Effect of additional solute elements (X= Al, Ca, Y, Ba, Sn, Gd and Zn) on crystallographic anisotropy during the dendritic growth of magnesium alloys

Journal of Alloys and Compounds 775 (2019) 322e329

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Effect of additional solute elements (X¼ Al, Ca, Y, Ba, Sn, Gd and Zn) on crystallographic anisotropy during the dendritic growth of magnesium alloys Jinglian Du a, b, Ang Zhang a, c, Zhipeng Guo a, c, *, Manhong Yang a, c, Mei Li d, Feng Liu b, Shoumei Xiong a, c, ** a

School of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, China Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing, 100084, China d Materials Research Department, Research and Innovation Center, Ford Motor Company, MD3182, P.O Box 2053, Dearborn, MI48121, USA b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 April 2018 Received in revised form 11 October 2018 Accepted 12 October 2018 Available online 13 October 2018

Based on the first-principles calculations and crystallographic anisotropy analysis, the effect of additional solute elements on the dendritic growth behavior of binary Mg-X (X ¼ Al, Ca, Y, Ba, Sn, Gd and Zn) alloys are investigated in terms of the orientation-dependent surface energy. The preferred growth direction of the a-Mg dendrite is found to be dependent on the magnitude of the anisotropic surface energy and the difference of crystallographic anisotropy between the matrix Mg and the additional solute X. The most densely packed crystallographic planes are found to be the energetically favorable planes with the minimum surface energy, as exemplified by the f111g plane of Al with fcc (face-centered cubic) structure, the f110g plane of Ba with bcc (body-centered cubic) structure, and the f0001g plane of Y with hcp (hexagonal-close packed) structure. For all additional solute elements studied, Zn exhibits the maximum anisotropy and the according effect on the growth behavior of the a-Mg dendrite is the most significant, which could also be reflected by the complex growth patterns of the Mg-Zn alloy dendrite observed in experiments. Compared with Zn, the crystallographic anisotropy of the other additional solutes is weaker, and their effect on the a-Mg dendrite growth is not as significant as Zn, which is reflected by their similar eighteen-primary branch dendritic morphology in 3D. © 2018 Elsevier B.V. All rights reserved.

Keywords: Magnesium alloy a-Mg dendrite Crystallographic anisotropy Additional solute elements Orientation-dependent surface energy

1. Introduction As one of the most lightweight metallic structural materials, magnesium alloys have attracted considerable attentions because they are considered as the promising candidates for materials used in automobile, aeroplane and biomedical research fields [1e5]. The a-Mg dendrite, which forms according to a first order phase transition driving by non-equilibrium thermodynamics and kinetics at the solid/liquid interface, is the primary phase of magnesium alloys [6e9]. Therefore, the microstructural features of the primary a-Mg

dendrite, together with the precipitated phases and impurity segregation, such as the grain size, growth direction and morphological distribution, play important roles in determining the mechanical properties and practical performances of magnesium alloys [10e17]. It has been confirmed that the dendritic microstructure of magnesium alloys is influenced by the additional solute elements [18e21]. For instance, the a-Mg dendrite of most magnesium alloys, including Mg-Al, Mg-Ba, Mg-Ca, Mg-Sn, Mg-Y and Mg-Gd, exhibits a typical eighteen-primary-branch morphology in 3D, among which six grow along < 1120 > in basal plane and the other twelve along < 112x > in non-basal planes, such as < 1123 > and

* Corresponding author. School of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China. ** Corresponding author. School of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China. E-mail addresses: [email protected] (Z. Guo), smxiong@ tsinghua.edu.cn (S. Xiong). https://doi.org/10.1016/j.jallcom.2018.10.145 0925-8388/© 2018 Elsevier B.V. All rights reserved.

< 2245 > (i.e., < 112 2:5 > ) [22e25]. Besides, an apparent dendrite orientation transition (DOT) phenomenon is observed for Mg-Zn alloys [26e28], which is similar to the DOT behavior observed for Al-Zn alloys [29e32]. Such complex growth pattern of the a-Mg

J. Du et al. / Journal of Alloys and Compounds 775 (2019) 322e329

dendrite is further demonstrated by the atomistic simulations based on density functional theory [33,34]. Nevertheless, the underlying reason behind the dendritic growth behavior of magnesium alloys with different additional elements is still unclear to date. During solidification, the dendritic growth orientations and morphological preferences are dependent on the crystallographic anisotropy of both the additional solute and the matrix components, and the final mechanical properties of magnesium alloys generally exhibit distinctions along different crystallographic orientations with respect to the hexagonal symmetry structure [11,14,17,35e40]. In this work, the effect of different additional solute elements on the dendritic growth behavior of binary magnesium alloys is investigated based on the crystallographic anisotropy. These additional elements with different atomic structures, including fcc-Al, bcc-Ba, fcc-Ca, bct-Sn, hcp-Y, Gd and Zn, have significant scientific and technological importance on the development of Mg-based alloys with favorable structure and desired properties. For instance, Al and Zn can enhance the strength and ductility, Sn can improve the ductility, Ca can increase the creep resistance, and the rare elements Y and Gd have advantages in both the microstructures and the properties of magnesium alloys. The microstructure pattern and orientation selection of the a-Mg dendrite is characterized by synchrotron X-ray tomography and electron backscattered diffraction (EBSD) techniques. Quantitative analysis on the orientation-dependent surface energy and related anisotropy of the matrix Mg, the additional solutes X and binary Mg-X alloys, is performed via the first-principles calculations. The strong anisotropy of Zn is found to be responsible for the complex growth patterns of the a-Mg dendrite in Mg-Zn alloys. The crystallographic anisotropy of the other additional solutes is not so significant as that of Zn, and thus their influence on the orientation selection and 3D morphology of the a-Mg dendrite is relatively weaker, as reflected by their similar eighteen-primary-branch dendritic morphologies and preferred growth directions observed in experiment.

2. Model and methodology 2.1. Theoretical method The crystallographic information of both Mg and the additional solute element X (X ¼ Al, Ba, Ca, Sn, Gd, Y and Zn) is referred from Pearson handbook [41] and listed in Table 1. The atomic structure of binary Mg-X alloys is simulated via the solid solution model [11,42], where certain number of the Mg atom is substituted randomly by

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the X atom within the Mg supercell. The atomic configuration for the anisotropic surface energy calculation is constructed using the slab model under periodic boundary condition [43,44]. It has been confirmed that the position of the substituted atoms in the solid solution model do not significantly affect the simulated results on orientation-dependent surface energy [27]. The first-principles calculations are performed within the framework of density functional theory (DFT), as implemented in the Vienna Ab initio Simulation Package (VASP) [45,46]. The interaction between ions and valence electrons is modeled using the projector-augmented wave (PAW) potential [47,48]. The exchange and correlation interaction is described in the local density approximation (LDA) method [49]. The pseudopotential employed in this work treats two valence electrons for magnesium (Mg 3s2), three for aluminum (Al 3s23p1), ten for barium (Ba 5s25p66s2), eight for calcium (Ca 3p64s2), four for tin (Sn 5s25p2), ten for gadolinium (Gd 4f86s2), eight for yttrium (Y 4p54d15s2) and twelve for zinc (Zn 3d104s2). A plane wave cutoff energy of 400 eV is used for the matrix Mg and the additional solute X, and 420 eV for binary Mg-X (X ¼ Al, Ba, Ca, Sn, Y, Gd and Zn) alloys. Brillouin zone integration is modeled using the Monkhorst-Pack k-point mesh [50], and the k-point separation in the Brillouin zone of the reciprocal space is set as 0.01 Å1 for each unitcell. Numerical tests with respect to the supercell size and the computational scheme are performed to ensure the convergence of the DFT-based calculations. The total energy converges to 5  107 eV/atom with respect to electronic, ionic and unitcell. The orientation-dependent surface energy (g), together with the related crystallographic anisotropy, is employed to analyze the dendritic growth behavior. It is defined as the energy required to form a unit area of a certain crystallographic plane [51e53], and can be obtained via:

g¼

En  n*Eb 2*A

(1)

where En is the total energy of the surface slab structure after optimization, n is the atomic layers' number of the surface slab model, Eb is the total energy of the bulk unitcell structure after optimization, A is the surface area of the slab model, and the constant 2 represents the two equivalent surfaces in the slab model. The calculated surface energy is satisfactorily converged to <1  103 eV/Å2 with respect to the slab size, the vacuum thickness and the relaxed atomic layers during optimization, as shown in Supplementary Fig. S1. The computational details for convergence tests of the surface energy are provided in Supplementary Material.

Table 1 Basic information of the matrix Mg and additional solute elements X in binary magnesium alloys, including the crystallographic data, the size of atomic radius (r), the mass density (r), the enthalpy of mixing (DH) between solvent and solute elements, and the solid solubility of the additional element X in the Mg matrix. Element

Lattice structure

Space group

Lattice parameter (Å)

r (Å)

DH (kJ/mol)

r (kg/m3)

Maximum Solubility (at.%)

Reference

Mg

HCP

P63/mmc

Al

FCC

Fm3m

a ¼ 3.2094 a ¼ 3.2065 a ¼ 4.0495

c ¼ 5.2105 c ¼ 5.2256 e

1.60 e 1.43

e e 2

1736.67 e 2698.85

e e 11.58

This work Ref. [41] This work

Ba

BCC

Im3m

a ¼ 4.0502 a ¼ 5.0190

e e

e 2.17

e 4

e 3607.39

e ~0.011

Ref. [41] This work

Ca

FCC

Fm3m

a ¼ 5.5820

e

1.98

6

1530.62

0.48

This work

a ¼ 5.5884 a ¼ 5.7918 a ¼ 5.8197 a ¼ 3.6451 a ¼ 3.6475 a ¼ 3.6315 a ¼ 3.6330 a ¼ 2.6649 a ¼ 2.6650

e c ¼ 3.1227 c ¼ 3.1750 c ¼ 5.7305 c ¼ 5.7307 c ¼ 5.7770 c ¼ 5.7739 c ¼ 4.9468 c ¼ 4.9470

e 1.51 e 1.80 e 2.54 e 1.39 e

e 9 e 6 e 6 e 4 e

e 7525.96 e 4477.84 e 7915.26 e 7136.86 e

e 3.23 e 3.73 e 4.53 e 2.59 e

Ref. [41] This work Ref. [41] This work Ref. [41] This work Ref. [41] This work Ref. [41]

Sn

BCT

I41 =amd

Y

HCP

P63/mmc

Gd

HCP

P63/mmc

Zn

HCP

P63/mmc

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Based on the definition of anisotropy introduced by Miller and Chadwick [38,54e56], the crystallographic anisotropy (a) is determined as the ratio of the orientation-dependent surface energy of a certain fhklg crystallographic plane versus that of the most closely packed crystallographic plane, as expressed by the following formula:

.

a ¼ gcerainfhklg g closest packed

(2)

Relevant benchmark calculations on the bulk phases of both the matrix Mg and the additional solutes X are performed to ensure the accuracy of computational method. The lattice parameters after optimization, together with the experimental values are listed in Table 1. The results indicate that the optimized lattice parameters coincide well with the experimental values [41], confirming that the computational scheme is reliable. 2.2. Experimental method In this work, the binary Mg-30 wt% Gd alloy is employed as a reference to characterize and analyze the microstructure of the aMg dendrite. The samples are prepared by melting pure magnesium (99.95 wt%) and pure gadolinium (99.95 wt%) in a mild steel crucible at 800  C with a protected gas atmosphere of N2 and SF6 mixture [22,23]. The melting alloy is then solidified in a permanent mold (preheated to 300  C) for 30 min and cooled in air. Cylindrical specimens of 10 mm in diameter and 30 mm in height are machined and sealed in a quartz tube with argon as a protective gas and then quenched in water. The final cylindrical samples with 1 mm in diameter and 5 mm in height are then extracted for subsequent synchrotron X-ray tomography and EBSD experiments. The sample is scanned via synchrotron X-ray tomography at the BL13W1 beamline of the Shanghai Synchrotron Radiation Facility (SSRF). The sample is continuously rotated over 180 , during which a high-speed CCD camera is used to record the transmitted intensity of a monochromatic X-ray beam with 22e28 KeV energy to penetrate the sample. The distance between the sample and the CCD camera is 20 cm and the exposure time is one second per projection. An according 900 image slices are collected and further used to reconstruct the dendritic microstructure. The reconstruction is performed in a volume of 20483 with a voxel size of ~0.65 mm. The sample for the EBSD experiment is grinded with SiC paper and electro-polished by a stainless cathode with a DC of 2.5 V voltage and 0.25 A current. The electrolytic solution is a mixture of 35 ml phosphoric acid and 65 ml ethyl alcohol. The electropolishing lasts about 3e4 minutes at ambient conditions. The

EBSD experiment is performed on a TESCAN MIRA3 LMH scanning microscope with HKL Channel 5 system. 3. Results and discussion 3.1. Crystallographic information A graphic illustration for the face-centered cubic (fcc), bodycentered tetragonal (bct), body-centered cubic (bcc) and hexagonal-close packed (hcp) atomic structure of Mg and the additional solute X is shown in Fig. 1aed, and the most closely packed crystallographic planes are marked by red dot lines, like the f111g of fcc Al and Ca, the f010g of bct Sn, the f110g of bcc Ba, and the f0001g of hcp Y, Gd and Zn. The lattice parameters and mass density after optimization are listed in Table 1, together with those available values known from literature. The calculated values coincide well with both experimental and previous theoretical results [41]. Among these additional solute elements, the mass density of the matrix Mg (1736.67 kg/m3) is larger than that of Ca (1530.62 kg/m3) and smaller than that of the other additional solutes. The mass density difference between the matrix Mg and the additional solute Zn (7136.86 kg/m3) and Sn (7525.96 kg/m3) is much more significant than the others, i.e., 75.67% and 76.92%, respectively. In addition to difference of the lattice structure and the mass density, difference also exhibits for the electronic configuration, the size of atomic radius and the enthalpy of mixing (DH) between the matrix Mg and the additional elements X (X ¼ Al, Ba, Ca, Sn, Y, Gd and Zn), which can be used to reflect the interatomic interactions [57e59], as shown in Table 1. 3.2. Typical microstructure of the a-Mg dendrite Fig. 2 shows a typical growth pattern of the a-Mg dendrite for binary Mg-Gd alloys, together with the corresponding dendritic orientation selection. Fig. 2a shows the reconstructed 3D morphology of the a-Mg dendrite based on the 900 image slices captured during the synchrotron X-ray tomography experiment. The growth pattern is further analyzed by cutting the a-Mg dendrite via one horizontal section (P0), and three vertical sections (P1, P2, and P3). The according dendritic pattern profiles with these sections are shown in Fig. 2cef, respectively. The a-Mg dendrite exhibits six primary branches with six-fold symmetry in the P0 section, and twelve primary branches with each four of them in the P1, P2 and P3 sections. As a result, the dendritic morphology exhibits a typical eighteen-primary-branch pattern in 3D, with six growing along the basal directions and the other twelve growing along the

Fig. 1. Schematic illustration for the atomic lattice structure of the additional solutes X in binary Mg-X (X ¼ Al, Ba, Ca, Sn, Gd and Zn) alloys, the corresponding most densely packed crystallographic plane of each lattice structure is labeled by the red dash lines. (a) face-centered cubic (fcc) structure, (b) body-centered tetragonal (bct) structure, (c) body-centered cubic (bcc) structure, and (d) hexagonal-close packed (hcp) structure. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

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Fig. 2. Growth pattern and orientation selection of the a-Mg dendrite of binary Mg-Gd alloys, analyzed by the synchrotron X-ray tomography and the EBSD techniques. (a) the reconstructed 3-D dendritic morphology, (bef) the dendritic pattern profiles with different horizontal and vertical sections, and (g) the dendritic preferred growth directions.

non-basal directions. Based on analysis from the hcp lattice structure, it is clear that the growth orientations of the a-Mg dendrite are < 1120 > or < 1010 > in the basal plane, and < 112x > or < 101x > in non-basal planes. To quantify the dendritic growth directions, the EBSD experiments are performed, results of which are shown in Fig. 2g. The preferred growth direction of the a-Mg dendrite in the basal plane is < 1120 > , while that in non-basal planes is < 1123 > . These experimental findings agree well with the previous work on the dendritic microstructure of other magnesium alloys [22,23]. Accordingly, it is concluded that the 3D morphology of the a-Mg dendrite exhibits a typical eighteenprimary-branch pattern, and the preferred growth directions are < 1120 > and < 1123 > . 3.3. Crystallographic anisotropy and dendritic growth behavior The surface energy and related anisotropy are calculated by performing the first-principles calculations to understand the dendritic growth pattern of different magnesium alloys. During solidification, the evolution of microstructure is determined by both thermodynamic and kinetic effects [35,39,54,60e63]. However, the growth pattern of the dendrite is primarily determined by the thermodynamic effect associated with the underlying lattice structure [36,64,65]. The kinetic effect becomes significant only in rapid solidification with large cooling rate [66,67]. Based on our experiment [15,22,26,27], it is found that for most Mg-based alloys, changing cooling temperature, cooling rate and/or initial concentration of additional elements, would not change the eighteenprimary-branch pattern of the a-Mg dendrite, and the difference only happens to the dendritic morphology of the secondary arms including spacing and size [26,27]. Accordingly, the anisotropic surface energy of both Mg and additional solute elements are calculated based on Eq. (1), results of which are provided in Table 2 and Fig. 3. It is found that the surface energy exhibits an apparent orientation-dependent behavior, and the most densely packed crystallographic planes of different lattice structures are generally those energetically favorable planes with the minimum surface

energy, as exemplified by the f111g plane of fcc-Al, the f110g plane of bcc-Ba, the f010g plane of bct-Sn, and the f0001g basal plane of hcp-Mg, Zn and Y. This result is consistent with previous predictions [38,68e70]. Besides, those crystallographic planes with the same atomic packing density of a certain lattice structure have the same magnitude of surface energy, such as f100g, f010g, f001g and f110g, f101g planes of fcc-Al and bcc-Ba, as reflected in Fig. 3. Comparing with Zn, which has considerable surface energy distinctions between the most close packed f0001g basal plane and other planes [70], the difference of the orientation-dependent surface energy of the other additional elements is not as significant. The crystallographic anisotropy is calculated based on Eq. (2), and the results are provided in Table 2. Fig. 4a shows the correlation between the crystallographic anisotropy and the inter-planar distance of both the matrix Mg and the additional solute X. As reflected that the anisotropy of Zn is higher than that of the other additional elements by almost one order of magnitude. Fig. 4b shows the surface anisotropy difference between Mg and X. The anisotropic difference from the matrix Mg is more significant for Zn [70], which is about two orders of magnitude larger than that for other additional solutes X (X ¼ Al, Ba, Ca, Sn and Y). The strong anisotropy of Zn is responsible for the complex growth patterns of Mg-Zn alloy dendrite observed in experiment [26,27]. Because of a weaker anisotropy strength of other additional elements, the growth pattern and orientation selection of the according a-Mg dendrites exhibit analogous 3D morphology, i.e., an eighteenprimary-branch pattern and the same growth direction within both the basal and non-basal planes [22,23,27]. Nevertheless, the weak anisotropy of different additional solutes still affects the dendritic microstructure, as reflected by the primary arm length and pattern of the secondary and higher order arms [26]. It has been generally accepted that crystal usually grows along those directions with higher surface energy and crystallographic anisotropy [43,71,72]. To further investigate the dendritic growth orientation selection of different magnesium alloys. The surface energy along both basal and non-basal directions of the matrix Mg, the additional solute X and the binary Mg-X alloys are calculated. Because the average composition of solid Mg dendrite is usually

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Table 2 Surface energy g (J/m2) and its anisotropy a referred to the closest-packing crystallographic plane of the additional solute elements X (X ¼ Al, Ba, Ca, Sn, Y and Zn), the matrix Mg, and the binary Mg-X alloys obtained from the DFT-based atomistic calculations. Element

ð100Þ

ð010Þ

ð001Þ

ð101Þ

ð110Þ

Al

g ¼ 1.1112 a ¼ 1.137 g ¼ 0.4185 a ¼ 1.015 g ¼ 0.5663 a ¼ 1.026 g ¼ 0.5961 a ¼ 1.045

g ¼ 1.1112 a ¼ 1.137 g ¼ 0.4184 a ¼ 1.015 g ¼ 0.5662 a ¼ 1.026 g ¼ 0.5703 a ¼ 1.000

g ¼ 1.1112 a ¼ 1.137 g ¼ 0.4185 a ¼ 1.015 g ¼ 0.5664 a ¼ 1.026 g ¼ 0.7211 a ¼ 1.264

g ¼ 1.1771 a ¼ 1.203

g ¼ 1.1772 a ¼ 1.204 g ¼ 0.4121 a ¼ 1.000 g ¼ 0.6417 a ¼ 1.163 g ¼ 0.7151 a ¼ 1.254

Ba Ca Sn

e e e e e e

ð011Þ

ð111Þ

e e

g ¼ 0.4122 a ¼ 1.000

e e

g ¼ 0.6320 a ¼ 1.108

g ¼ 0.9774 a ¼ 1.000 g ¼ 0.5078 a ¼ 1.232 g ¼ 0.5518 a ¼ 1.000 g ¼ 0.7137 a ¼ 1.252

Element

ð0001Þ

ð1010Þ

ð1011Þ

ð1120Þ

ð1121Þ

ð1122Þ

ð1123Þ

ð1124Þ

ð1125Þ

ð1126Þ

ð1127Þ

ð1128Þ

Mg

g ¼ 0.7030 a¼1 g ¼ 0.0969 a¼1 g ¼ 1.1373 a¼1 g ¼ 0.5409 a¼1 g ¼ 0.6400 a¼1

g ¼ 0.7340 a ¼ 1.044 g ¼ 1.1573 a ¼ 11.944 g ¼ 1.1511 a ¼ 1.012 g ¼ 0.6070 a ¼ 1.122 g ¼ 0.6696 a ¼ 1.046

g ¼ 0.7598 a ¼ 1.081 g ¼ 1.1888 a ¼ 12.269 g ¼ 1.1522 a ¼ 1.013 g ¼ 0.7195 a ¼ 1.330 g ¼ 0.8326 a ¼ 1.301

g ¼ 0.8193 a ¼ 1.166 g ¼ 1.4511 a ¼ 14.977 g ¼ 1.1819 a ¼ 1.039 g ¼ 0.7039 a ¼ 1.301 g ¼ 0.8724 a ¼ 1.363

g ¼ 0.8819 a ¼ 1.255 g ¼ 1.3105 a ¼ 13.525 g ¼ 1.3003 a ¼ 1.143 g ¼ 0.7123 a ¼ 1.317 g ¼ 0.8417 a ¼ 1.315

g ¼ 0.8223 a ¼ 1.169 g ¼ 1.3151 a ¼ 13.573 g ¼ 1.2578 a ¼ 1.106 g ¼ 0.7495 a ¼ 1.386 g ¼ 0.8677 a ¼ 1.356

g ¼ 0.8705 a ¼ 1.231 g ¼ 1.4179 a ¼ 14.634 g ¼ 1.2804 a ¼ 1.126 g ¼ 0.7271 a ¼ 1.344 g ¼ 0.8601 a ¼ 1.344

g ¼ 0.8657 a ¼ 1.238 g ¼ 1.3450 a ¼ 13.881 g ¼ 1.2862 a ¼ 1.131 g ¼ 0.7101 a ¼ 1.313 g ¼ 0.8498 a ¼ 1.328

g ¼ 0.9463 a ¼ 1.346 g ¼ 1.1402 a ¼ 11.768 g ¼ 1.2748 a ¼ 1.121 g ¼ 0.7601 a ¼ 1.405 g ¼ 0.9164 a ¼ 1.432

g ¼ 0.7963 a ¼ 1.133 g ¼ 1.3001 a ¼ 13.418 g ¼ 1.3035 a ¼ 1.146 g ¼ 0.6071 a ¼ 1.122 g ¼ 0.7697 a ¼ 1.203

g ¼ 0.8626 a ¼ 1.227 g ¼ 1.1728 a ¼ 12.105 g ¼ 1.2748 a ¼ 1.121 g ¼ 0.5571 a ¼ 1.030 g ¼ 0.6940 a ¼ 1.084

g ¼ 0.8452 a ¼ 1.202 g ¼ 0.7610 a ¼ 7.853 g ¼ 1.2764 a ¼ 1.122 g ¼ 0.5424 a ¼ 1.003 g ¼ 0.6594 a ¼ 1.030

Zn Y Mg-Gd Mg-Al

Fig. 3. Orientation-dependent surface energy of different additional solute elements in binary magnesium alloys. (a) fcc-Al, bcc-Ba, fcc-Ca and bct-Sn, (b) hcp-Zn and hcp-Y, respectively.

Fig. 4. Crystallographic anisotropy of the additional solute elements in binary Mg-X (X ¼ Al, Ba, Ca, Sn, Y and Zn) alloys. (a) shows the correlation between surface anisotropy and inter-planar distance of the matrix Mg and the additional solutes X. (b) shows the magnitude of anisotropic distinctions between the matrix Mg and the additional solutes X.

lower than the nominal composition, the first-principles calculations are limited to dilute Mg-based alloys, whose compositions are

chosen based on the solid solubility of the additional element X in the matrix Mg [11,22]. As shown in Table 1, the selected alloying

J. Du et al. / Journal of Alloys and Compounds 775 (2019) 322e329

content, i.e., 1.56 at% is within the solubility limit of most additional elements (including Al, Sn, Y, Gd and Zn) in the Mg matrix except for Ba and Ca. For the convenience of comparison, the alloy composition is maintained at 1.56 at% to investigate the effect of additional elements on the crystallographic anisotropy of the magnesium alloy dendrite. Fig. 5 shows the according orientationdependent surface energy of the crystallographic planes f101kg and f112kg (k ¼ 1, 2… 8) of the matrix Mg, the additional solute Zn, and the binary Mg-X (X ¼ Gd and Zn) with the hcp lattice structure, respectively. The surface energy along < 112x > is higher than that along < 101x > , indicating that the a-Mg dendrite prefers to grow along < 112x > rather than < 101x > . Accordingly, more attention is focused on those crystallographic planes f112kg and orientations < 112x > of the binary Mg-X alloys in our subsequent investigation. Moreover, the surface energy deceases with the addition of 1.56 at% Gd in the Mg matrix, which can be understood in terms of the difference in the electronic configuration, the atomic size and the enthalpy of mixing (DH) between the additional Gd and the Mg matrix. Theoretically, a larger negative value of DH implies a stronger atomic interaction between the solvent and the solute [57,58]. Such difference alters the surface energy and the according crystallographic anisotropy with respect to dendritic growth. It is worthwhile to mention that the dendritic pattern formation and growth direction is believed to be primarily determined by the thermodynamic associated anisotropic surface energy in terms of

327

the intrinsic lattice structure [36,54,61,70,73]. In this respect, the surface energy of both Mg and binary Mg-X (X ¼ Al, Ba, Ca, Sn, Y, Gd and Zn) alloys along different crystallographic directions is calculated. Fig. 6a shows the correlation between surface energy and inter-planar distance of those high symmetrical low index crystallographic planes, including f0001g, f1010g, f1011g and f1120g. The results indicate that in the basal plane, the surface energy of the f1120g is always larger than that of the f1010g, signifying that the preferred growth direction of the aMg dendrite in the basal plane is < 1120 > rather than < 1010 > . Fig. 6b shows the orientation-dependent surface energy of those low symmetrical high index crystallographic planes, i.e., f112kg with k ¼ 0, 1, …8, where q represents the angle between a certain direction and the principal axis direction, i.e., < 0001 > . These crystallographic planes and directions are schematically illustrated in Fig. 6c. Among these high index f112kg planes, the surface energy of the f1125g plane is the maximum, indicating that its perpendicular direction is the preferred growth orientation of the a-Mg dendrite in non-basal planes. For hcp lattice structure, the crystallographic planes and orientations that perpendicular each other are associated with the axial ratio (c/a) [11,35], e.g. f112kg⊥ < 112x > is correlated via the following formula:

. k ¼ 2xðc=aÞ2 3

(3)

Fig. 5. Anisotropic surface energy of the crystallographic planes f101kg and f112kg (k ¼ 1, 2… 8) of the matrix Mg (a), the additional solute Zn (b), the binary Mg-Gd (c) and Mg-Zn (d) alloys.

Fig. 6. Orientation-dependent surface energy of Mg and binary Mg-X (X ¼ Al, Ba, Sn, Ca, Y, Gd and Zn) alloys. (a) shows the correlation between inter-planar distance and surface energy of the high symmetrical low-index crystallographic planes, including f0001g, f1010g, f1011g and f1120g. (b) shows the orientation-dependent surface energy of those high-index crystallographic planes, i.e. f112kg, k ¼ 1, 2, …, 8. (c) shows the graphic illustration for the corresponding crystallographic planes and orientations of Mg with the hcp lattice structure.

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Fig. 7. Surface anisotropy of pure Mg and binary Mg-X (X ¼ Al, Ba, Sn, Ca, Y, Gd and Zn) alloys. (a) shows the surface anisotropy of the high symmetrical low-index crystallographic planes, including f0001g, f1010g, f1011g and f1120g, while (b) shows that of the low symmetrical high-index crystallographic planes, i.e., f112kg, k ¼ 1, 2, …and 8, respectively.

Accordingly, the preferred growth direction for the a-Mg dendrite in non-basal planes is < 1123 > . Based on Eq. (2), the corresponding anisotropy of both Mg and binary Mg-X (X ¼ Al, Ba, Sn, Ca, Y, Gd and Zn) alloys is obtained and the results are shown in Fig. 7. It is found that in the basal plane, < 1120 > has higher anisotropy than < 1010 > , and in non-basal planes, the crystallographic anisotropy of < 1123 > is higher than that of the other directions, as also reflected in Fig. 7a and b, respectively. Accordingly, the a-Mg dendrite prefers to grow along < 1120 > in the basal plane and < 1123 > in non-basal planes. Remarkably, these theoretical predictions for the preferred growth direction of the aMg dendrite is in good agreement with the experimental findings [22,23,26,27].

Acknowledgements This work is financially supported by the National Natural Science Foundation of China (51701104), the National Key Research and Development Program of China (2016YFB0301001), the Postdoctoral Science Foundation of China (2017M610884), the Tsinghua University Initiative Scientific Research Program (20151080370), the Tsinghua Qingfeng Scholarship (THQF2018-15), and the UK Royal Society Newton International Fellowship Scheme. The authors acknowledge the supports from Shanghai Synchrotron Radiation Facility for the provision of beam time, and the National Laboratory for Information Science and Technology in Tsinghua University for access to supercomputing facilities. Appendix A. Supplementary data

4. Conclusion In summary, the effect of the additional elements X with different atomic lattice structure, including fcc-Al, bcc-Ba, fcc-Ca, bct-Sn, hcp-Y, Gd and Zn, on the growth behavior of the a-Mg dendrite is investigated in terms of the crystallographic anisotropy. Results show that the growth direction and pattern formation of the a-Mg dendrite are highly dependent on the crystallographic anisotropy of the additional solutes. For all of these elements, the most closely packed crystallographic planes are generally those energetically favorable planes with a minimum magnitude of surface energy, such as the f111g of fcc-Al, the f110g of bcc-Ba, and the f0001g of hcp-Y. The crystallographic anisotropy is thus determined as the surface energy ratio of a certain crystallographic plane versus the most closely packed plane. Accordingly, it is found that the crystallographic anisotropy of the additional Zn is one order of magnitude larger than that of the other additional solutes, which is responsible for the complex growth patterns of Mg-Zn alloy dendrite observed in experiments. The other additional solutes are associated with relatively small anisotropy, and their effects on the dendritic growth behavior are not as significant as Zn, as reflected by their analogous eighteen-primary-branch dendritic morphology and dendritic preferred growth directions in both the basal and non-basal planes. The results of our investigation offers deep insight into understanding the effects of additional solutes on the hcp a-Mg dendrite growth, and thus provides theoretical guidance for the developments of new magnesium alloys with desired microstructure and favorable performances.

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