Trans. Nonferrous Met. Soc. China 24(2014) 2034-2040

Crystallographic study of Al₃Zr and Al₃Nb as grain refiners for Al alloys

Feng WANG¹, Dong QIU¹, Zhi-lin LIU¹, John TAYLOR¹, Mark EASTON², Ming-xing ZHANG¹

1. School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia;

2. School of Physics and Materials Engineering, Monash University, Clayton, VIC 3800, Australia

Received 17 October 2013; accepted 25 April 2014

Abstract: The potency of Al₃Zr and Al₃Nb as grain refiners for Al alloys was investigated from a crystallographic point of view using the edge-to-edge matching (E2EM) model. The results show that both Al₃Zr and Al₃Nb have small values of interatomic spacing misfit and interplanar spacing mismatch with respect to Al. Furthermore, energetically favourable orientation relationships predicted by the model exist between Al and each of these two intermetallic phases. In the light of the edge-to-edge matching model predictions, it is suggested that both Al₃Zr and Al₃Nb are potent heterogeneous nucleation refiners for Al grains from the crystallographic point of view. The present crystallographic analysis provides a more reasonable explanation for the significant grain refinement obtained in the peritectic Al-Zr and Al-Nb alloys and also provides fresh insight into the understanding of the grain refinement mechanism of Al alloys.

Key words: Al alloy; A₃Zr; Al₃Nb; grain refinement; peritectic; crystallography; E2EM model

1 Introduction

In commercial production, the grain refinement of Al and its alloys through inoculation (i.e., adding master alloys/grain refiners into melt before casting) is common practice to obtain fine, uniform and equiaxed grain structure because fine grains can not only improve the soundness and mechanical properties of castings but also facilitate the subsequent deformation processing and hence ensure consistent performance of the final products [1-4]. Over the past 60 years, extensive research work has been carried out to develop efficient grain refiners for various Al alloys, and many theories/models have been proposed to clarify the mechanism underlying the obtained grain refinement [3-13]. In general, it is agreed that two components, numerous potent nucleants and sufficient effective solutes, are required to achieve effective grain refinement [1-5,9,11,14]. Potent nucleants promote the nucleation of α(Al) at small undercoolings while effective solutes provide constitutional undercooling to trigger further nucleation on adjacent nucleant particles. In spite of the common recognition of these two components, the details of the grain refinement mechanism are still of some controversy as none of the existing theories can fully explain all the observations in both experiments and practice. One of the major controversial and important issues is the determination of key factors that control the efficiency of grain refinement. For instance, a number of new grain refiners [15,16] developed for Mg-Al based alloys and Ti alloys show relatively low grain refining efficiency in comparison with that expected from the combined effect of nucleant particles and solutes. Therefore, it is expected that something important in controlling the grain refinement efficiency is still missing. In addition, it is also noted that the spotlight of the grain refinement of Al alloys is mainly focused on Al-Ti, Al-Ti-B and Al-Ti-C systems since they are the most widely-used grain refiners in the foundry [1,2,11]. However, it has been long realized that many other peritectic Al systems are also associated with appreciable grain refinement of Al such as Al-Zr, Al-Nb and Al-V alloys [17-19]. It is believed that, through the study of these peritectic Al systems, new light may be shed on the factors that control the grain refinement efficiency and hence on the grain refinement mechanism in Al alloys.

Most recently, the grain refining effect of a few peritectic-forming solutes including Zr and Nb on pure Al has been re-examined by WANG et al [20]. Significant grain refinement was obtained by adding Zr and Nb at levels above their maximum solubilities in Al.

Using the Q-value model, it is suggested that substantial grain size reduction induced by the addition of Zr and Nb is mainly attributed to the introduction of newly-formed nucleant particles that promote the grain refinement via the enhanced heterogeneous nucleation. Based on the scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD) and thermal analysis results, these in-situ-formed nucleant particles are further identified to be Al₃Zr and Al₃Nb pro-peritectic particles, respectively. Nevertheless, little evidence was provided to confirm the potency of Al₃Zr and Al₃Nb particles as heterogeneous nucleation sites for Al. Therefore, one of the major aims of the this work is to evaluate the nucleation potency of Al₃Zr and Al₃Nb to verify the mechanism proposed in the previous paper.

2 Introduction to edge-to-edge matching model

It is well known that the interfacial energy between the nucleant particle and the metal matrix is of critical significance in determining the potency of nucleant particles [1,2]. In general, good crystallographic matching favours the formation of a low-energy interface between the nucleant particle and the metal matrix, which facilitates the heterogeneous nucleation and hence promotes the grain refinement. Conventionally, the crystallographic matching was simply examined through the calculation of lattice matching based on the lattice parameters [21]. However, in real situations, a great majority of nucleant particles have complex crystal structure, of which crystallographic matching with metal matrix is more than lattice matching because it is the real atoms that form the interface between phases. To overcome the shortcoming of simple calculation of lattice matching, an edge-to-edge matching (E2EM) model was employed.

The edge-to-edge matching model was originally developed by ZHANG and KELLY [22,23] for the examination of actual atomic matching across an interface between adjacent phases of diffusion-controlled phase transformations in solids. It has the ability to predict possible orientation relationship (OR) and the corresponding habit plane/interface with matrix from the first principles. The model is based on a critical assumption that the interfacial crystallographic features are governed by the minimization of the interfacial strain energy through the maximization of atomic matching in the two phases. In general, the atomic row-matching condition can be fulfilled when the atomic rows along the edges of a pair of conjugate crystallographic plane meet at the interface, as shown in Fig. 1 [22,23]. To maximize the atomic matching along the parallel rows, the matching rows should be close packed (CP) or nearly CP directions with small interatomic spacing misfit (f_r). The value of f_r should be less than 10% for a reproducible OR. The matching rows can be either straight or zigzag but the model requires that straight rows match with the straight rows, while zigzag rows match with the zigzag rows. In addition, the conjugate planes containing the matching rows should be a pair of CP or nearly CP planes with similar interplanar spacings. They are termed matching planes. The smaller the interplanar spacing mismatch (f_d<10%) is, the easier the interface meets the row-matching requirement. Once the above conditions are fulfilled, an energetically favourable OR between the two phases can be constructed and expressed in terms of the parallelism of the matching rows and near parallelism of the matching planes. The accuracy of the OR and the orientation of the interface can be further refined by using the △g parallelism criterion [24,25].

Fig. 1 Schematic diagram of interface meeting edge-to-edge matching conditions [22,23]

In recent years, the E2EM model has been widely applied to the area of grain refinement through the inoculation during solidification. Great success has been achieved in many aspects such as evaluating the potency of grain refiners [26-28], understanding the mechanisms of grain refinement and poisoning phenomena [29-31] and discovering new and effective grain refiners [32] in both Al and Mg alloys. Following the preceding success, in this work, the E2EM model was used to examine the crystallographic matching between the Al matrix and Al₃Zr as well as Al₃Nb particles. As a result, the potency of Al₃Zr and Al₃Nb as nucleant substrates for Al can be evaluated from the crystallographic point of view.

3 Crystallography of Al₃Zr and Al₃Nb with Al matrix

In principle, the E2EM model calculation involves the following two major steps [27,28]: 1) the identification of CP or nearly CP atomic rows and planes of all the phases based on the crystal structure and atomic positions, and 2) the calculation of interatomic misfit, f_r, along the matching rows and the interplanar spacing mismatch, f_d, between the matching rows based on the corresponding lattice parameters. Table 1 lists the crystal structure, lattice parameters and atomic positions of Al, Al₃Zr and Al₃Nb phases [33]. Using these crystallographic data, the CP or nearly CP atomic rows and planes of these three phases can be identified. As a simple face-centred-cubic (FCC) structure, Al has three possible CP or nearly CP planes: {111}_Al, {020}_Al and {220}_Al. {111}_Al is the most CP plane that contains two CP directions:  and For convenience, superscripts of “S” and “Z” are used to distinguish straight and zigzag rows. The second most CP plane, {020}_Al, contains only one CP directions, i.e., , while the third most CP plane, {220}_Al, contains two CP directions of  and . The Al₃Zr phase has a tetragonal crystal structure with three CP or nearly CP planes. The most CP plane is the  plane, which contains three CP rows: ,  and . The second most CP plane of the Al₃Zr phase is the  plane that contains only one CP row of Another possible CP plane is  plane that contains two CP rows of  and . Having a similar structure as Al₃Zr, Al₃Nb also has three CP or nearly CP planes. They are and The  plane contains four CP or nearly CP rows that are  and  while the  contains only one CP row of . The  plane also contains only one CP row of . The atomic configurations of Al, Al₃Zr and Al₃Nb within their most CP planes are schematically shown in Fig. 2.

Based on the identified CP rows and CP planes, the interatomic spacing misfit along the CP rows between the Al matrix and Al₃Zr as well as Al₃Nb was calculated and listed in Table 2. It is important to note that the interatomic spacing misfit, f_r, is defined by

, rather than              (1)

where r_M is the interatomic spacing along a certain CP row of metal matrix, and r_P is the interatomic spacing along the corresponding matching CP row of inoculant particle. It can be seen from Table 2 that all the values of f_r are less than the critical value of 10%. Following that, the interplanar spacing mismatch, f_d, of the CP or nearly CP planes between the Al matrix and Al₃Zr as well as Al₃Nb was further calculated using the equation:

                              (2)

where d_M is the interplanar spacing of a certain CP plane of the metal matrix, and d_P is the interplanar spacing of the corresponding matching CP plane of the inoculant particle. The quantitative results of f_d are graphically illustrated in Fig. 3. As shown in Fig. 3(a), between Al and Al₃Zr, there are only three pairs of CP planes having smaller f_d than 10%. They are {111}_Al// with f_d=1.34%,  with f_d=1.05% and  with f_d=1.05%. Figure 3(b) shows the values of f_d between Al and Al₃Nb. It can be seen that four pairs of CP planes between Al and Al₃Nb have interplanar spacing mismatch, f_d, less than 10%. They are with f_d=1.78%,  with f_d=8.63%,  with f_d=5.93%, and  with f_d=5.43%.

Table 1 Crystal structure, lattice parameters and atomic positions of Al, Al₃Zr and Al₃Nb phases [33]

Fig. 2 Atomic configurations of Al (a), Al₃Zr (b) and Al₃Nb (c) on their respective most CP planes

Table 2 Interatomic spacing misfit, f_r, along CP matching rows between Al and Al₃Zr as well as Al₃Nb

According to the E2EM model [27,28], the construction of possible ORs requires that the matching rows must lie in the matching planes. Therefore, the CP row pairs with f_r less than 10% (Table 2) and the corresponding CP planes that contain these row pairs with f_d smaller than 10% (Fig. 3) are represented in Fig. 4. Since a given pair of rows often lie in one or more pair of planes, the arrows are used to indicate the associated plane pairs for a given row pair.

Figure 4(a) shows that, combining the matching row pairs with the plane pairs that contain the matching rows, six possible ORs between Al and Al₃Zr can be obtained. Using the △g parallelism criterion, these six possible ORs are finally refined to three distinguishable ORs which are listed in Table 3.

Following that, six possible ORs between Al and Al₃Nb are also obtained as shown in Fig. 4(b) by combining the matching row pairs with the plane pairs that carry the matching rows. After the refinement of these six possible ORs, three different ORs are finally predicted as shown in Table 4.

Fig. 3 Interplanar spacing mismatch, f_d, between Al and Al₃Zr (a) and between Al and Al₃Nb (b)

Table 3 Refined crystallographic ORs between Al and Al₃Zr

Table 4 Refined crystallographic ORs between Al and Al₃Nb

Fig. 4 Graphic representation of matching row pairs (Table 2) and related suitable matching plane pairs (Fig. 3) that carry matching row pairs between Al and Al₃Zr (a), Al and Al₃Nb (b), as predicted by E2EM model

4 Discussion

Based on the above crystallographic analysis using the E2EM model, the potency of Al₃Zr and Al₃Nb as nucleation sites for Al grains can be evaluated. According to the E2EM model, small f_r along the matching rows and low f_d between the matching planes can reduce the interfacial energy between the inoculant particles and metal matrix and hence correspond to high grain refining potency [26-28]. It can be seen from Table 2 and Fig. 3 that both the Al₃Zr and Al₃Nb phases have very small values of f_r and f_d with respect to Al, indicating that these two phases are good grain refiners for Al grains. In particular, the values of f_r and f_d between Al₃Nb and Al are very close to those between Al and Al₃Ti [27] that is one of the most effective grain refiners employed in the industrial practice. This implies that Al₃Nb has the same potential as Al₃Ti as grain refiners for Al grains from the crystallographic point of view.

In the practice of grain refinement by inoculation, it is found that an efficient grain refiner normally has one or more suitable and reproducible OR with the matrix [1,2,11]. Previous studies have proven that the great majority of the reported ORs between the common grain refiners and the Al or Mg matrix are consistent with the predicted ORs by E2EM model [27,28]. It can be seen from Tables 3 and 4 that both the Al₃Zr and Al₃Nb phases have been predicted to have three distinguishable ORs with Al by E2EM model. Unfortunately, unlike the common grain refiners for Al alloys, these predicted ORs between Al and Al₃Zr as well as Al₃Nb cannot be experimentally verified at this stage due to the lack of accurate experimental data on ORs. Currently, the authors are working on the experimental determination of ORs between Al and Al₃Zr as well as Al₃Nb using the electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The detailed results will be published in the future papers.

5 Conclusions

1) Both Al₃Zr and Al₃Nb have very small values of interatomic spacing misfit along the matching rows and interplanar spacing mismatch between the matching planes with respect to Al, indicating that these two phases are good nucleant particles for Al grains.

2) Three potential ORs between Al and Al₃Zr are predicted as follows:

OR A1: , 1.34° from ,  3.50° from ;

OR B1: ,  1.26° from , 0.04° from ;

OR C1: 0.68° from ,  1.30° from , 0.68° from .

Three distinguishable ORs between Al and Al₃Nb were predicted as follows:

OR A2:  2.13° from , // ,  1.07° from ;

OR B2: 1.85°from  1.64° from ,  1.76° from ;

OR C2: //,  1.92° from ,  0.24° from .

Acknowledgement

The authors are very grateful to the Australian Research Council for funding support. Feng WANG would also like to acknowledge the support of China Scholarship Council.

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Al₃Zr和Al₃Nb作为铝合金晶粒细化剂的晶体学研究

汪 锋¹，邱 冬¹，刘峙麟¹，John TAYLOR¹，Mark EASTON²，张明星¹

1. School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia;

2. School of Physics and Materials Engineering, Monash University, Clayton, VIC 3800, Australia

摘  要：利用edge-to-edge matching 模型从晶体学角度研究Al₃Zr 和 Al₃Nb两种金属间化合物作为铝合金晶粒细化剂的有效性。结果表明，Al₃Zr和Al₃Nb两种金属间化合物和铝之间的原子间距错配和面间距错配值都很小。此外，模型预测Al₃Zr和Al₃Nb两种金属间化合物与铝之间存在良好的晶粒取向关系。根据模型理论可以从晶体学角度证明这两种金属间化合物对铝合金是有效的晶粒异质形核细化剂。本晶体学研究为包晶铝合金Al-Zr和Al-Nb中出现的明显晶粒细化现象提供了合理解释，同时为理解晶粒细化机理提供了新方法。

关键词：铝合金；Al₃Zr；Al₃Nb；晶粒细化；包晶；晶体学；E2EM模型

(Edited by Wei-ping CHEN)

Corresponding author: Ming-xing ZHANG; Tel: +61-07-33468709; E-mail: mingxing.zhang@uq.edu.au

DOI: 10.1016/S1003-6326(14)63309-4