A Numerical Formula for General Prediction of Interface Bonding between Alumina and Aluminum-Containing Alloys

Interface termination between alumina and aluminum-containing alloys is discussed from a viewpoint of thermodynamics by extending the authors’ previous discussion on the interface termination between alumina and pure metal. A numerical formula to predict interface bonding at alumina-aluminum-containing alloys is proposed. The effectiveness of the formula is examined by extracting information on interface termination from experimental results and first-principle calculations in references. It is revealed that the prediction by the formula agrees quite well with the results reported in the references. According to the formula, a terminating species can be switched fromoxygen to aluminum, which had been actually demonstrated experimentally.The formula uses only basic quantities of pure elements and the formation enthalpy of oxides.Therefore it can be applied for most of aluminumcontaining alloys in the periodic table and is useful for material screening in developing interfaces with particular functions.


Introduction
Interface bonding between oxides and metals is one of the crucial factors that determine properties of materials such as bonding strength, Schottky barrier height, sensitivity of sensors, catalytic activity, and overpotential in batteries.Metal oxides, which are composed of metals and oxygen, can have differently terminated surfaces, for example, the topmost surface being occupied only by oxygen atoms or by the metal atoms that compose the oxide.When such differently terminated surfaces form the interface with metals, bonding strength and wetting properties at the interfaces depend on surface termination species [1][2][3][4][5].Electron energy level alignment between the Fermi level and oxides' valence bands (band alignment) also varies largely with surface terminating species [6][7][8][9][10].Regarding alumina/metal interface, which is one of the most extensively studied systems among various oxide/metal interfaces, we have studied the thermodynamics of interface termination and proposed a numerical formula to predict a terminating species at the interface [11].A software program that gives predicted results according to the formula has been released [12].
Under conditions where a stable interface termination is determined by a metal in contact, alloying (mixing two or more metals) is one of the most frequently used techniques for modifying interfaces, especially for electric device applications where an electrode metal works only as an electronic conductor but is not chemically functioning.Because the choice of oxides is based on specific properties of the oxides, modification should be made on electrode metals, not on oxides.In this paper, therefore, the discussion on the thermodynamics of interface termination in [11] is extended to the interface between alumina and alloys that contain aluminum, and then a numerical formula for predicting a stable interface terminating species at alumina/aluminum-containing alloy interfaces is proposed.

International Journal of Metals
This work aims to offer a new tool for predicting whether alloying with aluminum is effective or not for interface modification so that time-consuming trials and errors on each system would not be necessary.We believe that the formula proposed in this work would be of great use in material development.

Formula for Prediction
2.1.Varieties in Termination.The most stable phase of alumina is alpha, which has a corundum structure with hexagonal symmetry.The planes parallel to the -axis (plane) have differently terminated surfaces and could be Oterminated, Al-terminated, or Al-double-layer-terminated.Because experiments on the -plane have been mostly conducted using metal/alumina interfaces for both solidstate bonding and film growth experiments, the -plane is considered in this study.Therefore, the interface bonding species can be either Al (M-Al-alumina, including Al-double layer) or O (M-O-alumina) when an interface is formed with a metal (M).
The interface between pure metal (M) and alumina will be terminated by either (1) M-Al-alumina (Al-termination) or (2) M-O-alumina (O-termination).Here, the influence of the coverage is neglected as discussed in the previous paper [11].When the discussion is extended to the interface with aluminum-containing alloy (MAl), M-Al  -alumina (Altermination, Al  denotes terminating Al) in pure M system is replaced by (MAl)-Al  -alumina, where the atom that binds to Al  can be either M * or Al * in MAl (here, M * and Al * denote atoms from alloys).Likewise, M-O  -alumina (O-termination, O  denotes terminating O) is replaced by (MAl)-O  -alumina, where the atom that binds to O  can be either M * or Al * in MAl.Then, there would be four different types of termination at the interface: Although (D) is initially derived from the O-terminated interface between (MAl) alloy and alumina, it can be regarded as Al-termination because this is the same as either (A) or (B).

Procedure for Prediction.
Thermodynamic equilibrium among the four types of termination (A)-(D) has been considered.The equilibrium is determined by Gibbs energy difference among the terminations [11].In our previous paper on the interface between alumina and pure metal, we use M-Al and M-O bonding energy to obtain Gibbs energy difference among different terminations for simplicity [11].Here, for the interface between alumina and aluminum-containing alloy (MAl), we use M-Al, Al-Al, M-O, and Al-O bonding energy.
As in the previous paper, M-Al bonding energy is estimated either by the adsorption energy of Al on M (Approx-1) or by subtracting the adsorption energy of M on M from that of Al on M (Approx-2).The subtraction is considered because the values of adsorption energy include not only the influence of chemical interaction between Al and M but also that of cohesion energy.M-O bonding energy is estimated either by the adsorption energy of oxygen on M (Approx-1) or by subtracting the dissociation energy of molecular oxygen from the adsorption energy of oxygen on M (Approx-2).The reason of adopting adsorption energy of metals to estimate M-Al or Al-Al bonding energy and that of oxygen for M-O bonding energy is as follows: values of formation enthalpy of oxides and intermetallic compounds or of mixing enthalpy include terms not only from chemical interaction but also from structural change.At the interface structural relaxation occurs more easily than in bulk and the structural term would be smaller and can be neglected for rough estimation.
The adsorption energy of Al on M (=Al on Al when M = Al) and M on M were calculated using (1), which is based on Meadima's formula [13]: where Δ ad ( on ) is the adsorption energy of  on ,   , and   , and   and   are surface energy and surface area of  and , respectively.Δ sol ( in ) is the heat of mixing of  in ; Δ vap is vaporization enthalpy. is the portion of the area of  in contact with , which is typically around 0.4.Here, the energy is described per mol.Δ sol ( in ) is calculated by the following equation: where () is the molar volume of metal , (), and () are the electron density of  and  at the boundary of the Wigner-Seitz cell, Δ is the work function difference between  and , and , , and  are parameters. 0 is the Avogadro's number.The detail of the calculation and values for   and   , Δ vap , (), (), and (), Δ, and three parameters , , and  are described in [14].The values of the calculated adsorption energy for each M-Al combination were obtained using the software [15] released by one of the authors and listed in Table 1.
The adsorption energy of oxygen on M is estimated in the following way.It has been reported [16] that the initial heat of adsorption of oxygen on some metals [17] has linear dependence on the standard enthalpy of formation [18] of the corresponding oxides with the highest oxidation state.The values of the formation enthalpy and the valence of the corresponding oxides were reexamined using other references [19,20].We decided to use the values from [20] to correlate the initial heat of adsorption of oxygen (Hads) with the formation enthalpy of the corresponding oxide with the highest oxidation state (Hform) except Cr.The following numerical relationship has been obtained with the correlation coefficient of 0.977: We use values of Hads calculated by (3) as the adsorption energy of oxygen on M. In Table 2, formation enthalpy of various oxides to be used for the calculation (after [20] except those in italics which are from [19]) and the calculated adsorption energy values are listed.For readers' convenience, values for metals that were not reported in references we discuss later are also given.
In the previous paper, the following two expressions were used in order to predict whether the interface termination is either M-Al-alumina or M-O-alumina between pure metal and alumina.
Approx-1 is Approx-2 is where O 2 dissociation energy = 493.07kJ/mol [21].Approx-2 has been proposed because the value of (AlonM) includes both chemical interaction between Al and M and cohesive energy of atomic Al, and therefore, in order to extract the term caused by only chemical interaction, subtraction of cohesive energy is necessary.The situation is the same for (OonM), where both chemical interaction between O and M and cohesive energy of atomic O are included and the subtraction of cohesive energy Therefore, in order to predict which one of terminations is realized at the interface with aluminum-containing alloy, we first predict whether M-Al-alumina or M-O-alumina is realized at the interface without aluminum in the alloy using either Approx-1 or Approx-2.Once M-Al-alumina is predicted, the second step is to predict whether the interface is (A) or (B) at the interface with aluminum-containing alloy.When M-O-alumina is predicted, the second step is to predict whether the interface is (C) or (D).Whether (A) or (B) is realized is determined by comparing the value of (AlonAl) with that of (AlonM).If (AlonAl) > (AlonM), Al-Al bonding is preferred to M-Al bonding and the termination becomes (B).Similarly, (C) or (D) is determined by the value of (OonAl) with respect to (OonM).Here, the value of (OonAl) is obtained by calculating (OonM) with M = Al and is 833.06 kJ/mol.If (OonAl) > (OonM), Al-O bonding is preferred to M-O bonding and the termination becomes (D), which is regarded as Al-termination.Here, comparison between (AlonAl) and (AlonM) or between (OonAl) and (OonM) does not need subtraction like in (5), because the as well as for (OonAl) and (OonM) Therefore, the expressions for each termination for aluminumcontaining alloy (Approx-1) are as follows, where the flow chart for finding an expression is shown in Figure 1(a): When Approx-2 is used in the first step to predict whether M-Al-alumina or M-O-alumina is realized at the interface Figure 1: Flow chart for finding an expression that predicts termination.

If (d) or (d 󸀠
) is satisfied, the interface between alumina and pure metal M is O-terminated, whereas the interface with M alloyed with Al is Al-terminated.This is the key to switch interface termination species from oxygen to aluminum by adding Al to metals that satisfy (d) or (d  ).Whether this switching of interface termination species occurs or not is governed by the adsorption energy of oxygen on M and Al.As in the expressions (d) and (d  ), when the adsorption energy of oxygen on Al is larger than that on M, Al-O bonding is preferred at the interface and type (D) termination, that is, Al-termination, is formed.On the other hand, it is clear that switching Al-terminated interface to O-terminated one by alloying with Al is impossible from the expressions (a)-(d).
It should be noted that the systems where different termination is predicted in the first step using by either Approx-1 or Approx-2 are limited only to Ru, Rh, Ir, Pt, and Hg (predictions for these systems are M-Al-alumina with Approx-1 and M-O-alumina with Approx-2).Furthermore, aluminumcontaining alloys of these metals are predicted to be Alterminated whether interface termination is predicted as M-Al-alumina or M-O-alumina in the first step (termination (A) or (D)).Therefore, we may be able to use Approx-1 in the first step for predicting the interface in aluminum-containing alloy.In summary, to find a type of interface bonding in aluminum-containing alloy (MAl), interface termination at alumina-corresponding pure metal (without aluminum in the alloy) should be first examined.Then, if the interface with pure metal is Al-terminated, values of (AlonM) and (AlonAl) are to be compared.For O-terminated interface with pure metal, values of (OonM) and (OonAl) should be compared.This procedure gives the type of interface bonding in aluminum-containing alloy from expressions (A)-(D).After looking for M that satisfies (AlonAl) > (AlonM) (M = Ga, Ge, In, Sn, Hg, Pb, Bi in Table 1), we found that there is no M with (OonM) < (AlonM).Therefore, there is no M that satisfies expression (B).
It should be noted that the values of (OonM) are derived from the standard formation enthalpy of corresponding oxide, which is defined at 1 bar pressure.Because both oxidation and reduction of metal can occur in the same system at different oxygen pressure, a terminating species would vary with oxygen pressure, especially for metals with relatively small standard formation enthalpy values.
There is one more thing to be noted.In all the above discussion, the possibility of alumina reduction is excluded.However, if the oxide formation enthalpy of metal M per mol-O is larger than that of alumina, formation of oxide with M and reduction of alumina should occur, which is expected for M = La, Hf in Table 2.

Termination in Aluminum-Containing
Alloys in References

Experimental Results.
There are only a limited number of references that handle interface termination between alumina and aluminum-containing alloys.We have investigated interface termination using NiAl(110) and Cu-9Al(111) [10] and showed that Al 2p XPS peak is a good measure to judge a type of termination.If Al 2p peak has a component between that for Al 2 O 3 and metallic Al, the component is attributed to the interface and the interface is Al-terminated.For NiAl(110), the shoulder in Al 2p peak in oxidized substrate has been known [22], which were attributed to Al that binds the substrate and alumina film using calculation and STM [23].
Although other references did not discuss interface termination, by examining the reported Al 2p XPS spectra, a type of interface termination can be estimated in the above way.For FeAl, a similar shoulder in Al 2p peak as in NiAl and Cu-9Al was reported [31], which indicates that the interface between FeAl and alumina formed by the oxidation of FeAl was Al-terminated though the authors of the paper did not mention it.In addition to NiAl(110), when NiAl(111), a different orientation of the same intermetallic, was oxidized, a similar shoulder in Al 2p was reported [32].
There are XPS studies on the oxidation of TiAl and Ti 3 Al, but well resolved Al 2p spectra were not reported.However, we are able to estimate the interface termination difference by examining the reported Al 2p binding energies in the following way.In Table 3, Al 2p binding energy values of alumina and of intermetallics taken from references [10,[24][25][26][27][28][29][30] are listed.In the case of Cu and Ni systems, where all the data come from our laboratory under the same energy calibration conditions, differences of Al 2p 3/2 values in alumina (Al 2p 3/2 (ox)) with respect to the ones in M-Al (Al 2p 3/2 (MAl)) for Al-terminated samples (2.3-2.4 eV) are clearly different from those for O-terminated ones (1.5-1.6 eV).For Ti systems, the energy difference between Al 2p (ox) and Al 2p (MAl) falls in two categories, one 3.2-3.3eV and the other 2.6-2.7 (in the references, Al 2p 3/2 and Al 2p 1/2 were not resolved).The smaller energy difference appears to suggest O-termination, while the larger one is for Al-termination.If we examine the preparation conditions for all these experiments in Table 3, it seems that the suggested terminating species is dependent on the oxidation potential during the interface formation.In the case of lower oxygen pressure and/or higher temperature (=lower oxidation potential), larger energy difference, that is, Al-termination, appears to be realized.The interface termination deduced from reported experiments is schematically summarized in Table 4.

Theoretical Results.
To the authors' knowledge, there is no reference that calculates the stability of interface termination at alumina/aluminum-containing alloy (including intermetallics) by first-principle calculations.The references that discuss the chemical potential of Al, Δ Al , as a parameter in the thermodynamic study of interface termination for alumina-Ni, Cu, Ag, and Au [33][34][35] interfaces handle Alcontaining intermetallics.Their conclusion is that an interface terminating species changes from oxygen to aluminum according to the increase of the chemical potential of Al in metals as schematically shown in Figure 2.This Δ Al is a function of both oxygen partial pressure and aluminum activity  Al in metals.The figure assumes that alumina is more stable than oxide of metal M, MO.Here, using Figure 2, we discuss the influence of aluminum activity under constant oxygen partial pressure, where alumina is stable.From the right to the left in the figure, metal composition changes from pure metal to Al intermetallics.On the border B at the right side in Figure 2

Comparison between Prediction and Results in References
Here, we examine the prediction derived from the proposed expressions for each system and compare with the results deduced from the reported results.
In Table 5, the prediction for pure metal (M), the examination of the expression described in Section 2.2 (both Approx-1 and Approx-2), and the resulting prediction for aluminum-containing alloy (MAl) are listed for various metals.The results from the experimental references are also shown in the table.For M on which experimental results both for M and MAl are available (M = Fe, Ni, Cu), the interface is terminated by oxygen for pure M. Therefore, the termination for MAl should be either (C) or (D).Because (OonM) is   For M = Ti, where the expression (c) or (c  ) is satisfied, our formula predicts O-termination.In the experimental reports, both O-termination and Al-termination appear to be obtained depending on the conditions (oxygen potential) for the interface formation as discussed in Section 3.1.Altermination, which is in disagreement with the prediction, was obtained under low oxygen pressure at high temperature.Under such condition, adsorbed oxygen is known to dissolve into bulk Ti [36].For Ti, although (OonAl) < (OonM), it appears that dissolution of oxygen at the interface into Ti occurs, resulting in Al-termination.The dissolution of oxygen into metal or alloy is highly dependent on a kind of metals or alloy and is not taken into account in the prediction formula.Among Si, Ti, Zr, Nb, Ta, and W, which satisfy expression (c) or (c  ), similar behavior as for Ti is expected for Zr, Nb, and Ta, because these three metals dissolve considerable amount of oxygen according to the phase diagrams.
One more thing to be noted is that all the metals that satisfy expression (c) or (c  ) have a mixed oxide phase described as MAlO in Figure 2 As mentioned in Section 3.2, interface for these metals could be Al 2 O 3 /MAlO (border C in Figure 2), which contains Al-O-M-O-bonding at the interface and hence is regarded as O-termination in this paper.When the formation enthalpy of metal oxide increases, approaching that of alumina, the position of borders B and C shifts toward left side in Figure 2, while the position of border A is not influenced by oxide formation enthalpy but mainly by the strength of M-Al bonding (if the M-Al bonding is stronger, the position of border A moves toward right side).The features shown in Figure 2 in the theoretical study are based on thermodynamics and are common among all the systems calculated.Therefore, we can expect the features to be universal for any metal.Then, when the interface is Alterminated, alumina is expected to be in equilibrium with aluminum-containing alloys or intermetallics under oxygen partial pressure that metal is not oxidized.This guides the practically useful technique to switch interface bonding from an originally O-terminated interface to Al-termination by adding Al in a metal M. The exception of the application of this technique is the case where (OonAl) < (OonM) (expression (c) or (c  ) is satisfied).Interface bonding for metals that satisfy expression (c) or (c  ) would be processdependent in practice, because the thermodynamic stability of Al-terminated and O-terminated interface is very close for metals that satisfy both (OonAl) < (OonM) and (formation enthalpy of oxide of metal M) < (formation enthalpy of Al 2 O 3 ).For such case, prediction is possible by observing which one of metal elements is preferentially oxidized in Al-containing alloys or intermetallics.If Al is preferentially oxidized, the interface would be Al-terminated, whereas the preferential oxidation of M would results in O-terminated.
It should be noted that if MO is more stable than Al 2 O 3 , interface Al/MO instead of Al 2 O 3 /M should be formed under thermodynamic equilibrium.Among metals we consider in Table 2, Mg, La, and Hf correspond to the case.
By incorporating the discussion on Figure 2 into the expressions presented here, we can make an algorithm to find interface termination in Al-containing alloy as in Figure 3.This algorithm guides a novel method to control interface termination; for a metal with (OonM) < (OonAl), an interface that exhibits O-termination in pure metal can be switched to Al-termination by alloying the metal with Al.It also concludes that a stable Al-terminated interface cannot be formed for metals with (OonM) > (OonAl) under equilibrium conditions if oxygen partial pressure is not low enough to reduce Al 2 O 3 .Therefore, for such metals, utilizing a quenching process is necessary to obtain Al-terminated interfaces.One example of a quenching process is depositing Al on metals followed by oxidation without sufficient annealing, which avoids atomic diffusion needed to reach thermodynamically stable O-termination.
The influence of oxygen partial pressure is not taken into account in (1) and ( 3), which are used to calculate the adsorption energies of Al on M and oxygen on M, respectively.On the other hand, the strengths of M-O and Al-O bonds should depend on the oxygen partial pressure.Therefore, prediction by this method is not accurate, especially for easily reduced metals.However, it provides a guide for termination, which we believe is quite useful for material development.

Conclusions
Interface bonding between alumina and aluminum-containing alloy (MAl) has been investigated.A method to predict an interface terminating species is proposed by extending the prediction method already proposed for the interface between alumina and pure metals.In the method, to find the most stable interface termination, the interface bonding energies of differently terminated interfaces, which are estimated using the adsorption energy of Al on base-metal M and that of M on M, and the adsorption energy of oxygen on M and Al are compared.In the algorithm for prediction, interface termination at alumina-pure metal interface should be first examined.Then, if the interface with pure metal is Al-terminated, values of (AlonM) and (AlonAl) are compared.For O-terminated interface with pure metal, values of (OonM) and (OonAl) should be compared.This procedure gives the type of interface bonding in aluminum-containing alloy according to the expressions (a)-(d) or (a  )-(d  ) in the text.Based on the algorithm, it is also revealed that O-terminated interface can be switched to Al-terminated one by adding Al to pure metal M.
The predicted results are compared with those deduced from experimental studies.The agreement is very good.For aluminum-containing alloys where there is little difference bonding is preferred to M-O bonding and if (AlonM) < (OonM), M-O bonding is preferred.With Approx-2, prediction goes as follows: if (5) is positive, that is, {(AlonM) − (MonM)} > {(OonM) − 1/2(O 2 dissociation energy)}, M-Al bonding is preferred, and vice versa.Four types of terminations (A)-(D) for aluminumcontaining alloy, as described in Section 2.1, are derived from either M-Al-alumina or M-O-alumina interface in pure metal, where (A) and (B) are derived from M-Alalumina and (C) and (D) are derived from M-O-alumina.
without aluminum in the alloy, the comparison between (OonM) and (AlonM) should be made by replacing (OonM) by {(OonM) − 1/2(O 2 dissociation energy)} and (AlonM) by {(AlonM) − (MonM)}.Then the corresponding expressions to (a)-(d) become as follows, where the flow chart for finding an expression is shown in Figure 1(b): , the interface is not Al 2 O 3 /M (pure metal) but Al 2 O 3 /MO  (metal oxide).When  Al is larger than that at the border B, the interface is O-terminated.If mixed oxide phase MAlO exists, the border C appears in the figure and the interface with alumina would be Al 2 O 3 /MAlO  instead of Al 2 O 3 /MO  .The interface Al 2 O 3 /MAlO  is regarded as O-terminated from a bonding point of view, because M-O bonding, not M-Al, exists at the interface.On the border A at the left side in Figure 2, Al 2 O 3 reduces to Al metal that forms an intermetallic compound MAl, such as Cu 3 Al and Ni 3 Al, and the interface is Al 2 O 3 /MAl, not Al 2 O 3 /M.Therefore, the reference tells us that the interface between MAl (M = Ni, Cu, Ag and Au) and alumina is Al-terminated.

Figure 2 :
Figure 2: Schematic diagram of interface energy and preferred interface termination as a function of Δ Al (chemical potential of Al) for M with intermetallic compound (MAl) and oxides (MO) formation taken into account.On the left side of the border A, Al 2 O 3 reduces to Al metal.On the right side of the border B, the interface is not Al 2 O 3 /M (pure metal) but Al 2 O 3 /MO  (metal oxide).When  Al is larger than that at the border B, the interface is O-terminated.If mixed oxide phase MAlO exists, the border C appears in the figure and the interface with alumina would be Al 2 O 3 /MAlO  instead of Al 2 O 3 /MO  .

Figure 3 :
Figure 3: Flow chart for predicting a termination type among (A)∼ (D) in the text.

Table 1 :
Adsorption energy of Al and other metals (M) on M and their subtracted values.

Table 2 :
Values of oxide formation enthalpy and calculated adsorption energy of oxygen on various metals (M) and related values.

Table 3 :
Binding energies of Al 2p in Ti-Al compounds prepared in various conditions compared to those in alumina on Cu and Ni related metals as references.

Table 4 :
Schematic representation of interface terminating species at interfaces with alumina reported in experiments.
interface is not Al 2 O 3 /M (pure metal) but Al 2 O 3 /MO  (metal oxide).When  Al is larger than that at the border B, the interface is O-terminated.If mixed oxide phase MAlO exists, the border C appears in the figure and the interface with alumina would be Al 2 O 3 /MAlO  instead of Al 2 O 3 /MO  .

Table 5 :
The interface prediction for pure metal (M), examination of interface type and interface prediction for aluminum-containing alloy, and experimental results on interface termination in references.