Electronic and structural properties of low-index L12–Al3Zr surfaces by first-principle calculations

Calphad 66 (2019) 101645

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Electronic and structural properties of low-index L12–Al3Zr surfaces by firstprinciple calculations

T

Tianxing Yanga, Xiujun Hanb,*, Zongye Dinga, Yuanxu Wangc, Jianguo Lia a

Laboratory of Advanced Materials and Solidification, School of Materials Science and Engineering, Shanghai Jiao Tong University, 200240, Shanghai, PR China School of Materials Science and Engineering, Qilu University of Technology, Jinan, 250353, Shandong, PR China c Institute for Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng, 475004, PR China b

A R T I C LE I N FO

A B S T R A C T

Keywords: L12 –Al3Zr First-principles calculation Surface energy Atomic relaxation

The atomic relaxations, electronic properties and surface energies of low index L12-Al3Zr surfaces were studied by using the first-principles method based on the density functional theory. Five low index surfaces with different terminations are studied systematically. The study shows that atomic relaxations occur mainly within the outermost two layers. The stoichiometric (111), non-stoichiometric (110) and (001) surfaces with different terminations are investigated. The (111) surface which has the lowest surface energy and is independent on the chemical potential of Al atom is found to be the most thermodynamically stable surface. For the non-stoichiometric surfaces, the AlZr terminated (001) surface and Al terminated (110) surface are metastable under an Zrrich and Al-rich condition respectively. These results are in consistant with the results of density of states. The lattice misfit between α-Al and L12-Al3Zr is not more than 1.65% by our calculation, indicating L12-Al3Zr is a potent effective heterogeneous nucleating agent for α-Al.

1. Introduction ―During the past decades, Al-based alloys have attracted considerable attentions because of their good thermal stability, high strength, low density, and high melting point [1–3]. As a promising structural and a functionally graded material, the ordered Al-rich transition metal trialuminide Al3Zr, with tetragonal D023 structure, has been investigated extensively [4–10]. One important application of Al3Zr is that it can be used as a grain refiner of Al alloys. It has been found that with the addition of Zr the properties of aluminum alloys could be improved significantly [11–14]. In these Al alloys doped with Zr, Al3Zr precipitates at nanometer scale were observed and thought to contribute to the grain refinement. It should be noted that the Al3Zr precipitate exhibits a metastable cubic L12 structure, which is quite different from its ground state of tetragonal D023 structure. Due to the feature of metastable state, the experimental study of L12-Al3Zr is quite difficult, although it could be stabilized by the addition of the third element, such as Cu, Ni and Mn by mechanical alloying [1]. Up to now, why the metastable L12-Al3Zr could refine the grain size of Al alloys is still unclear. We now only know that there is a small lattice mismatch between L12-Al3Zr and α-Al [14,16]. Until now, there is little information about the surface properties and stability of L12-Al3Zr. It has been demonstrated that the

*

surface properties, such as surface energy, electronic properties and surface relaxations, play key roles in understanding the bonding of two heterogeneous phases [15], which is the essential issue in the grain refinement. Therefore, it’s crucial to study the properties of different L12-Al3Zr surfaces to elucidate its grain refinement mechanism. The first principle methods have been widely employed to study the surface properties of many systems and some novel results have been obtained. Recently, the properties of low indexed surfaces of Al3Sc [39] and Al3Nb [40] were investigated intensively. The results showed that the (001)-AlSc terminated and (111) surfaces of Al3Sc are thermodynamically stable, while for Al3Nb the (110)-Al terminated and (111) surfaces are more stable. The bulk properties of L12-Al3Zr have been studied by using first principle calculations. And some experimental and theoretical works have been focused on the structural stability, and mechanical properties [17–20]. These results give us deeper insights into the properties between the bulk and intrinsic crystal. However, there is no available information about the properties and stabilities of L12-Al3Zr surfaces. In this research, the atomic relaxations, electronic structures and surface energies of low index surfaces with different terminations of L12-Al3Zr have been studied. The rest of this paper is organized as follows: in Section 2, we describe the computational methods. The bulk properties, atomic relaxations, electronic and surface properties of low

Corresponding author. E-mail address: [email protected] (X. Han).

https://doi.org/10.1016/j.calphad.2019.101645 Received 8 March 2019; Received in revised form 8 June 2019; Accepted 8 July 2019 Available online 15 July 2019 0364-5916/ © 2019 Elsevier Ltd. All rights reserved.

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experimental lattice constant was a = 4.08 Å [28]. In Table 1, the lattice constants, elastic constants and bulk modulus of pure Al, pure Zr and L12-Al3Zr are presented. The results of the PBE functional are in good agreement with other theoretical and experimental data, which means that the PBE functional can ensure the precision of our studies. So, PBE functional is applied in the following calculations. To estimate the stability, the formation enthalpy of L12–Al3Zr is calculated as,

index surfaces are given in Section 3. And we end with a summary in Section 4. 2. Computational details All the first-principle calculations in this work were performed using the plane-wave pseudopotential based on the density functional theory (DFT), as implemented in the Cambridge sequential total energy package (CASTEP) code [21,22]. The valence electrons considered in their pseudopotential were described by Al 3s23p1 and Zr 4s24p64d25s2 respectively. By solving Kohn–Sham equation [23] with the self-consistent field (SCF) procedure, the ground state can be found; And the SCF convergence threshold was set 5.0 × 10−7 eV/atom. The Broyden–Fletcher–Goldfarb–Shannon (BFGS) [24] algorithm was iterated to achieve the geometry optimization. In BFGS minimization, the convergence tolerances for the energy, force, stress and displacement were set as 5.0 × 10−6 eV/atom, 0.01 eV/Å, 0.02 GPa and 5 × 10−4Å, respectively. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional [26], the local-density approximation (LDA) [25], and Perdew-Wang-91 functional (PW91) [27] were utilized and evaluated at the first step by calculating the bulk properties of L12-Al3Zr, pure Al and pure Zr, such as lattice constant and elastic constants and bulk modulus. The Monkhorst–Pack scheme was used for K point sampling in the first irreducible Brillouin zone (BZ). The K points separation in the Brillouin zone of the reciprocal space were 25 × 25 × 25 for bulk fcc-Al, 20 × 20 × 15 for bulk hcp-Zr, 25 × 25 × 25 for bulk L12-Al3Zr and 25 × 25 × 1 for all the surfaces. The plane wave energy cutoff of 350eV was used for Al(fcc), L12-Al3Zr and the following surface calculations, and a larger cutoff of 550eV was used for Zr(hcp). The plane slab method was used to model the slab supercell, and a vacuum region of 15 A was included to eliminate the interactions between surface atoms. The low-index surfaces of (001), (110) and (111) were discussed in this work.

ΔHAl3 Zr = (EAl3 Zr − 3EAl − EZr )/4

(1)

where EAl3 Zr is the total energy of a L12–Al3Zr unit cell, and EAl, EZr are the respective total energy of a bulk Al and Zr atom. The calculated formation enthalpy of L12–Al3Zr and other reference values are given in Table 2. It’s clear to see that the value of the formation enthalpy has a negative value, which means the interaction between Al and Zr atoms is strong, and thus the Cu3Au-type L12–Al3Zr is stable. To characterize the electronic structure and the bonding of the crystal, the density of states (DOS) and the charge density difference of L12-Al3Zr are computed, and the results are presented in Figs. 2 and 3, respectively. Obviously, the density of states at Fermi level (Ef), marked as dashed line in Fig. 2, is not zero, which is an indication of the metallic feature of L12–Al3Zr. The total density of states is mainly contributed by Zr-4d and Al-3p, and there is an obvious pseudogap near the Fermi level, which characterizes the strong covalent bonding. From the charge density and its difference illustrated in Fig. 3, we can clearly see the strong covalent and metallic interaction between Al and Zr atoms. 3.2. Structural relaxations of L12-Al3Zr The five relaxed surfaces are constructed in this work as follows: the stoichiometric AlZr-terminated (111) surface, the non-stoichiometric (001) and (110) surfaces, which both have AlZr-terminated and Alterminated surfaces, as illustrated in Fig. 4. All these five surfaces are symmetric, and the topside layer is defined as the first layer. Some parameters are defined to quantitatively characterize the degree of the relaxation. For each atom, the relaxation degree is defined by:

3. Results and discussion 3.1. Bulk properties of L12-Al3Zr

ΔZ = z − z 0 Firstly, we calculated the bulk structure of cubic Al3Zr. As shown in Fig. 1, the crystal structure belongs to the Cu3Au-type, with a symmetry of Pm-3m (space group). And the Al atoms occupy the 3c(0, 0.5, 0.5) Wyckoff positions, while the Zr atoms occupy 1a(0, 0, 0). The

and

δz = ΔZ/d0 × 100% where z and z0 are the z coordinate after and before relaxation, and (d0 is the bulk interlayer distance. A positive ΔZ indicates that the atom moves towards the vacuum side, while a negative value means the atom move towards the bulk. The interlayer space dij(j = i+1) represents the average distance between the ith and jth layer. And Δdij is calculated as (di,j − d0)/d0 × 100. The distance between the two layers will extend if Δdij is positive, which is called interlayer expansion. Especially, the rumpling phenomenon [33] will occur if one layer contains both Al and Zr atoms, which means the two kinds of atoms move in the opposite direction. Then the parameter ri = (z iZr − z iAl ) /d0 × 100% is defined to explain the rumpling phenomenon, where z iZr and z iAl are the average z value of Zr and Al atoms in the ith layer, respectively. All the parameters mentioned above for different surfaces are listed in the tables from Tables 3–7. For all these five surfaces, it’s clear to find that the atomic displacements of the first two layers are obviously larger than the interior ones. For the AlZr-terminated (001), AlZr- terminated (110) and (111) surfaces, the largest relaxations occur in the first layer; while for the Alterminated (001) and (110) surfaces, they occur to the second layer. For the AlZr-terminated and Al-terminated (001) surfaces, the interlayer reduction appears in all layers except the second layer of the former surface and the first layer of the latter surface. The relaxation of the Al atom in the AlZr-terminated (001) surface is larger than that of the Zr atom, while for the Al-terminated (001) surface the result is reversed.

Fig. 1. Crystal model of L12–Al3Zr. The gray and purple balls stand for the Zr and Al, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 2

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Table 1 The lattice constants, elastic constants and bulk modulus of pure Al, pure Zr and Al3Zr.

Al

Zr

Al3Zr

PBE PW91 LDA Cal. [29] Expt. PBE PW91 LDA Cal. [30] Expt [31] PBE PW91 LDA Cal [20] Cal [19]

a(Å)

c(Å)

C11(GPa)

C12(GPa)

C13(GPa)

C33(GPa)

C44(GPa)

C66(GPa)

B(GPa)

4.049 4.050 3.97 4.048 4.05 3.23 3.225 3.146 3.232 – 4.117 4.113 4.029 4.111 4.096

– – – – – 5.173 5.176 5.081 5.173 – – – – – –

116.1 114.2 130.7 105.6 107 154.2 154.7 154.8 152.73 155.4 167.6 169.1 198.6 184.8 185.7

55.8 52.9 59.6 63.05 61 53.7 55.6 62.5 55.75 67.2 60.1 60.8 67.0 59.9 59.2

– – – – – 65.8 70.4 80.8 65.39 64.6 – – – – –

–

41.2 38.6 45.8 33.29 28 25.9 27.3 17.4 26.23 36.3 69.5 69.1 84.4 72 62.7

– – – – – 50.2 49.5 46.1 45.25 44.1 – – – – –

75.9 73.3 83.3 77.2 76 93.3 95.7 102.5 93.22 97.3 95.9 94.9 110.9 101.5 103.1

– – 163.6 163.6 178.1 161.74 172.5 – – – – –

Table 2 The calculated formation enthalpies(ΔH) of L12–Al3Zr. Intermetallic

L12-Al3Zr

ΔH(kJ/mol)

others

PBE

PW91

LDA

−45.192

−45.391

−47.850

−44.417 [18]

−44.760 [19]

Fig. 2. Total density of states of L12–Al3Zr.

Fig. 3. The charge density and charge density difference of L12–Al3Zr crystal. (a) the charge density (b) the charge density difference.

3

−44.6 [32]

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Fig. 4. Low index surfaces of L12–Al3Zr crystal (a) AlZr terminated (001) (b) Al terminated (001) (c) AlZr terminated (110) (d) Al terminated (110) (e) (111). The first four layers of AlZr terminated (001) surface we defined are shown, which are the same for the rest surfaces. Z direction is the relaxation direction. Table 3 Atomic relaxation of (001)-AlZr surface.

Table 6 Atomic relaxation of (110)-Al surface.

Layer

Atom

ΔZ(Å)

δz(%)

ri(%)

Δdij(j = i+1)(%)

Layer

Atom

ΔZ(Å)

δz(%)

ri(%)

Δdij(j = i+1)(%)

1

Al Zr Al Al Zr Al

0.1482 −0.0681 0.0680 0.0312 0.0236 0.0377

7.195 −3.306 3.302 1.517 1.146 1.834

−10.502

−1.413

1 2

0 −5.033

3.095 −1.335

0

−0.038

−2.165 13.590 −5.340 0.952 0.373 −4.660 −0.809 −1.288 0.389

−6.290 3.172

1.915 −0.558

−0.0315 0.1978 −0.0777 0.0138 0.0054 −0.0678 −0.0117 −0.0187 0.0056

0 −18.931

0 −0.371

Al Al Zr Al Al Zr Al Al Zr

0 1.677

−0.359 −1.128

2 3 4

3 4 5 6

Table 4 Atomic relaxation of (001)-Al surface. Layer

Atom

ΔZ(Å)

δz(%)

ri(%)

Δdij(j = i+1)(%)

1 2

Al Al Zr Al Al Zr Al

0.0269 0.0225 −0.0930 −0.0310 −0.0080 −0.0238 0.0243

1.306 1.095 −4.516 −1.505 −0.393 −1.159 1.179

0 −5.612

2.961 −0.261

0 −0.766

−0.784 −2.011

0

−1.482

3 4 5

Table 7 Atomic relaxation of (111) surface. Layer

Atom

ΔZ(Å)

δz(%)

ri(%)

1

Al Zr Al Zr Al Zr Al Zr

0.1885 −0.1236 0.0448 −0.0801 0.0102 −0.0015 −0.0098 0.0449

7.932 −5.202 1.884 −3.370 0.430 −0.065 0.414 1.892

−13.134

4.078

−5.254

0.263

−0.495

−0.476

1.478

0.287

2 3 4

Table 5 Atomic relaxation of (110)-AlZr surface. Layer

Atom

ΔZ(Å)

δz(%)

ri(%)

Δdij(j = i+1)(%)

1

Al Zr Al Al Zr Al

0.1607 −0.0759 0.1419 0.0068 0.0332 0.0016

11.040 −5.218 9.751 2.286 0.472 0.113

−16.258

−6.839

0 −1.814

8.371 1.266

0

2.746

2 3 4

Δdij(j=i+1)(%)

Except the first layer of the AlZr-terminated (110) and the third layer of the (111) surface, all the other layers have an interlayer expansion. For the Al-terminated (110) surface, the second and third layers have an interlayer expansion, and the rest layers have an interlayer reduction. We can clearly find that (110) surfaces have a larger interlayer expansion or reduction than the (001) and (111) surfaces. This means that the (001) and (111) surfaces may be more stable than the (110) surfaces. 4

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As illustrated in Tables from 3–7, if there are both Al and Zr atoms in one layer, the atomic relaxations therein are antisymmetric, the Al atoms moving toward the vacuum but Zr atoms toward the bulk, or vice versa. Obviously, for the AlZr-terminated (001), (110) and (111) surfaces, the Al atoms in the first layer move outwards, whereas the Zr atoms move inwards. For the (001) AlZr terminated surface, the Al atoms in the first layer move outwards with a distance about 7.195% of the interlayer space of bulk crystal in z axis, while for the Zr atoms it is about 3.3% in the opposite direction. For the case of (111) surface, the displacements for Al and Zr atoms are respective 7.068% and 8.742%, but in the opposite directions. The opposite directions for Al and Zr atoms in one layer will result in the rumpling of the surface. The rumpling of the five surfaces are mainly concentrated in the first and second layers. The ri value decreases fast from the first layer to the interior ones. It means that, with the increasing No. of atomic layer of the surface, the influence of the rumpling will decrease, and the surface will be more stable. Compare the values of ri and Δdij from these tables, we can also conclude that the (001) and (111) surfaces are more stable than the (110) surfaces.

γs =

1 slab slab (Eslab − NAl × μAl − NZr × μZr − PV − TS ) 2A

(2)

where A is area of the surface unit cell, Eslab is the total energy of a fully slab slab relaxed surface slab, μAl and μZr are the chemical potential of Al or Zr atoms in a surface slab, NAl and NZr are the respective total number of Al and Zr atoms in the slab, and P, V, T, and S represent the pressure, volume, temperature, and entropy of the system, respectively. At 0K and the low pressure conditions, the TS equals 0 and PV can be neglected. If we assume that the Al3Zr surface is in equilibrium with bulk Al3Zr bulk slab slab μAl = 3μAl + μZr 3 Zr

(3)

is the chemical potentials for bulk Al3Zr, then the γs can be where expressed as bulk μAl 3 Zr

γs =

1 slab + (3NZr − NAl ) × μAl (Eslab − NZr × μAlbulk ) 3 Zr 2A

(4)

Because it’s difficult to calculate accurately the chemical potential slab ), we use the method in Ref. [33] to get rid of this of Al in the slab ( μAl trouble. And the surface energies for stoichiometric (3NZr = NAl ) and non-stoichiometric surfaces (3NZr ≠ NAl .) can be obtained by the following equations,

3.3. Electronic structure of the surfaces In order to clarify the electronic structure of the L12–Al3Zr surfaces, the total densities of states (TDOS) and the partial densities of states (PDOS) of the five surfaces, namely, the (001)-AlZr, (001)-Al, (110)AlZr, (110)-Al and (111) surfaces, are calculated, and the results are presented in Fig. 5. The energy zero represents the Fermi level (Ef). Generally, the TDOS of the five surfaces have significant changes, compared with the TDOS of the bulk L12–Al3Zr. For the surface layer, whatever Al-terminated or AlZr-terminated, the PDOS is different from the inner layer’s. This is because the atoms at the surface layer has a new environment, and their properties will be easily disturbed. However, the PDOS of the inner layer, containing two kinds of atoms or only Al atoms, is similar to the TDOS of the surface. For AlZr-terminated (001) and (110) surfaces, as respectively shown in Fig. 5a and b, the surface and the third layers contain both Al and Zr atoms. The PDOS of these two layers are mainly contributed by the Al3p and Zr-4d electrons, but the PDOS of surface layer shifts to the Fermi level. For the second and fourth layer, which only contains Al atoms, their PDOS are similar to each other. From Fig. 5c and d we can get the same conclusion for Al-terminated (001)-Al and (110)-Al surfaces. For the stoichiometric and non-polar (111) surface, all layers contain both Al and Zr atoms, the PDOS are demonstrated in Fig. 5e. It’s easy to find that the PDOS of the four layers is quite similar to the TDOS of (111) surface. However, the surface layer shows a different behavior of PDOS. The peak under Fermi level shifts significantly to the Fermi level. It is understandable, since the surface layer forms the surface, whereas the other inner layers are more like the bulk Al3Zr. It may be caused by the fact that the co-existence of Al and Zr atoms on the surface layer will effectively compensate the dangling bonds and reduce the influence from the environment. The parameter Δ was defined to illustrate this energy difference between the local minimum and the Fermi level, and it was shown in Table 9. The TDOS of these five surfaces show that the occupied states at Fermi level are at or near the local minimum for the AlZr-terminated (001), Al-terminated (110) and (111) surfaces. Therefore, these surfaces are more stable than the other two surfaces.

γsto =

1 (Eslab − NZr × μAlbulk ) 3 Zr 2A

γnon − sto =

1 Al AlZr Al AlZr bulk + Eslab − (NZr + NZr ) × μAl [Eslab ] 3 Zr 4A

Al Eslab and

(5) (6)

AlZr Eslab

are the total energy of the Al-terminated and AlZrwhere AlZr Al terminated surfaces after relaxation, NZr and NZr are the total number of Zr atoms in the Al- and AlZr- terminated surfaces, respectively. The energies for the stoichiometric surfaces calculated by Eqs. (4) and (5) are given in Table 8. The surface energies of these three surfaces follow the sequence of (110) > (001) > (111). So, the structural stability of Al3Zr surfaces from strong to weak is (111) > (001) > (110), which agrees well with the general rule mentioned in Ref. [36], and also shows the (111) surface is the most stable. In this work, the definition given by Refs. [37,38] is used for calculating the surface energies of the five surfaces. The chemical potential of bulk Al3Zr is related to its formation enthalpy ΔH f0 , bulk bulk bulk μAl = 3μAl + μZr + ΔH f0 3 Zr

(7)

Combining Eqs. (3) and (7), we can get bulk μZr

slab bulk slab − μZr + ΔH f0 = 3(μAl − μAl )

(8)

The formation enthalpy of L12–Al3Zr is negative, as listed in Table 2, and the chemical potentials for the two species in surfaces must be smaller than their respective values in the bulk phases. Therefore, bulk slab slab bulk μZr − μZr > 0 and μAl − μAl <0

(9)

It’s easy to get the following relationship,

1 slab bulk ΔH f0 < μAl − μAl <0 3

(10)

Combining Eqs. (4) and (10), we can get the surface energy for nonslab bulk , stoichiometric surfaces of L12–Al3Zr with the variation of μAl − μAl

γnon − sto = 3.4. Surface energies of low index surfaces The thermodynamic stability of surfaces is usually studied by the surface energy, γs. For the surface system, which is modeled by a slab with two equivalent surfaces, the surface energy can be defined as [34,35]:

1 bulk slab bulk + (3NZr − NAl )(μAl + (μAl − μAl )) ] [Eslab − NZr × μAlbulk 3Zr 2A (11)

According to Eqs. (3) and (11), we can obtain the energies for the stoichiometric (111) surface and the rest non-stoichiometric surfaces. The calculation results are presented in Fig. 6. It’s clear to conclude that, for the stoichiometric (111) surface, its surface energy is 5

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Fig. 5. The total DOS and layer partial DOS of low index surfaces of L12–Al3Zr crystal. (a) (001)-AlZr (b) (001)-Al (c) (110)-AlZr (d) (110)-Al (e) (111). The arrow in each subgraph indicates the local minimum near the Fermi level. Table 8 Surface energies of L12–Al3Zr calculated by the method of Ref. [37] (unit is J/ m2). Surface

(001)

(110)

(111)

γ

1.36

1.39

0.929

Table 9 The energy difference between the local minimum and the Fermi level in Fig. 5.

Δ(eV)

(001)-AlZr

(001)-Al

(110)-AlZr

(110)-Al

(111)

−0.01

−0.64

−0.38

−0.33

−0.25

of the ΔμAl , whereas the values for the Al-terminated surfaces decrease. The stability for the low index surfaces of L12–Al3Zr could be concluded from the surface energies. The stability under Al-rich condition is: (111) > (110)-Al > (001)-Al > (001)-AlZr > (110)-AlZr, while under the Al deficient condition, the sequence is changed as: (111) > (001)-AlZr > (110)-AlZr > (110)-Al > (001)-Al.

independent to the chemical potential of Al, and it’s the smallest among these surfaces, which means the (111) surface is the most stable one. For the four non-stoichiometric surfaces, the surface energies are rebulk lated to the variation of ΔμAl = μslab Al − μAl . For instance, the surface energies of the AlZr-terminated surfaces increase with the enhancement 6

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as Al, which is quite significant for understanding the grain refinement mechanism of L12-Al3Zr. Conflicts of interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work is sponsored by National Key Research and Development Program of China (Grant Nos. 2016YFB0701202, 2017YFB0305300) and National Natural Science Foundation of China (Grant Nos. 51671134, 51671133, and 51171115). References Fig. 6. Relationships between surface energy of L12–Al3Zr and ΔμAl , only (111) is stoichiometric surface, and the other four surfaces are non-stoichiometric.

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Obviously, the stoichiometric (111) surface is most stable. But under an Al-rich or Zr-rich conditions for non-stoichiometric surface, a Al-terminated (110) or AlZr-terminated (001) surfaces are relatively more stable. These results agree well with atomic relaxations reported in 3.2. 3.5. Analysis on L12-Al3Zr as heterogeneous nucleation of α-Al The Bramfitt misfit theory [41] for heterogeneous nucleation shows that the mismatch for the most effective nucleus is less than 6%. And the lattice misfit between α-Al and L12-Al3Zr is not more than 1.65% by our calculation, which means L12-Al3Zr is a potent effective heterogeneous nucleating agent for α-Al. The surface and interface properties of heterogeneous nucleating agent play a key role during the heterogeneous nucleation process [42]. Experiment show that the grains with the lowest surface energy is easier to form and grow [43]. Compared with our results, under the Zr rich condition, L12-Al3Zr (111) surface and the AlZr terminated (001) surface have the lowest and the second minimum surface energy, indicating the grains with these two surfaces are easier to form. And the interface properties of Al(001)/L12-Al3Zr (001) [44] and Al(111)/L12-Al3Zr(111) [45] have been detected and studied experimentally in different Al-alloys during the heterogeneous nucleation process, which also shows that these two surfaces are easier to form and play a key role in refining the α-Al. The calculated results of surface energy in this study can provide a theoretical method to evaluate the more suitable surfaces for the grain refiner of heterogeneous nucleation. 4. Conclusion The first-principle calculations based on density functional theory were applied to study the electronic and structural properties of the low-index surfaces of L12–Al3Zr. In the present work, we calculated the atomic relaxation, density of states and surface energies for five different surfaces. The calculated surface energy indicates that (111) surface is most stable among these surfaces. This conclusion is consistent with the studies of atomic relaxation and density of states. For the non-stoichiometric, the stability sequence under Zr-rich conditions is (001)-AlZr > (110)-AlZr > (110)-Al > (001)-Al, while under Alrich conditions it changes to (110)-Al > (001)-Al > (001)AlZr > (110)-AlZr. From the calculation of surface energy, it allows us to control the chemical reactivity of different surfaces by varying the chemical potential of different elements for preparation. The results in this work is quite meaningful to the further study on the energetics and structure of the interface formed by L12-Al3Zr and other materials, such 7

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