation of W-based materials is extremely difficult. After many trials by various techniques, a method for thin foil preparation was successfully elaborated and a transmission electron microscope (TEM) investigation was carried out. A pure tungsten specimen was investigated as a reference material. The application of TEM and focused ion beam–scanning electron microscopy techniques enables the identification of some creep-induced features in pure tungsten and the determination of the size and morphology of three-dimensional pores and particles in W–TiC-based alloy. PACS number: 28.52.Fa
temperature (low border) and increases significantly after recrystallization and neutron irradiation [8]. The upper border of the operating temperature window depends on the tungsten recrystallization temperature (TR ) [5–7]. The requirement for divertor design is a material having a low DBTT and TR of about 1570 K [9]. To improve the high-temperature properties of tungsten, two approaches can be applied. One method involves dispersion strengthening of tungsten by oxides and/or carbides, i.e. Y2 O3 , La2 O3 , Ce2 O, ThO2 , HfC or TiC [9–12]. The effect of dispersion strengthening is almost independent of the type of dispersoids. Addition of particles leads to
1. Introduction Tungsten (W) and its alloys are considered as potential candidates for plasma-facing materials, especially for divertor and first-wall applications in nuclear fusion reactors due to the low sputtering rate, high thermal conductivity, high strength at elevated temperatures and low tritium inventory [1–4]. The operating temperature window for these materials appears to be currently established between 1070 and 1470 K [5–7]. For pure tungsten and tungsten-based materials the ductile–brittle transition temperature (DBTT) is much higher than room 0031-8949/11/014043+04$33.00
1
© 2011 The Royal Swedish Academy of Sciences
Printed in the UK
Phys. Scr. T145 (2011) 014043
S Milc et al
an improvement of creep and tensile strength and to an increase of TR , and enables better component machining. Another way to improve the ductility of tungsten is doping by solution-hardening elements, such as in [6, 13].
2. Material and experimental details Two materials, pure tungsten and W–1.7%TiC alloy, were studied. The investigated pure tungsten material proposed for fusion application was produced by Plansee by sintering, forging and annealing (containing 99.97% tungsten, ASTM grain size 7), whereas the W–1.7%TiC alloy was manufactured by mechanical alloying and hot isostatic pressing. The pure tungsten was creep tested at 1370 K and 80 MPa for 2000 and 5000 h. The head of creep specimens was used as undeformed reference specimens. The microstructural analyses were performed by transmission electron microscopy (TEM) using a JEM-2010 ARP from JEOL and scanning electron microscopy (SEM) accomplished by qualitative energy dispersive x-ray spectroscope (EDS) analyses using an FEG NEON 40EsB CrossBeam from Zeiss. The low ductility of the material was one of the main reasons for difficulty of TEM specimen preparation. It is the reason why no mechanical treatment at the last thinning steps was applicable. Specimens for TEM observation were electrolytically cut in NaOH solution to 3 mm discs. Because of the high electron absorption due to the high atomic weight, very thin specimens of W-based materials for TEM investigations are required. Therefore the 3 mm W discs were subsequently slowly perforated by electro-polishing in TENUPOL 5 (manufactured by Struers) using 10% NaOH solution with a voltage of 5 V at room temperature. Focused ion beam (FIB) tomography was applied for the characterization of the W–1.7%TiC microstructure (shape and size of strengthening particles). Electron tomography images were recorded using a dual-beam workstation (Neon 40EsB CrossBeam of Zeiss) equipped with an FIB column with Ga ions. A series of 314 back-scattered secondary electron (BSE) images was recorded during FIB slicing (the distance between slices was about 5 nm). Due to the configuration of the NEON 40EsB, there was no need for mechanical tilt of the specimen between slicing and imaging during acquisition of tomography series. The recorded micrographs were transformed into a voxel-based data volume. In order to align the images, slightly shifted during the acquisition, FIJI software was used. A three-dimensional (3D) reconstruction was made with the Avizo Fire 6 program.
Figure 1. Ashby map for tungsten [14] with a marker indicating the creep tests conditions performed. Reprint with permission from [14] copyright 1972, with permission from Elsevier.
parameter curves are lines of constant creep rate. The marker indicates the creep test conditions performed (T = 1270 K, TH = 0.37, σ = 80 MPa, G = 161 GPa, σ/G = 5.10–4). Based on the Ashby map, it can be concluded that under given creep conditions, the diffusion creep by the Coble mechanism dominates the creep process and dislocation creep plays only a secondary role. The microstructure of the pure tungsten reference specimen is presented in figure 2. Well-developed sub-grain microstructure was observed after long-term thermal exposure at 1370 K without applied stress (figure 2(a)). The dislocation density within sub-grains was very low which can be caused by the production process (sintering, forging and annealing) (figure 2(b)). After creep deformation for 2000 h at 1370 K and 80 MPa applied stress, a slight increase of dislocation density was visible, but still only a few dislocations were present (figure 3(a)). Due to the small transparent regions of the examined thin foils, the dislocation density could not be estimated. Dislocations were not uniformly distributed. In the tungsten microstructure, sub-grain/low-angle grain boundaries (figure 3(b)) and a small amount of gliding dislocation inside the grains were observed (figure 3(c)). In some areas of the microstructure, very early stages of the formation of creep-induced dislocation meshes were found (figure 3(c)). This fact indicates an early creep state. A longer creep test (5000 h) of the other specimen did not result in pronounced changes in the microstructure of tungsten. A few dislocations inside the grains as well as low-angle grain boundaries were observed (figure 4(a)). The dislocation density was similar to that after 2000 h of creep under the same test conditions. The formation of dislocation meshes was observed as well (figure 4(b)). As the microstructure of tungsten in the gauge length and the head of the creep-deformed specimen were very similar, there were no signs of severe dislocation-controlled creep under these test conditions. Only very early stages of the early primary creep were documented. The findings observed in
3. Results and discussion 3.1. Pure tungsten Figure 1 shows the Ashby map with a marked point, corresponding to the creep test conditions. The Ashby map, with homologous temperature TH (T /TM ) and normalized tensile stress (σ/G) as coordinates, shows the parameter field for different creep mechanisms, mainly the diffusioncontrolled Coble and Nabarro–Herring creep as well as the dislocation movement and climb-controlled creep. The 2
Phys. Scr. T145 (2011) 014043
S Milc et al
Figure 2. Microstructure of pure tungsten (reference specimen): (a) sub-grain boundaries and (b) dislocations inside the grains.
Figure 3. Microstructure of pure tungsten after creep at a temperature of 1370 K and stress of 80 MPa for 2000 h: (a) dislocations inside the grains, (b) sub-grain boundaries and (c) the formation of dislocation meshes.
Figure 4. Microstructure of pure tungsten after creep at a temperature 1370 K and stress of 80 MPa for 5000 h: (a) low-angle grain boundary and (b) the initial formation of dislocation meshes.
the microstructure of tungsten indicate a diffusion-controlled creep and agree with the estimation of the creep behaviour with the help of the Ashby map.
presence of both phases in the investigated alloy was qualitatively confirmed by SEM–EDS mapping. Figure 5(b) shows a 3D visualization of the alloy investigated (volume 4.7 × 2.4 × 1.7 µm3 ), where both pores and particles are included. The relative volume of both features in this volume was estimated to be 5.2 ± 1.4%. The distribution, shape and size of pores and particles are presented in figures 5(c) and (d), respectively. The pores exhibited variable shape and size. The size of pores was larger than that of strengthening particles. The dispersoids, mostly regular in shape, were rather randomly distributed in the matrix. Figure 5(e) shows
3.2. W–1.7%TiC alloy Figure 5(a) presents one of the 314 SEM–BSE images used for the electron tomography investigation of the W1.7%TiC alloy. In this image, the pores and particles (titanium carbides and oxides) are visible. Using only SEM imaging, titanium carbides and oxides cannot be distinguished; however, the 3
Phys. Scr. T145 (2011) 014043
S Milc et al
Figure 5. 3D characterization of W–1.7%TiC alloy microstructure using FIB tomography: (a) microstructure of W–1.7%TiC alloy as seen by SEM–BSE imaging, (b) 3D visualization of pores and particles, (c) 3D visualization of pores, (d) 3D visualization of particles and (e) histogram of particle diameters.
a histogram of the particle diameter. The mean diameter of the particles in that volume was estimated to be 33 ± 19 nm.
fusion energy materials. We acknowledge financial support from the Polish Ministry of Science and Higher Education and the German DAAD. This work, partially supported by the European Communities under the contract of association between EURATOM/Forschungszentrum Jülich, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Finally, we thank Professor Kurishira for his helpful suggestions on the preparation of TEM specimens.
4. Conclusions No pronounced differences in the microstructure of the head and gauge length of the creep deformed pure tungsten specimen were found. The dislocation density was low and sub-grain boundaries, mostly as low-angle grain boundaries, were observed. No significant changes in the microstructure of W specimens were found after creep tests. Only the very early stages of the early primary creep were documented, indicating diffusion-controlled creep. These results agree with the estimation of the creep behaviour with the help of the Ashby map. The microstructure W–1.7%TiC alloy consists of the tungsten matrix as well as carbide and oxide particles, mostly globular in shape with a diameter of 33 ± 19 nm. The W–1.7%TiC alloy exhibited pronounced porosity with irregularly shaped pores of various sizes. The relative volume of both pores and particles was estimated by FIB/SEM tomography to be 5.2 ± 1.4%.
Published under license from EURATOM.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Acknowledgments The study was conducted under cooperation between AGH University of Science and Technology and Forschungszentrum Jülich within the bilateral project on
4
Garcia-Rosales C 1994 J. Nucl. Mater. 211 202 Petti D A et al 1996 J. Nucl. Mater. 233–237 37 Tanabe T et al 1992 J. Nucl. Mater. 196–198 11 Roth J et al 2009 J. Nucl. Mater. 390 1 Norajitra P et al 2004 J. Nucl. Mater. 329 1594 Zinkle S J and Ghoniem N M 2011 J. Nucl. Mater. 417 2 Zinkle S J and Ghoniem N M 2000 Fusion Eng. Des. 51–52 55 Fujitsuka M et al 1996 J. Nucl. Mater. 233–237 638 Chen Y et al 2008 Int. J. Refract. Met. Hard Mater. 26 525 Song G M et al 2003 Int. J. Refract. Met. Hard Mater. 21 1 Mabuchi M et al 1997 Mater. Sci. Eng. A 237 241 Itoh Y et al 1996 JSME Int. J. A 39 42 Wurster H O 2010 Int. J. Refract. Met. Hard Mater. 28 692 Ashby M F 1972 Acta Metall. 20 887
