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CRYSTALLOGRAPHY
ISSN: 1600-5767

Transmission electron microscopy analysis of the crystallography of precipitates in Mg–Sn alloys aged at high temperatures

aSchool of Physics and Technology, Center for Electron Microscopy and MOE Key Laboratory of Artificial Micro- and Nano-structures, Wuhan University, Wuhan, Hubei 430072, People's Republic of China, bNew Materials, Shandong Academy of Sciences, Jinan, Shandong 250014, People's Republic of China, and cCenter for Nanoscale Characterization and Devices, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science, Wuhan, Hubei 430074, People's Republic of China
*Correspondence e-mail: dszhao@whu.edu.cn

(Received 22 March 2014; accepted 29 August 2014; online 30 September 2014)

The crystallographic orientation relationships (ORs) of precipitated β-Mg2Sn particles in Mg–9.76 wt% Sn alloy aged at 573 K for 5 h, corresponding to its peak hardness, were investigated by advanced transmission electron microscopy (TEM). OR-3 of (110)β//(0001)α and [[\overline 1]11]β//[1[\overline 2]10]α and OR-4 of (110)β//(0001)α and [001]β//[2[\overline 1\overline 1]0]α are the key ORs of β-Mg2Sn particles in the alloy. The proportions of β-Mg2Sn particles exhibiting OR-3 and OR-4 were determined as 75.1 and 24.3%, respectively. Crystallographic factors determined the predominance of OR-3 in the precipitated β-Mg2Sn particles. This mechanism was analyzed by a three-dimensional invariant line model constructed using a transformation matrix in reciprocal space. Models of the interface of precipitated β-Mg2Sn and the α-Mg matrix were constructed via high-resolution TEM and atomic resolution high-angle annular dark-field scanning TEM.

1. Introduction

Magnesium-based alloys are lightweight structural materials that have elicited great interest because of their ability to reduce the weight of automobiles (Luo, 2004[Luo, A. A. (2004). Int. Mater. Rev. 49, 13-30.]; Nie, 2012[Nie, J. F. (2012). Metall. Mater. Trans. A, 43, 3891-3939.]; Yoon & Park, 2014[Yoon, J. & Park, S. (2014). Mater. Des. 55, 300-308.]). Among those alloys, Mg–Al-based alloys are widely used in many areas because of their superior castability and ideal mechanical behavior at room temperature (Celloto, 2000[Celloto, S. (2000). Acta Mater. 48, 1775-1787.]; Zheng et al., 2009[Zheng, O., Zhou, J. P., Zhao, D. S., Wang, J. B., Wang, R. H., Gui, J. N., Xiong, D. X. & Sun, Z. F. (2009). Scr. Mater. 60, 791-794.]; Zhou et al., 2007[Zhou, J. P., Zhao, D. S., Wang, R. H., Sun, Z. F., Wang, J. B., Gui, J. N. & Zheng, O. (2007). Mater. Lett. 61, 4707-4710.], 2009[Zhou, J. P., Zhao, D. S., Zheng, O., Wang, J. B., Xiong, D. X., Sun, Z. F., Gui, J. N. & Wang, R. H. (2009). Micron, 40, 906-910.]). However, Mg–Al alloys exhibit poor creep resistance at temperatures between 393 and 573 K because their secondary precipitate, γ-Mg17Al12, has a low melting point (735 K) and is a poor strengthening phase at high temperatures (Hort et al., 2006[Hort, N., Huang, Y., Abu Leil, T., Maier, P. & Kainer, K. U. (2006). Adv. Eng. Mater. 8, 359-364.]). Mg–Sn-based alloys have recently been studied for their potential high-temperature applications (Kang et al., 2005[Kang, D. H., Park, S. S. & Kim, N. J. (2005). Mater. Sci. Eng. A, 413-414, 555-560.]; Wei et al., 2008[Wei, S. H., Chen, Y. G., Tang, Y. B., Liu, H. M., Xiao, S. F., Niu, G., Zhang, X. P. & Zhao, Y. H. (2008). Mater. Sci. Eng. A, 492, 20-23.]). These alloys can be developed into precipitation-hardenable alloys according to their binary phase diagrams (Murray, 1997[Murray, J. L. (1997). Alloy Phase Diagrams, ASM Handbook, edited by H. Baker & H. Okamoto. Materials Park: ASM International.]) because the maximum solid solubility of Sn in α-Mg is 14.85 wt% at a eutectic temperature 834 K and decreases to 0.45 wt% at 473 K. The equilibrium volume fraction of Mg–10.0 wt% Sn alloy precipitated at 573 K is approximately 11.1%. These precipitates are the equilibrium phase of β-Mg2Sn, which has a face-centered cubic (f.c.c.) structure.

The α-Mg matrix exhibits a hexagonal close-packed (h.c.p.) structure. The lattice parameters for the β-Mg2Sn phase and α-Mg matrix are aβ = 6.759 Å (space group Fm[\overline 3]m; JCPDS 65-2997) and aα = 3.209, cα = 5.210 Å (space group P63/mmc; JCPDS 89-5003), respectively. Liu et al. (2007[Liu, H. M., Chen, Y. G., Tang, Y. B., Wei, S. H. & Niu, G. (2007). J. Alloys Compd. 440, 122-126.]) analyzed as-cast Mg–(1–10) wt% Sn alloys and suggested that the Mg–5 wt% Sn alloy exhibits the best ductility and creep resistance, whereas the Mg–10 wt% Sn alloy manifests the highest hardness. Van der Planken (1969[Van Der Planken, J. (1969). J. Mater. Sci. 4, 927-929.]) found that the time required by Mg–7.75 wt% Sn alloys aged at 473, 523 and 573 K to reach their peak hardness decreases with increasing temperature. Mendis et al. (2006a[Mendis, C. L., Bettles, C. J., Gibson, M. A., Gorsse, S. & Hutchinson, C. R. (2006a). Philos. Mag. Lett. 86, 443-456.]) revealed that the morphology, orientation relationships (ORs), and unit volume density of precipitates of Mg–6 wt% Sn-based alloys markedly affect their properties after annealing and aging at 473 K to peak hardness. Derge et al. (1937[Derge, G., Kommell, A. R. & Mehl, R. F. (1937). Trans. AIME, 124, 367-378.]) examined the ORs between the β-Mg2Sn phase and α-Mg matrix using X-ray diffractometry and optical microscopy and reported that the β-Mg2Sn phase presents a plate-like morphology (Table 1[link]). According to Henes & Gerold (1962[Henes, V. S. & Gerold, V. (1962). Z. Metallkd. 53, 743-748.]), the β-Mg2Sn phase in an Mg–Sn alloy exhibited OR-1 and OR-2 at temperatures between 473 and 573 K, and exhibited OR-3 and OR-4 at temperatures between 403 and 473 K (Table 1[link]). The frequencies of these ORs and their precise morphologies, however, remain unknown, and information on Mg–Sn alloys remains unclear despite the availability of related studies. Zhang et al. (2007[Zhang, M., Zhang, W. Z., Zhu, G. Z. & Yu, K. (2007). Trans. Nonferrous Metals Soc. 17, 1428-1432.]), Sasaki et al. (2006[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2006). Scr. Mater. 55, 251-254.]) and Shi et al. (2012[Shi, Z. Z., Dai, F. Z. & Zhang, W. Z. (2012). Mater. Sci. Technol. 28, 411-414.]) reported the OR-5, OR-6, OR-7 and OR-8 forms of the β-Mg2Sn phase (Table 1[link]). The presence of several ORs and the influence of crystallographic factors on their formation have yet to be determined.

Table 1
Reported ORs and morphologies between a precipitated β-Mg2Sn particle (f.c.c.) and the α-Mg matrix (h.c.p.) in Mg–Sn systems

Name OR-1 OR-2 OR-3 OR-4
OR [{(111)_\beta }//{(0001)_\alpha }] [{[1\overline 10]_\beta }//{[2\overline 1\overline 10]_\alpha }] [{(111)_\beta }//{(0001)_\alpha }] [{[2\overline 1\overline 1]_\beta }//{[2\overline 1\overline 10]_\alpha }] [{(110)_\beta }//{(0001)_\alpha }] [{[\overline 111]_\beta }//{[1\overline 210]_\alpha }] [{(110)_\beta }//{(0001)_\alpha }] [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }]
Morphology Lath shaped, plate shaped and polygon shaped Lath shaped and plate shaped Lath shaped and plate shaped Lath shaped
References Derge et al. (1937[Derge, G., Kommell, A. R. & Mehl, R. F. (1937). Trans. AIME, 124, 367-378.]); Henes & Gerold (1962[Henes, V. S. & Gerold, V. (1962). Z. Metallkd. 53, 743-748.]); Kang et al. (2007[Kang, D. H., Park, S. S., Oh, Y. S. & Kim, N. J. (2007). Mater. Sci. Eng. A, 449-451, 318-321.]); Mendis et al. (2006a[Mendis, C. L., Bettles, C. J., Gibson, M. A., Gorsse, S. & Hutchinson, C. R. (2006a). Philos. Mag. Lett. 86, 443-456.],b[Mendis, C. L., Bettles, C. J., Gibson, M. A. & Hutchinson, C. R. (2006b). Mater. Sci. Eng. A, 435-436, 165-171.]); Sasaki et al. (2006[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2006). Scr. Mater. 55, 251-254.], 2011[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2011). Mater. Sci. Eng. A, 530, 1-8.]); Zhang et al. (2007[Zhang, M., Zhang, W. Z., Zhu, G. Z. & Yu, K. (2007). Trans. Nonferrous Metals Soc. 17, 1428-1432.]) Derge et al. (1937[Derge, G., Kommell, A. R. & Mehl, R. F. (1937). Trans. AIME, 124, 367-378.]); Henes & Gerold (1962[Henes, V. S. & Gerold, V. (1962). Z. Metallkd. 53, 743-748.]); Sasaki et al. (2011[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2011). Mater. Sci. Eng. A, 530, 1-8.]) Derge et al. (1937[Derge, G., Kommell, A. R. & Mehl, R. F. (1937). Trans. AIME, 124, 367-378.]); Henes & Gerold (1962[Henes, V. S. & Gerold, V. (1962). Z. Metallkd. 53, 743-748.]); Mendis et al. (2006b[Mendis, C. L., Bettles, C. J., Gibson, M. A. & Hutchinson, C. R. (2006b). Mater. Sci. Eng. A, 435-436, 165-171.]); Sasaki et al. (2006[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2006). Scr. Mater. 55, 251-254.], 2011[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2011). Mater. Sci. Eng. A, 530, 1-8.]) Henes & Gerold (1962[Henes, V. S. & Gerold, V. (1962). Z. Metallkd. 53, 743-748.]); Sasaki et al. (2009[Sasaki, T. T., Ju, J. D., Hono, K. & Shin, K. S. (2009). Scr. Mater. 61, 80-83.]); Zhang et al. (2007[Zhang, M., Zhang, W. Z., Zhu, G. Z. & Yu, K. (2007). Trans. Nonferrous Metals Soc. 17, 1428-1432.])
Name OR-5 OR-6 OR-7 OR-8
OR [(111)_\beta//(0001)_\alpha], [[2 \overline 1 \overline 1 0]_\alpha] 9° from [[1 \overline 1 0]_\beta] [{(111)_\beta }//{(01\overline 10)_\alpha }] [{[1\overline 10]_\beta }//{[2\overline 1\overline 10]_\alpha }] [{(110)_\beta }//{(0001)_\alpha }] [{[1\overline 11]_\beta }//{[01\overline 10]_\alpha }] [{(110)_\beta }//{(0001)_\alpha }] [{[001]_\beta }//{[01\overline 10]_\alpha }]
Morphology Plate shaped Lath shaped Lath shaped Lath shaped
References Zhang et al. (2007[Zhang, M., Zhang, W. Z., Zhu, G. Z. & Yu, K. (2007). Trans. Nonferrous Metals Soc. 17, 1428-1432.]) Sasaki et al. (2011[Sasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2011). Mater. Sci. Eng. A, 530, 1-8.]) Shi et al. (2012[Shi, Z. Z., Dai, F. Z. & Zhang, W. Z. (2012). Mater. Sci. Technol. 28, 411-414.]) Shi et al. (2012[Shi, Z. Z., Dai, F. Z. & Zhang, W. Z. (2012). Mater. Sci. Technol. 28, 411-414.])

In this paper, the ORs and interface structures of the β-Mg2Sn phase in an Mg–9.76 wt% Sn alloy were analyzed using high-resolution transmission electron microscopy (HRTEM) and high-angle annular dark-field scanning TEM (HAADF-STEM).

2. Experimental

Ingots of as-cast Mg–9.76 wt% Sn alloy were prepared and cut into bars/slices by electrical discharge machining. The resultant bars/slices were initially heat treated at 823 K for 12 h under the protection of argon flow to dissolve the β-Mg2Sn phase and achieve a homogeneous tin distribution. Subsequently, these samples were immediately quenched in water. All of the alloys were aged at 573 K in a muffle furnace for various aging times immediately after annealing. Age hardening responses were measured at the internal regions of α-Mg grains using a micro-Vickers hardness tester (HXD-1000TMC/LCD) under a load of 1 kg. Each hardness value is reported as the average of at least six individual measurements. The overall phase structures of the test alloys were analyzed using X-ray diffractometry (XRD) and scanning electron microscopy (SEM). XRD was performed on a Bruker AXS D8 Advance X-ray diffractometer with Cu Kα radiation (λ = 0.1542 nm). SEM observations were carried out on a SIRON TMP field-emission scanning electron microscope equipped with an EDAX energy dispersive X-ray spectrometer. The SEM samples were mechanically polished and then etched with a solution of 5 vol% nitric acid + absolute ethanol prior to characterization. The alloy slices were mechanically thinned to approximately 50 µm, and 3 mm-wide discs were punched and electrochemically polished. The alloy specimens were then ion milled using a Gatan precision ion polishing system (operating voltage, 3.0 kV). Conventional TEM was conducted using a JEOL JEM-2010 (HT) (high-angle tilt) microscope (LaB6 gun) operated at a voltage of 200 kV. High-resolution TEM and energy dispersive X-ray spectroscopy (EDS) analysis of the same specimen were performed on a JEOL JEM-2010 FEF (UHR) electron microscope with a field emission gun and an in-column Ω-type energy filter operated at 200 kV. The JEM-2010 FEF instrument was coupled to an EDAX energy dispersive X-ray spectrometer and a Gatan Model-894 CCD digital camera. Aberration-corrected HAADF-STEM images were acquired using an FEI Titan G2 60-300 transmission electron microscope (Prob Cs Corrector UHRSTEM) at an accelerating voltage of 300 kV.

3. Results and discussion

Ingots of as-cast Mg–9.76 wt% Sn alloy were heat treated at 823 K for 12 h until completely dissolved and then aged at 573 K. Fig. 1[link] shows that the hardness of the samples rapidly increases, reaching a maximum (63.5 HV) at 5 h and then gradually decreasing with further increases in time. The peak hardness and aging time of the present alloy were similar to those of Mg–7.75 wt% Sn alloys (60 HV and about 5 h) obtained after annealing and aging at 823 and 573 K, respectively (Van der Planken, 1969[Van Der Planken, J. (1969). J. Mater. Sci. 4, 927-929.]).

[Figure 1]
Figure 1
Age hardening curve of the as-cast Mg–9.76 wt% Sn alloy aged at 573 K after annealing at 823 K for 12 h.

Fig. 2[link] shows the powder XRD patterns of supersaturated Mg–9.76 wt% Sn alloys annealed at 573 K for 0, 1, 3 and 5 h. All of the XRD peaks could be indexed to either an α-Mg structure with lattice parameters of aα = 3.198, cα = 5.201 Å or a β-Mg2Sn structure with a lattice parameter of aβ = 6.747 Å. The peak aging time (5 h) was investigated to correlate the hardness of the sample alloys with the microstructures formed. Fig. 3[link](a) shows the SEM secondary electron image of the supersaturated Mg–9.76 wt% Sn alloy before aging. Figs. 3[link](b) and 3[link](c) show different magnifications of SEM secondary electron images of the supersaturated Mg–9.76 wt% Sn alloy aged at 573 K for 5 h to peak hardness. The results show that the precipitated β-Mg2Sn particles are densely distributed in the internal region of the α-Mg grains. The dark areas marked by arrows in Fig. 3[link](b) correspond to the β-Mg2Sn phase formed in the boundary regions of α-Mg grains. Fig. 3[link](c) illustrates the internal area of an α-Mg grain [white square in Fig. 3[link](b)]. Most of the precipitated β-Mg2Sn particles with bright contrast exhibit complicated lath-shaped morphologies. Typical β-Mg2Sn particles are indicated by arrows in Fig. 3[link](c).

[Figure 2]
Figure 2
XRD patterns of as-cast Mg–9.76 wt% Sn alloys aged for different times at 573 K after annealing at 823 K for 12 h.
[Figure 3]
Figure 3
(a) SEM secondary electron images of as-cast Mg–9.76 wt% Sn alloys aged (a) for 0 h and (b) at 573 K for 5 h after annealing at 823 K for 12 h. (c) Magnified SEM secondary electron image corresponding to the area marked by a white square in (b).

Fig. 4[link](a) shows a bright-field TEM image of the pre-aged Mg–9.76 wt% Sn alloy, and Fig. 4[link](b) shows the corresponding selected area electron diffraction (SAED) pattern. Figs. 4[link](a) and 4[link](b) indicate that the total dissolution of the β-Mg2Sn phase was achieved after heat treatment at 823 K for 12 h and confirm the XRD results in Fig. 2[link] and the SEM result in Fig. 3[link](a). Fig. 4[link](c) shows a bright-field TEM image taken along the [{[2\overline 1\overline 10]_\alpha }] direction of the Mg–9.76 wt% Sn alloy aged at 573 K for 5 h to peak hardness. Tilting and SAED results confirm that the precipitated particles [marked as P1, P2 and P3; Fig. 4[link](c)] of the β-Mg2Sn phase with OR-4 were platelet like (thickness 60 nm) along the [{[0001]_\alpha }] direction of the α-Mg matrix. Figs. 4(d) and 4(f), respectively, reveal the corresponding SAED patterns of P1 and the matrix along the [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }] and [{[1\overline 10]_\beta }//{[01\overline 10]_\alpha }] directions. Figs. 4(e) and 4[link](g) show simulated electron diffraction patterns based on the kinematic diffraction theory, which correspond to the real images of Figs. 4[link](d) and 4[link](f), respectively.

[Figure 4]
Figure 4
(a) TEM bright-field image of the as-cast Mg–9.76 wt% Sn alloy after annealing at 823 K for 12 h and before aging. (b) Corresponding SAED pattern obtained from the internal region of an α-Mg grain in (a). (c) TEM bright-field image of the Mg–9.76 wt% Sn alloy aged at 573 K for 5 h to peak hardness. The inset shows a high-magnification image of the particle marked as P1. (d) SAED pattern of particle P1 and the matrix [in (c)] along the [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }] direction. (e) Corresponding simulated electron diffraction pattern of (d). Open circles represent β-Mg2Sn and filled circles represent α-Mg. (f) SAED pattern of P1 and the matrix [in (c)] along the [{[1\overline 10]_\beta }//{[01\overline 10]_\alpha }] direction. (g) Corresponding simulated electron diffraction pattern of (f). Open circles represent β-Mg2Sn and filled circles represent α-Mg. (h) SAED pattern of particle Q1 and the matrix [in (c)] along the [{[\overline 111]_\beta }//{[1\overline 210]_\alpha }] direction. (i) Corresponding simulated electron diffraction pattern of (h). Open circles represents β-Mg2Sn and filled circles represent α-Mg. (j) TEM bright-field image of the Mg–9.76 wt% Sn alloy aged at 573 K for 5 h, corresponding to its peak hardness, along the [{[0001]_\alpha }] direction. (k) SAED pattern of the matrix [in (j)] along the [{[0001]_\alpha }] direction.

A typical particle Q1 (Fig. 4[link]c) of the β-Mg2Sn phase with OR-3 exhibited platelets (length 600 nm, thickness 25 nm). The corresponding SAED and kinematically simulated electron diffraction patterns of Q1, Q2, Q3, Q4 and Q5 along the [{[\overline 111]_\beta }//{[1\overline 210]_\alpha }] direction are shown in Figs. 4[link](h) and 4[link](i), respectively. The results suggest that these particles exhibit an OR of OR-3 with the α-Mg matrix. Figs. 4[link](j) and 4[link](k), respectively, show a bright-field TEM image and the corresponding SAED pattern taken along the [{[0001]_\alpha }] direction of the α-Mg matrix for the Mg–9.76 wt% Sn alloy aged at 573 K for 5 h. β-Mg2Sn particles marked as Q6, Q7, Q8, Q9, Q10, Q11, Q12 and Q13 were identified to be of OR-3, while those marked as P4 and P5 were associated with OR-4 (Fig. 4[link]j). The growth direction of β-Mg2Sn particles with OR-3 was parallel to the [{\langle {1\overline 12} \rangle _\beta }//{\langle {10\overline 10} \rangle _\alpha }] direction. The angle between the growth directions of β-Mg2Sn particles with OR-3 (Q6, Q7 and Q8) was 120° (Fig. 4[link]j). The growth direction of the β-Mg2Sn particle with OR-4 (P4) was parallel to the [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }] direction (Fig. 4[link]j). The growth directions of the β-Mg2Sn particles with OR-3 and OR-4 are in agreement with those reported by Zhang et al. (2007[Zhang, M., Zhang, W. Z., Zhu, G. Z. & Yu, K. (2007). Trans. Nonferrous Metals Soc. 17, 1428-1432.]). In Fig. 4[link](j), a typical particle Q7 of the β-Mg2Sn phase with OR-3 shows platelets with dimensions of 380 nm length and 70 nm width, and a β-Mg2Sn particle P5 with OR-4 shows platelets with dimensions of 260 nm length and 55 nm width.

With the obtained lattice parameters for the α-Mg matrix and β-Mg2Sn phase in Fig. 2[link], the stereographic projections of OR-1–OR-8 were calculated as shown in Figs. 5[link](a)–5[link](h), respectively. In Fig. 5[link], the thin lines indicate the plane traces of the α-Mg matrix, and the directions marked by h1–h8 represent [[03\overline 31]], [[03\overline 32]], [[01\overline 11]], [[02\overline 23]], [[01\overline 12]], [[11\overline 21]], [[22\overline 43]] and [[11\overline 23]], respectively. In Fig. 5[link], the thick lines represent plane traces of the β-Mg2Sn phase, and the directions marked by B1–B3 correspond to [100], [[1\overline 10]] and [[1\overline 11]], respectively. When the β lattice is rotated clockwise at about 5.23° around the [{[0001]_\alpha }] direction while retaining the condition of [{[0002]_\alpha }//{[220]_\beta }] or [{(0002)_\alpha }//{(220)_\beta }], OR-3 could be reached from OR-4 based on a comparison of Figs. 5[link](c) and 5[link](d).

[Figure 5]
Figure 5
Calculated stereographic projections of (a) OR-1, (b) OR-2, (c) OR-3, (d) OR-4, (e) OR-5, (f) OR-6, (g) OR-7 and (h) OR-8.

Three crystallographic ORs (OR-1, OR-3 and OR-4) were observed via SAED and tilting techniques. Table 2[link] lists the statistical results of the crystallographic ORs of 334 β-Mg2Sn particles of Mg–9.76 wt% Sn alloy aged at 573 K for 5 h. About 75.1 and 24.3% of the β-Mg2Sn particles exhibited OR-3 and OR-4, respectively. OR-3 was formed by most of the particles of the β-Mg2Sn phase in the alloy with the α-Mg matrix (Table 2[link], and Figs. 4[link]c and 4[link]j).

Table 2
Statistical survey of the ORs and morphologies of precipitated β-Mg2Sn particles in the Mg–9.76 wt% Sn alloy aged at 573 K for 5 h

Length range of the long axis of lath-shaped particles of β-Mg2Sn (nm) Number of lath-shaped particles with OR-1 Number of lath-shaped particles with OR-3 Number of lath-shaped particles with OR-4
<100 0 5 8
100–200 0 43 25
200–500 1 134 40
500–1000 0 53 8
>1000 1 16 0
Sum of the above 2 251 81

To elucidate the statistical results (Table 2[link]) in terms of a three-dimensional invariant line model (Zhang & Purdy, 1993[Zhang, W. Z. & Purdy, G. R. (1993). Acta Metall. 41, 543-551.]; Luo & Weatherly, 1987[Luo, C. P. & Weatherly, G. C. (1987). Acta Metall. 35, 1963-1972.]; Dahmen, 1982[Dahmen, U. (1982). Acta Metall. 30, 63-73.]), the transformation matrices A0 in real space and [A{'_0}^{ - 1}] in reciprocal space ([A{'_0}] corresponding to the transposed matrix of A0) must be determined. A0 - 1 was determined under the condition that the base vectors of each phase are correlated by small displacements [\Delta {\bf g}] in reciprocal space. The SAED patterns (Figs. 4[link]d and 4[link]f) reveal that three small noncoplanar [\Delta {\bf g}] values must be considered as follows: [\Delta {\bf g} _1 = {(0\overline 110)_\alpha }] − [{(\overline 220)_\beta }], [\Delta {\bf g} _2 = {(2\overline 1\overline 10)_\alpha } - {(004)_\beta }] and [\Delta {\bf g} _3 =] [{(0002)_\alpha } - {(220)_\beta }]. For OR-4 [[{(0\overline 110)_\alpha }//{(\overline 220)_\beta }], [{(2\overline 1\overline 10)_\alpha }//{(004)_\beta }] and [{(0002)_\alpha }//{(220)_\beta }]], [A{'_0}^{ - 1}] expressed in the orthogonal basis with three unit vectors along [{(0\overline 110)_\alpha }], [{(2\overline 1\overline 10)_\alpha }] and [{(0002)_\alpha }] is diagonal. The ratios [{\eta _1} = {d_{0\overline 1{{10}_\alpha }}}/] [{d_{\overline 2{{20}_\beta }}}], [{\eta _2} = {d_{2\overline 1\overline 1{0_\alpha }}}/{d_{{{004}_\beta }}}] and [{\eta _3} =] [ {d_{{{0002}_\alpha }}}/{d_{{{220}_\beta }}}] were found to be [{\rm Tr}(A{'_0}^{ - 1}) =] [ ({\eta _1},{\eta _2},{\eta _3})] = (1.161, 0.948, 1.090). According to three-dimensional invariant line theory (Zhang & Purdy, 1993[Zhang, W. Z. & Purdy, G. R. (1993). Acta Metall. 41, 543-551.]; Luo & Weatherly, 1987[Luo, C. P. & Weatherly, G. C. (1987). Acta Metall. 35, 1963-1972.]; Dahmen, 1982[Dahmen, U. (1982). Acta Metall. 30, 63-73.]), when the β lattice is rotated clockwise by θ around the [{[0001]_\alpha }] direction from the OR-4's OR while retaining the condition of [{(0002)_\alpha }//{(220)_\beta }], an invariant line in reciprocal space may be obtained as follows:

[\eqalignno{&\left({\matrix{ {\cos \theta } & { - \sin \theta } & 0 \cr {\sin \theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right)\left({\matrix{ {{\eta _1}} & 0 & 0 \cr 0 & {{\eta _2}} & 0 \cr 0 & 0 & {{\eta _3}} \cr } } \right){\left(\matrix{ h \hfill \cr k \hfill \cr l \hfill \cr} \right)_\beta } \cr & = {\left(\matrix{ h \hfill \cr k \hfill \cr l \hfill \cr} \right)_\beta }. &(1)}]

The eigenvalue equation yields [\cos \theta =] [(1 + {\eta _1}{\eta _2})/({\eta _1} + {\eta _2})], and [\theta = {5.11 }]° based on the measured transformation matrix A0 - 1. Hence, the β-Mg2Sn lattice reaches an orientation relationship of OR-3 as shown in Figs. 5[link](c) and 5[link](d). Owing to the existence of an invariant line, the interface (habit plane) between the β phase with OR-3 and the matrix is a low-strain energy interface. Hence, β-Mg2Sn particles with OR-3 precipitates are predominantly obtained (Table 2[link]).

Fig. 6[link](a) shows an HRTEM image obtained along the [{[2\overline 1\overline 10]_\alpha }] direction, which corresponds to the area bounded by dashed lines marked as II in the inset in Fig. 4[link](c). The interface structure between precipitated β-Mg2Sn particles with OR-4 and the α-Mg matrix is observable in Fig. 6[link](a). Fig. 6[link](b) illustrates an atomic resolution HAADF-STEM image of the interface area [large dashed square, Fig. 6[link](a)]. Each bright dot represents Sn-rich columns (Fig. 6[link]b) because the brightness of individual columns in HAADF–STEM is approximately the square of the average atomic number (Nie et al., 2013[Nie, J. F., Zhu, Y. M., Liu, J. Z. & Fang, X. Y. (2013). Science, 340, 957-960.]). Fig. 6[link](b) shows that the transition layer of the interface between the β-Mg2Sn particles and the nearby α-Mg matrix is about 1.67 nm thick and covers approximately four layers each of the [{(220)_\beta }] and [{(0002)_\alpha }] planes. Hence, an atomic structure model of the interface between the [{(220)_\beta }] plane of β-Mg2Sn particles with OR-4 and the [{(0001)_\alpha }] plane of the α-Mg matrix could be constructed and projected along the [{[001]_\beta }] and [{[2\overline 1\overline 10]_\alpha }] directions [inset, Fig. 6[link](b)]. The proposed atomic model is shown in the inset in Fig. 6[link](b). The corresponding simulated HRTEM image [inset, small dashed rectangle, Fig. 6[link](a)] was based on the proposed atomic model and showed agreement with the experimental HRTEM image of the interface between β-Mg2Sn particles with OR-4 and the α-Mg matrix (Fig. 6[link]a).

[Figure 6]
Figure 6
(a) HRTEM image of the area bounded by a dashed lines marked as II in the inset in Fig. 4[link](c) for the as-cast Mg–9.76 wt% Sn alloy aged at 573 K for 5 h, along the [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }] direction. The inset shows a simulated HRTEM image created according to the atomic structure model of the interface. (b) Atomic resolution HAADF-STEM image corresponding to the area enclosed by the large dashed square in (a) along the [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }] direction. The inset shows the proposed atomic structure model of the interface between the [{(220)_\beta }] plane of a β-Mg2Sn particle with OR-4 and the [{(0001)_\alpha }] plane of the α-Mg matrix projected along the [{[001]_\beta }] and [{[2\overline 1\overline 10]_\alpha }] directions. (c) HRTEM image of the area bounded by the dashed lines marked as I in Fig. 4[link](c), along the [{[\overline 111]_\beta }//{[1\overline 210]_\alpha }] direction. The inset shows the corresponding simulated HRTEM image. (d) Atomic resolution HAADF-STEM image of the area in (c). The inset shows the proposed atomic structure model of the interface between the [{(220)_\beta }] plane of a β-Mg2Sn particle with OR-3 and the [{(0001)_\alpha }] plane of the α-Mg matrix projected along the [{[\overline 111]_\beta }] and [{[1\overline 210]_\alpha }] directions.

Fig. 6[link](c) shows an HRTEM image obtained along the same direction as in Fig. 6[link](a); this image corresponds to the area marked by I in Fig. 4[link](c). The interface structure between the precipitated β-Mg2Sn particle with OR-3 and the α-Mg matrix could be observed in Fig. 6[link](c). Fig. 6[link](d) shows an atomic resolution HAADF–STEM image corresponding to the area in Fig. 6[link](c). Thus, an atomic structure model of the interface between the [{(220)_\beta }] plane of β-Mg2Sn particles with OR-3 and the [{(0001)_\alpha }] plane of the α-Mg matrix may be proposed and projected along the [{[\overline 111]_\beta }] and [{[1\overline 210]_\alpha }] directions [inset, Fig. 6[link](d)]. Using the atomic structure model shown in Fig. 6[link](d), the corresponding calculated HRTEM image [inset, Fig. 6[link](c)] may be obtained, and the results show good agreement with the experimental HRTEM image of the interface between β-Mg2Sn particles with OR-3 and the α-Mg matrix (Fig. 6[link]c). Figs. 6[link](c) and 6[link](d) indicate that the d-value misfits between [{({1\overline 12} )_\beta }] and [{({10\overline 10} )_\alpha }], between [{({220} )_\beta }] and [{({0002} )_\alpha }], and between [{({\overline 222} )_\beta }] and [{({1\overline 210} )_\alpha }] are 0.71, 8.62 and 19.2%, respectively. Hence, β-Mg2Sn particles with OR-3 grow along the [{[{1\overline 12} ]_\beta }//{ [{10\overline 10} ]_\alpha }] direction. Similarly, β-Mg2Sn particles with OR-4 grow along the [{[001]_\beta }//{[2\overline 1\overline 10]_\alpha }] direction because of the low d-value misfit (5.18%) between [{({004} )_\beta }] and [{({2\overline 1\overline 10} )_\alpha }]. Hence, β-Mg2Sn particles with OR-3 exhibit longer platelet morphologies than those with OR-4 (Table 2[link] and Fig. 4[link]j). This result is attributable to the low d-value misfits of β-Mg2Sn particles with OR-3 along the corresponding growth direction.

4. Conclusions

The crystallographic orientation relationships (ORs) of precipitated β-Mg2Sn particles in Mg–9.76 wt% Sn alloy aged at 573 K for 5 h, corresponding to its peak hardness, were investigated by advanced TEM. OR-3 of [{(110)_\beta }//{(0001)_\alpha }] and [{[\overline 111]_\beta }//{[1\overline 210]_\alpha }] and OR-4 of [{(110)_\beta }//{(0001)_\alpha }] and [{[001]_\beta }//][{[2\overline 1\overline 10]_\alpha }] are the key ORs of β-Mg2Sn particles in the alloy. The proportions of β-Mg2Sn particles exhibiting OR-3 and OR-4 were determined as 75.1 and 24.3%, respectively. Crystallographic factors influenced the predominance of OR-3. The corresponding mechanism was explained by a three-dimensional invariant line model constructed by a measured transformation matrix in reciprocal space. Atomic interface structures between the [{(220)_\beta }] plane of the β-Mg2Sn phases with OR-3 and OR-4 and the [{(0001)_\alpha }] plane of the α-Mg matrix were constructed via HRTEM and atomic resolution HAADF-STEM.

Supporting information


Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant Nos. 51371130, 51171130 and 51271134) and the Fundamental Research Funds for the Central Universities.

References

First citationCelloto, S. (2000). Acta Mater. 48, 1775–1787.  Google Scholar
First citationDahmen, U. (1982). Acta Metall. 30, 63–73.  CrossRef CAS Web of Science Google Scholar
First citationDerge, G., Kommell, A. R. & Mehl, R. F. (1937). Trans. AIME, 124, 367–378.  CAS Google Scholar
First citationHenes, V. S. & Gerold, V. (1962). Z. Metallkd. 53, 743–748.  CAS Google Scholar
First citationHort, N., Huang, Y., Abu Leil, T., Maier, P. & Kainer, K. U. (2006). Adv. Eng. Mater. 8, 359–364.  Web of Science CrossRef CAS Google Scholar
First citationKang, D. H., Park, S. S. & Kim, N. J. (2005). Mater. Sci. Eng. A, 413–414, 555–560.  Web of Science CrossRef Google Scholar
First citationKang, D. H., Park, S. S., Oh, Y. S. & Kim, N. J. (2007). Mater. Sci. Eng. A, 449–451, 318–321.  Web of Science CrossRef Google Scholar
First citationLiu, H. M., Chen, Y. G., Tang, Y. B., Wei, S. H. & Niu, G. (2007). J. Alloys Compd. 440, 122–126.  Web of Science CrossRef CAS Google Scholar
First citationLuo, A. A. (2004). Int. Mater. Rev. 49, 13–30.  Web of Science CrossRef CAS Google Scholar
First citationLuo, C. P. & Weatherly, G. C. (1987). Acta Metall. 35, 1963–1972.  CrossRef CAS Web of Science Google Scholar
First citationMendis, C. L., Bettles, C. J., Gibson, M. A., Gorsse, S. & Hutchinson, C. R. (2006a). Philos. Mag. Lett. 86, 443–456.  Web of Science CrossRef CAS Google Scholar
First citationMendis, C. L., Bettles, C. J., Gibson, M. A. & Hutchinson, C. R. (2006b). Mater. Sci. Eng. A, 435–436, 165–171.  Web of Science CrossRef Google Scholar
First citationMurray, J. L. (1997). Alloy Phase Diagrams, ASM Handbook, edited by H. Baker & H. Okamoto. Materials Park: ASM International.  Google Scholar
First citationNie, J. F. (2012). Metall. Mater. Trans. A, 43, 3891–3939.  Web of Science CrossRef CAS Google Scholar
First citationNie, J. F., Zhu, Y. M., Liu, J. Z. & Fang, X. Y. (2013). Science, 340, 957–960.  Web of Science CrossRef CAS PubMed Google Scholar
First citationSasaki, T. T., Ju, J. D., Hono, K. & Shin, K. S. (2009). Scr. Mater. 61, 80–83.  Web of Science CrossRef CAS Google Scholar
First citationSasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2006). Scr. Mater. 55, 251–254.  Web of Science CrossRef CAS Google Scholar
First citationSasaki, T. T., Oh-ishi, K., Ohkubo, T. & Hono, K. (2011). Mater. Sci. Eng. A, 530, 1–8.  Web of Science CrossRef CAS Google Scholar
First citationShi, Z. Z., Dai, F. Z. & Zhang, W. Z. (2012). Mater. Sci. Technol. 28, 411–414.  Web of Science CrossRef CAS Google Scholar
First citationVan Der Planken, J. (1969). J. Mater. Sci. 4, 927–929.  CrossRef CAS Google Scholar
First citationWei, S. H., Chen, Y. G., Tang, Y. B., Liu, H. M., Xiao, S. F., Niu, G., Zhang, X. P. & Zhao, Y. H. (2008). Mater. Sci. Eng. A, 492, 20–23.  Web of Science CrossRef Google Scholar
First citationYoon, J. & Park, S. (2014). Mater. Des. 55, 300–308.  Web of Science CrossRef CAS Google Scholar
First citationZhang, M., Zhang, W. Z., Zhu, G. Z. & Yu, K. (2007). Trans. Nonferrous Metals Soc. 17, 1428–1432.  Web of Science CrossRef Google Scholar
First citationZhang, W. Z. & Purdy, G. R. (1993). Acta Metall. 41, 543–551.  CrossRef CAS Web of Science Google Scholar
First citationZheng, O., Zhou, J. P., Zhao, D. S., Wang, J. B., Wang, R. H., Gui, J. N., Xiong, D. X. & Sun, Z. F. (2009). Scr. Mater. 60, 791–794.  Web of Science CrossRef CAS Google Scholar
First citationZhou, J. P., Zhao, D. S., Wang, R. H., Sun, Z. F., Wang, J. B., Gui, J. N. & Zheng, O. (2007). Mater. Lett. 61, 4707–4710.  Web of Science CrossRef CAS Google Scholar
First citationZhou, J. P., Zhao, D. S., Zheng, O., Wang, J. B., Xiong, D. X., Sun, Z. F., Gui, J. N. & Wang, R. H. (2009). Micron, 40, 906–910.  Web of Science CrossRef PubMed CAS Google Scholar

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