Insights into Poisoning Mechanism of Zr by First Principle Calculation on Adhesion Work and Adsorption Energy between TiB₂, Al₃Ti, and Al₃Zr

Abstract

Al-Ti-B intermediate alloys are widely used as grain refiners in aluminum alloys owing to the presence of Al₃Ti and TiB₂ phases. However, the existence of Zr in aluminum alloy melts often results in coarse grain size, leading to Al-Ti-B failure called Zr poisoning. There are three kinds of poisoning mechanisms related to TiB₂, Al₃Ti, and a combination of TiB₂ and Al₃Ti for Zr. First, Zr forms ZrB₂ or Ti₂Zr with TiB₂ in Al-Ti-B to reduce the nucleation ability. Second, Zr existing in the aluminum melt with a high melting point Al₃Zr then attracts Ti to reduce the dispersion of Ti as a growth inhibitor. Third, Zr reacts with Al₃Ti on TiB₂ surface to form Al₃Zr, thereby increasing the degree of mismatch with Al and diminishing the refiner’s ability as a nucleation substrate. To gain a better understanding of the mechanism of Zr poisoning, the first principle was used in this study to calculate the adhesion works (ZrB₂//Al₃Ti), (Ti₂Zr//Al₃Ti), (Al₃Zr//Al₃Ti), (Al₃Ti//Al), (TiB₂//Al₃Zr), and (Al₃Zr//Al), as well as the surface energy of Al₃Zr and adsorption energies of Al to Al₃Ti or Al₃Zr. The results demonstrated that Zr poisoning originated from the second guess. Zr element exiting in aluminum melt led to the formation of an Al₃Zr (001) surface. The interfacial adhesion work of Al₃Zr (001)//Al₃Ti (001) was not weaker than that of TiB₂//Al₃Ti. As a result, Al₃Zr first combined with Al₃Ti to significantly decline the adsorption of Al₃Ti (001) on Al, losing its role as a nucleating agent and grain coarsening. Overall, to prevent failure of the grain refiner in Zr containing aluminum melt, the adhesion work interface between the generated phase of the grain refiner and Al₃Zr must remain lower to avoid the combination of the generated phase of grain refiner with Al₃Zr. In sum, these findings look promising for evaluating future effects of grain refinement in Zr containing aluminum melt.

1. Introduction

Aluminum is a metal with lower cost and lighter weight, thereby widely used in furniture, automobile, aerospace, and navigation. However, higher strength and toughness aluminum alloys are increasingly required for various practical applications. In this regard, grain refinement could be used to improve the microstructure, strength, and toughness of aluminum alloys, as well as reduce defects like component segregation, shrinkage porosity, and cracking.

Among refiners, Al-5Ti-1B is widely used in various fields. With the progress of time, three nucleation mechanisms take place: boride particle theory, peritectic reaction theory, and double nucleation theory [1,2]. Meanwhile, TiB₂ employed as a heterogeneous core with a high melting point possesses an orientation relationship between TiB₂ (0001)//Al (111) and Al. In this respect, Cibula et al. [3] proposed the boride particle theory with TiB₂ as the main nucleation core. By comparison, the peritectic reaction theory mainly considers Al₃Ti phase precipitated in the refiner as the nucleation core. For instance, Crossley et al. [4] proposed a peritectic reaction (L + Al₃Ti → α- Al) nucleation. However, both theories suffer from defects. For example, Gru’zleski et al. [5] directly added large amounts of TiB₂ particles to the melt and noticed the possible exclusion of TiB₂ toward the aluminum grain boundary, showing TiB₂ is not the main nucleating material. On the other hand, Ti content introduced into the refiner often does not reach 0.01 wt.%, thereby preventing the occurrence of peritectic reactions due to the very far lower Ti content than the level of peritectic reaction. The latest theory has to do with the dual nucleation theory, suggesting the formation of a thin layer of Al₃Ti on the TiB₂ surface. In this regard, Jones et al. [6] reported the easy segregation of Ti on TiB₂ surface by calculating the chemical formula in the melt. Qi et al. [7] noticed higher Ti content around TiB₂ in the refined aluminum alloy than that around TiB₂ in the refiner. Fan et al. [8] observed two-dimensional Al₃Ti by transmission electron microscopy. Schumacher et al. [9] recorded coating of a TiB₂ surface with Al₃Ti by transmission imaging after adding the refiner to aluminum-based glass alloy, further confirming the reliability of the double nucleation theory.

For aluminum alloys containing Zr, the effect of Al-5Ti-1B refiner would be significantly reduced [10]. Some studies dealing with Zr poisoning have so far been reported, and three kinds of Zr poisoning mechanisms have been recorded: targeting TiB_2,Al₃Ti and (TiB₂//Al₃Ti). Jones and Pearson suggested the association between Zr and TiB₂. They first proposed the replacement of Ti atoms by Zr on a TiB₂ surface in combination with boride particle theory. Under these conditions, ZrB₂ was also formed on TiB₂ surface, thereby affecting the ability of TiB₂ as a nucleation substrate. Wang et al. also noticed the associated Zr to TiB₂ and confirmed the dual nucleation theory through transmission imaging by observing Zr atoms on TiB₂ refiner surface in Al alloys containing Zr with Ti₂Zr formed on the surface. In this case, Zr may have caused the dissolution of Al₃Ti bimetallic compounds formed on the surface of TiB₂. Johnsson et al. [11] employed the peritectic reaction theory to propose Zr poisons free Al₃Ti in the melt, as well as a combination of Al₃Ti with Al₃Zr forming ternary compounds. The last kind of guess consisted of Zr poisoning (TiB₂//Al₃Ti), where Zr reacted with Al₃Ti thin layer on the TiB₂ surface, and Zr replaced Ti atom in Al₃Ti.

In the present study, vasp program was used to carry out calculations. For dual nucleation theory, calculations corresponding to three kinds of guesses for Zr poisoning mechanisms were performed. The first consisted of an Al melt without Zr: TiB₂ (0001)//Al₃Ti (112), Al₃Ti (112)//Al (111). The second dealt with Zr poisoning TiB₂ by calculating the works of TiB₂-ZrB₂ (0001)//Al₃Ti (112) and TiB₂-Ti₂Zr (0001)//Al₃Ti (112). The third had to do with Zr adsorption free Ti, where the minimum energy surface of Al₃Zr was first calculated followed by Al₃Ti (112)//Al₃Zr (114) and Al₃Ti (001)//Al₃Zr (001). Fourth, Zr poisoned Al₃Ti on a TiB₂ surface was explored by calculating TiB₂ (0001)//Al₃Ti-Al₃Zr (112) and TiB₂ (0001)//Al₃Zr (114). Finally, calculations related to Al₃Ti and Al₃Zr in contact with an Al melt were performed, including Al₃Ti (001)//Al (001), Al₃Zr (001)//Al (001), Al₃Ti-Al₃Zr (112)//Al (111), and Al₃Zr (114)//Al (111). Note that Al atoms were adsorbed by Al₃Ti and Al₃Zr.

The three kinds of guesses for the Zr poisoning mechanism and the first principle calculations are summarized in

Table 1. The three kinds of guesses for Zr poisoning mechanism and the first principle calculations.

Zr Poison Target	Toxic Products	Adhesion Work Calculation	Adsorption Energy Calculation
Not containing Zr in Aluminum melt		TiB2 (0001)//Al3Ti (112)
		Al3Ti (112)//Al (111)	Al3Ti (112) adsorbed Al
TiB2	ZrB2	TiB2-ZrB2 (0001)//Al3Ti (112)
	Ti2Zr	TiB2-Ti2Zr (0001)//Al3Ti (112)
Free Al3Ti	(Al3Ti//Al3Zr)	Al3Ti (001)//Al3Zr (001)
		Al3Ti (001)//Al (001)	Al3Ti (001) adsorbed Al
		Al3Zr (001)//Al (001)	Al3Zr (001) adsorbed Al
		Al3Ti (112)//Al3Zr (114)
Al3Ti on TiB2 surface	(TiB2//Al3Zr)	TiB2 (0001)//Al3Ti-Al3Zr (112)
		Al3Ti-Al3Zr (112)//Al (111)
		TiB2 (0001)//Al3Zr (114)
		Al3Zr (114)//Al (111)	Al3Zr (114) adsorbed Al

.

2. Computing Method

2.1. First Principle

All simulations in this paper were carried out by vasp5.4 package. To this end, crystal models of various compounds were first established with interface cut by Material studio software. Next, TiB₂ (0001), Al₃Ti (112), Al (111), and other surfaces were all obtained, and vasp package was optimized to yield stable structures and surface energies. Further calculations were then carried out under stable structures, and the atomic adsorption calculations were performed on the surface followed by calculations of adhesion works at the interfaces.

The wave function was generated by the program itself, and charge density was induced by superimposing charges using the conjugate gradient method. The self-consistent convergence energy was set to 1E-5, the pseudo-potential was PBE, and truncation energy was 1.0~1.3 times the energy of the highest pseudo-potential of elements in the compound. The vacuum layer thickness adopted a height of 15 Å, and the interface was calculated by the relaxation method. The adsorption calculations were based on the method of relaxing the upper three layers and fixing the lower three layers.

2.2. Adhesion Work

The adhesion work can be defined as the energy required to separate the interface and the reversible work per unit area required to separate the X and Y condensed phase interface to generate two free surfaces. The adhesion work can mainly be reflected in the stability and bonding ability between the two interfaces, where bigger energies would yield more stability. The calculation formula can be expressed by Equation (1):

$${\mathrm{W}}_{\mathrm{ab}}=({\mathrm{E}}_{\mathrm{XY}}-{\mathrm{E}}_{\mathrm{X}}-{\mathrm{E}}_{\mathrm{Y}})/\mathrm{A}$$

(1)

where E_XY represents the total interface energy when X is combined with Y, E_X and E_Y are, respectively, the total surface energies of surfaces X and Y, and A refers to the area of the contact surface [12,13].

2.3. Surface Energy

Surface energy can be defined as the energy required to create the surface of matter. In the melt, lower energy required to form the surface would lead to the easy spontaneous formation of the surface. This can be calculated according to Equation (2):

$${\mathrm{E}}_{\mathrm{surf}}=({\mathrm{E}}_{\mathrm{slab}}-{\mathrm{N}}_{\mathrm{i}}{\mathrm{E}}_{\mathrm{ibulk}})/2\mathrm{A}$$

(2)

where E_slab represents the total energy of the surface, N_i is the number of i atoms in the structure, E_ibulk refers to the average atomic energy of i atoms in the single substance of the structure, and A denotes the surface area [14,15].

2.4. Adsorption Energy

The adsorption energy can be defined as the energy required to adsorb atoms on the surface. This can be calculated according to Equation (3):

$${\mathrm{E}}_{\mathrm{ads}}={\mathrm{E}}_{\mathrm{all}}-{\mathrm{E}}_{\mathrm{surf}}-{\mathrm{E}}_{\mathrm{atom}}$$

(3)

where E_all represents the total energy of the adsorption system, E_surf is the energy of a clean surface, and E_atom refers to the energy of isolated atoms [16,17].

3. Results and Discussion

3.1. Adhesion Work TiB₂ (0001)//Al₃Ti (112) and Al₃Ti (112)//Al (111)

In dual nucleation theory, TiB₂ with a high melting point (2980 °C) was taken as the base core to solidify on TiB₂ surface and form an Al₃Ti thin layer. Next, Al underwent nucleation on Al₃Ti surface to yield the orientation relationship of TiB₂ (0001)//Al₃Ti (112) and Al₃Ti (112)//Al (111). Note that dual nucleation theory was the most accepted nucleation mechanism theory to date. The formation of Al₃Ti thin layer was also confirmed by Fan [8] and Schumacher [9].

As shown in Figure 1, the graph of interface structure revealed TiB₂ (0001), Al₃Ti (112), and Al (111) all with the same atomic arrangement order. Additionally, only small differences in atomic spacing were noticed, suggesting good bonding ability between the interfaces between TiB₂ (0001), Al₃Ti (112), and Al (111).

As shown in

Table 2. The initial and final interface distance, contact area, and adhesion work calculated on TiB₂ (0001)//Al₃Ti (112) and Al₃Ti (112)//Al (111).

Interfaces	Initial d (Å)	WAB (eV/Å2)	A (Å2)	Final d (Å)
TiB2 (0001)//Al3Ti (112)	3	−0.228	63.82	2.25
Al3Ti (112)//Al (111)	3	−0.139	55.39	2.31

, the adhesion work of (TiB₂ (0001)//Al₃Ti (112)) was calculated as −0.228 eV/Ų, a value much greater than that of (Al₃Ti (112)//Al (111)) (−0.139 eV/Ų). The binding of Al₃Ti (112) to TiB₂ (0001) was more stable than that of Al₃Ti (112) to Al (111), revealing the experimental formation of Al₃Ti thin layer on TiB₂ surface. Accordingly, the Zr poisoning theory was further studied.

3.2. Adhesion Work TiB₂-ZrB₂ (0001)//Al₃Ti (112) and TiB₂-Ti₂Zr (0001)//Al₃Ti (112)

The first kind of Zr poisoning guess was mainly aimed to study the action of TiB₂ particles precipitated in the refiner. Jones and Pearson suggested the replacement of Ti by Zr on TiB₂ surface to form ZrB₂, leading to increased degree of mismatch. Wang et al. confirmed dual nucleation theory through transmission imaging, where Zr atoms existing on TiB₂ surface led to the formation of Ti₂Zr on TiB₂ surface. They believed that Zr caused the dissolution of Al₃Ti on TiB₂ surface. Thus, the interface model was calculated in both cases.

As shown in Figure 2, the left part replaced all Ti ends of TiB₂ surface layer with Zr to yield ZrB₂ surface, while the right part replaced part of Ti with Zr to form a thin Ti₂Zr surface layer. Therefore, the respective values of adhesion work with Al₃Ti were calculated.

As presented in

Table 3. The initial and final interface distance, contact area, and adhesion work calculated on TiB₂-ZrB₂ (0001)//Al₃Ti (112) and TiB₂-Ti₂Zr (0001)//Al₃Ti (112).

Interfaces	Initial d (Å)	WAB (eV/Å2)	A (Å2)	Final d (Å)
TiB2-ZrB2 (0001)//Al3Ti (112)	3	−0.226	63.82	2.47
TiB2-Ti2Zr (0001)//Al3Ti (112)	3	−0.224	63.82	2.08

, the adhesion work between TiB₂-ZrB₂ (0001)//Al₃Ti (112) interface was calculated to −0.226 eV/Ų, and that between TiB₂-Ti₂Zr (0001)//Al₃Ti (112) interface was −0.224 eV/Ų. By replacing Ti on TiB₂ surface with Zr, the binding abilities of ZrB₂ and Ti₂Zr to Al₃Ti decreased slightly by 0.002 eV/Ų and 0.004 eV/Ų, respectively. However, these reductions were too small to affect the combination with Al₃Ti surface.

3.3. Adhesion Work Al₃Ti (001)//Al₃Zr (001) and Al₃Ti (112)//Al₃Zr (114)

The second kind of poisoning guess proposes Zr poisons-free Al₃Ti in the melt. Since the melting point of Al₃Ti was low, the melting upon addition of Al melt followed gradual precipitation during solidification. In this case, the Ti atoms released by melting could inhibit the growth of Al. In this view, Johnsson et al. [11] proposed that the high melting point Al₃Zr would agglomerate Ti atoms in the melt, as well as reduce the uniform dispersion of Ti in the melt and decline its growth inhibition. Xiao et al. [18] used scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS) techniques to show the bounding and wrapping of Al₃Ti with Al₃Zr on Al₃Zr surface, where Al₃Zr was the core of the aggregate. In this case, Zr poisoning was caused by the combination of Al₃Ti and Al₃Zr to form Al₃ (Zr, Ti).

For precipitation and crystallization of Al₃Zr in the melt with a high melting point, Liu et al. [19] determined the precipitation of (011) and (110) in Al₃Zr through transmission electron microscopy (TEM) microstructures and corresponding diffraction patterns. In the present study, multiple modeling and pair screening of Al₃Ti and Al₃Zr crystal planes revealed the existence of (110), (114), and (001) planes of Al₃Zr with the same atomic structure arrangement as Al₃Ti (110), Al₃Ti (112), and Al₃Ti (001) surface, respectively.

The surface of Al₃Zr (110), Al₃Zr (114), and Al₃Zr (001) surface were shown in Figure 3. Since (110), (114), and (001) planes of Al₃Zr were the most easily combined planes with Al₃Ti, a better understanding of which crystal plane Al₃Zr would most likely crystallize or grow in the high-temperature melt can be determined. According to Equation (2), the surface energies of Al₃Zr (110), (114), and (001) were calculated as −0.008 eV/Ų, −0.109 eV/Ų, and −0.136 eV/Ų, respectively. Hence, Al₃Zr crystallized most easily in (001) plane among the three planes. The second consisted of (114) plane, and the lowest was (110) plane. The energy of (110) plane was close to zero, and its crystallization ability was much lower than those of the other two planes. Hence, Al₃Zr (114) and Al₃Zr (001) surfaces and Al₃Ti were selected to calculate the adhesion capacities.

The interface of Al₃Ti (001)//Al₃Zr (001) and Al₃Ti (112)//Al₃Zr (114) interfaces were shown in Figure 4. As presented in

Table 4. The initial and final interface distance, contact area, and adhesion work calculated on Al₃Ti (001)//Al₃Zr (001) and Al₃Ti (112)//Al₃Zr (114).

Interfaces	Initial d (Å)	WAB (eV/Å2)	A (Å2)	Final d (Å)
Al3Ti (001)//Al3Zr (001)	3	−0.223	61.00	2.28
Al3Ti (112)//Al3Zr (114)	3	−0.168	110.6	2.38

, the adhesion works between Al₃Zr (001) and (114) with Al₃Ti were calculated as −0.223 eV/Ų and −0.168 eV/Ų, respectively. The previous calculations of surface energy revealed Al₃Zr (001) surface as the easiest to crystallize in the melt, and its adhesion work with Al₃Ti (001) was calculated to −0.223 eV/Ų. Compared to the adhesion work between TiB₂ (111) and Al₃Ti (112) surface in the melt, the difference was calculated to be only 0.005 eV, confirming the heterogeneous nucleation of Al₃Zr with a high melting point in the melt to compete with TiB₂ for Al₃Ti. In other words, Al₃Ti would be wrapped on Al₃Zr surface, consistent with the experimental results reported by Xiao et al. [18].

3.4. Adhesion Work TiB₂ (0001)//Al₃Ti-Al₃Zr (112) and TiB₂ (0001)//Al₃Zr (114)

The third kind of poisoning guess suggested the action of Zr on an Al₃Ti thin layer wrapped on a TiB₂ surface, and replacement of Ti atoms in Al₃Ti by Zr to reduce the effect of Al₃Ti. Wang et al. [20] observed the adsorption of Zr atoms on a TiB₂ (0001) surface by scanning transmission electron microscopy and showed that Zr may replace Ti of Al₃Ti on a TiB₂ surface. In the present study, two models were established. The first consisted of Zr replacing the Ti atom of Al₃Ti (112) to form Al₃Ti-Al₃Zr (112), and the second considered Al₃Zr (114) surface crystallization on a TiB₂ surface.

According to Figure 5 and

Table 5. The initial and final interface distance, contact area, and adhesion work calculated on TiB₂ (0001)//Al₃Ti-Al₃Zr (112) and TiB₂ (0001)//Al₃Zr (114).

Interfaces	Initial d (Å)	WAB (eV/Å2)	A (Å2)	Final d (Å)
TiB2 (0001)//Al3Ti-Al3Zr (112)	3	−0.221	63.82	2.28
TiB2 (0001)//Al3Zr (114)	3	−0.255	110.6	2.22

, when Zr replaced Ti of Al₃Ti (112),the adhesion work between Al₃Zr (112) and TiB₂ (0001) was calculated to −0.221 eV. This value was 0.007 eV lower than that of TiB₂ (0001)//Al₃Ti (112) without Zr(as shown in Table 2). The adhesion work of TiB₂ (0001)//Al₃Zr (114) was 0.027 eV higher than that of TiB₂ (0001)//Al₃Ti (112). However, the increasing or decreasing range was very small, meaning that the adhesion of Al₃Ti and Al₃Zr to TiB₂ surface was almost the same, meaning that Zr may replace the Ti atom in the representative layer. Meanwhile, the melting point of Al₃Zr represented by Zr was higher, making it easier to produce Al₃Zr (114) instead of Al₃Ti-Al₃Zr (112).

3.5. Adhesion Work Al₃Ti-Al₃Zr (112)//Al (111) and Al₃Zr (114)//Al (111)

The previous calculations revealed that Zr may replace the Al₃Ti thin layer on TiB₂ surface. Hence, the adhesion work between Al₃Ti-Al₃Zr (112) and Al₃Zr (114) with Al (111) surface was further calculated to clarify the binding ability with Al from an energetic standpoint.

The interface of Al₃Ti-Al₃Zr (112)//Al (111) and Al₃Zr (114)//Al (111) interfaces were shown in Figure 6. As illustrated in

Table 6. The initial and final interface distance, contact area, and adhesion work calculated on Al₃Ti-Al₃Zr (112)//Al (111) and Al₃Zr (114)//Al (111).

Interfaces	Initial d (Å)	WAB (eV/Å2)	A (Å2)	Final d (Å)
Al3Ti-Al3Zr (112)//Al (111)	3	−0.141	55.39	2.36
Al3Zr (114)//Al (111)	3	−0.126	110.6	2.39

, the adhesion work of Al₃Ti-Al₃Zr (112) //Al (111) was 0.002 eV higher than that of Al₃Ti (112) //Al (111) (as shown in Table 2). Additionally, the adhesion work of Al₃Zr (114) //Al (111) was 0.013 eV lower than that of Al₃Ti (112) //Al (111), but the adhesion work of TiB2 (0001) //Al₃Zr (114) was higher than that of TiB2 (0001) //Al₃Ti (112). Thus, Zr reduced the nucleation ability in Zr-containing alloys, but with a small impact.

3.6. Adhesion Work Al₃Ti (001)//Al (001) and Al₃Zr (001)//Al (001)

The previous calculations mentioned that the presence of Zr element may lead to precipitation of Al₃Zr (001) plane crystallization in the melt, as well as the coating of Al₃Ti (001) plane on Al₃Zr (001) surface. Note that Al₃Ti-Al₃Zr (112) and Al₃Zr (114) were in contact with Al in the melt, while Al₃Ti (001) and Al₃Zr (001) were in contact with Al. Hence, their adhesion works with Al were calculated.

The Al₃Ti (001)//Al (001) and Al₃Zr (001)//Al (001) interfaces were shown in Figure 7. According to

Table 7. The initial and final interface distance, contact area, and adhesion work calculated on Al₃Ti (001)//Al (001) andAl₃Zr (001)//Al (001).

Interfaces	Initial d (Å)	WAB (eV/Å2)	A (Å2)	Final d (Å)
Al3Ti (001)//Al (001)	3	−0.140	58.98	2.08
Al3Zr (001)//Al (001)	3	−0.133	64.96	2.09

, the values of adhesion work between (001) surface of (Al₃Ti and Al₃Zr) with Al were calculated as −0.140 eV/Ų and −0.133 eV/Ų, respectively. Compared to Al₃Ti (112)//Al (111), the difference was also very small, meaning good bonding abilities of Al₃Ti(001) and Al₃Zr (001) with Al (001).

3.7. Adsorption Energy of Al on Al₃Ti (001) or Al on Al₃Zr (001)

In addition to the adhesion work used to understand the binding ability between the refiner and Al in the melt, the adsorption energy could also be employed to clarify the adsorption ability of the refiner to Al atoms. The adsorption ability of the refiner to Al atoms in the solute would determine the possible aggregation of Al atoms on its surface to form a new crystal surface. In previous calculations, the second guess of Zr poisoning confirmed the coating of Al₃Ti on Al₃Zr surface in the melt, with a relationship of site determined as Al₃Ti (001)//Al₃Zr (001). After surface energy calculations, the adsorption of Al atoms on its stable surface was calculated by considering the adsorption behavior of Al atoms on the surface. As shown in Figure 8, the following four points were considered:

The initial adsorption site and final site of Al₃Ti (001) and Al₃Zr (001) surfaces were shown in Figure 9. The top sites were all located above the Al atoms, as well as Zr and Ti atoms. Bridge sites were then built between Al-Zr and Al-Ti atoms, and hollows were formed in the center of Al-Zr and Al-Ti quadrilateral. In Figure 9, the adsorption site at the top site remained almost unchanged and stayed at the top site from the beginning to the end of the adsorption process. After completion of the adsorption process of the bridge site, the adsorption site shifted to the top site of the Al atom, while the adsorption site of the hollow site remained unchanged. Both the beginning and end stayed at the hollow site.

Referring to

Table 8. Adsorption energies of Al on Al₃Ti (001) or Al on Al₃Zr (001) surfaces, initial and final site of adsorption, and distance between adsorption end and plane top layer.

Surfaces	Initial Site	DAl-sur(Å)	Easd(eV)	Final Site
Al3Ti(001)	AlTop	1.67	−4.653	AlTop
	TiTop	2.34	−4.258	TiTop
	Bridge	1.63	−4.650	AlTop
	Hollow	1.85	−4.664	Hollow
Al3Zr(001)	AlTop	1.96	−3.848	AlTop
	ZrTop	2.96	−2.303	ZrTop
	Bridge	1.96	−3.845	AlTop
	Hollow	2.37	−3.069	Hollow

for Al₃Ti (001) surface, the energy at the hollow site was the most conducive to Al adsorption, with the adsorption energy at the hollow site calculated to −4.664 eV. The Al top site was the second priority adsorption site with an adsorption energy of −4.653 eV. For Al₃Zr (001), the Al top site consisted of the highest adsorption energy, thereby the most conducive to the adsorption of Al atoms with the energy of −3.848 eV. The second energy was obtained on the bridge site with a value calculated to −3.845 eV. However, the bridge site moved to the top site after adsorption, and the adsorption energy of Al₃Zr (001) for Al atoms was lower than that of Al₃Ti (001). This further confirmed that Al₃Ti could easily attract Al atoms when compared to Al₃Zr, and was thereby better as a core of nucleation.

3.8. Adsorption Energy of Al on Al₃Ti (112) or Al on Al₃Zr (114)

The dual nucleation theory is the most acceptable for the refinement mechanism consisting of forming a thin layer of Al₃Ti (112) on TiB₂ (0001) surface. Previous calculations suggested greater adhesion work between Al₃Zr (114) and TiB₂ (0001) than that between Al₃Ti (112) and TiB₂ (0001). As shown in Figure 10, the adsorption energies of Al on Al₃Ti (112) or Al on Al₃Zr (114) surfaces were calculated by selecting seven points for adsorption based on the complexity of Al₃Ti (112) and Al₃Zr (114) surfaces.

As shown in Figure 11, a total of seven adsorption points existed, with two sites at the top of Al atom and Ti atom. Three sites were selected at the bridge site: between Al-Ti atoms, between Al-Al atoms and away from Ti atoms, and between Al-Al atoms and close to Ti atoms. Hollow 1 was located at the center of Al-Al-Ti equilateral triangle, and hollow 2 was situated at the center of Al-Al-Al equilateral triangle. For adsorption of 7 sites, both the top and bridging sites crowded out the adjacent Al atoms to enter the hollow site after completion of the adsorption process.

In

Table 9. Adsorption energy of Al on Al₃Ti (112) surface, initial and final site of adsorption, and distance between adsorption end and plane top layer.

Surface	Initial Site	DAl-sur(Å)	Easd(eV)	Final Site
Al3Ti(112)	AlTop	1.565	−23.202	Hollow2
	TiTop	2.007	−22.886	Hollow1
	Bridge1	1.984	−22.885	Hollow1
	Bridge2	1.528	−23.204	Hollow2
	Bridge3	2.185	−22.732	Hollow2
	Hollow1	1.940	−22.881	Hollow1
	Hollow2	2.177	−22.732	Hollow2

, the highest adsorption energy was obtained at bridge site 2 with an energy of −23.204 eV. The secondary preferential adsorption was observed at the top of Al with energy of −23.202 eV. The energies of all sites were greater than 20 eV, and the adsorption energy of Al₃Ti (112) surface for Al atoms was about 4–5 times higher than that of Al₃Ti (001). Thus, Zr atoms existing in the melt led to significantly lower adsorption capacity for refining to Al. Similarly, the nucleation core with Al₃Zr (001)//Al₃Ti (001) mainly formed the crystal surface of Al (001) for growth and nucleation core with TiB₂ (0001)//Al₃Ti (112) as the base grown on Al (111) surface. Note that the surface energy of Al (001) was higher than that of Al (111). Al-related studies showed Al mainly nucleated with Al (111). As a result, Al (001) was more difficult to grow than Al (111).

As shown in Figure 12, the initial and final site of the Al adsorption site of Al₃Zr (114) were the same as those of Al₃Ti (112), with the top site located above Al and Zr atoms. A total of three sites were selected for the bridge site, namely between Al-Zr atoms, between Al-Al atoms and away from Zr atoms, and between Al-Al atoms and close to Zr atoms. Hollow 1 was located at the center of Al-Al-Zr equilateral triangle, and hollow 2 was situated at the center of Al-Al-Al equilateral triangle. Except for bridge site 1 that remained at its location after completion of the adsorption, other adsorption ends moved toward the hollow site. The original hollow site may also crowd out nearby Al atoms to form a larger hollow.

The adsorption energies of Al₃Zr (114) for Al are listed in

Table 10. Adsorption energy of Al on Al₃Zr (114) surface, initial and final site of adsorption, and distance between adsorption end and plane top layer.

Surface	Initial Site	DAl-sur(Å)	Easd(eV)	Final Site
Al3Zr(114)	AlTop	1.391	−23.058	Hollow2
	ZrTop	2.169	−22.153	Hollow1
	Bridge1	2.188	−22.175	Bridge1
	Bridge2	1.364	−23.695	Hollow2
	Bridge3	1.418	−22.056	Hollow2
	Hollow1	2.219	−22.156	Hollow1
	Hollow2	1.427	−23.695	Hollow2

. The most preferred adsorption point was based on hollow 2. The energy at the center of Al-Al-Al equilateral triangle was calculated to −23.695 eV, and the second was located at the top site directly above the Al atoms, thereby squeezing the Al atoms away to form a new hollow 2 with an energy of −23.058 eV. In general, hollow 2 can be considered as the optimal adsorption point. The highest adsorption energy of Al₃Zr (114) for Al was 0.491 eV superior, and the lowest adsorption energy was 0.579 eV inferior to that of Al₃Ti (112). However, the adsorption energy for Al atoms fluctuated between 22 and 23 eV when compared the whole, indicating both Al₃Ti (112) and Al₃Zr (114) surfaces with the same nucleation abilities in Al melt.

4. Conclusions

(1)

For the first kind of Zr poisoning guess, the adhesion work relationship between ZrB₂ and Ti₂Zr with Al₃Ti (112) surface was calculated and the results showed lower values for ZrB₂ and Ti₂Zr than TiB₂ and Al₃Ti (112). The replacement of Ti by Zr revealed reduced binding of Al₃Ti (112), but the reduction was not significant.

(2)

For the second kind of Zr poisoning guess, Al₃Zr in Zr containing melt showed a high melting point and was precipitated as Al₃Zr (001). The adhesion work between Al₃Zr (001) and Al₃Ti (001) was almost the same as that between TiB₂ (0001) and Al₃Ti (112), meaning that Al₃Ti (001) would accumulate on the Al3Zr (001) surface as precipitates. This agreed well with the experimental results reported by Xiao et al. [18]. The adsorption energy of Al on Al₃Ti (001) was only 1 / 5 ~ 1 / 4 of that of Al on Al₃Ti (112), and the energy required to form Al (001) surface was higher than that required to form Al (111). Hence, Al₃Zr (001) would compete with TiB₂ (0001) to seize Al₃Ti in the melt and then Al₃Ti (001) crystallized on Al₃Zr (001) surface. This seriously affected the condensation of Al, thereby reducing the probability of nucleation and producing Zr poisoning effect.

(3)

For the third kind of Zr poisoning guess, Zr acted on Al₃Ti (112) of the TiB₂ surface. The calculations showed higher adhesion work of TiB₂//Al₃Zr (114) than that of TiB₂//Al₃Ti (112). Thus, Al₃Ti on the TiB₂ surface may be replaced by Zr, and TiB₂ could bind to Al₃Zr. However, the calculated adhesion work and adsorption energy of the Al₃Zr (114) surface to Al illustrated Al₃Zr (114) surface with almost the same effect as Al₃Ti (112). The adhesion work and adsorption energy were similar to those of Al₃Ti (112). As a result, Zr may replace Ti, but its function remained the same as that of Ti without toxic effect.