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A bulk nanocrystalline Mg–Ti alloy with high thermal stability and strength
Materials Letters 210 (2018) 121–123
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Materials Letters journal homepage: www.elsevier.com/locate/mlblue
A bulk nanocrystalline Mg–Ti alloy with high thermal stability and strength X.C. Cai, J. Song, T.T. Yang, Q.M. Peng, J.Y. Huang, T.D. Shen ⇑ State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, PR China
a r t i c l e
i n f o
Article history: Received 8 August 2017 Accepted 1 September 2017 Available online 7 September 2017 Keywords: Thermal stability Nanocrystalline Magnesium Mechanical alloying
a b s t r a c t Nanocrystalline metals are often strong but with a low thermal stability. In this study, a bulk nanocrystalline Mg-1.5at%Ti alloy with a high thermal stability is successfully fabricated by mechanical alloying and subsequent high-temperature/high-pressure consolidation. The rapid grain growth of nanocrystalline Mg and Mg-1.5at%Ti alloy starts at 100 °C (0.40 Tm) and 450 °C (0.78 Tm), respectively. The high thermal stability of nanocrystalline Mg-1.5at%Ti alloy can be attributed to the segregation of Ti atoms at grain boundaries. The high thermal stability of nanocrystalline Mg-Ti alloy enables us to consolidate the alloy powders at a high temperature of 400 °C (0.73 Tm) under a pressure of 4 GPa, yielding a bulk nanocrystalline Mg-Ti alloy with a high strength of 202 MPa and a large fracture strain of above 0.8. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Nanocrystalline Mg-based materials are particularly attractive in the field of lightweight structural materials [1,2]. However, their applications are limited by their low thermal stability – grain growth occurs even at room temperature (RT) [3] – and more often than not, their abnormal grain growth (AGG). These provide a significant obstacle to use a high temperature to consolidate nanocrystalline powders to bulk form and subsequently deform the bulk to remove any remaining porosity. In general, there are two basic strategies to inhibit grain growth. Kinetically, second phase or solute drag can be used to slow down the migration of grain boundaries (GBs) [4,5]. Thermodynamically, grain growth can be inhibited by grain boundary (GB) segregation of solute atoms, which can reduce the GB free energy and thus lower the driving force for grain growth. The thermodynamic strategy exhibits weak temperature dependence and has been extensively studied in some systems [6–8]. Ti is a typical stabilizing solute in Mg, as predicted by Darling et al. [7], since 1) the atom size misfit between Ti and Mg reaches 10%, 2) the equilibrium solubility of Ti in Mg is negligible at RT, and 3) Ti and Mg do not form an intermetallic compound. Besides, our recent research (not published) and previous studies [9] have showed that the solubility of Ti in Mg can be largely extended by nonequilibrium methods, which allows sufficient solutes to segregate at GBs at elevated temperatures. Moreover, as predicted by ⇑ Corresponding author. E-mail address: [email protected] (T.D. Shen). http://dx.doi.org/10.1016/j.matlet.2017.09.021 0167-577X/Ó 2017 Elsevier B.V. All rights reserved.
Seah [10], Ti is a GB strengthening solute in Mg compared with other predicted stabilizing solutes (e.g., K, Ba, Na and Sr). Thus, a Mg-Ti binary system is selected to study the thermal stability of nanocrystalline Mg(Ti) alloy, aimed at fabricating a bulk nanocrystalline Mg alloy with high mechanical properties. 2. Experimental Elemental Mg (Alfa Aesar, 99.9+%) and Ti (Alfa Aesar, 99.5+%) powders were weighed to achieve a nominal composition of Mg1.5 at.% Ti. For comparison, pure Mg was also studied. The mass ratio of hardened-steel milling balls to powder is 10:1. 5 ml hexane was added to the hardened-steel milling vial to inhibit agglomeration of the ductile Mg powders. The mechanical alloying was performed in a SPEX 8000 M mill for 50 h inside an argon-filled glove box containing less than 1 ppm oxygen. The as-milled powders were degassed under vacuum at RT for 10 h and then compacted in a cubic-anvil press (CS-1B) under a pressure of 4 GPa at RT. The compacts were annealed for 1 h to study the thermal stability. The XRD was carried out on a D/MAX-2500/PC diffractometer with CuKa radiation. The peak position and the instrumental broadening were calibrated by using standard Si powders. The lattice parameters were obtained by using the Nelson-Riley method [11]. Microhardness was measured with a Vickers hardness tester (FM-ARS-9000) with a load of 50 g and a dwelling time of 15 s, respectively. Compression tests were performed with an 1120 INSTRON testing machine at a strain rate of 10–3 s-1 at RT. The samples for compression were achieved by consolidating the as-milled powders at different temperatures under 4 GPa. The microstruc-
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X.C. Cai et al. / Materials Letters 210 (2018) 121–123
tures were observed on a JEOL 2010 transmission electron microscopy (TEM) operated at 200 kV. More than 200 nanograins were counted from dark-field TEM images to obtain an average grain size. The scanning transmission electron microscopy (STEM) observation and the electron energy loss spectroscopy (EELS) analysis were performed on an TITAN G2 microscope operated at 300 kV with a Fischione high-angle annular dark-field detector (with a resolution of 0.136 nm in STEM image mode) and an oxford instruments EELS detector (with a spatial resolution of 1 nm).
3. Results and discussion Fig. 1a shows the grain size versus annealing temperature for nanocrystalline Mg and Mg-Ti. The initial grain size of both samples is about 70 nm. A rapid grain growth of nanocrystalline Mg and Mg-Ti alloy occurs at 100 °C (0.40 Tm, where Tm is the melting point of pure Mg) and 450 °C (0.78 Tm), respectively, suggesting that the latter has a much higher thermal stability. In addition, a bimodal microstructure appears in nanocrystalline Mg at 200 °C, where several isolated large micron-sized grains due to an AGG coexist with ultrafine-grained (325 nm) matrix, as shown Fig. 1b. The coarse grains are observed throughout the sample above 250 °C and the average grain size of pure Mg reaches 23 mm at 400 °C. In contrast, the average grain size of Mg-Ti alloy is still as
small as 135 nm, as shown in Fig. 1c. However, annealing above 400 °C causes the entire microstructure of Mg-Ti to rapidly grow. Fig. 2a shows the lattice parameter of nanocrystalline Mg and Mg-Ti samples as a function of annealing temperature. The lattice parameter of pure Mg is almost constant throughout annealing whereas that of Mg-Ti increases with annealing. The lattice parameter of as-milled Mg-Ti is much smaller than that of pure Mg, suggesting that a Mg(Ti) solid solution be formed. Based on the relationship between lattice parameter and Ti content established for Mg-Ti alloys [9], 1.2 at.% Ti is dissolved in Mg lattice. The lattice parameter of Mg-Ti increases rapidly above 250 °C and approaches that of pure Mg at 400 °C. Note that both XRD analysis (not shown here) and TEM image show no Ti phase in as-milled and annealed Mg-Ti. Thus, the increases of the lattice parameter of Mg-Ti during annealing can be explained by the decomposition of Mg(Ti), i.e., the diffusion of Ti atoms from grain interiors to GBs. Fig. 2b shows the STEM image of Mg-Ti alloy annealed at 400 °C for 1 h. Brighter contrast shown in this image represents the distribution of a heavier element (Ti), which is mainly located in grainboundary regions. The corresponding EELS line scan (Fig. 2c) across three adjacent Mg grains indicated by the green line in Fig. 2b also confirms the segregation of Ti atoms in grain-boundary regions. This segregation lowers the GB energy of Mg-Ti and thermodynamically inhibits the growth of grains. While no precipitate such as Ti nanoparticle is observed in as-milled and annealed Mg-Ti, mechan-
Fig. 1. (a) Grain size of nanocrystalline Mg and Mg-Ti as a function of annealing temperature. (b) and (c) Bright-field TEM images of nanocrystalline Mg annealed at 200 °C and Mg-Ti annealed at 400 °C, respectively.
Fig. 2. (a) Lattice parameter of nanocrystalline Mg and Mg-Ti as a function of annealing temperature. (b) STEM image of Mg-Ti annealed at 400 °C. (c) The EELS line scan of Ti across three adjacent Mg grains indicated by the green line in (b).
X.C. Cai et al. / Materials Letters 210 (2018) 121–123
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Fig. 3. (a) Microhardness of nanocrystalline Mg and Mg-Ti as a function of annealing temperature. (b) Room-temperature stress-strain curve of bulk Mg and Mg-Ti alloys.
ical alloying inevitably introduces such impurities as Fe that kinetically pin the grains. Thus, the thermodynamic and kinetic mechanisms may be coupled to make a contribution. However, our experimental results suggest that the thermodynamic stabilization by the segregation of Ti atoms at GBs should be the dominant factor for the observed high thermal stability of our Mg-Ti alloy. This is because the content of impurities in nanocrystalline Mg should be similar to that in Mg-Ti alloy. However, the former has a thermal stability much lower than the latter. Fig. 3a shows the microhardness of nanocrystalline Mg and MgTi as a function of annealing temperature. The microhardness of nanocrystalline Mg starts to decrease at 100 °C. In contrast, the microhardness of Mg-Ti does not largely decrease until 400 °C. Note from Fig. 1a that pure Mg and Mg-Ti start to exhibit a large increase in the grain size at 100 and 450 °C, respectively. The significant decrease in the microhardness of annealed Mg and Mg-Ti is clearly related to their grain growth. Fig. 3b shows the compressive stress–strain curve of bulk Mg (consolidated at 400 °C) and Mg-Ti alloys (consolidated at both RT and 400 °C). Consolidating the pure Mg powders at 400 °C results in a coarse-grained bulk Mg with a low yield strength of 92 MPa. In contrast, the bulk Mg-Ti consolidated at 400 °C has a high yield strength of 202 MPa. Note that consolidating the MgTi alloy powders at 400 °C under 4 GPa maintains a fine matrix (112 nm, as shown in the inset of Fig. 3b), which can be attributed to the high thermal stability of Mg-Ti combined with the inhibiting effect of high pressure on grain growth [5,12]. In addition, the fracture strain (above 0.8) of the Mg-Ti consolidated at 400 °C is much higher than that (0.43) of Mg-Ti consolidated at RT. This can be explained by the better binding between powder particles after consolidated at a high temperature. 4. Conclusions A bulk thermally stable and strong nanocrystalline Mg-Ti alloy is successfully fabricated by mechanical alloying and high-
temperature/high-pressure consolidation. The thermal stability is largely enhanced from 100 °C for nanocrystalline Mg to 450 °C for Mg-Ti alloy. STEM observation and EELS analysis suggest that the enhanced thermal stability in Mg-Ti alloy be mainly attributed to the thermodynamic stabilization, i.e., the segregation of Ti solute at GBs during annealing. The excellent thermal stability of Mg-Ti alloy enables us to consolidate the alloy powders at a high temperature of 400 °C under 4 GPa and achieve a bulk nanocrystalline Mg-Ti alloy with both a high strength of 202 MPa and a large fracture strain of above 0.8. Acknowledgement This work was supported by the High-level Talents Research Program of the Yanshan University under Grant number 606001101. References [1] L.Y. Chen, J.Q. Xu, H. Choi, M. Pozuelo, X.L. Ma, S. Bhowmick, J.M. Yang, S.N. Mathaudhu, X.C. Li, Nature 528 (2015) 539–543. [2] M. Pozuelo, Y.W. Chang, J.M. Yang, Mater. Sci. Eng. A 594 (2014) 203–211. [3] M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater. Sci. 51 (2006) 427–556. [4] H.Y. Tong, B.Z. Ding, H.G. Jiang, Z.Q. Hu, L. Dong, Q. Zhou, Mater. Lett. 16 (1993) 260–264. [5] X.C. Cai, T.T. Yang, H. Yu, B.R. Sun, Q.M. Peng, T.D. Shen, Mater. Lett. in press. [6] T. Chookajorn, H.A. Murdoch, C.A. Schuh, Science 337 (2012) 951–954. [7] K.A. Darling, M.A. Tschopp, B.K. VanLeeuwen, M.A. Atwater, Z.K. Liu, Comput. Mater. Sci. 84 (2014) 255–266. [8] K.A. Darling, B.K. VanLeeuwen, J.E. Semones, C.C. Koch, R.O. Scattergood, L.J. Kecskes, S.N. Mathaudhu, Mater. Sci. Eng. A 528 (2011) 4365–4371. [9] G. Liang, R. Schulz, J. Mater. Sci. 38 (2003) 1179–1184. [10] M.P. Seah, Acta Meter. 28 (1979) 955–962. [11] J.B. Nelson, D.P. Riley, Proc. Phys. Soc. 57 (1945) 160–177. [12] M. Krasnowski, T. Kulik, Intermetallics 15 (2007) 1377–1383.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
A bulk nanocrystalline Mg–Ti alloy with high thermal stability and strength X.C. Cai, J. Song, T.T. Yang, Q.M. Peng, J.Y. Huang, T.D. Shen ⇑ State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, PR China
a r t i c l e
i n f o
Article history: Received 8 August 2017 Accepted 1 September 2017 Available online 7 September 2017 Keywords: Thermal stability Nanocrystalline Magnesium Mechanical alloying
a b s t r a c t Nanocrystalline metals are often strong but with a low thermal stability. In this study, a bulk nanocrystalline Mg-1.5at%Ti alloy with a high thermal stability is successfully fabricated by mechanical alloying and subsequent high-temperature/high-pressure consolidation. The rapid grain growth of nanocrystalline Mg and Mg-1.5at%Ti alloy starts at 100 °C (0.40 Tm) and 450 °C (0.78 Tm), respectively. The high thermal stability of nanocrystalline Mg-1.5at%Ti alloy can be attributed to the segregation of Ti atoms at grain boundaries. The high thermal stability of nanocrystalline Mg-Ti alloy enables us to consolidate the alloy powders at a high temperature of 400 °C (0.73 Tm) under a pressure of 4 GPa, yielding a bulk nanocrystalline Mg-Ti alloy with a high strength of 202 MPa and a large fracture strain of above 0.8. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Nanocrystalline Mg-based materials are particularly attractive in the field of lightweight structural materials [1,2]. However, their applications are limited by their low thermal stability – grain growth occurs even at room temperature (RT) [3] – and more often than not, their abnormal grain growth (AGG). These provide a significant obstacle to use a high temperature to consolidate nanocrystalline powders to bulk form and subsequently deform the bulk to remove any remaining porosity. In general, there are two basic strategies to inhibit grain growth. Kinetically, second phase or solute drag can be used to slow down the migration of grain boundaries (GBs) [4,5]. Thermodynamically, grain growth can be inhibited by grain boundary (GB) segregation of solute atoms, which can reduce the GB free energy and thus lower the driving force for grain growth. The thermodynamic strategy exhibits weak temperature dependence and has been extensively studied in some systems [6–8]. Ti is a typical stabilizing solute in Mg, as predicted by Darling et al. [7], since 1) the atom size misfit between Ti and Mg reaches 10%, 2) the equilibrium solubility of Ti in Mg is negligible at RT, and 3) Ti and Mg do not form an intermetallic compound. Besides, our recent research (not published) and previous studies [9] have showed that the solubility of Ti in Mg can be largely extended by nonequilibrium methods, which allows sufficient solutes to segregate at GBs at elevated temperatures. Moreover, as predicted by ⇑ Corresponding author. E-mail address: [email protected] (T.D. Shen). http://dx.doi.org/10.1016/j.matlet.2017.09.021 0167-577X/Ó 2017 Elsevier B.V. All rights reserved.
Seah [10], Ti is a GB strengthening solute in Mg compared with other predicted stabilizing solutes (e.g., K, Ba, Na and Sr). Thus, a Mg-Ti binary system is selected to study the thermal stability of nanocrystalline Mg(Ti) alloy, aimed at fabricating a bulk nanocrystalline Mg alloy with high mechanical properties. 2. Experimental Elemental Mg (Alfa Aesar, 99.9+%) and Ti (Alfa Aesar, 99.5+%) powders were weighed to achieve a nominal composition of Mg1.5 at.% Ti. For comparison, pure Mg was also studied. The mass ratio of hardened-steel milling balls to powder is 10:1. 5 ml hexane was added to the hardened-steel milling vial to inhibit agglomeration of the ductile Mg powders. The mechanical alloying was performed in a SPEX 8000 M mill for 50 h inside an argon-filled glove box containing less than 1 ppm oxygen. The as-milled powders were degassed under vacuum at RT for 10 h and then compacted in a cubic-anvil press (CS-1B) under a pressure of 4 GPa at RT. The compacts were annealed for 1 h to study the thermal stability. The XRD was carried out on a D/MAX-2500/PC diffractometer with CuKa radiation. The peak position and the instrumental broadening were calibrated by using standard Si powders. The lattice parameters were obtained by using the Nelson-Riley method [11]. Microhardness was measured with a Vickers hardness tester (FM-ARS-9000) with a load of 50 g and a dwelling time of 15 s, respectively. Compression tests were performed with an 1120 INSTRON testing machine at a strain rate of 10–3 s-1 at RT. The samples for compression were achieved by consolidating the as-milled powders at different temperatures under 4 GPa. The microstruc-
122
X.C. Cai et al. / Materials Letters 210 (2018) 121–123
tures were observed on a JEOL 2010 transmission electron microscopy (TEM) operated at 200 kV. More than 200 nanograins were counted from dark-field TEM images to obtain an average grain size. The scanning transmission electron microscopy (STEM) observation and the electron energy loss spectroscopy (EELS) analysis were performed on an TITAN G2 microscope operated at 300 kV with a Fischione high-angle annular dark-field detector (with a resolution of 0.136 nm in STEM image mode) and an oxford instruments EELS detector (with a spatial resolution of 1 nm).
3. Results and discussion Fig. 1a shows the grain size versus annealing temperature for nanocrystalline Mg and Mg-Ti. The initial grain size of both samples is about 70 nm. A rapid grain growth of nanocrystalline Mg and Mg-Ti alloy occurs at 100 °C (0.40 Tm, where Tm is the melting point of pure Mg) and 450 °C (0.78 Tm), respectively, suggesting that the latter has a much higher thermal stability. In addition, a bimodal microstructure appears in nanocrystalline Mg at 200 °C, where several isolated large micron-sized grains due to an AGG coexist with ultrafine-grained (325 nm) matrix, as shown Fig. 1b. The coarse grains are observed throughout the sample above 250 °C and the average grain size of pure Mg reaches 23 mm at 400 °C. In contrast, the average grain size of Mg-Ti alloy is still as
small as 135 nm, as shown in Fig. 1c. However, annealing above 400 °C causes the entire microstructure of Mg-Ti to rapidly grow. Fig. 2a shows the lattice parameter of nanocrystalline Mg and Mg-Ti samples as a function of annealing temperature. The lattice parameter of pure Mg is almost constant throughout annealing whereas that of Mg-Ti increases with annealing. The lattice parameter of as-milled Mg-Ti is much smaller than that of pure Mg, suggesting that a Mg(Ti) solid solution be formed. Based on the relationship between lattice parameter and Ti content established for Mg-Ti alloys [9], 1.2 at.% Ti is dissolved in Mg lattice. The lattice parameter of Mg-Ti increases rapidly above 250 °C and approaches that of pure Mg at 400 °C. Note that both XRD analysis (not shown here) and TEM image show no Ti phase in as-milled and annealed Mg-Ti. Thus, the increases of the lattice parameter of Mg-Ti during annealing can be explained by the decomposition of Mg(Ti), i.e., the diffusion of Ti atoms from grain interiors to GBs. Fig. 2b shows the STEM image of Mg-Ti alloy annealed at 400 °C for 1 h. Brighter contrast shown in this image represents the distribution of a heavier element (Ti), which is mainly located in grainboundary regions. The corresponding EELS line scan (Fig. 2c) across three adjacent Mg grains indicated by the green line in Fig. 2b also confirms the segregation of Ti atoms in grain-boundary regions. This segregation lowers the GB energy of Mg-Ti and thermodynamically inhibits the growth of grains. While no precipitate such as Ti nanoparticle is observed in as-milled and annealed Mg-Ti, mechan-
Fig. 1. (a) Grain size of nanocrystalline Mg and Mg-Ti as a function of annealing temperature. (b) and (c) Bright-field TEM images of nanocrystalline Mg annealed at 200 °C and Mg-Ti annealed at 400 °C, respectively.
Fig. 2. (a) Lattice parameter of nanocrystalline Mg and Mg-Ti as a function of annealing temperature. (b) STEM image of Mg-Ti annealed at 400 °C. (c) The EELS line scan of Ti across three adjacent Mg grains indicated by the green line in (b).
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Fig. 3. (a) Microhardness of nanocrystalline Mg and Mg-Ti as a function of annealing temperature. (b) Room-temperature stress-strain curve of bulk Mg and Mg-Ti alloys.
ical alloying inevitably introduces such impurities as Fe that kinetically pin the grains. Thus, the thermodynamic and kinetic mechanisms may be coupled to make a contribution. However, our experimental results suggest that the thermodynamic stabilization by the segregation of Ti atoms at GBs should be the dominant factor for the observed high thermal stability of our Mg-Ti alloy. This is because the content of impurities in nanocrystalline Mg should be similar to that in Mg-Ti alloy. However, the former has a thermal stability much lower than the latter. Fig. 3a shows the microhardness of nanocrystalline Mg and MgTi as a function of annealing temperature. The microhardness of nanocrystalline Mg starts to decrease at 100 °C. In contrast, the microhardness of Mg-Ti does not largely decrease until 400 °C. Note from Fig. 1a that pure Mg and Mg-Ti start to exhibit a large increase in the grain size at 100 and 450 °C, respectively. The significant decrease in the microhardness of annealed Mg and Mg-Ti is clearly related to their grain growth. Fig. 3b shows the compressive stress–strain curve of bulk Mg (consolidated at 400 °C) and Mg-Ti alloys (consolidated at both RT and 400 °C). Consolidating the pure Mg powders at 400 °C results in a coarse-grained bulk Mg with a low yield strength of 92 MPa. In contrast, the bulk Mg-Ti consolidated at 400 °C has a high yield strength of 202 MPa. Note that consolidating the MgTi alloy powders at 400 °C under 4 GPa maintains a fine matrix (112 nm, as shown in the inset of Fig. 3b), which can be attributed to the high thermal stability of Mg-Ti combined with the inhibiting effect of high pressure on grain growth [5,12]. In addition, the fracture strain (above 0.8) of the Mg-Ti consolidated at 400 °C is much higher than that (0.43) of Mg-Ti consolidated at RT. This can be explained by the better binding between powder particles after consolidated at a high temperature. 4. Conclusions A bulk thermally stable and strong nanocrystalline Mg-Ti alloy is successfully fabricated by mechanical alloying and high-
temperature/high-pressure consolidation. The thermal stability is largely enhanced from 100 °C for nanocrystalline Mg to 450 °C for Mg-Ti alloy. STEM observation and EELS analysis suggest that the enhanced thermal stability in Mg-Ti alloy be mainly attributed to the thermodynamic stabilization, i.e., the segregation of Ti solute at GBs during annealing. The excellent thermal stability of Mg-Ti alloy enables us to consolidate the alloy powders at a high temperature of 400 °C under 4 GPa and achieve a bulk nanocrystalline Mg-Ti alloy with both a high strength of 202 MPa and a large fracture strain of above 0.8. Acknowledgement This work was supported by the High-level Talents Research Program of the Yanshan University under Grant number 606001101. References [1] L.Y. Chen, J.Q. Xu, H. Choi, M. Pozuelo, X.L. Ma, S. Bhowmick, J.M. Yang, S.N. Mathaudhu, X.C. Li, Nature 528 (2015) 539–543. [2] M. Pozuelo, Y.W. Chang, J.M. Yang, Mater. Sci. Eng. A 594 (2014) 203–211. [3] M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater. Sci. 51 (2006) 427–556. [4] H.Y. Tong, B.Z. Ding, H.G. Jiang, Z.Q. Hu, L. Dong, Q. Zhou, Mater. Lett. 16 (1993) 260–264. [5] X.C. Cai, T.T. Yang, H. Yu, B.R. Sun, Q.M. Peng, T.D. Shen, Mater. Lett. in press. [6] T. Chookajorn, H.A. Murdoch, C.A. Schuh, Science 337 (2012) 951–954. [7] K.A. Darling, M.A. Tschopp, B.K. VanLeeuwen, M.A. Atwater, Z.K. Liu, Comput. Mater. Sci. 84 (2014) 255–266. [8] K.A. Darling, B.K. VanLeeuwen, J.E. Semones, C.C. Koch, R.O. Scattergood, L.J. Kecskes, S.N. Mathaudhu, Mater. Sci. Eng. A 528 (2011) 4365–4371. [9] G. Liang, R. Schulz, J. Mater. Sci. 38 (2003) 1179–1184. [10] M.P. Seah, Acta Meter. 28 (1979) 955–962. [11] J.B. Nelson, D.P. Riley, Proc. Phys. Soc. 57 (1945) 160–177. [12] M. Krasnowski, T. Kulik, Intermetallics 15 (2007) 1377–1383.