metals

Review
Research Progress of First Principles Studies on Oxidation
Behaviors of Ti-Al Alloys and Alloying Influence
Yue Li, Jianhong Dai * and Yan Song

School of Materials Science and Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road,
Weihai 264209, China; 18b909049@stu.hit.edu.cn (Y.L.); sy@hitwh.edu.cn (Y.S.)
* Correspondence: daijh@hit.edu.cn; Tel.: +86-0631-5687-157

Abstract: Ti-Al alloys have good prospects in the aerospace, automobile, and other fields because of
their excellent mechanical properties. However, the lack of high temperature oxidation resistance
limits their practical applications. Various ways have been used to study their oxidation behaviors.
Besides numerous experimental studies focused on the oxidation resistance properties of Ti-Al alloys,
theoretical research based on first principles calculations has been carried out on the oxidation
mechanisms on the atomic and electronic scales. In recent years, these theoretical studies have
provided strong support for understanding the oxidation mechanisms and designing anti-oxidation
modification measures. This review will focus on the surface oxidation reactions, element diffusion
behaviors and interface bonding properties. The influencing mechanisms of alloying elements on the
oxidation properties will be discussed in detail.

Keywords: Ti-Al alloys; oxidation; alloying elements; ab-initio calculations







Citation: Li, Y.; Dai, J.; Song, Y. 1. Introduction

Research Progress of First Principles Ti-Al intermetallic alloys show promising applications in the aerospace, vehicle, and
Studies on Oxidation Behaviors of other fields. Due to their high contents of aluminum, their weight reduction effects are
Ti-Al Alloys and Alloying Influence.
extremely remarkable. Furthermore, Ti-Al alloys have high specific strength, good high-
Metals 2021, 11, 985. https://doi.org/
temperature fracture toughness, and strong creep resistance, providing obvious advantages
10.3390/met11060985
over traditional high temperature alloys. In elevated temperature environments (600 ◦ C to
800 ◦ C), the specific strength of Ti-Al based alloys is close to that of nickel-based alloys. One
Academic Editor: Filippo Berto
of the tendencies in aero-engine materials design is to introduce intermetallic alloys, metal
matrix composites and polymer matrix composites to gradually replace high temperature
Received: 21 April 2021
Accepted: 15 June 2021
steels and nickel alloys. Ti-Al intermetallics are suitable for the preparation of the rotor
Published: 20 June 2021
blades and integral blade rings of the compressor, low pressure shafts, high/low pressure
turbine blades and other parts [1,2].
Publisher’s Note: MDPI stays neutral
However, there are also some obstacles that hinder the applications of Ti-Al alloys,
with regard to jurisdictional claims in
among them their oxidation behavior is one of the most critical problems. Titanium and
published maps and institutional affil- aluminum both are easily passivated metals, they will spontaneously form dense oxide
iations. films in an air environment at room temperature. The dense oxide films will help to
protect the matrix from further oxidation or corrosion. Low electrode potential and high
chemical activity endow them with the ability of self-protection in severe environments.
Nevertheless, for the Ti-Al alloys, the affinity energy difference between oxygen and metal
Copyright: © 2021 by the authors.
elements in oxides TiO2 and Al2 O3 is very small [3], which leads to bonding competition
Licensee MDPI, Basel, Switzerland.
between Ti and Al with oxygen at high temperature. Therefore, the mixed oxides, e.g., TiO2
This article is an open access article
and Al2 O3 will often appear in the oxide scale during the Ti-Al alloy oxidation process,
distributed under the terms and due to the similar formation energies of the oxides. The mixed oxides are not always dense
conditions of the Creative Commons and uniform, and are often accompanied by large nodular-like or needle-like TiO2 oxides.
Attribution (CC BY) license (https:// Such irregular oxide layers are mixed with a large number of vacancies, crystal boundaries,
creativecommons.org/licenses/by/ and other defects, which provides diffusion paths for oxygen atoms into the alloy matrix
4.0/). and accelerates the progress of Ti-Al alloy oxidation.

Metals 2021, 11, 985. https://doi.org/10.3390/met11060985 https://www.mdpi.com/journal/metals

Metals 2021, 11, 985 2 of 18

In the initial stage of oxidation progress, both the TiO2 and Al2 O3 oxides form simul-
taneously and have the same growth orientation. The activation energy for TiO2 grain
growth is much lower than that of A12 O3 , so the surface of the Ti-Al matrix will be quickly
become covered by titanium oxide. An aluminum-rich zone caused by the Ti consumption
will be formed between the titanium oxide layer and the matrix, and A12 O3 scale will be
produced due to the element diffusion behaviors. By the end of the oxidation process, the
final oxidation products can be divided into the titanium oxide, the aluminum oxide, the
mixed oxide layers, and the oxygen-affected zone. A large amount of mass transfer can
take place between TiO2 grains and irregular oxide grain boundaries, which may weaken
the bonding between the oxides and the matrix. Therefore, the oxidation may damage the
mechanical properties of Ti-Al and even leads to the failure of the materials. In recent years
researchers have also focused on applying new Ti-Al alloy manufacturing methods such as
electron beam melting (EBM), spark plasma sintering (SPS), and so on. Nevertheless, the
poor high temperature oxidation resistance problem always remains, as the formation of
mixed oxides and the rapid weight growth at high temperature can hardly be avoided and
this may bring risks to the performance of the materials [4–6].
At present, many experimental and theoretical studies focus on the oxidation behav-
iors of Ti-Al alloys. In this paper, the experimental studies on the oxidation properties of
Ti-Al are briefly introduced, and first principles calculations of the oxidation mechanism of
Ti-Al alloys and the effects of alloying elements on their oxidation resistance properties
will be emphasized.

2. Alloying Methods
There are two main pathways to improve the high-temperature oxidation resistance
properties of Ti-Al alloys: one is to change the composition through element doping in order
to improve the overall performance of the alloys; the other is through surface modification
by forming an anti-oxidation film to protect the material matrix from oxidation, such
as laser cladding and micro-arc oxidation. This paper will mainly focus on the alloying
methods, which are closely related to the current research progress of the theoretical studies.
Alloying is a widely used method to improve the oxidation resistance of Ti-Al alloys,
which can be realized in the material preparation stage without subsequent surface treat-
ments. Although there is a high content of Al element in Ti-Al alloys, a single Al2 O3 layer
cannot be formed in the oxidation process, mainly because of the close equilibrium oxygen
partial pressure of Al/A12 O3 and Ti/TiO2 and the similar formation energies of the A12 O3
and TiO2 oxides [7]. The core idea of the alloying method is to promote the formation of
stable oxide films on the surface. The protective oxide films should possess good thermody-
namic stability in a high temperature environment, inhibition of mutual diffusion of oxygen
and metal ions, low saturation vapor pressure of oxygen, certain self-healing ability, good
combination and thermo-mechanical compatibility with the matrix. Introducing alloying
elements can help to improve oxidation resistance through the following ways: (1) Valence
control mechanism, that is, inhibiting the formation of titanium oxide and promoting the
formation of aluminum oxide; (2) Diffusion barrier effect, forming a dense and protective
film on the alloy surface to prevent oxygen atoms from further invading into the matrix;
(3) Selective formation of initial oxides, making aluminum oxide selectively generate in the
initial stage of oxidation [8]. The influence mechanics of representative elements on the
oxidation properties of Ti-Al alloys such as Nb, Si, Cr, Mo, Zr, and so on will be discussed
in the following sections.
As rutile TiO2 is a non-stoichiometric compound, a lot of defects such as oxygen vacan-
cies and Ti ion vacancies will be easily produced in this oxide. Replacing tetravalent Ti with
pentavalent Nb can reduce the aggregation of interstitial Ti ions, reduce the concentration
and mobility of cracks, decrease the diffusion rate of oxygen and metal ions, and thus
inhibit the formation of titanium oxide [9]. Other high cation valence elements like Mo,
Ta, and W also share a similar role [10,11]. In addition, Nb can weaken the interactions
between Al and other elements in the Ti-Al system and strengthen the combinations of Ti
Metals 2021, 11, 985 3 of 18

with the surrounding environment. Therefore Nb can improve the activity of Al relative to
Ti, promote the formation of A12 O3 , and reduce the necessary Al content for the formation
of protective oxides [8]. Doping a small amount of Nb in Ti-Al alloys can also reduce the
solid solubility and diffusion coefficient of oxygen, thus inhibiting the formation of oxides.
Nb has been proved to be effective in enhancing the formation of titanium nitrides, the
stabilized nitrides can hardly be converted to titanium oxides, therefore controlling the
rate of oxidation [12]. When alloying with Si element, a dense and continuous SiO2 oxide
layer can be formed on the surface of the Ti-Al alloys and the Ti5 Si3 can be formed by the
reactions between the Ti and Si. Therefore, the Si element can reduce the activity of Ti ions
and control their outward diffusion [13]. Si doping can cause the formation of the titanium
nitride layer or isolated nitride particles between the oxide layer and the matrix, which
prevents the further inward diffusion of oxygen atoms, and reduces the weight gain rate
in oxidation experiments [14]. With the increase of Si content, the thickness of the oxide
layer gradually decreases. Furthermore, the Si can even improve the oxidation resistance
of the alloys at 1200 K [15]. By comparing the weight change and the morphologies of the
oxidized surfaces of the TiAl alloys with and without Si element, when the content is not
enough for segregate and form a separate SiO2 layer, the Si alloying can still reduce the
thickness of the oxide scales [16]. Cr doping offers a combination of valence, initial oxide
control, and diffusion barrier effects. Although the substitution of Ti4+ with low cation
valence Cr3+ can increase the defect concentration in TiO2 and lead to an increased growth
rate, a higher Cr content can reduce the necessary aluminum content for the formation of
protective aluminum oxide layer by promoting the formation of A12 O3 [17]. Moreover,
Cr element itself will form Cr2 O3 in an air environment under high temperature, which
is even more compact, playing a positive role in protecting the alloy matrix and isolating
the external environment. Mo element mainly promotes the formation of A12 O3 between
the oxide layer and the matrix, and at the same time participates in the reaction to form
Ti2 AlMo. These two products hinder the further diffusion of oxygen atoms into the alloy
matrix, and therefore they will improve the high-temperature oxidation resistance, how-
ever, the extent of compressive residual stress and strain may increase with the growth of
A12 O3 and lead to oxide spalling [18]. Mo can reduce the solubility and diffusion rate of
oxygen in Ti-Al alloys by occupying Ti4+ sites with Mo6+ , hindering the formation of the
outer TiO2 layer, which depends on the outward diffusion of Ti4+ and inward diffusion
of oxygen [19]. Some experimental results show that some elements can optimize the
structure of the oxide, for instance, doped Sn element can react with Ti to form a Ti3 Sn
phase, which promotes the formation of Al2 O3 pegs, leading to the formation of a single
and continuous Al2 O3 layer, the Ti3 Sn phase impedes inward diffusion of oxygen and the
outward diffusion of Ti ions, relatively contributing to the diffusion of Al. Zr can control
the grain size of oxide by increasing the nucleation rate of the oxides at the initial stage
of oxidation, improve the compactness of the oxide and hinder the inward diffusion of
oxygen atoms [8,20].
As the effect of single element substitution on the oxidation resistance is still relatively
limited, numerous studies on mixed doping with multiple elements have been carried
out. For example, the oxidation kinetics curve of Ti2 AlNb alloy doped with Mo, Zr, and Si
through isothermal oxidation experiments from 650 ◦ C to 800 ◦ C can always maintain a
parabolic shape, only becoming a little bit faster at 800 ◦ C. Compared with the traditional
titanium alloy, the weight gain rate and the thickness of oxygen-rich α layer are significantly
decreased. The main role of these alloy elements is to reduce the diffusion rate of oxygen
atoms and inhibit the formation of brittle oxides, and therefore they can improve the high
temperature oxidation resistance [21]. In Ti-Al alloys with high Nb content, Sn doping can
reduce the thickness of the oxide film, change the structure of the oxide film and inhibit
the formation of cracks in the oxide layer. The Sn and Nb segregate in the transition layer
between oxide film and substrate, forming a barrier layer to hinder the oxygen diffusion. At
the same time, the addition of Sn stabilizes the TiN in the alloy and prevents the diffusion
of Ti ions from the matrix to the oxide layers, thus reducing the thickness of the oxide
Metals 2021, 11, 985 4 of 18

film and improving the oxidation resistance of the alloy [22]. The Ti-Al-Nb-Mo-X(TNM)
alloy, which has already been used by GE (America) for producing low pressure turbine
(LPT) blades for PW1100G™ engines [1], also benefits from the combined effect of Nb and
Mo elements. A continuous and dense Al2 O3 oxide film can be formed and can prevent
oxygen atoms from spreading inward and reduce the oxidation rate [23]. There are also
methods that use elements with positive effects to balance the negative influence of other
elements, for instance, Mn can diffuse rapidly in Ti-Al alloys at high temperature and be
oxidized to Mn2 O3 , which finally incorporates with TiO2 , weakening the strength of the
bonds between the oxides and the matrix. By Mn-W co-alloying, the selective oxidation of
Al is promoted by the W element and that of the Mn element is suppressed [24].
Combined with different processing and heat treatment methods, the alloyed Ti-
Al alloys present corresponding micro-structures which may greatly alter the oxidation
resistance. For instance, in Ti-48Al-2Cr-2Nb alloys, samples with lamellar structures show
better oxidation resistance than ones with duplex microstructures. The smaller the grain
size is, the more compact the oxide layer will be. Furthermore, Ti-Al alloys with smaller
grain size have better high temperature oxidation resistance [25]. Boron addition with 0.5 at.
% B can refine the microstructure of the Ti-45Al-8Nb alloy, reduce the lamellar structure
size from 400 µm to 70 µm. The refinement behavior reduces the thermal stress inside the
oxides and prevents spalling. The grain refinement also provides more Al2 O3 oxide pegs,
enhancing the strength between the oxide layer and the matrix [26]. By doping Co element
into a Ti-48Al-2Cr-2Nb alloy, Co-rich phases of CoAl2 Ti form along the grain boundaries,
and a Co-rich layer also forms between the oxide layer and the matrix, such structures
can hinder the diffusion of oxygen and metal ions, thereby suppressing the growth of the
oxides and preventing spallation [27].

3. Theoretical Study
The adsorption and dissolution properties of oxygen on the surface of the Ti-Al alloys
are the key factors that control the initial stage of high temperature oxidation behavior.
After the adsorption process, the diffusion properties of oxygen and metal ions through the
oxides and alloy matrix further affect the oxidation process. Furthermore, the stability and
strength of interfaces between the phases and oxides in Ti-Al alloys also affect the oxidation
resistance properties. However, these processes involve the reactions and interactions on
an atomic scale, which are difficult to analyze or test by experimental methods. For the
anti-oxidation protection of the alloys, alloying methods are some of the most effective
ways, which not only improves the oxidation resistance of the alloys but also provides
comprehensive properties such as mechanical properties, such as Si and Zr element can
improve the creep resistance of the alloys. The multiple-elements alloying is one of the
development directions of the Ti-Al alloys, it is worth predicting the role and influence
mechanics of various alloy elements in the oxidation process. However, it is hard to provide
more information on them using experimental methods.
With the rapid development of chip technology, high-performance computing clusters
have been greatly developed and widely used at present. Different kinds of computation
methods are used to simulate the physical and chemical properties of materials, and to
understand the phenomena and characteristics of materials from micro to macro scale
appeared one after another. Among them, first principles computation methods based
on density functional theory (DFT) can help to explore the geometry, electronic structure,
magnetic, optical, and mechanical properties of materials. In recent years, researchers
have employed first principles calculation methods to study the chemical and physical
properties of various materials in different environments, including the oxidation process
of Ti-Al alloys. For instance, as shown in Figure 1, the oxygen adsorption properties of
surface, interface, and bulk systems can be studied by applying first principles calculations.
The research progress will be introduced from three aspects.
Metals 2021, 11, 985 5 of 18

Figure 1. Schematic of the adsorption sites of the Ti2 AlNb alloy (a) On the (010) surface and inside the bulk (top views),
(b) Interstitial sites at the O(110)/B2(211) interface (side views), red, blue, orange, and gray balls denote O, Al, Nb, and Ti
atoms, respectively.
3.1. Surface Oxidation Properties
The oxidation process always takes place firstly on the surface, and the surface prop-
erties of materials, e.g., the terminal elements and atomic arrangement determine the
oxygen adsorption properties. For Ti-Al alloys, due to the very similar formation energies
of TiO2 and Al2 O3 , the competitions between Al and Ti will inevitably lead to the failure
of protective oxide layer formation. With the increase of oxygen coverage, the oxygen
adsorption on the surfaces tends to be saturated, then the surface structures are destroyed
and reconstructed, which will cause the subsequent diffusion behaviors of oxygen and
metal ions.
Our group has studied the adsorption behaviors of oxygen on the low indexes surfaces
of γ-TiAl. When performing DFT calculations, the chosen surfaces generally obey the
following rules: Firstly, the surface like γ-TiAl (111) has been proved by experiments
that can form interface with Al2 O3 , the related lattice mismatch between the surfaces
of the oxide and the matrix is small. In addition, by applying calculations, the surfaces
with low surface energies can be found, which provides the possibility of the adsorption
behavior during the oxidation process. The surface energies are significantly affected by
the bonds between the metal atoms, once the surface has been cleavaged, the chemical
environment of the surface has been decided and that may greatly influence the oxygen
adsorption and the formation of oxides. The stabilities of (100), (001), (110), and (111)
surfaces were compared firstly [28], and it was found that the surface energy of (100)
with 1:1 stoichiometric distribution of Ti and Al was the lowest. The co-existence of the
two elements indicated that there might be a competition between TiO2 and Al2 O3 in the
initial oxidation process. By comparing the adsorption energies of different adsorption
sites, the results show that oxygen atoms tend to be adsorbed in the titanium-rich regions.
The adsorption energy is defined as follows, where E(x) stands for the total energy of the
system X:
1
Eads = E(O−TiAl) − ( E(slab
TiAl) + 2 E(O2 ) ) (1)

Table 1 shows the adsorption energies of an oxygen atom for the considered surfaces
(the (001) and (110) surfaces are divided into Al-terminated surfaces and Ti-terminated
ones). The adsorption energies for the (111) surface agree with the results that estimated by
Li et al [29], the fcc-Al site is the most stable with the adsorption energy of −5.18 eV; the
Metals 2021, 11, 985 6 of 18

A2 site is the most favorable site of the (100) surface, followed by the T2 site, the energies
are −4.51 eV and −4.39 eV; in the Ti or Al terminated surfaces, except for the (001) surface
with Al-terminal, the oxygen adsorption behaviors of other cases are all controlled by O-Ti
bonds, which indicates that TiO2 is easy to form on these surfaces.

Table 1. Adsorption energy of an oxygen atom on the considered surfaces. (For (001) and (110)
surfaces, B, T, and C stand for bridge site, top site, and center site, respectively. On the (100) surface,
the oxygen atoms are on top of the Al and Ti atoms in the topmost (A1 and T1) and second (A2 and
T2) layer.).

Surface Site E(O-TiAl) (eV) Eads (eV)

Al-(001) B −285.454 −3.94
T1 −283.557 −2.04
T2 −285.133 −3.62
Ti-(001) B −286.506 −5.08
T1 −287.196 −5.78
T2 −284.938 −3.51
Al-(110) T1 −140.811 −0.92
T2 −142.212 −2.32
C1 −144.114 −4.22
C2 −143.654 −3.76
Ti-(110) T1 −143.911 −3.86
T2 −145.203 −5.15
C1 −145.015 −4.97
C2 −145.401 −5.36
(100) A1 −287.049 −2.00
A2 −289.560 −4.51
T1 −288.023 −2.97
T2 −289.548 −4.39
(111) fcc-Al −150.912 −5.18
hcp-Al −150.815 −5.08
fcc-Ti −149.918 −4.18
hcp-Ti −149.871 −4.14

The oxidation properties are also greatly affected by the surface type. For γ-TiAl (100)
surface, in the absence of oxygen, the segregation energy of Al is lower than that of Ti, thus
being easier to form, but oxygen atoms are more easily adsorbed near Ti atoms, and the
strength of O-Ti bond is higher than that of O-Al bond. The oxygen adsorption behaviors
promote the segregation of Ti and even leads to the formation of a pure Ti-terminal surface,
which may lead to the selective oxidation of Ti [30]. With the increase of the coverage of
oxygen atoms, not only the sites on the surfaces but also interstitial sites between surface
and subsurface are occupied by oxygen, which may lead to further oxidation [31]. The
γ-TiAl (111) surface is found to be stable only when the chemical potential of oxygen is very
low, otherwise, it will become unstable, so it is easy to absorb oxygen atoms and it reaches
high coverage quickly. The adsorption in the interstitial sites can also be observed on the
γ-TiAl (111) surface with the high coverage of oxygen. However, different from the (100)
surface, the oxide-like structure on the surface become dense after relaxations and hinder
the subsequent oxygen adsorption, benefiting to the oxidation resistance [29,32]. For γ-TiAl
(110) and (001) surfaces, the interaction between O-Ti is much stronger than that between
O-Al. The Ti-terminal surfaces with oxygen adsorption are more stable, as only titanium
oxides may appear under such conditions. Compared with γ-TiAl, Al3 Ti based alloys
have higher Al content and therefore they own different adsorption properties of oxygen
atoms. Among Al3 Ti(110) surfaces, the Al-terminal one has the lowest surface energy.
When oxygen atoms adsorb on this surface, the Al-Al bridge sites are the most preferable.
According to the analysis of the state density, the p-orbital electrons of oxygen atom have
obvious bonding interactions with the d-orbital electrons of Ti atoms and p-orbital electrons
of Al atoms. The Al-O interaction is stronger compared to the Ti-O one, indicating that
Metals 2021, 11, 985 7 of 18

oxygen atoms tend to bond with aluminum atoms, which is obviously different from the
γ-TiAl system situation. Therefore, it is easier to form the protective aluminum oxide layer
in Ti-Al alloys with high Al content [33].
We have studied the adsorption behaviors of oxygen on the surfaces of orthorhombic
(O) phase Ti2 AlNb to clarify the interaction mechanisms between oxygen and Ti2 AlNb.
The stoichiometric (010) surface of O phase was found to be the most stable low index
surface evaluated by the surface energy. Oxygen atoms prefer to adsorb at fcc-hollow and
hcp-hollow sites. The electronic structures of adsorption systems containing the charge
difference distributions and the densities of states of the hcp site are shown in Figure 2.

Figure 2. (a) charge densities, (b) charge difference distributions (side views), and (c) densities of
states of oxygen adsorbed on the hcp site, red, blue, orange, and gray balls denote O, Al, Nb, and
Ti atoms, respectively, blue isosurface stands for loss of electrons and yellow isosurface stands for
capturing electrons.
Metals 2021, 11, 985 8 of 18

The charge transfer from Ti and Nb atoms to the adsorbed oxygen as well as the
overlaps between O p, Nb d, and Ti d orbitals indicate that O-Ti and O-Nb bonds are
stronger than the O-Al bond. At the initial oxidation stage under high temperature, the
O phase of Ti2 AlNb could not form protective alumina but instead Ti and Nb oxides [34].
The coverage of oxygen atoms is another main factor that may influence the adsorption
progress, which not only has an obvious effect on the adsorption energies of oxygen atoms,
but also significantly impact the surface morphology, oxide nucleation, oxygen atom
diffusion, and the interaction between elements. A clearer understanding can be obtained
through the surface phase diagram, which is also clearly reflected in the calculations of
other materials [35,36].
In addition to the clean surfaces of the Ti-Al alloys, recent studies began to focus
on the changes of oxidation resistance caused by the alloying elements. The segregation
of alloying elements has a significant impact on the oxygen adsorption and changes the
oxidation kinetics. Because such a phenomenon only occurs on the atomic scale during
the oxidation reaction processes, the DFT-based calculation method is very suitable for
this kind of study, and here are some typical results. The investigations on the influence of
Si-segregation on the oxygen adsorption properties on the γ-TiAl (111) surface are carried
out. Si atoms do not easily appear inside the bulk, but rather tend to replace Ti atoms
then segregate on the surface, which improves the Al/Ti ratio on the surface. According
to the comparison of the oxidation properties, oxygen atoms on the primary surface are
more easily adsorbed around Ti atoms, and the oxygen atoms are mutually exclusive.
However, the interaction between O-Al on the alloyed surface becomes stronger and the
oxygen atoms attract each other, promoting the formation of aluminum oxide [37,38]. The
element B, which prefers to segregate on γ-TiAl (111) surface, can also make a contribution
to improve the oxidation resistance. B addition can decrease the coverage of oxygen
and the binding energy of oxygen at the surface, and hinder the growth of A12 O3 and
TiO2 [39]. Cl is effective to prevent the adsorption of oxygen on γ-TiAl (111) surfaces. The
computation results show that the adsorption of the Cl atoms will weaken the bonding
interactions between the oxygen and metal atoms on the alloy surface. On the other
hand, the adsorption competition between Cl and oxygen atoms will reduce the overall
coverage of O on the surface, thus weakening the oxidation [40]. The influence of transition
metal elements with 4d valence electrons as well as the third and fourth main group
elements on the oxidation resistance of γ-TiAl (100) surface have been analyzed. When
the transition metal replaced the Ti atoms on the surface, the adsorption energies of the
oxygen atoms on HCP positions increases compared to the original surface. However, if Al
atoms are replaced, the condition will be opposite. Furthermore, the effect of Al-replacing
on adsorption energies is smaller than that of Ti. When doping with 4d transition metal
elements, the competition and the change of hybrid state among the ions are the main
factors that affect the adsorption energies. When the third and fourth main group elements
are doped, the reduction of hybrid energy makes the adsorption energies of oxygen atoms
decrease accordingly [41]. The Ta-W co-alloying on the γ-TiAl (111) surface changes the
favorable adsorption sites of the oxygen atoms, decreases the formation rate of Ti-O bonds,
and the electronic structure analysis also indicates that the existence of 5d orbital electrons
significantly reduces the activity of the Ti 3d orbital electrons, the combination of Ti and O
has been greatly reduced, these results agree with the experimental conclusions that the
high cation valence elements doping may inhibit the formation of titanium oxide [10,11].
The parallel experimental results also show that the Ta-W co-alloying can improve the high
temperature oxidation resistance of the γ-TiAl by inhibiting the diffusion of oxygen [42].
The elements like Y and Hf may segregate on the surfaces of γ-TiAl, then weaken the
interaction between oxygen atoms and the surfaces. Therefore, the Y and Hf are helpful
to slow down the oxidation rate and inhibit the growth of the oxide layer. The bonding
between oxygen atoms and γ-TiAl surfaces can be an ionic bond or a covalent bond, while
Y and Hf elements mainly weaken the covalent bonding. In addition, Cr, Mo and other
Metals 2021, 11, 985 9 of 18

elements also have positive effects on improving the oxidation resistance and affecting the
oxygen adsorption behavior when doping on different surfaces [43,44].

3.2. Stability and Adhesion Properties of the Interfaces

As the oxidation reaction is happening, the oxide layer begins to form and the oxida-
tion behaviors of the alloys are no longer controlled by the original crystal surfaces. The
interfaces between the oxide and the matrix provide channels for the internal diffusion of
oxygen atoms. At the same time, the bonding strength determines whether oxide spalling
occurs. On the other hand, Ti-Al alloys are two-phase or three-phase alloys with a lot of
phase boundaries. The mechanical properties and oxidation resistance might be affected
by such defects. First principles calculation methods can explore the interface structure
evolution, stability, and mechanical properties.
To shed light on the adhesion and mechanical properties of the interfaces, here are
some of the available methods based on DFT calculations. Due to the different thermal
expansion coefficient and thermo-mechanical properties between the oxide and matrix, the
interfaces will produce tensile and shear stress. Firstly, for the simulations of the tensile
tests, the interfacial fracture under tension by applying the strain between atomic layers
has been studied. When the local stress concentration occurs and the strain exceeds 80%,
the fracture of an interface can be identified. It provides a good reference for the analysis
of oxide spalling from the alloy matrix [45,46]. Secondly, to explore the sliding friction and
shear behaviors of the atomic layers of the interface system, the effect on the sliding barrier
can be calculated. When the relative position of the interface changes, the bond length
and bond energy vary accordingly. As the periodic change of the atomic arrangement, the
energy correspondingly has the highest and lowest points thus forming a potential barrier.
In order to overcome the potential barrier and maintain the sliding within the atomic layers,
it is necessary to calculate the force of horizontal friction. The lower initial energy indicates
that the interface is easier to slide, and the sliding barriers reflect the stability and shear
resistance of the interfaces [47,48]. Similar to the surface system, alloying elements can
also segregate in the interface. The segregation behavior can not only affect the chemical
properties and mechanical properties of the interface but also the diffusion properties of
metal ions at the interface, which has significant influence on the oxidation process of Ti-Al
alloys [49,50].
For the Ti-Al alloys, we have studied the stability and adhesion property of the γ-
TiAl/Al2 O3 and γ-TiAl/TiO2 interfaces [51–54]. The influence of different stacking forms
and relative positions on the stability was investigated. It was found that Al2 O3 and TiO2
tend to bond with Al and Ti atoms respectively on the surfaces of the γ-TiAl alloy. The
results also indicate that the alloying elements and defects can affect the strength of the
interfaces. The Y, Nb, and Pd have the largest strength effect on the TiO2 /TiAl interface,
they will help to prevent the oxide from peeling off and may improve the oxidation
resistance in cyclic oxidation conditions [53]. For the Al2 O3 /TiAl interface system, to
evaluate the strength, the work of adhesion is defined as follows:

Wad = ( Ea−i − Ea−s−i − Es−i )/A (2)

where Ea−i is the total energy of the interface, Ea−s−i and Es−i stand for the energy of the
Ti-Al and Al2 O3 slabs, respectively, A stands for the interface area. The fitting curves are
obtained using the universal binding energy relation (UBER) curve [55,56]:

x − x0 x − x0
   
Ea−i = Ea−s−i + Es−i − 2AWad 1 + exp − (3)
λ λ

where x is the distance between the slabs, x0 is the equilibrium distance, λ is a Thomas-
Femi screening length specific to the materials of the two sides of the interface. The
plane-averaged charge (PAC) describes the charge distributions along with the c directions
of the two kinds of interfaces, where the positive and negative values stand for the gaining
Metals 2021, 11, 985 10 of 18

and losing of charges for forming the interfaces. As shown in Figure 3, the influence
of alloying elements on the interactions of γ-TiAl/Al2 O3 is limited, while they greatly
enhance the adhesion strength of α2 -Ti3 Al/Al2 O3 interface. The enhancement of strength
may result from the strong interactions between the alloying elements and the Al2 O3 . Other
investigations also proved that alloying elements like Mo can decrease the adhesion energy
of the TiO2 /γ-TiAl interface and cause negative effects [57]. The segregation of B and Nb
elements at the interfaces of α-Al2 O3 (0001)/γ-TiAl(111) and TiO2 (110)/γ-TiAl(111) has
been founded. The B addition can significantly enhance the adhesion of the Al2 O3 /γ-TiAl
interface, while the effect of the Nb on the adhesive strength of the TiO2 /γ-TiAl interface is
insignificant [58,59].

Figure 3. Variation of work of adhesion via the separation of (a) γ-TiAl/Al2 O3 and (b) α2 -Ti3 Al/Al2 O3 . Differences of
PACs between interface and separated slabs displayed along the direction perpendicular to the interface (c) γ-TiAl/Al2 O3
and (d) α2 -Ti3 Al/Al2 O3 .
As stated before, Ti-Al alloys may contain a large number of interfaces between
different phases, some researches also revealed their effects on the oxidation progress.
For the Ti2 AlNb alloy [60], the calculation results about the binding force, stability and
electronic structure of O(001)/B2(110) interface indicate that the thick atomic layers of
the two phases have similar properties to the bulk structure. The Ti-Nb and Ti-Al bonds
Metals 2021, 11, 985 11 of 18

maintain the adhesion of the interface. Similar conclusions were also obtained in our
calculations, in which the stability and oxygen adsorption properties of the O(110)/B2(211)
interface were studied. As shown in Figure 4, the influence of relative positions on the
stability has been systematically calculated. For turning the relative position between the
O and B2 phases, in the a–b plane, eight steps complete a period in each direction. The
HCP stacked interfaces (in which the frontal atoms of the O phase are located at the top of
the atoms in the second layer of the B2 phase) display the lowest formation energy values.
The oxygen adsorption in the interface is thermodynamically stable, but the adsorption
energies are higher than that of oxygen on the O(010) surface. Therefore the O/B2 coherent
interface without defects has limited influence on the oxidation resistant properties of the
Ti2 AlNb alloys.
For the TiAl/Ti3 Al interface, the adsorption behavior will lead to the deterioration
of mechanical properties. The oxygen adsorption can affect the shear strength of the
TiAl/Ti3 Al interface, the oxygen atoms tend to combine with Ti atoms at the interface. In
the four interface models with different stacking, although the formation energy of the
oxygen-containing system is lower, the addition of oxygen will lead to the decrease of
shear strength. If the oxidation occurs at the interface, the mechanical properties of the
alloy will deteriorate [61,62]. The existence of P element can decrease the bonding strength
of TiAl/Ti3 Al interface, since the P is more likely to bond with Ti, causing the weakness of
Ti-Al bonding. This indicates that the addition of P has a negative effect on the plasticity of
TiAl/Ti3 Al interface [63].

3.3. Bulk Properties

Due to the adsorption and diffusion of oxygen atoms on the alloy surface, mixed
oxides form under the competition of each component in the alloys. The thermodynamic
stability properties of the oxides are important due to the great influence on the formation
and growth of the oxides.
Al2 O3 is slightly easier to form compared to TiO2 according to the calculated formation
energy. The influence of 26 elements including the second to the fifth period on the
stability of Al2 O3 and TiO2 was investigated. Almost all these elements can decrease the
stability of the oxides. The Nb, Mo, W, Re, and other elements can significantly reduce
the stability of Al2 O3 relative to TiO2 . Therefore, they can reduce the internal oxidation
of aluminum, promoting the formation of dense oxide film structure and improving the
oxidation resistance of the alloy [57,64,65]. The theoretical calculations have revealed
the nuclear and growth of oxides, for example, through phonon calculations, the bond
length and bond energy in the oxide can be quantified to analyze the growth trend of the
oxide. The parameters like melting point, bulk modulus and enthalpy of formation can be
analyzed as well [66,67]. By performing such investigations, the alloying elements Cr, Ti,
Zr, Hf, Y, and Nb are found to increase the Al-O bonding. Therefore, elements like Nb can
promote the formation of A12 O3 and inhibit the formation of TiO2 , thus forming a compact
and stable A12 O3 oxide film on the surface of the TiAl alloys and improving the oxidation
resistance [68].
Diffusion of elements is another key problem during the oxidation of alloys. The diffu-
sion of elements is a very complex process, which is affected by the external environment,
micro-structure, defects, and so on. With the progress of the oxidation behavior, the oxygen
adsorption on the surface gradually approaches saturation. At high temperature, the
activity of both the oxygen and the metal ions are greatly improved. The interfaces, oxides,
and even the grain boundaries will become the channels for the diffusion of elements. The
continuous diffusion behavior is the main control factor of oxide growth.
Metals 2021, 11, 985 12 of 18

Figure 4. (a) Schematics of “OT” stack of the O/B2 interface (b) schematics of “HCP” stacks of the O/B2 interface (side
views), (c) formation energy surface against the relative positions between O and B2 phases. Gray, orange, and blue balls
denote Ti, Nb, and Al atoms, respectively.
Metals 2021, 11, 985 13 of 18

First principles calculations have been applied to systematically explore the dissolution
and diffusion behavior of oxygen atoms in TiAl. Compared with the tetrahedral interstitial
sites, oxygen tends to be adsorbed in octahedral sites, especially in the Ti-rich environment.
After relaxations, some oxygen atoms migrate to the adjacent "α" and "β" positions, and
phonon calculations show that these adsorption sites can be used as ideal starting and
ending points in the diffusion simulations. Through the Nudged Elastic Band (NEB)
calculations, the minimum barrier that oxygen atoms need to cross when it diffuse from
the β to α position is about 0.2 eV. The relationship between temperature and diffusion
rate is also considered, and the calculation conclusions are consistent with the relevant
experiments [69]. Combining first principles calculation results with other theoretical
models, the diffusion behavior can be analyzed more deeply. For instance, the mathematical
statistics and Landman model can be applied to fit the curve of temperature and diffusion
rate, which is difficult to be obtained from the experiments since the impurity of the sample
and the oxygen concentrations are hard to be controlled accurately [70].
The diffusion behaviors of elements in the Ti-Al alloys are more complex than that of
the original system. Generally, only the chemical environment around the diffusion path of
solute atoms should be considered, and the structure far away from the path is regarded as
the original component without alloying. The effects of alloying elements can be divided
into three categories: local short-range-trapping effect, local long-range-trapping effect, and
non-trapping effect. According to the studies of the effect of Nb doping on the diffusion
properties of oxygen atoms in γ-TiAl bulk, Nb can inhibit the activity of oxygen atoms.
The closer the distance between Nb and O is, the more obvious the inhibition effect is. This
finding is consistent with the experimental results showing that doping an appropriate
amount of Nb in TiAl can reduce the formation of TiO2 [71]. The addition of Nb has a
significant effect on increasing the diffusion barrier of oxygen atoms in TiAl alloy, and with
the increase of Nb contents, the ability to hinder the diffusion also increases, indicated by
the drop of the diffusion coefficient of O [68]. At the same time as the diffusion of oxygen,
the metal ions also continue to diffuse in both the matrix and the oxides. The Si and Y can
be double doped in the Ti-Al alloys. When both of them replace the Ti atoms, the diffusion
of Ti vacancies becomes more difficult. Therefore, the formation of TiO2 is inhibited, and
Al vacancies are easy to diffuse. That is to say, Al atoms are easier to move and diffuse
to the surface and bonding with oxygen atoms, thus promoting the formation of a dense
Al2 O3 oxide layer [72]. In order to explore the influence of alloying elements on the growth
rate of TiO2 , the stability of TiO2 after alloying with Si, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo,
Pd, Ag, Sn, La, Ce, Hf, Ta, and Pt and the diffusion properties of these alloying elements
in TiO2 were investigated [73]. Si, Nb, Hf, Ce, La, and Ta can stably replace Ti atoms in
TiO2 . The formation energies of Ce, Hf, and Ta doped systems are negative. In contrast, the
formation energy of interstitial doping is generally lower than that of displacement doping.
The bonding between the alloying elements and the oxide is strong. Four kinds of diffusion
paths of alloying elements in TiO2 are considered, in which the Sub-VAC-short defect has
lower formation energy than the Sub-VAC-long defect. According to NEB calculation
results, when alloying elements diffuse along the inter-inter path, the barrier is the smallest,
less than 1 eV (Figure 5), which may cause the diffusion of elements during the oxidation
of Ti-Al alloys. Incidentally, when applying DFT-based calculations on the oxides like TiO2 ,
there are matters needing attention, such as the use of the DFT+U method. Though the
electronic structure features can be described by using the local density approximation
(LDA) and the generalized gradient approximation (GGA), the bandgap of semiconductors
is usually underestimated since the existence of strongly correlated d-electrons. To avoid
the unacceptable increase of cost carried by using hybrid DFT, the Hubbard U correction
method (DFT+U) can offer a more efficient way to treat the problem in describing partially
filled electronic states, though such an approximate method can not totally eliminate the
band gap underestimation [74,75]. The DFT+U method has been widely used in the first
principles calculations related to transition metals, such as applying correction on the Ti 3d
orbital in the TiO2 system.
Metals 2021, 11, 985 14 of 18

Figure 5. The diffusion paths of alloying element in TiO2 system (side views). (a) Inter-Inter, (b) Sub-
Vac-long, and the minimum energy path (MEP) of (c) Inter-Inter, (d) Sub-Vac-short.

4. Summary
Oxidation behaviors of Ti-Al-based alloys have been widely studied, and a clear
understanding of their oxidation products, microstructure, and oxidation kinetics has
been established. In the absence of anti-oxidation protection films, the elemental compe-
tition leads to the inevitable formation of mixed oxides, and it is difficult to guarantee
the oxidation-resistant performance of materials at high temperatures. Among the anti-
oxidation modifications of Ti-Al alloys, alloying has been widely studied because of its
simplicity and effectiveness. In order to explore the reaction mechanism and the effects of
alloying elements during the oxidation process of Ti-Al alloys, theoretical studies based on
first principles calculations have been greatly employed. The specific research contents can
be divided into three parts:
(1) The surface oxidation properties of Ti-Al alloys such as the surface stability, oxygen
adsorption properties, and doping effects have received the most attention. Although
there is a strong tendency to form TiO2 on the original alloy surfaces, the interactions
Metals 2021, 11, 985 15 of 18

between oxygen and titanium can be inhibited to a certain extent by alloying. The
alloying elements like B, Si, Cl show an obvious segregation tendency on the surfaces
of the alloys and weaken the binding between oxygens and metal atoms. The high
cation valence elements like Ta and W are effective in hinder the reaction between Ti
and O, agreeing with the valence control mechanism.
(2) In order to explore the bonding properties between the oxides and the alloy matrix,
the interface systems are greatly studied, mainly focusing on the representative oxides
(TiO2 and Al2 O3 ) and Ti-Al matrix. Not surprisingly, the alloy elements have different
influences on the stability and adhesion properties of the interfaces, such as Nb can
enhance the strength of the TiO2 /γ-TiAl interface while Mo may play a negative role
in this system, generally, the elements that own obvious segregation tendency may
have more effects on the adhesion strength.
(3) The diffusion properties and the stability of the oxides have also been studied. Some
typical alloying elements such as Nb can not only segregate in the oxides and optimize
the structure of the oxides. They also reduce the diffusion rate of oxygen atoms, and
thus inhibit the rapid growth of the oxide.
Theoretical studies have provided valuable suggestions on the atomic and electronic
scales and can help to optimize and promote the oxidation resistant properties of Ti-Al
alloys. However, the oxidation process of Ti-Al alloys are complex due to the competi-
tion between various oxides, e.g., TiO2 and Al2 O3 . Further studies can be expected by
combining theoretical and experimental methods on the kinetic and phase transformation
properties during the oxidation process of Ti-Al alloys.

Author Contributions: Literature search, figures, data collection, data analysis, data interpretation,
writing, Y.L.; literature search, figures, data collection, data analysis, data interpretation, writing, J.D.;
literature search, figures, data collection, data analysis, data interpretation, writing, Y.S. All authors
have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data available on request due to restrictions eg privacy or ethicalThe
data presented in this study are available on request from the corresponding author.
Acknowledgments: This work was supported by The National Key Research and Development
Program of China, Grant No. 2016YFB0701301, the Natural Science Foundation of Shandong, China,
Grant ZR2020ME003, and the Weihai construction projects Grant No. 2014DXGJ12.
Conflicts of Interest: The authors declare no conflict of interest.

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