- Email: [email protected]
Al2CO interfaces
Applied Surface Science 285P (2013) 879–884
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
First-principles calculations on Mg/Al2 CO interfaces F. Wang, K. Li ∗ , N.G. Zhou School of Mechanical and Electrical Engineering, Nanchang University, Nanchang 330031, China
a r t i c l e
i n f o
Article history: Received 1 July 2013 Received in revised form 2 September 2013 Accepted 2 September 2013 Available online 12 September 2013 Keywords: First-principles calculation Interface Al2 CO Grain refining Magnesium alloy
a b s t r a c t The electronic structure, work of adhesion, and interfacial energy of the Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface were studied with the first-principles calculations to clarify the heterogeneous nucleation potential of Al2 CO particles in Mg melt. AlO-terminated Al2 CO(0 0 0 1) slabs with seven atomic layers were adopted for interfacial model geometries. Results show that the “Over O” stacking interface is more stable than the “Over Al” stacking interface due to the larger interfacial adhesion and stronger mixed ionic/metallic bond formed across the interface. The calculated interfacial energies of Mg/Al2 CO depend on the value of Al + C , proving Al2 CO particles can exist stably in Mg–Al alloys melt and become effective nucleation substrate for ␣-Mg grain under certain conditions. The above calculation and corresponding analysis provide strong theoretical support to the Al2 CO nucleus hypothesis from interfacial atomic structure and atomic bonding energy considerations. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Magnesium alloys have the advantages of light weight, high strength, excellent damping vibration capacity and good machinability [1,2]. However, during the production of magnesium alloys cast parts, the casting flaws such as porosity, segregation and hot tearing are common due to the coarse primary dendrite Mg grain. Therefore, how to control the solidification behavior of magnesium alloys, to decrease the grain size and casting flaw, and to improve the quality and property of the casting ingot are critical for expanding the application scope and developing high-performance magnesium alloys [3–5]. Presently, the study on the refinement mechanism of casting structure of magnesium alloys mainly focuses on the promoting of exogenous particles on nucleation, the inhibition of grain growth and the effect of solute on the nucleation rate [5]. Among grain refining approaches developed for Mg–Al based alloys, carbon inoculation by introducing carbon powder [6] or different carbon-containing compound, such as C2 Cl6 [7], SiC [8] and MgCO3 [9], is one of the major and effective one. The most commonly accepted grain refinement mechanism of carbon inoculation is Al4 C3 nucleus hypothesis [10,11], which was used to explain the excellent grain refining performance of carbon inoculation process. In addition, some experimental works [6,8,10] reported that particles containing Al, C, O elements were easily observed in the central
∗ Corresponding author at: School of Mechanical and Electrical Engineering, Nanchang University, 999 Xuefu Road, Honggutan District, Nanchang 330031, China. Tel.: +86 18970029945; fax: +86 79183969622. E-mail address: [email protected] (K. Li). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.09.006
region of ␣-Mg grain, and thus the Al2 CO hypothesis was proposed as another reasonable mechanism to explain the grain refinement of Mg–Al base alloys. It was discovered in earlier researches [12,13] that Al2 CO is the intermediate products in the sequence of transformations Al2 O3 → Al4 O4 C → Al2 CO → Al4 C3 . The nucleation potency of a potential heterogeneous substrate depends on the interfacial atomic structures and energy between the nucleating crystal and substrate [14]. The interfacial structure between Al4 C3 and ␣-Mg has been investigated and discussed according to the lattice disregistry theory [10] and the edge-to-edge matching model [15] from a crystallographic point of view. Our previous work [16] within an energy framework also demonstrated that Al4 C3 particles can act as heterogeneous nucleus for magnesium grains. As for Al2 CO, calculations in Ref. [15] revealed that the inter-atomic spacing matching along the close-packed rows between Mg1 0 1 0 and Al2 CO0 0 0 1 is 8.65 and the d-value mismatches between close-packed planes in Mg(0 0 0 2) and Al2 CO(0 0 0 2) is only 2.5, indicating that Al2 CO can act as effective nucleating substrate of ␣-Mg and is even superior to A14 C3 . This prediction is consistent with most experimental results recently [6,8]. Additionally, the deeper identification of interfacial structures at the atomic scale and theoretical calculations of the interfacial energy are necessary to demonstrate the nucleation potency of Al2 CO particles for ␣-Mg grain. However, it is difficult to quantitatively measure the interfacial energy with experimental method at present. In recent years, the first-principles methods have been successfully applied to investigate the stabilities of compound surfaces with different atomic termination [17], predict the interfacial energy and the interfacial structure between primary phase and
880
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
Table 1 Structure parameters of Al2 CO phase. Phase Al2 CO
Structure Trigonal/rhombohedra
Atom number in cell 2Al, 1C, 1O
heterogeneous nucleus, such as Mg/A14 C3 , Al/TiB2 , Al/AlB2 and Si/AlP [16,18–20]. In this work, Mg(0 0 0 2)/Al2 CO(0 0 0 1) interfacial properties are studied using the first-principles method, and the stability and refinement performance of Al2 CO particles in Mg melt is also discussed within an energy framework based on the calculations. 2. Computational methodology All calculations in this work were performed by using a total energy plane-wave pseudo-potential method based on the Density Functional Theory (DFT) [21]. The BFGS algorithm [22] is the recommended algorithm to reach the minimum total energy of the system and the ultrasoft pseudo-potential [23] was used to describe the interactions between ionic core and valence electrons. The generalized gradient approximation (GGA) of PBE approach [24,25] was chosen for exchange-correlation energy calculations. The planewave energy cutoff was selected as 310 eV. The Monkhorst–Pack k-point grid employed 3 × 3 × 1 for the interface calculation of Al2 CO. All atoms were relaxed to their equilibrium positions when the total energy changes during the optimization finally converged to less than 2 × 10−5 eV/atom, the forces on each atom were converged to 0.05 eV/Å, the stress on each atom was converged to ˚ More 0.1 GPa, and the displacement was converged to 0.002 A. details of the computational method can be found in our previous work [26].
Group(No.)
Atom site
P63mc(186)
Al1(0.333, 0.667, 0) C/O(0.333, 0.667, 0.3821)
Mg(0 0 0 2) slab with five atomic layers was adopted in the following interface geometries. Also, our previous calculation work [26] demonstrated that the AlO-terminated surface is thermodynamically more stable than AlC-terminated surface. The 2 × 2 × 2 supercell model of AlO-terminated Al2 CO(0 0 0 1) slab was shown in Fig. 1. It is noted that the slab is complementary mutually with AlC and AlO layer, indicating that the surface of Al2 CO is classified as a polar surface. An asymmetric geometry induces a spurious dipole moment within the supercell, which can bias atomic forces and energies [29]. Therefore, the symmetric slab ranging from 3 to 9 layers thick, with AlO-termination, was adopted in the surface convergence tests to eliminate the spurious dipole effects. Accordingly, the surface interlayer relaxations ij , which is defined as the change of the interlayer spacing in percent of the bulk spacing of Al2 CO free surface after full relaxation, are calculated and listed in Table 2. The similar method was presented in Refs. [16,17]. It is found that the slab exhibit an oscillatory expansion/contraction behavior along the Z direction, and the relaxation effects are mainly localized in the first atomic layer. Actually, the 5-layer slab can achieve convergence easily. However, the contraction of the first layer on 5-layer slab (12 = 4.4542%) is much larger than others. Considering the relaxation stability and bearing capacity of the computer, the 7-layer AlO-terminated Al2 CO(0 0 0 1) slab was used in the following interface geometries.
3. Bulk and convergence tests 3.1. Bulk properties of Al2 CO The calculating bulk properties for Mg were presented in an earlier study of the Mg/Al4 C3 interface [16], in which the calculated lattice constant, bulk modulus, and cohesive energy obtained with a GGA–PBE approach were in good agreement with experimental and other first-principles calculations. The model of Al2 CO phase was built with the parameters in ˚ Table 1. The calculated lattice constants of Al2 CO, a = 3.474 A, c = 4.095 A˚ and its volume, V0 = 42.785, are in good agreement ˚ c = 5.078 A˚ and the volwith the experimental values, a = 3.170 A, ume V0 = 44.192 [27]. The three independent elastic constants are also calculated (C11 = 259.5043 GPa, C12 = 132.9899 GPa and C44 = 174.7822 GPa) and all constants for Al2 CO are positive and satisfy the generalized criteria [28] for mechanically stable crystals: (C11 –C12 > 0), (C11 + 2C12 > 0), C44 > 0. These results show that the adopted parameters can ensure enough precision. 3.2. Convergence tests In order to study the interface between Mg and Al2 CO bulk, the selected slabs of both sides should be thick enough to show the bulk-like character interiors. For this reason, we have conducted convergence tests on the Mg(0 0 0 2) and Al2 CO(0 0 0 1) slabs in preparation for their interface calculations. We already presented calculation results for the convergence of the Mg(0 0 0 2) surface [16]. It was found that a Mg(0 0 0 2) slab consisting of five atomic layers was sufficient to converge. Therefore, the symmetric
Fig. 1. The supercell model of Al2 CO(0 0 0 1) slab with AlO-termination.
F. Wang et al. / Applied Surface Science 285P (2013) 879–884 Table 2 Al2 CO(0 0 0 1) surface relaxation as a function of slab thickness(ij : change of the interlayer spacing, %; −/+ represents expansion/contraction of atoms, respectively). Termination
AlO
Interlayer
12 23 34 45 56 67 78 89
Table 3 Work of adhesion (Wad ) and rate of interfacial separation change (d0 ). Termination
Stacking
d0 (Å)
d1 (Å)
d0 (%)
Wad (J/m2 )
AlO
“Over Al” “Over O”
3.248 3.250
3.182 3.106
2.0 4.4
0.427 0.551
Slab thickness (n) 3
5
7
9
1.6602 0.977
4.4542 0.1954 0.4883 3.1265
2.3495 −0.098 −0.293 0.342 0.3906 2.6869
1.7587 −0.195 0.0977 −0.391 0.3908 0.6348 0.2931 1.416
4. Interfaces 4.1. Interfacial model geometry We have confined our investigation to the interface formed between Mg(0 0 0 2) and hcp Al2 CO(0 0 0 1) because the stable interfaces are commonly formed between most stable surfaces [30,31]. The AlO-terminated Al2 CO(0 0 0 1) slab was employed to simulate the Mg/Al2 CO interface. Based on the convergence test, the interfacial model geometry consists of 5-layers Mg(0 0 0 2) slab and 7-layers AlO-terminated Al2 CO(0 0 0 1) slab. A 10 A˚ vacuum region was included to prohibit interactions between the free surfaces of Mg and Al2 CO slab with an in-plane periodicity. The interfacial orientation relationship, (0 0 0 2)[1 1 2¯ 0]Mg //(0 0 0 1)[1 2¯ 1 0]Al2 CO with a lattice mismatch of about 0.9%, was adopted in the interface models [15]. In order to make up the mismatch and satisfy the periodic boundary conditions, the Mg(0 0 0 2) slab was stretched with the coherent interface approximation. The “Over X” stacking with the interfacial Mg atom directly placed on the top of O or Al atoms of Al2 CO(0 0 0 1) slab was considered. Hence, two different interfacial model geometries for AlO-terminated Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface, as shown in Fig. 2, were discussed in this study. In our calculation, atoms in
881
the systems were allowed to relax freely in three directions during geometry optimization. 4.2. Interfacial structure and work of adhesion The ideal work of adhesion, Wad , is defined as the reversible work needed to separate an interface into two free surfaces. It can be estimated using the total energy difference between the interface and its isolated slabs [16,32–34]: Wad =
1
2Asurface
total total total EMg + EAl − EMg/Al CO
2 CO
2
total , E total and E total where EMg Al CO Mg/Al 2
2 CO
(1)
are the total energies of the
relaxed Mg(0 0 0 2), Al2 CO(0 0 0 1) slab and Mg/Al2 CO interfacial system, respectively; Asurface is the area of the interface unit cell. The calculated values of Wad and the rate of interfacial separation change (d0 ) for different interfacial geometries are summarized in Table 3, where d0 and d1 are interfacial spacing before and after full relaxation, respectively. The interfacial spacing between Mg atoms and AlO-terminated Al2 CO slab changes slightly, only about 2.0% and 4.4% for “Over Al” and “Over O” stacking geometries, suggesting that the interaction between Mg and Al/O is weak than that of between Mg and C. By comparing the corresponding values of Wad , it can be seen that the “Over O” stacking geometry possess the larger interfacial adhesion (Wad = 0.551) and separation change (d0 = 4.4), indicating the “Over O” surfaces are more reactive and readily to form strong bonds. Unfortunately, no experimental data could be cited to compare the calculated Wad values yet. Thus, the “Over O” stacking geometry for AlO-termination is the favorable structure for Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface. 4.3. Electronic structure and bonding The mechanical properties of an interface are closely related to the interfacial atomic bonding [34]. Hereby, the charge density difference is used to explain the interfacial electronic structures. In the case of Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface, the electron density difference, can be expressed as [35]: = Mg(0 0 0 2)/Al2 CO(0 0 0 1) − (Mg(0 0 0 2) + Al2 CO(0 0 0 1) )
Fig. 2. Two stacking sequences for AlO-terminated Mg/Al2 CO interface, (a) “Over O” and (b)“Over Al” (gray ball: C, green ball: Mg, red color ball: O, and pink ball: Al). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
(2)
where Mg(0 0 0 2)/Al2 CO(0 0 0 1) is the electron density of the total Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface system, Mg(0 0 0 2) and Al2 CO(0 0 0 1) are the unperturbed electron densities of the isolated Mg(0 0 0 2) and Al2 CO(0 0 0 1) slabs, respectively. We note that the electron charge rearrangements are mainly confined to two atomic layers near the interface, as shown in Fig. 3. The more negative or red the mark is in the figure, the more electrons the atoms lose. Thus, the O- and Al-site, which are intermediate to build the interface, possess different charge density difference. For “Over O” stacking interface, the area of charge depletion extend to cover the interstitial regions, including the O, Mg and Al atoms, as shown in Fig. 3(a). This signal clearly illustrates the formation of a new bonding across the interface by the contribution of O and Al atoms in lateral Al2 CO and the reduction in lateral Mg–Mg metallic bonds. And the electrons in Mg-layer are pushed into the interfacial region to form the mixed ionic/metallic bonds. In contrast, for “Over Al” stacking interface, high charge density with concentric contour can only be observed at the Al and Mg atoms near the interface, the effect of O atom is quite poor,
882
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
Fig. 3. The charge density difference for (a) “Over O” and (b)“Over Al” stacking AlO-terminated Mg/Al2 CO interface along (1 1 2¯ 0) plane (the dashed lines indicate the location of the interfaces).
which gives an evident of metallic bond formed between Mg and Al atoms, as shown in Fig. 3(b). Compared with the “Over O” stacking, the charge transfer in the interfacial regions of “Over Al” stacking model is weaker. In additional, it can be seen that the curve profiles of Al and C atoms in the second layer of the lateral Al2 CO for both stacking sequences are very similar, indicating their similar effects on the interfacial bonding. These atomic preferable interfacial bonding have also been observed in other interface systems, such as Al/WC, Al/TiC, Al/TiN and Fe/WC [32–35]. Further evidence of interface bonding can be seen from layer partial density of states (PDOS) for both stacking sequences, as shown in Fig. 4, where solid line presents s states, dotted line presents p states. Total DOS means the sums of every atomic partial density of states for each stacking sequence. The ␣-interface is Layer-projected PDOS of the ␣ atom near the interface and An (n = 2, 3) is Layer-projected PDOS of the A atom in the n-layer, for example, the Al2 means the Layer-projected PDOS of the Al atom in the 2-layer. Despite of the different stacking sequences of two models, there are some common features of the interface electronic structure. First of all, we note that the interfacial charge redistribution is confined to the first layer on each side nearby the interface, because the interface layer PDOS shapes in Al, C and Mg atom are dissimilar to other layers in two models. This is consistent with the change of interlayer relaxations shown in Table 2. Secondly, it can be seen that the Total DOS of both stacking models are mainly occupied by p orbital electrons, and the contributions of the s orbital electrons are relatively small. Moreover, the DOS of “Over Al” model has a larger value at the Fermi level than that of “Over O” model, indicating the stronger metallic feature for the “Over Al” stacking Mg/Al2 CO interface.
where C = slab − bulk ; Al = slab − bulk ; bulk = C C Al Al Al 1 bulk 1 bulk 1 bulk bulk bulk bulk bulk bulk bulk E ; C = 4 EC ; Al CO = EAl CO ; Mg = 2 EMg , EAl CO , EAl 4 Al 2 2 2 and ECbulk are the bulk energy for Al2 CO,Al and Graphite, respectively; Asurface is the interface area; EMg/Al2 CO is the total energy of fully relaxed interfacial supercell; NAl, NC, NO and NMg are the
4.4. Interfacial stability It is know that the stable interfacial structure minimizes the interfacial energy [16,18]. Hereby, we determine the interfacial energy so as to quantitatively analyze the interface stability and provide a basis for how deeply to understand the mechanism of heterogeneous nucleation of ␣-Mg on the Al2 CO particles surfaces. The interfacial energy of the stoichiometric Mg(0 0 0 2)/Al2 CO(0 0 0 1), Mg/Al2 CO , was calculated by [36]: Mg/Al2 CO =
1 [E − NO bulk Al2 CO 2Asurface Mg/Al2 CO + (2NO − NAl )slab + (NO − NC )slab − NMg bulk Mg ] C Al
(3)
Fig. 4. Total DOS and Layer-projected PDOS for (a) “Over Al” and (b)“Over O” stacking AlO-terminated Mg/Al2 CO interface (the vertical dashed lines indicate the location of Fermi level).
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
numbers of Al, C, O and Mg atoms in the Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface respectively; bulk , bulk and bulk are the chemical Mg C Al potentials of Mg atoms in bulk magnesium phase, Al atoms in bulk aluminum phase and C atoms in graphite respectively; slab and slab are the chemical potentials of Al and C in the C Al
Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface respectively; bulk is the Al CO 2
bulk chemical potentials of Al2 CO. For an equilibrium system, the , Hf0 , bulk relationship of bulk , bulk , bulk , slab , slab , slab C O C O Al CO Al Al 2
were given as follows: bulk = 2slab + slab + slab C O Al CO Al
(4)
bulk = 2bulk + bulk + bulk + Hf0 C O Al CO Al
(5)
2
2
Combining Eqs. (4) and (5), the following relation can be given: 2slab − 2bulk = bulk − slab + bulk − slab + Hf0 C C O O Al Al
883
the interfacial stability of Mg/Al2 CO interface is determined by the range of Al + C from thermodynamic consideration. And the interfacial energy for both stacking model was divided into two parts, one of which is larger than 0.1 J/m2 and another less than 0.1 J/m2 . While Al + C ≤ −2.71 eV for “Over O” stacking and Al + C ≤ −2.84 eV for “Over Al” stacking, the interface energy was less than 0.1 J/m2 , a stable ordered interfacial structure will be in favor of the stacking of liquid Mg atoms. Namely, the Al2 CO(0 0 0 1) surfaces will act as effective nucleation substrate for ␣-Mg under the condition of low undercooling. This explains well on the previous experimental phenomenon that particles composed of Al, C, O elements were easily observed in the central region of ␣-Mg grain [6,10,38]. The above calculations and analysis provided strong theoretical support to the Al2 CO nucleus hypothesis for ␣-Mg grains from interfacial atomic structure and atomic bonding energy considerations.
(6) 5. Conclusions
Using the above relationships, Eq. (3) can be rewritten to be: Mg/Al2 CO = (Al2 CO(0 0 0 1)) −
2 Asurface
(Al + C )
(7)
where (Al2 CO(0 0 0 1)) =
1 bulk [E − NO EAl 2 CO 2Asurface Mg/Al2 CO 1 bulk 1 + (2NO − NAl ) EAl + (NO − NC ) ECbulk 4 4
(8)
As (Al2 CO(0 0 0 1)) can be calculated as a constant, the results of interfacial energy, Mg/Al2 CO for both stacking sequence as a function of Al + C can be calculated according to Eq. (7) and plotted in Fig. 4. From Fig. 4 it can be seen that the Mg/Al2 CO interfacial energy increases with the increasing value of Al + C . Within the entire range of −8.1 eV ≤ Al + C ≤ 0, the interfacial energy of the “Over-Al” model is approximately 0.13 J/m2 larger than those of the “Over-O” model, indicating the latter stacking model is more stable. Note the shadow region in Fig. 4, which indicates the region where the bulk phases begin to form. Under the condition of Al + C ≤ −8.1 eV, Al2 CO tends to change into O2 . Otherwise, single Al and Graphite may be formed when Al + C ≥ 0. Actually, these regions would not be of interest because Mg/Al2 CO interfaces can only be formed under the condition of −8.1 eV ≤ Al + C ≤ 0. It has been deduced through crystallographic analysis that stable Mg/Al2 CO interface can be formed with combination of closepacked planes in Mg and Al2 CO crystal [15]. In addition, from Table 3 we can see that the “Over-O” model has a larger work of adhesion. It results in the lower interfacial energy for AlOtermination over the whole range of Al + C . Therefore, the most favorable Mg(0 0 0 2)/Al2 CO(0 0 0 1) interfacial structure is the AlO-terminated “Over-O” stacking interface. 4.5. Heterogeneous nucleation of Al2 CO In general, the First-principle calculations were performed at 0 K levels. It has been proved that the calculated results match well with experimental study for solid phase structure and solid–liquid interface [18,37]. Therefore, we discuss the heterogeneous nucleation mechanism by this method. According to the classical spherical cap model or adsorption model, it is thermodynamically believed that the interfacial energy between nucleation particles and ␣-Mg must be less than the interfacial energy between ␣-Mg and magnesium melts, which is 0.1 J/m2 for solid–liquid interface in Mg melt [36]. As can be seen in Fig. 4,
In order to understand the heterogeneous nucleation potential of Al2 CO for ␣-Mg grain in Mg–Al alloys melt, the interface atomic structure, work of adhesion and interfacial energy of the Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface were studied with the firstprinciples calculations. The main conclusions are summarized as follows. (1) Surface convergence test revealed that for AlO-terminated Al2 CO(0 0 0 1) slab, the relaxation effects are mainly localized in the first atomic layer. And the Al2 CO(0 0 0 1) slab with more than five atomic layers can exhibit bulk-like interior feature. (2) Analysis on electronic structure and bonding of AlO-terminated Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface shown that the mixed ionic/metallic bonds are formed near the “Over O” stacking interface, while the “Over Al” stacking interface exhibits predominantly metallic bonding character. Further comparison on the work of adhesion and interfacial energy indicated that “Over-O” stacking interface is more stable than “Over Al” stacking interface. Therefore, the Mg atoms prefer to directly stack on O atoms with an “Over O” stacking sequence when Mg atoms grow on Al2 CO(0 0 0 1) slab. (3) The calculated interfacial energies of Mg/Al2 CO with “Over O” and “Over Al” stacking sequence both depend on the value of Al + C . In the range of −8.1 eV < Al + C ≤ −2.71 eV for “Over O” stacking and −8.1 eV < Al + C ≤ −2.84 eV for “Over Al” stacking, the Mg/Al2 CO interfacial energies are less than that between ␣-Mg and magnesium melts. Namely, the Al2 CO particles will become effective nucleation substrate for ␣-Mg under certain conditions. The above calculation and analysis thermodynamically proved the Al2 CO nucleus hypothesis and explain some experimental phenomenon observed recently. Acknowledgements The authors gratefully acknowledge the financial supports from National Natural Science Foundation of China (No. 51264032) and the Ministry of Education Scientific Research Foundation for the returned overseas (Lot. 44). References [1] A. Luo, Recent magnesium alloy development for elevated temperature applications, International Materials Reviews 49 (2004) 13–30. [2] H. Friedrich, S. Schumann, Research for a new age of magnesium in the automotive industry, Journal of Materials Processing Technology 117 (2001) 276–281.
884
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
[3] S.F. Liu, L.Y. Liu, L.G. Kang, Refinement role of electromagnetic stirring and strontium in AZ91 magnesium alloy, Journal of Alloys and Compounds 450 (2008) 546–550. [4] J. Du, J. Yang, M. Kuwabara, W. Li, J. Peng, Improvement of grain refining efficiency for Mg–Al alloy modified by the combination of carbon and calcium, Journal of Alloys and Compounds 470 (2009) 134–140. [5] D.H. StJohn, M. Qian, M.A. Easton, P. Cao, Z. Hildebrand, Grain refinement of magnesium alloys, Metallurgical and Materials Transactions A 36 (2005) 1669–1679. [6] E. Yano, Y. Tamura, T. Motegi, E. Sato, Effect of carbon powder on grain refinement of an AZ91E magnesium alloy, Materials Transactions (Japan) 44 (2003) 107–110. [7] Y.M. Kim, C.D. Yim, B.S. You, Grain refining mechanism in Mg–Al base alloys with carbon addition, Scripta Materialia 57 (2007) 691–694. [8] T.J. Chen, X.D. Jiang, Y. Ma, Y.D. Li, Y. Hao, Grain refinement of AZ91D magnesium alloy by SiC, Journal of Alloys and Compound 496 (2010) 218–225. [9] K.F.W.A.N.G. Li, Q. Wang, N.G. Zhou, Study on grain refining mechanism of carbon inoculation on Mg–Al alloy, Journal of Shanghai Jiaotong University 17 (2012) 301–305. [10] M. Qian, P. Cao, Discussions on grain refinement of magnesium alloys by carbon inoculation, Scripta Materialia 52 (2005) 415–420. [11] Y.H. Liu, X.F. Liu, X.F. Bian, Grain refinement of Mg–Al alloys with Al4 C3 –SiC/Al master alloy, Materials Letter 58 (2004) 1282–1287. [12] V. Klimov, G. Bergman, O. Karlina, Thermodynamic properties of aluminum monooxycarbide Al2 OC, Russian Journal of Physical Chemistry 80 (2006) 1816–1818. [13] J.M. Lihrmann, T. Zambetakis, M. Daire, High temperature behavior of the aluminum oxycarbide Al2 OC in the system Al2 O3 –Al4 C3 and with additions of aluminum nitride, Journal of the American Ceramic Society 72 (1989) 1704–1709. [14] M.-X. Zhang, P. Kelly, M. Easton, J. Taylor, Crystallographic study of grain refinement in aluminum alloys using the edge-to-edge matching model, Acta Materialia 53 (2005) 1427–1438. [15] M.X. Zhang, P.M. Kelly, M. Qian, J.A. Taylor, Crystallography of grain refinement in Mg–Al based alloys, Acta Materialia 53 (2005) 3261–3270. [16] K. Li, Z.G. Sun, F. Wang, N.G. Zhou, X.W. Hu, First-principles calculations on Mg/Al4 C3 interfaces, Applied Surface Science 270 (2013) 584–589. [17] Y.F. Han, Y.B. Dai, D. Shu, J. Wang, B.D. Sun, First-principles study of TiB2 (0 0 0 1) surface, Journal of Physics: Condensed Matter 18 (2006) 4197–4205. [18] Y. Han, Y. Dai, D. Shu, J. Wang, B. Sun, First-principles calculations on the stability of Al/TiB2 interface, Applied Physics Letters 89 (2006) 144107. [19] Y.F. Han, Y.B. Dai, J. Wang, D. Shu, B.D. Sun, First-principles calculations on Al/AlB2 interfaces, Applied Surface Science 257 (2011) 7831–7836. [20] H. Dai, J. Du, L. Wang, C. Peng, X. Liu, First-principle study of the AlP/Si interfacial adhesion, Physica B: Condensed Matter 405 (2010) 573–578.
[21] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Physical Review B 136 (1964) 864. [22] B.G. Pfrommer, M. Côté, S.G. Louie, M.L. Cohen, Relaxation of crystals with the quasi-Newton method, Journal of Computational Physics 131 (1997) 233–240. [23] K. Laasonen, A. Pasqurello, R. Car, C. Lee, D. Vanderbilt, Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Physical Review B 47 (1993) 10142–10153. [24] J. White, D. Bird, Implementation of gradient-corrected exchange-correlation potentials in Car-Parrinello total-energy calculations, Physical Review B 50 (1994) 4954. [25] M. Marlo, V. Milman, Density-functional study of bulk and surface properties of titanium nitride using different exchange-correlation functionals, Physical Review B 62 (2000) 2899. [26] F. Wang, K. Li, M.Q. Zhan, First-principles study of surface properties for Al2 CO, in: The 10th Asia Thermophysical Properties Conference, Jeju, Korea, 2013 (in press). [27] 2002 JCPDS-International Centre for Diffraction Data, PCPDFWIN v.2.3. [28] S. Yip, J. Li, M. Tang, J. Wang, Mechanistic aspects and atomic-level consequences of elastic instabilities in homogeneous crystals, Materials Science and Engineering A 317 (2001) 236–240. [29] J. Neugebauer, M. Scheffler, Adsorbate–substrate and adsorbate–adsorbate interactions of Na and K adlayers on Al (1 1 1), Physical Review B 46 (1992) 16067. [30] Y. Wang, M. Xia, Z. Fan, X. Zhou, G. Thompson, The effect of Al8 Mn5 intermetallic particles on grain size of as-cast Mg–Al–Zn AZ91D alloy, Intermetallics 18 (2010) 1683–1689. [31] A. Arya, E.A. Carter, Structure, bonding, and adhesion at the TiC (1 0 0)/Fe (1 1 0) interface from first principles, The Journal of Chemical Physics 118 (2003) 8982. [32] D.J. Siegel, L.G. Hector Jr., J.B. Adams, Adhesion, stability, and bonding at metal/metal-carbide interfaces: Al/WC, Surface Science 498 (2002) 321–336. [33] L. Liu, S. Wang, H. Ye, First-principles study of polar Al/TiN (1 1 1) interfaces, Acta Materialia 52 (2004) 3681–3688. [34] Y. Li, Y. Gao, B. Xiao, T. Min, S. Ma, D. Yi, Theoretical calculations on the adhesion, stability, electronic structure, and bonding of Fe/WC interface, Applied Surface Science 257 (2011) 5671–5678. [35] L. Liu, S. Wang, H. Ye, Adhesion and bonding of the Al/TiC interface, Surface Science 550 (2008) 46–56. [36] Q. Jiang, H. Lu, Size dependent interface energy and its applications, Surface Science Reports 63 (2008) 427–464. [37] J. Wang, A. Horsfield, U. Schwingenschlögl, P.D. Lee, Heterogeneous nucleation of solid Al from the melt by TiB2 and Al3 Ti: an ab initio molecular dynamics study, Physical Review B 82 (2010) 184203. [38] E. Yano, Y. Tamura, T. Motegi, E. Sato, Effect of pure carbon powder on grain refining of cast magnesium alloy AZ 91, Journal of Japan Institute of Light Metals 51 (2001) 599–603.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
First-principles calculations on Mg/Al2 CO interfaces F. Wang, K. Li ∗ , N.G. Zhou School of Mechanical and Electrical Engineering, Nanchang University, Nanchang 330031, China
a r t i c l e
i n f o
Article history: Received 1 July 2013 Received in revised form 2 September 2013 Accepted 2 September 2013 Available online 12 September 2013 Keywords: First-principles calculation Interface Al2 CO Grain refining Magnesium alloy
a b s t r a c t The electronic structure, work of adhesion, and interfacial energy of the Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface were studied with the first-principles calculations to clarify the heterogeneous nucleation potential of Al2 CO particles in Mg melt. AlO-terminated Al2 CO(0 0 0 1) slabs with seven atomic layers were adopted for interfacial model geometries. Results show that the “Over O” stacking interface is more stable than the “Over Al” stacking interface due to the larger interfacial adhesion and stronger mixed ionic/metallic bond formed across the interface. The calculated interfacial energies of Mg/Al2 CO depend on the value of Al + C , proving Al2 CO particles can exist stably in Mg–Al alloys melt and become effective nucleation substrate for ␣-Mg grain under certain conditions. The above calculation and corresponding analysis provide strong theoretical support to the Al2 CO nucleus hypothesis from interfacial atomic structure and atomic bonding energy considerations. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Magnesium alloys have the advantages of light weight, high strength, excellent damping vibration capacity and good machinability [1,2]. However, during the production of magnesium alloys cast parts, the casting flaws such as porosity, segregation and hot tearing are common due to the coarse primary dendrite Mg grain. Therefore, how to control the solidification behavior of magnesium alloys, to decrease the grain size and casting flaw, and to improve the quality and property of the casting ingot are critical for expanding the application scope and developing high-performance magnesium alloys [3–5]. Presently, the study on the refinement mechanism of casting structure of magnesium alloys mainly focuses on the promoting of exogenous particles on nucleation, the inhibition of grain growth and the effect of solute on the nucleation rate [5]. Among grain refining approaches developed for Mg–Al based alloys, carbon inoculation by introducing carbon powder [6] or different carbon-containing compound, such as C2 Cl6 [7], SiC [8] and MgCO3 [9], is one of the major and effective one. The most commonly accepted grain refinement mechanism of carbon inoculation is Al4 C3 nucleus hypothesis [10,11], which was used to explain the excellent grain refining performance of carbon inoculation process. In addition, some experimental works [6,8,10] reported that particles containing Al, C, O elements were easily observed in the central
∗ Corresponding author at: School of Mechanical and Electrical Engineering, Nanchang University, 999 Xuefu Road, Honggutan District, Nanchang 330031, China. Tel.: +86 18970029945; fax: +86 79183969622. E-mail address: [email protected] (K. Li). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.09.006
region of ␣-Mg grain, and thus the Al2 CO hypothesis was proposed as another reasonable mechanism to explain the grain refinement of Mg–Al base alloys. It was discovered in earlier researches [12,13] that Al2 CO is the intermediate products in the sequence of transformations Al2 O3 → Al4 O4 C → Al2 CO → Al4 C3 . The nucleation potency of a potential heterogeneous substrate depends on the interfacial atomic structures and energy between the nucleating crystal and substrate [14]. The interfacial structure between Al4 C3 and ␣-Mg has been investigated and discussed according to the lattice disregistry theory [10] and the edge-to-edge matching model [15] from a crystallographic point of view. Our previous work [16] within an energy framework also demonstrated that Al4 C3 particles can act as heterogeneous nucleus for magnesium grains. As for Al2 CO, calculations in Ref. [15] revealed that the inter-atomic spacing matching along the close-packed rows between Mg1 0 1 0 and Al2 CO0 0 0 1 is 8.65 and the d-value mismatches between close-packed planes in Mg(0 0 0 2) and Al2 CO(0 0 0 2) is only 2.5, indicating that Al2 CO can act as effective nucleating substrate of ␣-Mg and is even superior to A14 C3 . This prediction is consistent with most experimental results recently [6,8]. Additionally, the deeper identification of interfacial structures at the atomic scale and theoretical calculations of the interfacial energy are necessary to demonstrate the nucleation potency of Al2 CO particles for ␣-Mg grain. However, it is difficult to quantitatively measure the interfacial energy with experimental method at present. In recent years, the first-principles methods have been successfully applied to investigate the stabilities of compound surfaces with different atomic termination [17], predict the interfacial energy and the interfacial structure between primary phase and
880
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
Table 1 Structure parameters of Al2 CO phase. Phase Al2 CO
Structure Trigonal/rhombohedra
Atom number in cell 2Al, 1C, 1O
heterogeneous nucleus, such as Mg/A14 C3 , Al/TiB2 , Al/AlB2 and Si/AlP [16,18–20]. In this work, Mg(0 0 0 2)/Al2 CO(0 0 0 1) interfacial properties are studied using the first-principles method, and the stability and refinement performance of Al2 CO particles in Mg melt is also discussed within an energy framework based on the calculations. 2. Computational methodology All calculations in this work were performed by using a total energy plane-wave pseudo-potential method based on the Density Functional Theory (DFT) [21]. The BFGS algorithm [22] is the recommended algorithm to reach the minimum total energy of the system and the ultrasoft pseudo-potential [23] was used to describe the interactions between ionic core and valence electrons. The generalized gradient approximation (GGA) of PBE approach [24,25] was chosen for exchange-correlation energy calculations. The planewave energy cutoff was selected as 310 eV. The Monkhorst–Pack k-point grid employed 3 × 3 × 1 for the interface calculation of Al2 CO. All atoms were relaxed to their equilibrium positions when the total energy changes during the optimization finally converged to less than 2 × 10−5 eV/atom, the forces on each atom were converged to 0.05 eV/Å, the stress on each atom was converged to ˚ More 0.1 GPa, and the displacement was converged to 0.002 A. details of the computational method can be found in our previous work [26].
Group(No.)
Atom site
P63mc(186)
Al1(0.333, 0.667, 0) C/O(0.333, 0.667, 0.3821)
Mg(0 0 0 2) slab with five atomic layers was adopted in the following interface geometries. Also, our previous calculation work [26] demonstrated that the AlO-terminated surface is thermodynamically more stable than AlC-terminated surface. The 2 × 2 × 2 supercell model of AlO-terminated Al2 CO(0 0 0 1) slab was shown in Fig. 1. It is noted that the slab is complementary mutually with AlC and AlO layer, indicating that the surface of Al2 CO is classified as a polar surface. An asymmetric geometry induces a spurious dipole moment within the supercell, which can bias atomic forces and energies [29]. Therefore, the symmetric slab ranging from 3 to 9 layers thick, with AlO-termination, was adopted in the surface convergence tests to eliminate the spurious dipole effects. Accordingly, the surface interlayer relaxations ij , which is defined as the change of the interlayer spacing in percent of the bulk spacing of Al2 CO free surface after full relaxation, are calculated and listed in Table 2. The similar method was presented in Refs. [16,17]. It is found that the slab exhibit an oscillatory expansion/contraction behavior along the Z direction, and the relaxation effects are mainly localized in the first atomic layer. Actually, the 5-layer slab can achieve convergence easily. However, the contraction of the first layer on 5-layer slab (12 = 4.4542%) is much larger than others. Considering the relaxation stability and bearing capacity of the computer, the 7-layer AlO-terminated Al2 CO(0 0 0 1) slab was used in the following interface geometries.
3. Bulk and convergence tests 3.1. Bulk properties of Al2 CO The calculating bulk properties for Mg were presented in an earlier study of the Mg/Al4 C3 interface [16], in which the calculated lattice constant, bulk modulus, and cohesive energy obtained with a GGA–PBE approach were in good agreement with experimental and other first-principles calculations. The model of Al2 CO phase was built with the parameters in ˚ Table 1. The calculated lattice constants of Al2 CO, a = 3.474 A, c = 4.095 A˚ and its volume, V0 = 42.785, are in good agreement ˚ c = 5.078 A˚ and the volwith the experimental values, a = 3.170 A, ume V0 = 44.192 [27]. The three independent elastic constants are also calculated (C11 = 259.5043 GPa, C12 = 132.9899 GPa and C44 = 174.7822 GPa) and all constants for Al2 CO are positive and satisfy the generalized criteria [28] for mechanically stable crystals: (C11 –C12 > 0), (C11 + 2C12 > 0), C44 > 0. These results show that the adopted parameters can ensure enough precision. 3.2. Convergence tests In order to study the interface between Mg and Al2 CO bulk, the selected slabs of both sides should be thick enough to show the bulk-like character interiors. For this reason, we have conducted convergence tests on the Mg(0 0 0 2) and Al2 CO(0 0 0 1) slabs in preparation for their interface calculations. We already presented calculation results for the convergence of the Mg(0 0 0 2) surface [16]. It was found that a Mg(0 0 0 2) slab consisting of five atomic layers was sufficient to converge. Therefore, the symmetric
Fig. 1. The supercell model of Al2 CO(0 0 0 1) slab with AlO-termination.
F. Wang et al. / Applied Surface Science 285P (2013) 879–884 Table 2 Al2 CO(0 0 0 1) surface relaxation as a function of slab thickness(ij : change of the interlayer spacing, %; −/+ represents expansion/contraction of atoms, respectively). Termination
AlO
Interlayer
12 23 34 45 56 67 78 89
Table 3 Work of adhesion (Wad ) and rate of interfacial separation change (d0 ). Termination
Stacking
d0 (Å)
d1 (Å)
d0 (%)
Wad (J/m2 )
AlO
“Over Al” “Over O”
3.248 3.250
3.182 3.106
2.0 4.4
0.427 0.551
Slab thickness (n) 3
5
7
9
1.6602 0.977
4.4542 0.1954 0.4883 3.1265
2.3495 −0.098 −0.293 0.342 0.3906 2.6869
1.7587 −0.195 0.0977 −0.391 0.3908 0.6348 0.2931 1.416
4. Interfaces 4.1. Interfacial model geometry We have confined our investigation to the interface formed between Mg(0 0 0 2) and hcp Al2 CO(0 0 0 1) because the stable interfaces are commonly formed between most stable surfaces [30,31]. The AlO-terminated Al2 CO(0 0 0 1) slab was employed to simulate the Mg/Al2 CO interface. Based on the convergence test, the interfacial model geometry consists of 5-layers Mg(0 0 0 2) slab and 7-layers AlO-terminated Al2 CO(0 0 0 1) slab. A 10 A˚ vacuum region was included to prohibit interactions between the free surfaces of Mg and Al2 CO slab with an in-plane periodicity. The interfacial orientation relationship, (0 0 0 2)[1 1 2¯ 0]Mg //(0 0 0 1)[1 2¯ 1 0]Al2 CO with a lattice mismatch of about 0.9%, was adopted in the interface models [15]. In order to make up the mismatch and satisfy the periodic boundary conditions, the Mg(0 0 0 2) slab was stretched with the coherent interface approximation. The “Over X” stacking with the interfacial Mg atom directly placed on the top of O or Al atoms of Al2 CO(0 0 0 1) slab was considered. Hence, two different interfacial model geometries for AlO-terminated Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface, as shown in Fig. 2, were discussed in this study. In our calculation, atoms in
881
the systems were allowed to relax freely in three directions during geometry optimization. 4.2. Interfacial structure and work of adhesion The ideal work of adhesion, Wad , is defined as the reversible work needed to separate an interface into two free surfaces. It can be estimated using the total energy difference between the interface and its isolated slabs [16,32–34]: Wad =
1
2Asurface
total total total EMg + EAl − EMg/Al CO
2 CO
2
total , E total and E total where EMg Al CO Mg/Al 2
2 CO
(1)
are the total energies of the
relaxed Mg(0 0 0 2), Al2 CO(0 0 0 1) slab and Mg/Al2 CO interfacial system, respectively; Asurface is the area of the interface unit cell. The calculated values of Wad and the rate of interfacial separation change (d0 ) for different interfacial geometries are summarized in Table 3, where d0 and d1 are interfacial spacing before and after full relaxation, respectively. The interfacial spacing between Mg atoms and AlO-terminated Al2 CO slab changes slightly, only about 2.0% and 4.4% for “Over Al” and “Over O” stacking geometries, suggesting that the interaction between Mg and Al/O is weak than that of between Mg and C. By comparing the corresponding values of Wad , it can be seen that the “Over O” stacking geometry possess the larger interfacial adhesion (Wad = 0.551) and separation change (d0 = 4.4), indicating the “Over O” surfaces are more reactive and readily to form strong bonds. Unfortunately, no experimental data could be cited to compare the calculated Wad values yet. Thus, the “Over O” stacking geometry for AlO-termination is the favorable structure for Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface. 4.3. Electronic structure and bonding The mechanical properties of an interface are closely related to the interfacial atomic bonding [34]. Hereby, the charge density difference is used to explain the interfacial electronic structures. In the case of Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface, the electron density difference, can be expressed as [35]: = Mg(0 0 0 2)/Al2 CO(0 0 0 1) − (Mg(0 0 0 2) + Al2 CO(0 0 0 1) )
Fig. 2. Two stacking sequences for AlO-terminated Mg/Al2 CO interface, (a) “Over O” and (b)“Over Al” (gray ball: C, green ball: Mg, red color ball: O, and pink ball: Al). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
(2)
where Mg(0 0 0 2)/Al2 CO(0 0 0 1) is the electron density of the total Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface system, Mg(0 0 0 2) and Al2 CO(0 0 0 1) are the unperturbed electron densities of the isolated Mg(0 0 0 2) and Al2 CO(0 0 0 1) slabs, respectively. We note that the electron charge rearrangements are mainly confined to two atomic layers near the interface, as shown in Fig. 3. The more negative or red the mark is in the figure, the more electrons the atoms lose. Thus, the O- and Al-site, which are intermediate to build the interface, possess different charge density difference. For “Over O” stacking interface, the area of charge depletion extend to cover the interstitial regions, including the O, Mg and Al atoms, as shown in Fig. 3(a). This signal clearly illustrates the formation of a new bonding across the interface by the contribution of O and Al atoms in lateral Al2 CO and the reduction in lateral Mg–Mg metallic bonds. And the electrons in Mg-layer are pushed into the interfacial region to form the mixed ionic/metallic bonds. In contrast, for “Over Al” stacking interface, high charge density with concentric contour can only be observed at the Al and Mg atoms near the interface, the effect of O atom is quite poor,
882
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
Fig. 3. The charge density difference for (a) “Over O” and (b)“Over Al” stacking AlO-terminated Mg/Al2 CO interface along (1 1 2¯ 0) plane (the dashed lines indicate the location of the interfaces).
which gives an evident of metallic bond formed between Mg and Al atoms, as shown in Fig. 3(b). Compared with the “Over O” stacking, the charge transfer in the interfacial regions of “Over Al” stacking model is weaker. In additional, it can be seen that the curve profiles of Al and C atoms in the second layer of the lateral Al2 CO for both stacking sequences are very similar, indicating their similar effects on the interfacial bonding. These atomic preferable interfacial bonding have also been observed in other interface systems, such as Al/WC, Al/TiC, Al/TiN and Fe/WC [32–35]. Further evidence of interface bonding can be seen from layer partial density of states (PDOS) for both stacking sequences, as shown in Fig. 4, where solid line presents s states, dotted line presents p states. Total DOS means the sums of every atomic partial density of states for each stacking sequence. The ␣-interface is Layer-projected PDOS of the ␣ atom near the interface and An (n = 2, 3) is Layer-projected PDOS of the A atom in the n-layer, for example, the Al2 means the Layer-projected PDOS of the Al atom in the 2-layer. Despite of the different stacking sequences of two models, there are some common features of the interface electronic structure. First of all, we note that the interfacial charge redistribution is confined to the first layer on each side nearby the interface, because the interface layer PDOS shapes in Al, C and Mg atom are dissimilar to other layers in two models. This is consistent with the change of interlayer relaxations shown in Table 2. Secondly, it can be seen that the Total DOS of both stacking models are mainly occupied by p orbital electrons, and the contributions of the s orbital electrons are relatively small. Moreover, the DOS of “Over Al” model has a larger value at the Fermi level than that of “Over O” model, indicating the stronger metallic feature for the “Over Al” stacking Mg/Al2 CO interface.
where C = slab − bulk ; Al = slab − bulk ; bulk = C C Al Al Al 1 bulk 1 bulk 1 bulk bulk bulk bulk bulk bulk bulk E ; C = 4 EC ; Al CO = EAl CO ; Mg = 2 EMg , EAl CO , EAl 4 Al 2 2 2 and ECbulk are the bulk energy for Al2 CO,Al and Graphite, respectively; Asurface is the interface area; EMg/Al2 CO is the total energy of fully relaxed interfacial supercell; NAl, NC, NO and NMg are the
4.4. Interfacial stability It is know that the stable interfacial structure minimizes the interfacial energy [16,18]. Hereby, we determine the interfacial energy so as to quantitatively analyze the interface stability and provide a basis for how deeply to understand the mechanism of heterogeneous nucleation of ␣-Mg on the Al2 CO particles surfaces. The interfacial energy of the stoichiometric Mg(0 0 0 2)/Al2 CO(0 0 0 1), Mg/Al2 CO , was calculated by [36]: Mg/Al2 CO =
1 [E − NO bulk Al2 CO 2Asurface Mg/Al2 CO + (2NO − NAl )slab + (NO − NC )slab − NMg bulk Mg ] C Al
(3)
Fig. 4. Total DOS and Layer-projected PDOS for (a) “Over Al” and (b)“Over O” stacking AlO-terminated Mg/Al2 CO interface (the vertical dashed lines indicate the location of Fermi level).
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
numbers of Al, C, O and Mg atoms in the Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface respectively; bulk , bulk and bulk are the chemical Mg C Al potentials of Mg atoms in bulk magnesium phase, Al atoms in bulk aluminum phase and C atoms in graphite respectively; slab and slab are the chemical potentials of Al and C in the C Al
Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface respectively; bulk is the Al CO 2
bulk chemical potentials of Al2 CO. For an equilibrium system, the , Hf0 , bulk relationship of bulk , bulk , bulk , slab , slab , slab C O C O Al CO Al Al 2
were given as follows: bulk = 2slab + slab + slab C O Al CO Al
(4)
bulk = 2bulk + bulk + bulk + Hf0 C O Al CO Al
(5)
2
2
Combining Eqs. (4) and (5), the following relation can be given: 2slab − 2bulk = bulk − slab + bulk − slab + Hf0 C C O O Al Al
883
the interfacial stability of Mg/Al2 CO interface is determined by the range of Al + C from thermodynamic consideration. And the interfacial energy for both stacking model was divided into two parts, one of which is larger than 0.1 J/m2 and another less than 0.1 J/m2 . While Al + C ≤ −2.71 eV for “Over O” stacking and Al + C ≤ −2.84 eV for “Over Al” stacking, the interface energy was less than 0.1 J/m2 , a stable ordered interfacial structure will be in favor of the stacking of liquid Mg atoms. Namely, the Al2 CO(0 0 0 1) surfaces will act as effective nucleation substrate for ␣-Mg under the condition of low undercooling. This explains well on the previous experimental phenomenon that particles composed of Al, C, O elements were easily observed in the central region of ␣-Mg grain [6,10,38]. The above calculations and analysis provided strong theoretical support to the Al2 CO nucleus hypothesis for ␣-Mg grains from interfacial atomic structure and atomic bonding energy considerations.
(6) 5. Conclusions
Using the above relationships, Eq. (3) can be rewritten to be: Mg/Al2 CO = (Al2 CO(0 0 0 1)) −
2 Asurface
(Al + C )
(7)
where (Al2 CO(0 0 0 1)) =
1 bulk [E − NO EAl 2 CO 2Asurface Mg/Al2 CO 1 bulk 1 + (2NO − NAl ) EAl + (NO − NC ) ECbulk 4 4
(8)
As (Al2 CO(0 0 0 1)) can be calculated as a constant, the results of interfacial energy, Mg/Al2 CO for both stacking sequence as a function of Al + C can be calculated according to Eq. (7) and plotted in Fig. 4. From Fig. 4 it can be seen that the Mg/Al2 CO interfacial energy increases with the increasing value of Al + C . Within the entire range of −8.1 eV ≤ Al + C ≤ 0, the interfacial energy of the “Over-Al” model is approximately 0.13 J/m2 larger than those of the “Over-O” model, indicating the latter stacking model is more stable. Note the shadow region in Fig. 4, which indicates the region where the bulk phases begin to form. Under the condition of Al + C ≤ −8.1 eV, Al2 CO tends to change into O2 . Otherwise, single Al and Graphite may be formed when Al + C ≥ 0. Actually, these regions would not be of interest because Mg/Al2 CO interfaces can only be formed under the condition of −8.1 eV ≤ Al + C ≤ 0. It has been deduced through crystallographic analysis that stable Mg/Al2 CO interface can be formed with combination of closepacked planes in Mg and Al2 CO crystal [15]. In addition, from Table 3 we can see that the “Over-O” model has a larger work of adhesion. It results in the lower interfacial energy for AlOtermination over the whole range of Al + C . Therefore, the most favorable Mg(0 0 0 2)/Al2 CO(0 0 0 1) interfacial structure is the AlO-terminated “Over-O” stacking interface. 4.5. Heterogeneous nucleation of Al2 CO In general, the First-principle calculations were performed at 0 K levels. It has been proved that the calculated results match well with experimental study for solid phase structure and solid–liquid interface [18,37]. Therefore, we discuss the heterogeneous nucleation mechanism by this method. According to the classical spherical cap model or adsorption model, it is thermodynamically believed that the interfacial energy between nucleation particles and ␣-Mg must be less than the interfacial energy between ␣-Mg and magnesium melts, which is 0.1 J/m2 for solid–liquid interface in Mg melt [36]. As can be seen in Fig. 4,
In order to understand the heterogeneous nucleation potential of Al2 CO for ␣-Mg grain in Mg–Al alloys melt, the interface atomic structure, work of adhesion and interfacial energy of the Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface were studied with the firstprinciples calculations. The main conclusions are summarized as follows. (1) Surface convergence test revealed that for AlO-terminated Al2 CO(0 0 0 1) slab, the relaxation effects are mainly localized in the first atomic layer. And the Al2 CO(0 0 0 1) slab with more than five atomic layers can exhibit bulk-like interior feature. (2) Analysis on electronic structure and bonding of AlO-terminated Mg(0 0 0 2)/Al2 CO(0 0 0 1) interface shown that the mixed ionic/metallic bonds are formed near the “Over O” stacking interface, while the “Over Al” stacking interface exhibits predominantly metallic bonding character. Further comparison on the work of adhesion and interfacial energy indicated that “Over-O” stacking interface is more stable than “Over Al” stacking interface. Therefore, the Mg atoms prefer to directly stack on O atoms with an “Over O” stacking sequence when Mg atoms grow on Al2 CO(0 0 0 1) slab. (3) The calculated interfacial energies of Mg/Al2 CO with “Over O” and “Over Al” stacking sequence both depend on the value of Al + C . In the range of −8.1 eV < Al + C ≤ −2.71 eV for “Over O” stacking and −8.1 eV < Al + C ≤ −2.84 eV for “Over Al” stacking, the Mg/Al2 CO interfacial energies are less than that between ␣-Mg and magnesium melts. Namely, the Al2 CO particles will become effective nucleation substrate for ␣-Mg under certain conditions. The above calculation and analysis thermodynamically proved the Al2 CO nucleus hypothesis and explain some experimental phenomenon observed recently. Acknowledgements The authors gratefully acknowledge the financial supports from National Natural Science Foundation of China (No. 51264032) and the Ministry of Education Scientific Research Foundation for the returned overseas (Lot. 44). References [1] A. Luo, Recent magnesium alloy development for elevated temperature applications, International Materials Reviews 49 (2004) 13–30. [2] H. Friedrich, S. Schumann, Research for a new age of magnesium in the automotive industry, Journal of Materials Processing Technology 117 (2001) 276–281.
884
F. Wang et al. / Applied Surface Science 285P (2013) 879–884
[3] S.F. Liu, L.Y. Liu, L.G. Kang, Refinement role of electromagnetic stirring and strontium in AZ91 magnesium alloy, Journal of Alloys and Compounds 450 (2008) 546–550. [4] J. Du, J. Yang, M. Kuwabara, W. Li, J. Peng, Improvement of grain refining efficiency for Mg–Al alloy modified by the combination of carbon and calcium, Journal of Alloys and Compounds 470 (2009) 134–140. [5] D.H. StJohn, M. Qian, M.A. Easton, P. Cao, Z. Hildebrand, Grain refinement of magnesium alloys, Metallurgical and Materials Transactions A 36 (2005) 1669–1679. [6] E. Yano, Y. Tamura, T. Motegi, E. Sato, Effect of carbon powder on grain refinement of an AZ91E magnesium alloy, Materials Transactions (Japan) 44 (2003) 107–110. [7] Y.M. Kim, C.D. Yim, B.S. You, Grain refining mechanism in Mg–Al base alloys with carbon addition, Scripta Materialia 57 (2007) 691–694. [8] T.J. Chen, X.D. Jiang, Y. Ma, Y.D. Li, Y. Hao, Grain refinement of AZ91D magnesium alloy by SiC, Journal of Alloys and Compound 496 (2010) 218–225. [9] K.F.W.A.N.G. Li, Q. Wang, N.G. Zhou, Study on grain refining mechanism of carbon inoculation on Mg–Al alloy, Journal of Shanghai Jiaotong University 17 (2012) 301–305. [10] M. Qian, P. Cao, Discussions on grain refinement of magnesium alloys by carbon inoculation, Scripta Materialia 52 (2005) 415–420. [11] Y.H. Liu, X.F. Liu, X.F. Bian, Grain refinement of Mg–Al alloys with Al4 C3 –SiC/Al master alloy, Materials Letter 58 (2004) 1282–1287. [12] V. Klimov, G. Bergman, O. Karlina, Thermodynamic properties of aluminum monooxycarbide Al2 OC, Russian Journal of Physical Chemistry 80 (2006) 1816–1818. [13] J.M. Lihrmann, T. Zambetakis, M. Daire, High temperature behavior of the aluminum oxycarbide Al2 OC in the system Al2 O3 –Al4 C3 and with additions of aluminum nitride, Journal of the American Ceramic Society 72 (1989) 1704–1709. [14] M.-X. Zhang, P. Kelly, M. Easton, J. Taylor, Crystallographic study of grain refinement in aluminum alloys using the edge-to-edge matching model, Acta Materialia 53 (2005) 1427–1438. [15] M.X. Zhang, P.M. Kelly, M. Qian, J.A. Taylor, Crystallography of grain refinement in Mg–Al based alloys, Acta Materialia 53 (2005) 3261–3270. [16] K. Li, Z.G. Sun, F. Wang, N.G. Zhou, X.W. Hu, First-principles calculations on Mg/Al4 C3 interfaces, Applied Surface Science 270 (2013) 584–589. [17] Y.F. Han, Y.B. Dai, D. Shu, J. Wang, B.D. Sun, First-principles study of TiB2 (0 0 0 1) surface, Journal of Physics: Condensed Matter 18 (2006) 4197–4205. [18] Y. Han, Y. Dai, D. Shu, J. Wang, B. Sun, First-principles calculations on the stability of Al/TiB2 interface, Applied Physics Letters 89 (2006) 144107. [19] Y.F. Han, Y.B. Dai, J. Wang, D. Shu, B.D. Sun, First-principles calculations on Al/AlB2 interfaces, Applied Surface Science 257 (2011) 7831–7836. [20] H. Dai, J. Du, L. Wang, C. Peng, X. Liu, First-principle study of the AlP/Si interfacial adhesion, Physica B: Condensed Matter 405 (2010) 573–578.
[21] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Physical Review B 136 (1964) 864. [22] B.G. Pfrommer, M. Côté, S.G. Louie, M.L. Cohen, Relaxation of crystals with the quasi-Newton method, Journal of Computational Physics 131 (1997) 233–240. [23] K. Laasonen, A. Pasqurello, R. Car, C. Lee, D. Vanderbilt, Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Physical Review B 47 (1993) 10142–10153. [24] J. White, D. Bird, Implementation of gradient-corrected exchange-correlation potentials in Car-Parrinello total-energy calculations, Physical Review B 50 (1994) 4954. [25] M. Marlo, V. Milman, Density-functional study of bulk and surface properties of titanium nitride using different exchange-correlation functionals, Physical Review B 62 (2000) 2899. [26] F. Wang, K. Li, M.Q. Zhan, First-principles study of surface properties for Al2 CO, in: The 10th Asia Thermophysical Properties Conference, Jeju, Korea, 2013 (in press). [27] 2002 JCPDS-International Centre for Diffraction Data, PCPDFWIN v.2.3. [28] S. Yip, J. Li, M. Tang, J. Wang, Mechanistic aspects and atomic-level consequences of elastic instabilities in homogeneous crystals, Materials Science and Engineering A 317 (2001) 236–240. [29] J. Neugebauer, M. Scheffler, Adsorbate–substrate and adsorbate–adsorbate interactions of Na and K adlayers on Al (1 1 1), Physical Review B 46 (1992) 16067. [30] Y. Wang, M. Xia, Z. Fan, X. Zhou, G. Thompson, The effect of Al8 Mn5 intermetallic particles on grain size of as-cast Mg–Al–Zn AZ91D alloy, Intermetallics 18 (2010) 1683–1689. [31] A. Arya, E.A. Carter, Structure, bonding, and adhesion at the TiC (1 0 0)/Fe (1 1 0) interface from first principles, The Journal of Chemical Physics 118 (2003) 8982. [32] D.J. Siegel, L.G. Hector Jr., J.B. Adams, Adhesion, stability, and bonding at metal/metal-carbide interfaces: Al/WC, Surface Science 498 (2002) 321–336. [33] L. Liu, S. Wang, H. Ye, First-principles study of polar Al/TiN (1 1 1) interfaces, Acta Materialia 52 (2004) 3681–3688. [34] Y. Li, Y. Gao, B. Xiao, T. Min, S. Ma, D. Yi, Theoretical calculations on the adhesion, stability, electronic structure, and bonding of Fe/WC interface, Applied Surface Science 257 (2011) 5671–5678. [35] L. Liu, S. Wang, H. Ye, Adhesion and bonding of the Al/TiC interface, Surface Science 550 (2008) 46–56. [36] Q. Jiang, H. Lu, Size dependent interface energy and its applications, Surface Science Reports 63 (2008) 427–464. [37] J. Wang, A. Horsfield, U. Schwingenschlögl, P.D. Lee, Heterogeneous nucleation of solid Al from the melt by TiB2 and Al3 Ti: an ab initio molecular dynamics study, Physical Review B 82 (2010) 184203. [38] E. Yano, Y. Tamura, T. Motegi, E. Sato, Effect of pure carbon powder on grain refining of cast magnesium alloy AZ 91, Journal of Japan Institute of Light Metals 51 (2001) 599–603.