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Wandering and nanolaminated structures of grain boundary triple junctions in tungsten
Materials Letters xxx (xxxx) xxx
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Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Wandering and nanolaminated structures of grain boundary triple junctions in tungsten T.I. Mazilova ⇑, E.V. Sadanov, I.V. Starchenko, I.M. Mikhailovskij Department of Condensed Matter, National Science Center ‘‘Kharkiv Institute of Physics and Technology”, Academichna Str. 1, 61108 Kharkiv, Ukraine
a r t i c l e
i n f o
Article history: Received 5 November 2019 Accepted 8 November 2019 Available online xxxx Keywords: Polycrystals Grain boundaries Triple junctions Field ion microscopy Tungsten
a b s t r a c t The peculiarities of nanomorphology triple junctions have been studied by the method of field ion microscopy in fine-grained high-textured tungsten using the phenomenon of atom-by-atom field evaporation. It was found evidence of the formation of double-kinks at the triple junction lines accompanied by a local intrusion of several atomic layers of one grain into another. Observed a double-kink mode of the wandering is geometrically related to revealed nanolaminated structures of triple junctions bounded by pairs of twist boundaries. Molecular statics calculations have shown that the grain boundary expansion and energetics for the laminated grains with incommensurate twist grain boundaries are essentially independent of their thickness in nano-scale region. Ó 2019 Elsevier B.V. All rights reserved.
1. Introduction Triple junctions (TJs) are usually considered as a linear object along which three grain boundaries (GBs) connect with each other. They are characterised by physical properties rather different from those exhibited by the interfaces that they bound [1–6]. Their effects on mechanical properties have been revealed as a particular path of high-yield nucleation and accumulation of strain, allowing to arise intensive plastic deformation in fine-grained materials [7–9]. The TJs are recognized as essential structural features in the context of GB susceptible nanomaterial properties [10–12], however, experimental data on the core structures of TJs are still exceptionally scarce. High-resolution electron microscopy reveals the comprehensive crystallography of the TJs but, rarely, their atomic structures. It was conjectured that the difficulty in obtaining such information at the atomic level is due to their possible non-linear character throughout the thickness of the specimen [13]. Such a non-linear profile of the TJ lines has been revealed in a field ion microscope (FIM) study of TJs in tungsten [12]. In this paper, we report experimental evidence for the existence of a double-kink mode of the TJ wandering and geometrically related to nanolaminated structures of TJs in fine-grained tungsten. 2. Experimental procedure The experiments were carried out in an FIM with needle-shaped specimens cooled to 21 and 77 K. The system was pumped to a ⇑ Corresponding author. E-mail address: [email protected] (T.I. Mazilova).
base pressure of 106 Pa; He was used as image gas under a pressure of 103 Pa. The specimens with an initial radius of about 20 nm at their top were prepared by electrochemical polishing from 0.01 to 0.2 mm ultrafine-grained tungsten wires of 99.98 at % with a h1 1 0i axial texture, which had been manufactured by multiple drawing metal-ceramic rods at 700–770 K. The drawn tungsten wires had a nanoscale fiber structure with average fiber diameters in the range of 80–220 nm. The taper angles near hemispherical specimen apexes were in the range of 2–5°. Before experiments, the specimen surface was cleaned and polished to an atomic level situ in the FIM using low-temperature field evaporation [14,15]. The crystallographic relationships of adjacent nanograins were determined from FIM images using standard stereographic procedures [15]. Authors used the unique to FIM possibilities to obtain detailed and clear information on defects inside the bulk region brought up to the surface using the phenomenon of atom-byatom low temperature field evaporation. So an FIM is able to produce an accurate reconstruction of three-dimensional location of atoms generating a high-precision real-space atomic-scale representation of the analyzed linear lattice defects. The depth resolution was in the range of 1.29–2.23 Å. The GBs in three-crystalline specimens can be described by rotations about the [1 1 0] axis which, within the experimental uncertainty (±2°), coincided with the centre of the FIM image projection. The misorientation of grains was determined from a large set (more than ten) of FIM images obtained during atom-by-atom field evaporation. The error of such a determination was less than ±1°; the specification of the boundary plane normal was made with an error of ±3°.
https://doi.org/10.1016/j.matlet.2019.126980 0167-577X/Ó 2019 Elsevier B.V. All rights reserved.
Please cite this article as: T. I. Mazilova, E. V. Sadanov, I. V. Starchenko et al., Wandering and nanolaminated structures of grain boundary triple junctions in tungsten, Materials Letters, https://doi.org/10.1016/j.matlet.2019.126980
2
T.I. Mazilova et al. / Materials Letters xxx (xxxx) xxx
3. Results and discussion The analysis of more than 2103 FIM images of three-crystals continuously dissected by field evaporation of successive atomic layers has given the experimental evidence for the atomic-scale wandering of the TJ line with the formation of double-kinks of different heights. The morphology of TJs with such double-kinks corresponds to formation of the geometrically related lamellar nanograins bounded predominately by two (1 1 0) twist GBs and relatively short tilt boundaries oriented along the [1 1 0] direction. A typical example of such structures is shown in Fig. 1. The misorientations of adjacent grains forming the TJ (marked by a rectangular box) are described by rotation angles of 35, 25, and 10° about the [1 1 0] axis. Such orientation relationships correspond to special non-coincident site lattice (CSL) boundaries with misorientation angles x equal to a half of the CSL misorientation angles [16] for R = 3, 11, and 33. High magnification images obtained at different stages of layer-by-layer field evaporation correspond to the rectangular region marked in Fig. 1(a). The initial pattern in Fig. 1(b) is acquired after field evaporation of grains designated as A, B, and C. Evaporation to a depth of about monolayer was accompanied by a jump-like displacement of the TJ [Fig. 1(c)] along the GB B–C at a distance of 1.8 nm from point 1 to 2 in the sketch (e). The FIM image in Fig. 1(d) is obtained after evaporation of the four individual (1 1 0) atomic layers accompanied by the jump of the TJ track at a distance of 1.5 nm from position 2 to 3 (the crossed area). A straightforward crystal geometric consideration of the data presented in Fig. 1 reveals a nanoscale lamella with the thickness of 0.67 nm bounded by the two (1 1 0) twist highangle and short lateral tilt GBs. The sizes of the TJ lamellae were usually in the range from 1 to 6 nm in the (1 1 0) plane common for all three grains in the longitudinal direction and from 0.5 to 2 nm in the transverse one. Depth profiling obtained by field evaporation has shown that the thickness of lamellae was in the range from 0.67 to 1.12 nm [from 3 to 5 (1 1 0) atomic layers]. Molecular statics calculations were performed using the reciprocal-space method [17]. High-angle twist (1 1 0) GBs show no distinctive dependence of the GB energy on the twist angle or the inverse density of coincident sites [18]. So, in our calculations, the universal case of twist GBs corresponding to the incommensurate interconnections of nanograins was used. The energy of the (1 1 0) incommensurate twist GB was found equal to 2.101 J/m2. The minimization of the lamella energy is accompanied by the relative displacement Dz of adjacent grains in the direction perpendicular to the GB which is an analogy of the GB expansion. The total relative displacement Dz for an isolated (1 1 0) twist GB was 0.245 Å. Fig. 2(a) illustrates the calculated variations of the interplanar separation produced by the three-layer nanolamella. The inset shows a cross-sectional view of the lamellar nanograin bounded by two (1 1 0) twist GBs (hatched regions). The total GB expansion Dz for the three-layer nanolamella is 0.462 Å. Fig. 2(b) shows an analogical dependence of interplanar separations for a fivelayer nanolamella. The data shown in Fig. 2(b) correspond to Dz = 0.472 Å. The dependence of the excess energy of multilayer nanolamellae on the number of atomic layers parallel to GBs is shown in Fig. 3. The excess energy for the three-layer nanolamella shown in Fig. 2a is 4.195 J/m2. This value is lower by only of 7 mJ/m2 than that for two (1 1 0) twist GBs. So, it was found that infinite nanolamellae have the total relative displacement Dz and energy close to twice for those of isolated (1 1 0) twist GBs. So, the formation of nanolaminated morphology in the vicinity of TJ illustrated
Fig. 1. An FIM image of tungsten three-crystal with TJ of special non-CSL GBs marked by arrows acquired at 21 K with applied potential of 15.12 kV (a) and corresponding high magnification images of a nanoscale lamella after evaporation of a linear part of the TJ (b), after a jump-like displacement of the triple line (c), and after field evaporation of the four individual (1 1 0) atomic layers (d) with corresponding schematic representation of the lamella (e).
in Fig. 1 is attributed to exceptionally low energy. Note, that by analogy to the surface meandering [19], the emergence of the double-kink on TJs allows the TJ to wander, increasing the configurational entropy and thus decreasing the free energy of the TJ. The results of our calculations compared with those obtained by conventional analysis of GB plane distributions in polycrystals [20] are found to be qualitatively reliable. Refining grains of metals producing highly-oriented nanoscale lamellae may greatly enhance their hardness and strength [21–23].
Please cite this article as: T. I. Mazilova, E. V. Sadanov, I. V. Starchenko et al., Wandering and nanolaminated structures of grain boundary triple junctions in tungsten, Materials Letters, https://doi.org/10.1016/j.matlet.2019.126980
T.I. Mazilova et al. / Materials Letters xxx (xxxx) xxx
3
4. Conclusions Field ion microscopic examination of tungsten three-crystals used the atomic layer-by-layer tomography has revealed the existence of double-kink mode of the TJ wandering and geometrically related with it nanolaminated structures of TJs. The formation of double-kinks with different amplitudes corresponds to the local intrusion of several atomic layers of one grain into another at the TJ. All of the TJs of GBs observed in the bulk of W specimens revealed a tendency toward the formation of radial lamella protrusions separated by linear segments of the TJs. Every double-kink produces the geometrically necessary nanolaminated grains of prolate shape at TJs bounded by pairs of twist boundaries normal to the [1 1 0] axis. The GB expansion and energetics of such nanolamelae are nearly independent of their thickness. Declaration of Competing Interest 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.
Acknowledgments The authors acknowledge the financial support of the National Academy of Sciences, Ukraine (Grants No. 32-08-15/1).
References
Fig. 2. The interplanar separation in the vicinity of (a) three- and (b) five-layer nanolamellae bounded by twist GBs vs. number of the (1 1 0) plane. The inset provides cross-sectional view of the lamella.
Fig. 3. The excess energy of multilayer nanolamellae vs. a total number of the (1 1 0) planes in a lamella.
[1] D. Mattissen, D.A. Molodov, L.S. Shvindlerman, G. Gottstein, Acta Mater. 53 (2005) 2049. [2] A.M. Glezer, E.V. Kozlov, N.A. Koneva, N.A. Popova, I.A. Kurzina, Plastic Deformation of Nanostructured Materials, CRC Press, 2017. [3] A.A. Mazilkin, B.B. Straumal, S.G. Protasova, M.F. Bulatov, B. Baretzky, Mater. Lett. 192 (2017) 101–103. [4] A.S. Lazarenko, I.M. Mikhailovskij, V.B. Rabukhin, O.A. Velikodnaya, Acta Metal. Mater. 43 (1995) 639–643. [5] A.A. Nazarov, Lett. Mater. 8 (2018) 372–381. [6] B.S. Bokstein, S.A. Gulevsky, A.L. Petelin, A.O. Rodin, Diffusion controlled grain triple junctions wetting in metals, Defect Diffusion Forum. 309 (2011) 231– 238. [7] A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials, Clarendon, Oxford, 2007. [8] Q. Zhao, W. Jiang, D.J. Srolovitz, W. Bao, Acta Mater. 128 (2017) 345. [9] V.Y. Novikov, Mater. Lett. 159 (2015) 510–513. [10] A.H. King, Scr. Mater. 62 (2010) 889–893. [11] I.A. Ovid’Ko, R.Z. Valiev, Y.T. Zhu, Prog. Mater. Sci. 94 (2018) 462–540. [12] E.V. Sadanov, I.V. Starchenko, V.A. Ksenofontov, I.M. Mikhailovskij, Metallogr. Microstruct. Anal. 7 (6) (2018) 755–760. [13] L. Priester, Grain boundaries From Theory to Engineering, Springer Series in Materials Science, 172, 2013. [14] V.A. Ksenofontov, T.I. Mazilova, I.M. Mikhailovskij, E.V. Sadanov, O.A. Velicodnaja, A.A. Mazilov, J. Phys.: Condensed Matter 19 (46) (2007) 466204. [15] M.K. Miller, A. Cerezo, M.G. Hetherington, G.D.W. Smith, Atom-probe Field ion Microscopy, Oxford University, Oxford, 1996. [16] E.V. Sadanov, T.I. Mazilova, V.A. Ksenofontov, I.V. Starchenko, I.M. Mikhailowskij, Mater. Lett. 145 (2015) 137–140. [17] I.M. Mikhailovskij, T.I. Mazilova, V.N. Voyevodin, A.A. Mazilov, Phys. Rev. B 83 (2011) 134115. [18] Z.-H. Liu, Y.-X. Feng, J.-X. Shang, Appl. Surf. Sci. 370 (2016) 19–24. [19] E.D. Williams, N.C. Bartelt, Science 251 (1991) 393–400. [20] W. Wang, C. Cai, G.S. Rohrer, X. Gu, Y. Lin, S. Chen, P. Dai, Mater. Charact. 144 (2018) 411. [21] L. Lu, X. Chen, X. Huang, K. Lu, Science 323 (2009) 607–610. [22] X. Zhou, X.Y. Li, K. Lu, Science 360 (2018) 526–530. [23] G. Cheng, H. Li, G. Xu, W. Gai, L. Luo, Sci. Rep. 7 (2017) 12393.
Please cite this article as: T. I. Mazilova, E. V. Sadanov, I. V. Starchenko et al., Wandering and nanolaminated structures of grain boundary triple junctions in tungsten, Materials Letters, https://doi.org/10.1016/j.matlet.2019.126980
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Wandering and nanolaminated structures of grain boundary triple junctions in tungsten T.I. Mazilova ⇑, E.V. Sadanov, I.V. Starchenko, I.M. Mikhailovskij Department of Condensed Matter, National Science Center ‘‘Kharkiv Institute of Physics and Technology”, Academichna Str. 1, 61108 Kharkiv, Ukraine
a r t i c l e
i n f o
Article history: Received 5 November 2019 Accepted 8 November 2019 Available online xxxx Keywords: Polycrystals Grain boundaries Triple junctions Field ion microscopy Tungsten
a b s t r a c t The peculiarities of nanomorphology triple junctions have been studied by the method of field ion microscopy in fine-grained high-textured tungsten using the phenomenon of atom-by-atom field evaporation. It was found evidence of the formation of double-kinks at the triple junction lines accompanied by a local intrusion of several atomic layers of one grain into another. Observed a double-kink mode of the wandering is geometrically related to revealed nanolaminated structures of triple junctions bounded by pairs of twist boundaries. Molecular statics calculations have shown that the grain boundary expansion and energetics for the laminated grains with incommensurate twist grain boundaries are essentially independent of their thickness in nano-scale region. Ó 2019 Elsevier B.V. All rights reserved.
1. Introduction Triple junctions (TJs) are usually considered as a linear object along which three grain boundaries (GBs) connect with each other. They are characterised by physical properties rather different from those exhibited by the interfaces that they bound [1–6]. Their effects on mechanical properties have been revealed as a particular path of high-yield nucleation and accumulation of strain, allowing to arise intensive plastic deformation in fine-grained materials [7–9]. The TJs are recognized as essential structural features in the context of GB susceptible nanomaterial properties [10–12], however, experimental data on the core structures of TJs are still exceptionally scarce. High-resolution electron microscopy reveals the comprehensive crystallography of the TJs but, rarely, their atomic structures. It was conjectured that the difficulty in obtaining such information at the atomic level is due to their possible non-linear character throughout the thickness of the specimen [13]. Such a non-linear profile of the TJ lines has been revealed in a field ion microscope (FIM) study of TJs in tungsten [12]. In this paper, we report experimental evidence for the existence of a double-kink mode of the TJ wandering and geometrically related to nanolaminated structures of TJs in fine-grained tungsten. 2. Experimental procedure The experiments were carried out in an FIM with needle-shaped specimens cooled to 21 and 77 K. The system was pumped to a ⇑ Corresponding author. E-mail address: [email protected] (T.I. Mazilova).
base pressure of 106 Pa; He was used as image gas under a pressure of 103 Pa. The specimens with an initial radius of about 20 nm at their top were prepared by electrochemical polishing from 0.01 to 0.2 mm ultrafine-grained tungsten wires of 99.98 at % with a h1 1 0i axial texture, which had been manufactured by multiple drawing metal-ceramic rods at 700–770 K. The drawn tungsten wires had a nanoscale fiber structure with average fiber diameters in the range of 80–220 nm. The taper angles near hemispherical specimen apexes were in the range of 2–5°. Before experiments, the specimen surface was cleaned and polished to an atomic level situ in the FIM using low-temperature field evaporation [14,15]. The crystallographic relationships of adjacent nanograins were determined from FIM images using standard stereographic procedures [15]. Authors used the unique to FIM possibilities to obtain detailed and clear information on defects inside the bulk region brought up to the surface using the phenomenon of atom-byatom low temperature field evaporation. So an FIM is able to produce an accurate reconstruction of three-dimensional location of atoms generating a high-precision real-space atomic-scale representation of the analyzed linear lattice defects. The depth resolution was in the range of 1.29–2.23 Å. The GBs in three-crystalline specimens can be described by rotations about the [1 1 0] axis which, within the experimental uncertainty (±2°), coincided with the centre of the FIM image projection. The misorientation of grains was determined from a large set (more than ten) of FIM images obtained during atom-by-atom field evaporation. The error of such a determination was less than ±1°; the specification of the boundary plane normal was made with an error of ±3°.
https://doi.org/10.1016/j.matlet.2019.126980 0167-577X/Ó 2019 Elsevier B.V. All rights reserved.
Please cite this article as: T. I. Mazilova, E. V. Sadanov, I. V. Starchenko et al., Wandering and nanolaminated structures of grain boundary triple junctions in tungsten, Materials Letters, https://doi.org/10.1016/j.matlet.2019.126980
2
T.I. Mazilova et al. / Materials Letters xxx (xxxx) xxx
3. Results and discussion The analysis of more than 2103 FIM images of three-crystals continuously dissected by field evaporation of successive atomic layers has given the experimental evidence for the atomic-scale wandering of the TJ line with the formation of double-kinks of different heights. The morphology of TJs with such double-kinks corresponds to formation of the geometrically related lamellar nanograins bounded predominately by two (1 1 0) twist GBs and relatively short tilt boundaries oriented along the [1 1 0] direction. A typical example of such structures is shown in Fig. 1. The misorientations of adjacent grains forming the TJ (marked by a rectangular box) are described by rotation angles of 35, 25, and 10° about the [1 1 0] axis. Such orientation relationships correspond to special non-coincident site lattice (CSL) boundaries with misorientation angles x equal to a half of the CSL misorientation angles [16] for R = 3, 11, and 33. High magnification images obtained at different stages of layer-by-layer field evaporation correspond to the rectangular region marked in Fig. 1(a). The initial pattern in Fig. 1(b) is acquired after field evaporation of grains designated as A, B, and C. Evaporation to a depth of about monolayer was accompanied by a jump-like displacement of the TJ [Fig. 1(c)] along the GB B–C at a distance of 1.8 nm from point 1 to 2 in the sketch (e). The FIM image in Fig. 1(d) is obtained after evaporation of the four individual (1 1 0) atomic layers accompanied by the jump of the TJ track at a distance of 1.5 nm from position 2 to 3 (the crossed area). A straightforward crystal geometric consideration of the data presented in Fig. 1 reveals a nanoscale lamella with the thickness of 0.67 nm bounded by the two (1 1 0) twist highangle and short lateral tilt GBs. The sizes of the TJ lamellae were usually in the range from 1 to 6 nm in the (1 1 0) plane common for all three grains in the longitudinal direction and from 0.5 to 2 nm in the transverse one. Depth profiling obtained by field evaporation has shown that the thickness of lamellae was in the range from 0.67 to 1.12 nm [from 3 to 5 (1 1 0) atomic layers]. Molecular statics calculations were performed using the reciprocal-space method [17]. High-angle twist (1 1 0) GBs show no distinctive dependence of the GB energy on the twist angle or the inverse density of coincident sites [18]. So, in our calculations, the universal case of twist GBs corresponding to the incommensurate interconnections of nanograins was used. The energy of the (1 1 0) incommensurate twist GB was found equal to 2.101 J/m2. The minimization of the lamella energy is accompanied by the relative displacement Dz of adjacent grains in the direction perpendicular to the GB which is an analogy of the GB expansion. The total relative displacement Dz for an isolated (1 1 0) twist GB was 0.245 Å. Fig. 2(a) illustrates the calculated variations of the interplanar separation produced by the three-layer nanolamella. The inset shows a cross-sectional view of the lamellar nanograin bounded by two (1 1 0) twist GBs (hatched regions). The total GB expansion Dz for the three-layer nanolamella is 0.462 Å. Fig. 2(b) shows an analogical dependence of interplanar separations for a fivelayer nanolamella. The data shown in Fig. 2(b) correspond to Dz = 0.472 Å. The dependence of the excess energy of multilayer nanolamellae on the number of atomic layers parallel to GBs is shown in Fig. 3. The excess energy for the three-layer nanolamella shown in Fig. 2a is 4.195 J/m2. This value is lower by only of 7 mJ/m2 than that for two (1 1 0) twist GBs. So, it was found that infinite nanolamellae have the total relative displacement Dz and energy close to twice for those of isolated (1 1 0) twist GBs. So, the formation of nanolaminated morphology in the vicinity of TJ illustrated
Fig. 1. An FIM image of tungsten three-crystal with TJ of special non-CSL GBs marked by arrows acquired at 21 K with applied potential of 15.12 kV (a) and corresponding high magnification images of a nanoscale lamella after evaporation of a linear part of the TJ (b), after a jump-like displacement of the triple line (c), and after field evaporation of the four individual (1 1 0) atomic layers (d) with corresponding schematic representation of the lamella (e).
in Fig. 1 is attributed to exceptionally low energy. Note, that by analogy to the surface meandering [19], the emergence of the double-kink on TJs allows the TJ to wander, increasing the configurational entropy and thus decreasing the free energy of the TJ. The results of our calculations compared with those obtained by conventional analysis of GB plane distributions in polycrystals [20] are found to be qualitatively reliable. Refining grains of metals producing highly-oriented nanoscale lamellae may greatly enhance their hardness and strength [21–23].
Please cite this article as: T. I. Mazilova, E. V. Sadanov, I. V. Starchenko et al., Wandering and nanolaminated structures of grain boundary triple junctions in tungsten, Materials Letters, https://doi.org/10.1016/j.matlet.2019.126980
T.I. Mazilova et al. / Materials Letters xxx (xxxx) xxx
3
4. Conclusions Field ion microscopic examination of tungsten three-crystals used the atomic layer-by-layer tomography has revealed the existence of double-kink mode of the TJ wandering and geometrically related with it nanolaminated structures of TJs. The formation of double-kinks with different amplitudes corresponds to the local intrusion of several atomic layers of one grain into another at the TJ. All of the TJs of GBs observed in the bulk of W specimens revealed a tendency toward the formation of radial lamella protrusions separated by linear segments of the TJs. Every double-kink produces the geometrically necessary nanolaminated grains of prolate shape at TJs bounded by pairs of twist boundaries normal to the [1 1 0] axis. The GB expansion and energetics of such nanolamelae are nearly independent of their thickness. Declaration of Competing Interest 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.
Acknowledgments The authors acknowledge the financial support of the National Academy of Sciences, Ukraine (Grants No. 32-08-15/1).
References
Fig. 2. The interplanar separation in the vicinity of (a) three- and (b) five-layer nanolamellae bounded by twist GBs vs. number of the (1 1 0) plane. The inset provides cross-sectional view of the lamella.
Fig. 3. The excess energy of multilayer nanolamellae vs. a total number of the (1 1 0) planes in a lamella.
[1] D. Mattissen, D.A. Molodov, L.S. Shvindlerman, G. Gottstein, Acta Mater. 53 (2005) 2049. [2] A.M. Glezer, E.V. Kozlov, N.A. Koneva, N.A. Popova, I.A. Kurzina, Plastic Deformation of Nanostructured Materials, CRC Press, 2017. [3] A.A. Mazilkin, B.B. Straumal, S.G. Protasova, M.F. Bulatov, B. Baretzky, Mater. Lett. 192 (2017) 101–103. [4] A.S. Lazarenko, I.M. Mikhailovskij, V.B. Rabukhin, O.A. Velikodnaya, Acta Metal. Mater. 43 (1995) 639–643. [5] A.A. Nazarov, Lett. Mater. 8 (2018) 372–381. [6] B.S. Bokstein, S.A. Gulevsky, A.L. Petelin, A.O. Rodin, Diffusion controlled grain triple junctions wetting in metals, Defect Diffusion Forum. 309 (2011) 231– 238. [7] A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials, Clarendon, Oxford, 2007. [8] Q. Zhao, W. Jiang, D.J. Srolovitz, W. Bao, Acta Mater. 128 (2017) 345. [9] V.Y. Novikov, Mater. Lett. 159 (2015) 510–513. [10] A.H. King, Scr. Mater. 62 (2010) 889–893. [11] I.A. Ovid’Ko, R.Z. Valiev, Y.T. Zhu, Prog. Mater. Sci. 94 (2018) 462–540. [12] E.V. Sadanov, I.V. Starchenko, V.A. Ksenofontov, I.M. Mikhailovskij, Metallogr. Microstruct. Anal. 7 (6) (2018) 755–760. [13] L. Priester, Grain boundaries From Theory to Engineering, Springer Series in Materials Science, 172, 2013. [14] V.A. Ksenofontov, T.I. Mazilova, I.M. Mikhailovskij, E.V. Sadanov, O.A. Velicodnaja, A.A. Mazilov, J. Phys.: Condensed Matter 19 (46) (2007) 466204. [15] M.K. Miller, A. Cerezo, M.G. Hetherington, G.D.W. Smith, Atom-probe Field ion Microscopy, Oxford University, Oxford, 1996. [16] E.V. Sadanov, T.I. Mazilova, V.A. Ksenofontov, I.V. Starchenko, I.M. Mikhailowskij, Mater. Lett. 145 (2015) 137–140. [17] I.M. Mikhailovskij, T.I. Mazilova, V.N. Voyevodin, A.A. Mazilov, Phys. Rev. B 83 (2011) 134115. [18] Z.-H. Liu, Y.-X. Feng, J.-X. Shang, Appl. Surf. Sci. 370 (2016) 19–24. [19] E.D. Williams, N.C. Bartelt, Science 251 (1991) 393–400. [20] W. Wang, C. Cai, G.S. Rohrer, X. Gu, Y. Lin, S. Chen, P. Dai, Mater. Charact. 144 (2018) 411. [21] L. Lu, X. Chen, X. Huang, K. Lu, Science 323 (2009) 607–610. [22] X. Zhou, X.Y. Li, K. Lu, Science 360 (2018) 526–530. [23] G. Cheng, H. Li, G. Xu, W. Gai, L. Luo, Sci. Rep. 7 (2017) 12393.
Please cite this article as: T. I. Mazilova, E. V. Sadanov, I. V. Starchenko et al., Wandering and nanolaminated structures of grain boundary triple junctions in tungsten, Materials Letters, https://doi.org/10.1016/j.matlet.2019.126980