Correlation between Growth Twinning and Crystalline Reorientation of

Communication pubs.acs.org/crystal

Correlation between Growth Twinning and Crystalline Reorientation of Faceted Growth Materials during Directional Solidification Dazhuang Kang, Jinghua Liu, Chengbao Jiang,* and Huibin Xu Key Laboratory of Aerospace Materials and Performance (Ministry of Education), School of Materials Science and Engineering, Beihang University, Beijing 100191, P. R. China

ABSTRACT: The correlation between growth twinning and crystalline reorientation of faceted growth materials during directional solidification was demonstrated through matrix calculation and Thompson regular tetrahedron model diagrams. The correlation is that the crystalline reorientation results from the mirror symmetry operation of initial orientation on different twin planes. In total, seven possibilities of crystalline reorientation caused by single-twinning from ⟨110⟩, ⟨111⟩, and ⟨112⟩ initial axial orientation were predicted, four of which were verified experimentally in the representative Tb0.3Dy0.7Fe2 alloys.

G

provide a better understanding for crystalline orientation control and properties. In this communication, we analyzed the correlation between GT and reoriented growth from ⟨110⟩, ⟨111⟩, and ⟨112⟩ initial axial orientations in faceted growth materials with facecentered-cubic (fcc) structure. All the possibilities of crystalline reorientation from these three orientations were calculated by matrix and intuitively shown through a Thompson regular tetrahedron model, and the results were confirmed experimentally in a representative alloy of Tb0.3Dy0.7Fe2. High-purity starting element terbium, dysprosium, and iron with a purity level of 99.99% were remelted four times by arc melting and drop cast in the chilled copper mold to obtain master rods with a diameter of 7.0 mm and length of 100 mm. Then the master polished rod was put into the thin alumina tube for zone melting directional solidification. Crystals of nominal composition of Tb0.3Dy0.7Fe2 were prepared in the FZT-4000-H type vertical optical floating zone melting furnace. The withdrawal rate was 10 mm/h. The crystalline orientations were detected by X-ray Laue back-reflection technique from transverse sections of samples. To investigate the correlation between GT and crystalline reorientation during directional solidification, the essence is to find the new crystallographic orientation of the initial axial orientation in the coordinate of twinned crystalline lattice. It is well-known that the crystallographic orientations between

rowth twinning (GT) has attracted much attention owing to its effects on the growth pattern, microstructure, crystalline orientation, and thus the property. The effects of GT on crystal growth were first discovered from Ge in the 1950s1 and has been extensively observed in metals, intermetallic compounds, semiconductors, and oxides, especially for the faceted growth materials with a large entropy of melting, for instance, Ge,1−4 Si,5−13 AlSi,14−19 and TbDyFe.20−25 Growth with GT is usually a major growth pattern for the faceted growth materials because twinning grooves can reduce the growth supercooling degree. Remarkable property anisotropy exists in almost all faceted growth materials. The excellent properties usually appear along specific crystalline orientation. For example, the magnetostriction along ⟨111⟩ orientation (λ111) is about 20 times of that along ⟨100⟩ orientation (λ100) in TbDyFe giant magnetostrictive alloys.26 Thus, the control of crystalline orientation along certain direction is of crucial importance for faceted growth materials. However, the phenomenon that the crystalline orientation can be changed by GT is frequently observed in faceted growth materials.14,24,27 Especially for directional solidification process, the axial orientation is usually changed even with a single crystal seed. For instance, it is observed that the axial orientation changes from ⟨110⟩ initial axial orientation to ⟨114⟩ in TbDyFe alloys,23,24 and a two-{111}-twin system growth model is proposed.24 However, because of lacking systematic theoretical analysis, the correlation between GT and crystalline reorientation remains still unclear. Investigating all possibilities of reorientation from different initial axial orientations could © XXXX American Chemical Society

Received: January 21, 2015 Revised: April 28, 2015

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DOI: 10.1021/acs.cgd.5b00096 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Communication

Figure 1. Thompson regular tetrahedron model: (a) ⟨110⟩ axial oriented tetrahedron with twinning occurrence on planes 1 and 3; (b) ⟨111⟩ axial oriented tetrahedron with twinning occurrence on planes 1 and 4; (c) ⟨112⟩ axial oriented tetrahedron with twinning occurrence on planes 1, 2, and 3 (the insets of panels a−c are ⟨110⟩, ⟨111⟩, and ⟨112⟩ axial oriented tetrahedron, respectively, with four surfaces as twin planes).

initial orientation, and ⟨112⟩, ⟨552⟩, or ⟨127⟩ for ⟨112⟩ initial orientation. For multiple-twinning, the final axial orientation will be the iteration result of several mirror symmetry operations on different {111} planes of different twinned crystals. The final results can be calculated by iterative calculation with the transformation matrix. To visualize this crystallographic relationship, we show the crystallographic elements in a Thompson regular tetrahedron model as follows. A regular tetrahedron is formed by {111} planes as four surfaces in one crystalline lattice. The ⟨110⟩ directions are the intersection line of any two {111} planes, and the ⟨112⟩ directions are the bisectors of angles on each triangular surface. This model describes crystallographic orientations and planes. In the inset of Figure 1a, a tetrahedron with ⟨110⟩ axial orientation is shown. Twinning could occur on each of its four surfaces. It can be directly observed that twinning on planes 1, 2 and planes 3, 4 shows the same effects on the axial orientation. Thus, there are in total two possibilities of crystalline reorientation caused by single-twinning for ⟨110⟩ initial axial orientation. The situation of twinning occurrence on planes 1 and 3 is shown in the form of tetrahedron combination in Figure 1a. The new axial orientation in the coordinate of twinned lattice is ⟨110⟩ when twinning occurrence on plane 1 and ⟨114⟩ for plane 3. Further, it should be noted that twinning on plane 1 is equivalent to a rotation of 70.5° along ⟨11̅ 0⟩, and similar phenomenon exists on the plane 3 along ⟨110⟩, in the cubic structure crystal. The tetrahedron with ⟨111⟩ axial orientation and the tetrahedrons combination when twinning occurrence on planes 1 and 4 are shown in Figure 1b. Twinning on planes 1, 2, and 3 show the same effects, seen directly in the inset. Thus, there are in total two possibilities. Twinning on plane 1, which is equivalent to a rotation of 70.5° along ⟨1̅10⟩, leads to a ⟨1̅1̅5⟩ reorientation. Twinning on plane 4, which is normal to the axis, do not change the ⟨111⟩ axial orientation but makes the lattice rotate 180° along the axis. The tetrahedron with ⟨112⟩ axial orientation and the tetrahedron combination with twinning occurrence on planes 1, 2, and 3 are shown in Figure 1c. In this, planes 3 and 4 are equivalent, as shown in the inset. Thus, there are in total three possibilities. Twinning occurrence on planes 1, 2, and 3 lead to ⟨112⟩, ⟨552⟩, and ⟨127⟩ reorientations, respectively. Further, from Figure 1a−c, it can be also observed that the axial orientation will change only if it is neither parallel nor normal to the twin planes. In sum, from the viewpoint of crystallography, crystalline reorientation is the result of mirror symmetry operation of

twinned crystals are of mirror symmetry to the {111} twin plane in the crystalline materials with fcc structure. Thus, to make mirror symmetry operation of initial orientation on all of the four {111} planes, respectively, then the possibilities of crystalline reorientation after single-twinning can be simulated. The new crystallographic orientation in the coordinate of twinned crystalline lattice could be calculated by matrix as follows.28 These four matrix are coordinate transformation matrices with {111} planes as mirror symmetry in cubic lattice system. ⎡ 1̅ 2 2 ⎤ ⎢ ⎥ = ⎢ 2 1̅ 2 ⎥ ⎢⎣ 2 2 1 ⎥⎦ ̅

(1)

⎡ 1̅ 2̅ 2 ⎤ ⎢ ⎥ T1 1̅ 1 = ⎢ 2̅ 1̅ 2̅ ⎥ ⎢⎣ 2 2 1 ⎥⎦ ̅ ̅

(2)

⎡ 1̅ 2̅ 2̅ ⎤ ⎢ ⎥ T1̅ 11 = ⎢ 2̅ 1̅ 2 ⎥ ⎢⎣ 2 2 1 ⎥⎦ ̅ ̅

(3)

⎡ 1̅ 2 2̅ ⎤ ⎢ ⎥ = ⎢ 2 1̅ 2̅ ⎥ ⎢⎣ 2 2 1 ⎥⎦ ̅ ̅ ̅

(4)

T111

T11 1̅

For ⟨110⟩ initial orientation, to multiply [110] and matrix (1−4), respectively, then the reorientations are as follows: [110]*T111 = [114];

[110]*T1 1̅ 1 = [3̅ 30] ̅

[110]*T1̅ 11 = [3̅ 30]; ̅

[110]*T11 1̅ = [114]̅

Similarly, for ⟨111⟩ initial orientation [111]*T111 = [333]; [111]*T1̅ 11 = [5̅ 1̅ 1̅ ];

[111]*T1 1̅ 1 = [ 1̅ 5̅ 1̅ ] [111]*T11 1̅ = [ 1̅ 1̅ 5]̅

For ⟨112⟩ initial orientation [112]*T111 = [552]; [112]*T1̅ 11 = [712]; ̅ ̅

[112]*T1 1̅ 1 = [172] ̅ ̅ [112]*T11 1̅ = [3̅ 3̅ 6]̅

Thus, there are in total seven possibilities of crystalline reorientation caused by single-twinning for ⟨110⟩, ⟨111⟩, and ⟨112⟩ initial orientations. The new orientation will be ⟨114⟩ or ⟨110⟩ for ⟨110⟩ initial orientation, ⟨115⟩ or ⟨111⟩ for ⟨111⟩ B

DOI: 10.1021/acs.cgd.5b00096 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Communication

initial orientation on different twin planes. There are in total seven possibilities of crystalline reorientation caused by single twinning for ⟨110⟩, ⟨111⟩, and ⟨112⟩ axial oriented crystals with fcc structure. The tetrahedron model is consistent with the calculation results. To verify the calculated results and the model, TbDyFe alloys are chosen to be the object of experiment. TbDyFe is a typical faceted growth material with fcc structure, whose best property orientation is ⟨111⟩,26 followed by ⟨110⟩ and ⟨112⟩.23 These three orientations are most commonly studied in TbDyFe alloys. Three rods were prepared by optical zone melting directional solidification method from ⟨110⟩, ⟨111⟩, and ⟨112⟩ twin-free single crystal seeds, respectively. From each rod, three transverse sections were cut to investigate the crystalline reorientation. With higher withdrawal rate (compared with the conditions for preparing a twin-free single crystal25), R = 10 mm/h, GTs were evoked and different results of reoriented growth were observed. Grown from ⟨110⟩ axial oriented single crystal seed, a sample named 1# was obtained. From transverse sections cut from sample 1#, three Laue spot photographs can be observed, as shown in Figure 2a−c. The main crystallographic elements are

Figure 3. Laue spot photographs taken from transverse sections cut from the oriented crystal with ⟨111⟩ single crystal seed: (a) photo of initial single crystal seed with ⟨111⟩ axial orientation; (b) photo of part of grown crystal with ⟨1̅1̅5⟩ axial orientation.

Figure 2. Laue spot photographs taken from transverse sections cut from the oriented crystal with ⟨110⟩ single crystal seed: (a) photo of initial single crystal seed with ⟨110⟩ axial orientation; (b) photo of part of grown crystal with ⟨114⟩ axial orientation; (c) photo of part of grown crystal with ⟨110⟩ axial orientation.

annotated in the figures in which Figure 2a is taken from the seed. Crystalline orientations of Figure 2b,c are the results of 70.5° rotation along ⟨1̅10⟩ and ⟨110⟩ axes of Figure 2a, seen directly from the figures, leading to new axial orientations ⟨114⟩ and ⟨110⟩, respectively. We know that the 70.5° rotation is equal to mirror symmetry operation under this condition, as analyzed in Figure 1a. Thus, these two crystalline reorientations are both caused by twinning. The experiment results are fully consistent with the calculated results and the tetrahedron model. Sample 2# was grown from ⟨111⟩ single crystal seed. Two Laue spot photographs taken from transverse sections are shown in Figure 3a,b. Figure 3a was taken from the seed, showing ⟨111⟩ axial orientation. Figure 3b, taken from the grown rod, is the result of 70.5° rotation along ⟨1̅10⟩ axis of Figure 3a, showing ⟨11̅ 5̅ ⟩ axial orientation. This result is consistent with one of the possibilities analyzed above. Sample 3# was grown from ⟨112⟩ single crystal seed. Figure 4a was taken from the transverse section of the seed, showing

Figure 4. Laue spot photographs taken from transverse sections cut from the oriented crystal with ⟨112⟩ single crystal seed: (a) photo of initial single crystal seed with ⟨112⟩ axial orientation; (b) photo of part of grown crystal with ⟨112⟩ axial orientation.

⟨112⟩ axial orientation. Figure 4b was taken from the transverse sections of the grown rod, showing ⟨112⟩ axial orientation as well. In this, the twin relationship is clear; Figure 4b is the result of mirror symmetry of Figure 4a on (111̅) plane. Furthermore, two sets of Laue spots belonging to two twinned crystals exist C

DOI: 10.1021/acs.cgd.5b00096 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Communication

(16) Wang, R.; Lu, W.; Hogan, L. M. Metall. Mater. Trans. A 1997, 28, 1233−1243. (17) Min, Z.; Xiangfa, L. Cryst. Growth Des. 2010, 10, 2443−2446. (18) Timpel, M.; Wanderka, N.; Schlesiger, R.; Yamamoto, T.; Lazarev, N.; Isheim, D.; Schmitz, G.; Matsumura, S.; Banhart, J. Acta Mater. 2012, 60, 3920−3928. (19) Pei, Y. T.; De Hosson, J. T. M. Acta Mater. 2001, 49, 561−571. (20) Verhoeven, J. D.; Gibson, E. D.; McMasters, O. D.; Baker, H. H. Metall. Mater. Trans. A 1987, 18, 223−231. (21) Wu, G. H.; Zhao, X. G.; Wang, J. H.; Li, J. Y.; Jia, K. C.; Zhan, W. S. Appl. Phys. Lett. 1995, 67, 2005−2007. (22) Mei, W.; Yoshizumi, M.; Okane, T.; Umeda, T. J. Alloys Compd. 1997, 258, 34−38. (23) Jiang, C.; Zhou, S.; Xu, H.; Wang, R. Mater. Sci. Eng., B 1999, 58, 191−194. (24) Zhao, Y.; Jiang, C.; Zhang, H.; Xu, H. J. Alloys Compd. 2003, 354, 263−268. (25) Kang, D.; Liu, J.; Jiang, C.; Xu, H. J. Alloys Compd. 2015, 621, 331−338. (26) Clark, A. E.; Cullen, J. R.; McMasters, O. D.; Callen, E. R. AIP Conf. Proc. 1976, 29, 192−193. (27) Xu, X.; Yang, H.; Liu, Y.; Zheng, Y.; Li, L.; Ji, Y.; Han, X. Acta Mater. 2011, 59, 7177−7188. (28) Kestenbach, H. J. Metallography 1977, 10, 189−199.

in Figure 4b, showing mirror symmetry relationship to each other, for instance, (111) and (111)′, and (233) and (233)′. This result is consistent with one of the possibilities analyzed above. The experiment results consist well with the calculated results and the Thompson regular tetrahedron models. Four results are observed directly from in total seven conjectured possibilities. There are three remaining possibilities that were not observed directly from the experiments, which could be due to fewer experiments or growth dynamics. In this communication, the correlation between growth twinning and crystalline reorientation during directional solidification are investigated both theoretically and experimentally. It was found that crystalline reorientation of faceted growth materials are caused by growth twinning. Essentially, it is the result of mirror symmetry operation of initial crystalline orientation on different {111} planes. There are in total seven possibilities of crystalline reorientation caused by singletwinning for ⟨110⟩, ⟨111⟩, and ⟨112⟩ axial oriented crystals with fcc structure, four of which were verified directly in experiments. These results should contribute to a better understanding of the crystalline reorientation, crystal growth control, and properties for faceted growth materials.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Tel: 8610-82338780/82316234. Fax: 86-10-82338200. Funding

This work is supported by the National Basic Research Program of China (973 Program) under Grant No. 2012CB619404, National High-tech R&D Program (863 Program) under Grant No. 2013AA030903, and National Natural Science Foundations of China (NSFC) under Grant Nos. 51331001, 51221163. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Billig, E. Proc. R. Soc. 1955, A229, 346−363. (2) Bennett, A. I.; Longini, R. L. Phys. Rev. 1959, 116, 53−61. (3) Wagner, R. S. Acta Metall. 1960, 8, 57−60. (4) Hamilton, D. R.; Seidensticker, R. G. J. Appl. Phys. 1960, 31, 1165−1168. (5) Nagashio, K.; Kuribayashi, K. Acta Mater. 2005, 53, 3021−3029. (6) Fujiwara, K.; Maeda, K.; Usami, N.; Sazaki, G.; Nose, Y.; Nakajima, K. Script. Mater. 2007, 57, 81−84. (7) Fujiwara, K.; Maeda, K.; Usami, N.; Nakajima, K. Phys. Rev. Lett. 2008, 101, 055503. (8) Fujiwara, K.; Maeda, K.; Usami, N.; Sazaki, G.; Nose, Y.; Nomura, A.; Shishido, T.; Nakajima, K. Acta Mater. 2008, 56, 2663− 2668. (9) Fujiwara, K.; Fukuda, H.; Usami, N.; Nakajima, K.; Uda, S. Phys. Rev. B 2010, 81, 224106. (10) Yang, X.; Fujiwara, K.; Gotoh, R.; Maeda, K.; Nozawa, J.; Koizumi, H.; Uda, S. Appl. Phys. Lett. 2010, 97, 172104. (11) Kutsukake, K.; Abe, T.; Usami, N.; Fujiwara, K.; Morishita, K.; Nakajima, K. Script. Mater. 2011, 65, 556−559. (12) Yang, X.; Fujiwara, K.; Maeda, K.; Nozawa, J.; Koizumi, H.; Uda, S. Appl. Phys. Lett. 2011, 98, 012113. (13) Yang, X.; Fujiwara, K.; Maeda, K.; Nozawa, J.; Koizumi, H.; Uda, S. Cryst. Growth Des. 2011, 11, 1402−1410. (14) Kobayashi, K. F.; Hogan, L. M. J. Mater. Sci. 1985, 20, 1961− 1975. (15) Lu, S.; Hellawell, A. Metall. Trans. A 1987, 18, 1721−1733. D

DOI: 10.1021/acs.cgd.5b00096 Cryst. Growth Des. XXXX, XXX, XXX−XXX