Journal of Materials Science & Technology  2019 , 35 (11): 2625-2629 https://doi.org/10.1016/j.jmst.2019.07.029

Orginal Article

The stability of deformation twins in aluminum enhanced by alloying elements

Linghong Liuab, Jianghua Chena*, Touwen Fana, Shunli Shangc, Qinqin Shaoa, Dingwang Yuana, Yu Daid

aCenter for High-Resolution Electron Microscopy, College of Materials Science and Engineering, Hunan University, Changsha, 410082, China
bCollege of Science, Central South University of Forestry and Technology, Changsha, 410004, China
cDepartment of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA
dAdvanced Corporation for Materials & Equipment, Changsha, 410111, China

Corresponding authors:   *Corresponding author.E-mail address: jhchen123@hnu.edu.cn (J. Chen).

Received: 2019-02-20

Revised:  2019-04-20

Accepted:  2019-05-5

Online:  2019-11-05

Copyright:  2019 Editorial board of Journal of Materials Science & Technology Copyright reserved, Editorial board of Journal of Materials Science & Technology

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Abstract

Introducing and stabilizing twins in aluminum is a challenge for metals research due to their high formation energy. Employing first-principles calculations, we investigated the twin boundary segregation of alloying elements and their impact on the twin boundary energy in aluminum. Alloying elements with small solubilities but strong interaction with twin boundary would significantly reduce twin boundary energies in aluminum at low temperatures. With increasing temperature, their segregation near twin boundary weakens, leading to their influence on twin boundary energies reduced. Some elements with large solubilities may greatly reduce the twin energies not only at low temperatures but also at high temperatures. Based on careful analysis of charge density and atomic radius, it has been found that chemical difference has little influence on twin boundary energy whereas the atomic size effect plays a leading role in causing the change of twin boundary energy.

Keywords: Twins ; Twin boundary energy ; Al alloy ; First-principles calculations

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Linghong Liu, Jianghua Chen, Touwen Fan, Shunli Shang, Qinqin Shao, Dingwang Yuan, Yu Dai. The stability of deformation twins in aluminum enhanced by alloying elements[J]. Journal of Materials Science & Technology, 2019, 35(11): 2625-2629 https://doi.org/10.1016/j.jmst.2019.07.029

1. Introduction

Stacking fault energy (SFE) and twin boundary energy (TBE) are two important intrinsic parameters for understanding the plastic deformation of metals [[1], [2], [3], [4]]. With reducing SFE, partial dislocation slip and twinning may be stimulated and twins may form in deformed metals. Twins may play very important roles in improving plasticity, strength and formability of metals [1]. On the one hand, twins can change the crystal orientation, thereby affecting the dislocation motion and thus coordinating the matrix deformation. On the other hand, twin boundary (TB) as a barrier may hinder the movement of dislocations, and result in work hardening. Therefore, deformation twins have the potentials to improve the strength and toughness of materials. In general, the SFE reflects the possibility of twin formation, whereas TBE mainly affects the stability of twins.

Thus far a large number of studies have shown great potentials of alloying elements for increasing the formation possibilities of twins in metals. For instance, the dark field scanning transmission electron microscope observation revealed that alloying elements can segregate to TBs, providing the pinning effect and causing the anomalous phenomenon of “annealing strengthening” [5,6]. The total energy change of a twin system before and after segregation is called the twin boundary segregation energy (TBSE) [7]. This energy is used to evaluate the segregation ability quantitatively and to predict the effect of alloying elements on twinning strengthening. Although it is closely related to the properties of alloys, the TBSE is difficult to be measured through experimental methods and also the available data are only for pure metals [8]. Alternatively, the first-principles calculation method can accurately predict such energy values. Using density functional theory (DFT), Zhang et al. [7] investigated the migration and segregation ability of solutes into TBs by computing the TBSE and the solute-diffusion activation enthalpy. Focusing on the structure and energy of TBs, Kumar et al. [9] found that those alloying elements with much greater or much smaller metallic radius than that of the matrix atoms (Mg, Ti and Zr) generally have a larger solubility at TB than that in bulk.

For aluminum, however, no investigation has been made about the interaction between alloying elements and twins, simply because it is hard to form twins in the Al-matrix. Al is a face centered cubic (fcc) metal with a high SFE of 110-160 mJ/m2 [[10], [11], [12], [13]], which intrinsically makes it difficult to introduce twins in the bulk Al material. Even though, a few studies have evidently shown the possibility to produce twins in the Al-matrix under circumstances. Molecular dynamics simulations and subsequently experimental observations has demonstrated that twinning mechanism does exist in nanocrystalline Al or Al alloys [[14], [15], [16], [17]]. Our previous study suggested that some alloying elements may drastically lower the SFE of Al alloys at low temperatures, indicating that it is possible to introduce twins in Al if alloyed with proper alloying elements [13]. In addition, it has been shown that the stress concentration near a crack tip can lead to deformation twinning in a pure polycrystalline Al [18]. In a recent study, deformation twins in an Al single crystal have been observed when the material was severely deformed via a novel dynamic equal channel angular pressing technique (D-ECAP) [19]. Hence, the following has become a meaningful issue: can the formed twins in a bulk Al be stabilized through adding proper alloying elements to reduce the TBE in the material?

Nonetheless, as mentioned above, on the one hand, there are no adequate experimental data available about the TBE values in Al alloys, since twins are difficult to form experimentally, On the other hand, there are very few theoretical studies about the TBE values of Al alloys in correlation with the environmental temperature, largely due to the methodology limitation of the traditional computation method. For example, the concentration of alloying elements cannot be chosen randomly and the influence of temperature is usually neglected [20]. In fact, to go beyond such methodology limitation, our previous studies have demonstrated that the TBE values of Al alloys in relation with the temperature and with the concentration of alloying elements can be obtained by calculations, using (1) the important physical quantity TBSE and (2) a method of the so-called single atom interaction energy model [13,21]. In the present study, using such an approach we will focus on seeking possible alloying elements to potentially lower the TBE values of Al alloys, providing a theoretical guidance for further understanding the twin properties in Al materials.

2. Computational method

The ideal stacking sequence of fcc Al is …ABCABCABC….with A, B and C being the closed-packed planes for {111} as shown in Fig. 1(a). If the upper layers identified by the orange shadow are displaced along the [11] direction by a distance a0/$\sqrt{6}$ (a0 is the lattice constant), and then the intrinsic stacking fault (ISF)…ABCBCABC… is created as shown in Fig. 1(b). On the basis of the ISF structure, if the upper layer (i.e. identified by the orange shadow in Fig. 1(b)) are displaced along [11] over a distance a0/$\sqrt{6}$ continually, the structure of a two-layer fault are formed. Then the fully symmetrical twinning structure (as shown in Fig. 1(c)) is created while continuing to slip 5 times in accordance with the same method. For convenience of description, we define the plane of the TB as layer 0, the planes nearest to the TB are defined as layer 1, and so are the other planes, respectively, named as layer 2, 3, 4,…n according to their distances to the TB. It is noteworthy that each supercell contains two TBs.

Fig. 1.   Selective schematic structures to explain the operations leading to the formation of stacking fault and twin: (a) perfect sequence, (b) intrinsic stacking fault configuration, (c) fully symmetrical twin structure, red line represents the TB.

TBE of pure Al can be calculated as follows [9]

ET=(ETB-EP)/2A, (1)

where ETB and EP are the total energies of the twinned and perfect structures, respectively. A is the area of the twin boundary, and “2” accounts for the two identical boundaries in the simulation model. Then, the increment of TBE caused by alloying elements can be determined according to Eq. (2) [13,21]

ΔET=∑cnEint-n/A, (2)

where cn is the concentration of alloying elements at the nth plane based on the Fermi-Dirac distribution [21]

cn=$\frac{1}{1+exp[(E_{int-n}-kTln\frac{c_0}{1-c_0})/kT]}$, (3)

where c0 is the initial concentration before atoms segregating to the TB (i.e., the concentration of alloying elements in the plane with Eint-n=0). Eint-n is the interaction energy between TB and alloying elements when they are located in the nth plane, i.e., TBSE [7]:

Eint-n=Es-n-Es-r, (4)

where Es-n and Es-r are the energies of the supercells with one alloying element located in the nth and rth layers, respectively. The rth layer is the reference layer. In the present study, the reference layer is chosen as layer 4 due to its far distance from the TB.

We perform the DFT based first-principles calculations using the Vienna Ab initio Simulation Package (VASP) [22] and the projector augmented waves (PAW) method [23]. The Perdew-Burke-Ernzerhof (PBE) parameterization of the generalized gradient approximation (GGA-PBE) [24] is used for exchange-correlation functional. In order to mimic the dilute distribution of alloying elements in matrix, a 144-atom supercell (with 16 (111) layer and 9 atoms per layer) is used as seen in Fig. 1(c). During the calculations, a cutoff energy of 350 eV is employed for the plane-wave basis ensuring an accurate result. For the Brillouin zone integration, a Monkhorst-Pack 7 × 7 × 1 k-point mesh is used for all calculations. The convergence criteria are selected as the Hellmann-Feyman force acting on atoms of 0.01 eV/Å and the total energy of 10-5 eV per unit-cell.

3. Results and discussion

For the purpose of studying the effects of alloying elements on the TBE of Al alloys, we firstly calculate the TBE of pure Al. The present TBE value of pure Al is 52 mJ/m2, which agrees well with the values (56-64 mJ/m2) from the previous first-principles calculations [3,10,12,25,26].

To find the alloying elements which would obviously reduce the TBE of Al alloys, 30 commonly and uncommonly used alloying elements in Al alloys are selected. The calculated Eint-n values are illustrated in Fig. 2. Note that negative value indicates that the alloying element prefers to stay at the TB, and make some effects on the TBE. The positive interaction energy means that the alloying element will be excluded by the TB, which would lead to a small concentration of alloying elements near the TB, so they have little effect on the TBE. Therefore, we mainly focus on the negative interaction energies. For conveniently describing the results, the uncommon and common alloying elements are displayed separately in Fig. 2(a) and (b). In general, the interactions of uncommon elements with TB are stronger than those of common elements. Furthermore, for most of the elements, the interactions are quite large when the alloying elements are located in layers 0 and 1, especially for the uncommon elements.

Fig. 2.   Eint-n between (a) uncommon elements, (b) common elements and TB as a function of distance from TB.

It is found that Eint(T) and cn(T) are two key quantities to determine the effect of alloying elements on the TBE. Because there is a one-to-one correlation between volume and temperature, and then temperature-dependence Eint(T) can be reflected by calculating the volume-dependence Eint(V) directly through first principles calculations [27]. The calculated results illustrate that changes of interaction energies with volume for all of the alloying elements are not obvious. For example, the maximum changes of Eint(V) for Sr and Y located in GB plane are 0.5% and 8%, respectively. The result agrees well with Ref. [13,28]. Therefore, it is reasonable to ignore the effect of temperature on the interaction energy by assuming that Eint(T) equals roughly to the energy at the ground state, i.e., Eint(0).

In this section, the effects of temperature and concentration will be discussed separately. Firstly, the temperature-dependence of the increment of TBE at the given nominal elements concentrations has been investigated, and the results are shown in Fig. 3. The initial concentration c0 of the common elements such as Mg, Zn, and Cu, are selected within the maximum solid solubility, while c0 of other elements with small or unknown solid solubility is taken as 10-5. Fig. 3(a) is about the uncommon elements in Al alloys, and their effects on TBE can be roughly divided into two different groups: (1) Alloying elements Pt, Cr, Ni, V, Be, Mo, Na, and Co have almost no effect on the TBE of Al alloys, while Hf can slightly increase the TBE at high temperatures (only 3.4 mJ/m2 at 900 K); (2) Alloying elements K, Cs, Er, Rb, Sr, Yb, Ba, La, Y and Ca can greatly reduce the TBE at low temperatures. At the initial concentration c0, alloying elements Yb and Er have relatively little effect on TBE, followed by Y. Other alloying elements can greatly reduce the TBE at the temperatures lower than 400 K, so as to stabilize the twins. With increasing temperature, the alloying elements tend to be evenly distributed in the whole supercell, and the degree of segregation in the vicinity of TB decreases. Then their effect on the TBE is gradually reduced. When the temperature is higher than 400 K, the effect is gradually reduced to 0. Fig. 3(b) is about the common alloying elements. It is found that alloying elements Zr, Si, Mn and Ti have very little influence on TBE, while elements Mg, Zn, Li, Cu, Ge, Ag, and Sc have great impacts on TBE. When the temperature is reduced to 200 K, elements Mg, Zn, Sc and Ag would reduce the TBE values to 0 or even negative. Compared with alloying elements in Fig. 3(a), the interaction between these common elements and TB is not very strong, but their solubilities in Al alloy are relatively large. Therefore, they can reduce the TBE greatly. Moreover, the decreasing effect on TBE of the common elements is also obvious at high temperatures.

Fig. 3.   Increment of TBE induced by (a) uncommon elements and (b) common elements, under various temperatures at given c0, respectively.

ΔET at 300 K are calculated for various initial concentrations c0, and the results are shown in Fig. 4. In general, the higher the concentration c0, the greater influence of the alloying elements will be on the TBE. As literature [20] reported, TBE of Al-Mg alloy decreases obviously with increasing Mg content. But for some alloys, the TBE is not sensitive to the concentration, such as V, Na, Be, Hf, Cr, Co, Pt, Ni and Mo as shown in Fig. 4(a), and Si and Mn as shown in Fig. 4(b). The ΔET curve is basically coinciding with a horizontal line, which means that they have little effect on the TBE of Al alloys under the temperature of 300 K. At first, atoms, such as V, Mo, Co, and Cr, are not easy to stay at TBs due to their repulsive interactions with TBs. Then, the interaction between the alloying elements and TBs is too small to affect the TBE, although the initial concentration c0 is large (such as the Be atom). Finally, atoms, such as Na, do interact to some extent with the TB and there is a little impact on TBE due to their small solubility in Al alloys.

Fig. 4.   Increment of TBE induced by (a) uncommon elements and (b) common elements, under various concentrations c0 at 300 K, respectively.

Fig. 4(a) shows that alloying elements (Y, Ca, Er and Yb) have little influence on the TBE which (<10 mJ/m2 under the concentration range we considered), while the reducing effect on TBE of other elements is more obvious at higher concentrations. Particularly, when c0>0.003 at.%, elements Ba, Cs, La and Rb can lower the TBE to a negative value. As aforementioned, the influence of the common alloying elements Mn and Si on TBE is negligibly small. Fig. 4 illustrates that high solubility elements such as Mg, Zn, Li, Cu, Ge, Ag and Sc can greatly reduce the TBE under the condition of high initial concentrations c0, while both Ti and Zr atoms would slightly increase TBE with increasing concentration and the increment of TBE is still less than 10 mJ/m2 when c0 increases to 10 at.%.

In order to interpret the effect of alloying elements on TBE from a microscopic point of view, we carefully examined the charge distributions of different structures. However, there is no obvious difference in charge distribution when alloying elements added to the different layers of the twinning structures. It indicates that chemical difference is not the main factor that causes the change of TBE. But some interesting results are obtained through comparing the atomic radius. The atomic radius is crucial to the stress caused by the difference in atomic size between the alloying element and matrix [29]. Fig. 5 illustrates atomic radii of 30 alloying elements versus Eint-1, which shows a secondary polynomial relationship. It is obvious that strong attraction occurs in atoms with a radius being 0.2 times longer than Al. While the atoms whose radius is equal to or less than Al exhibit weak attraction or repulsion interaction with TBs. The result shows that the size effect plays a key role in TBE.

Fig. 5.   Atomic radius of alloying elements versus Eint-1, which shows a secondary polynomial relationship.

Generally, SFE and TBE are closely related to the plastic deformation of materials [10,19]. For Al alloys with high SFE (110-160 mJ/m2) [[10], [11], [12], [13]], deformation twins can rarely form. Our previous work [13] indicated that the possibilities to introduce twins in Al materials can be increased significantly by some alloying elements such as Sr, Y and Sc, to significantly lower the SFEs with a relative high concentration at low temperature. Actually, the deformation twins in Al has been observed experimentally [18,19]. But these twins are only associated with ultra-high strains. They will reverse as the strains relaxes or during the subsequent processing. According to our present and previous results [13], it is found that alloying elements Sc, Sr and Y would reduce both SFE and TBE under certain circumstance, which will be of great help to design high performance Al alloys.

4. Conclusions

Using first-principles calculations, we investigated the effect of 30 kinds alloying elements on the TBE of Al alloys induced by TB segregation. The results can be summarized as follows.

(1) Due to their strong interaction with TB, those alloying elements (i.e. K, Cs, Er, Rb, Sr, Yb, Ba, La, Ca and Y) with small solubilities in Al alloys can significantly reduce the TBE at low temperatures. While their influence is weakened because of the homogeneous distribution of alloying elements at high temperature.

(2) Although the atom-TB interactions of Mg, Zn, Sc and Ag are not large enough, they can effectively reduce the TBE both at low and high temperatures, due to their relatively large solubilities in Al alloy.

(3) Chemical difference has little influence on TBE whereas the atomic size effect is the main factor that causes the change of TBE.

Acknowledgements

This work is supported financially by the National Natural Science Foundation of China (Nos. 51701243, 11427806, 51471067 and 51371081), the Hunan Provincial Natural Science Foundation of China (No. 2019JJ40544), the Specialized Research Found for the Doctoral Program of Higher Education of China (No. 20120161110036), the National Basic Research (973) Program of China (No. 2009CB623704) and the PhD Research Startup Foundation of Central South University of Forestry and Technology (No. 2017YJ020), as well as by the supercomputer TH-1A installed at Hunan University.


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