M Legrée

J.-L Bobet

F Mauvy

J Sabatier
email: jocelyn.sabatier@u-bordeaux.fr

Modeling hydrolysis kinetics of dual phase α-Mg/LPSO alloys

Keywords: Magnesium, LPSO, hydrolysis, kinetics modeling

This work proposes a new modeling of hydrolysis reaction in simulated seawater solution (35 g/L NaCl) with alloys containing α-Mg and Long Period Stacking Ordered (LPSO) phases. Alloys with different chemical compositions or thermal treatments were synthesized, leading to different (i) microstructures, (ii) α-Mg over LPSO phase fractions or (iii) LPSO type (18R or 14H). Classical nucleation and growth equation is used as an indicator of the reaction mechanisms but a new model is proposed to describe the complex kinetics curves (Vol(H 2 )=f(t)) obtained. This new model allow to (i) discriminate the contribution of each phase, (ii) could be applied to any alloy composed of two phases and (iii) is applied to the whole kinetics curves (i.e. from 0 to 100% yield). It is supported by the comparisons between the different alloys and SEM observations of their microstructure before and after exposure to the seawater solution.

Introduction

Between 1939 and 1941, Melvin Avrami popularized the probabilistic approach of kinetics of phase change in solids, initially proposed by Kolmogorov in 1937 and later by Mehl and Johnson [START_REF] Avrami | Kinetics of phase change. I: General theory[END_REF][START_REF] Avrami | Kinetics of phase change. II Transformation-time relations for random distribution of nuclei[END_REF][START_REF] Avrami | Granulation, phase change, and microstructure kinetics of phase change[END_REF][START_REF] Johnson | Reaction kinetics in processes of nucleation and growth[END_REF][START_REF] Kolmogorov | On the statistical theory of the crystallization of metals[END_REF]. This theory (known as JMAK theory) relies on a germ nucleation and growth process. Its purpose is to describe isothermal phase transformation in a crystalline material. The resulting general equation (often referred to as Avrami or Avrami-Erofeev equation) has the form:

y(t) = 1-exp(-k t n ) (1)
where y is the volume fraction of transformed material at time t, k is a kinetic related factor that notably depends on temperature and n is the Avrami exponent linked to the dimensionality of germ growth. The simplicity of this resulting equation along with its solid theoretical foundations made it extremely popular over the past 70 years [START_REF] Couillaud | Study of the hydrogenation mechanism of LaCuMg 8 ternary phase: The decomposition induces kinetics improvement[END_REF][START_REF] Takeichi | Hydrogen Absorption and Desorption Behavior of Magnesium Hydride : Incubation Period and Reaction Mechanism[END_REF][START_REF] Blázquez | On the use of JMAK theory to describe mechanical amorphization: A comparison between experiments, numerical solutions and simulations[END_REF]. The main application domains are crystallization kinetics, phase transformation or chemical reactions. It also happened to be a relevant expression of epidemic spreading [START_REF] Avramov | Kinetics of distribution of infections in networks[END_REF]. However, like any model, JMAK relies on several assumptions that limit its use in certain cases. Among the numerous efforts made to enlarge JMAK applicability domain and viability [START_REF] Blázquez | On the use of JMAK theory to describe mechanical amorphization: A comparison between experiments, numerical solutions and simulations[END_REF][START_REF] Dziembaj | Restatement and a new method of application of the[END_REF][START_REF] Fanfoni | The Johnson-Mehl-Avrami-Kolmogorov model: A brief review[END_REF], one can mention the work of Farjas and Roura to adapt JMAK to non-isothermal reactions [START_REF] Farjas | Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution[END_REF]. Under constant heating conditions, they obtained a transformation rate equation differing from the original one by a constant factor. Holloway and Hudson were the first to apply JMAK equation to surface science [START_REF] Holloway | The kinetics of the reaction between oxygen and sulfur on a Ni(111) surface[END_REF]. In order to suit their reaction's geometry (removal of sulfur segregated on a nickel surface) they assumed a growth of circular holes on a surface instead of spheres in a volume. Later on, Egert obtained satisfying results applying this version of the model to the corrosion of uranium protected with metallic coating [START_REF] Egert | Theory of the Corrosion of Substrates With Protective Metallic Coatings[END_REF].

Obtaining the The kinetic parameters k T of a reaction at different temperatures allows determining the activation energy (using Arrhenius-type law), which is a convenient way to compare the reactivity of different systems. This is probably the reason for such a wide use of JMAK model in the field of hydrogen production from hydrolysis with magnesium (Mg) based compounds [START_REF] Alasmar | Hydrogen generation from Nd-Ni-Mg system by hydrolysis reaction[END_REF][START_REF] Hou | Comparative investigation on feasible hydrolysis H2 production behavior of commercial Mg-M (M = Ni, Ce, and La) binary alloys modified by high-energy ball milling-Feasible modification strategy for Mg-based hydrogen producing alloys[END_REF][START_REF] Zhong | Effect of cations in chloride solutions on lowtemperature hydrolysis performances and mechanisms of Mg-Ca-based hydride[END_REF][START_REF] Huang | Hydrogen generation by hydrolysis of MgH2 and enhanced kinetics performance of ammonium chloride introducing[END_REF][START_REF] Awad | Effect of carbons (G and CFs), TM (Ni, Fe and Al) and oxides (Nb 2 O 5 and V 2 O 5 ) on hydrogen generation from ball milled Mg-based hydrolysis reaction for fuel cell[END_REF].

However, the model is used without considering its inherent assumptions, which comprise: i) An a priori assumption of phase transformation operating by nucleation and growth, ii) nucleation appears randomly in the volume, iii) the nucleus critical size is zero and iv) the growth is isotropic.

The second assumption cannot be considered as correct for is not true in the case of a corrosion reaction, which takes place at the material surface. As previously mentioned, the work of Holloway and Hudson [START_REF] Holloway | The kinetics of the reaction between oxygen and sulfur on a Ni(111) surface[END_REF] answered the geometry issue, but the general equation is still used instead of to their more complex version. Even considering only the surface, nucleation is still not random since corrosion initiates on preferential sites like impurities, defects or interphases [START_REF] Perez | ELECTROCHEMISTRY AND CORROSION SCIENCE[END_REF][START_REF] Ahmad | Principles of corrosion engineering and corrosion control[END_REF][START_REF] Yang | Corrosion Behavior of Pure Magnesium with Low Iron Content in 3.5 wt% NaCl Solution[END_REF][START_REF] Marcus | Atomic level characterization in corrosion studies[END_REF]. This remark also applies to the fourth assumption as corrosion is often tempted to propagate in preferential directions such as intergranular surfaces [START_REF] Perez | ELECTROCHEMISTRY AND CORROSION SCIENCE[END_REF][START_REF] Song | Understanding magnesium corrosion. A framework for improved alloy performance[END_REF][START_REF] Atrens | Advances in Mg corrosion and research suggestions[END_REF]. JMAK model for hydrolysis must be interpreted with much care and is, most of the time, not applicable to early and late reaction data (i.e. commonly applied between 0.15 and 0.5% yield). Kinetic models based on fundamental mechanisms seems to be a more relevant approach [START_REF] Berezovets | Kinetics and mechanism of MgH2 hydrolysis in MgCl2 solutions[END_REF][START_REF] Gonçalves | Dynamic Modeling of Hydrogen Generation via Hydrolysis of Sodium Borohydride[END_REF][START_REF] Bajger | Mathematical modelling of the degradation behaviour of biodegradable metals[END_REF][START_REF] Bajger | Modelling the Corrosion of Magnesium and Its Alloys[END_REF][START_REF] Thomas | Corrosion mechanism and hydrogen evolution on Mg[END_REF]. The idea is to consider the simple reactions that occur in the whole process (anodic Mg dissolution, Mg(OH) 2 formation, water reduction,…) and build the model from the laws describing the kinetics of the fundamental mechanisms. A model constructed this way suits a specific material or type of corrosion. This kind of approach is very powerful but designing a relevant model demands good preliminary knowledge of the mechanisms involved. On the other hand, the more mechanisms involved the more complex the model becomes and the harder it is to solve and apply properly.

In this study, 11 Mg alloys formed of α-Mg and/or Long Period Stacking Ordered (LPSO) phases are tested as materials for hydrolysis reaction in 0.6M NaCl solution. The modelling of the kinetic curves is discussed herein based on Scanning Electron Microscopy (SEM) and crosscomparison between alloys. Alloys considered in this study were designed in order to present specific differences such as the nature of the alloying elements, their proportions, the microstructure, the α-Mg/LPSO ratio or the nature of the LPSO phase (14H or 18R). The method used in this work is a novelty in that it to analyses the behavior of each of the phases composing the alloy, taking into account their galvanic coupling interactions. It allows proposing an original model that accounts independently for the hydrolysis of the two phases that contribute to the overall H 2 generation. This new model may help analysing hydrolysis results in future works. Especially since Mg alloy design is a common strategy for hydrogen production from Mg based materials and researchers struggle at modeling the whole data range of the reaction kinetics [START_REF] Hou | Comparative investigation on feasible hydrolysis H2 production behavior of commercial Mg-M (M = Ni, Ce, and La) binary alloys modified by high-energy ball milling-Feasible modification strategy for Mg-based hydrogen producing alloys[END_REF][START_REF] Oh | Design of Mg-Ni alloys for fast hydrogen generation from seawater and their application in polymer electrolyte membrane fuel cells[END_REF][START_REF] Li | Mg-Mg2X (X=Cu, Sn) eutectic alloy for the Mg2X nano-lamellar compounds to catalyze hydrolysis reaction for H2 generation and the recycling of pure X metals from the reaction wastes[END_REF][START_REF] Oh | Fabrication of Mg-Ni-Sn alloys for fast hydrogen generation in seawater[END_REF][START_REF] Hou | Enhanced hydrogen generation behaviors and hydrolysis thermodynamics of as-cast Mg-Ni-Ce magnesium-rich alloys in simulate seawater[END_REF][START_REF] Bai | H2 Production of As-Cast Multialloying Mg-Rich Alloys by Electrochemical Hydrolysis in NaCl Solution[END_REF][START_REF] Hou | H2 generation kinetics/thermodynamics and hydrolysis mechanism of high-performance La-doped Mg-Ni alloys in NaCl solution-A large-scale and quick strategy to get hydrogen[END_REF][START_REF] Yang | Hydrolysis H2 generation of Mg-Ni alloy catalyzed by expandable graphite / stannic oxide[END_REF][START_REF] Hou | Mg alloy waste modified by ( Mg10Ni ) 90 Ce 10 : A green hydrolysis hydrogen production strategy[END_REF].

Methods

The compounds with Mg content inferior to 93 % at. were synthesized using chunks of magnesium (99.9%) from Kojundo Chemical Laboratory Co., Ltd., copper (99.99%) and nickel (99.9%) from Furuuchi Chemical Co., and yttrium (99.9%) from Nippon Yttrium Co., Ltd. The elements were melted together in an induction furnace under a helium atmosphere. Due to its high vapor pressure, an excess of 7 wt.% of Mg was added. The compounds with Mg content superior to 93 % at. were synthesized using chunks of magnesium (99.9%) from Sigma, nickel (99.9%) from Strem chemicals and yttrium (99.9%) from Smart elements. The elements were sealed in tantalum crucible under low Argon atmosphere to avoid Mg evaporation during induction melting. All the obtained ingots were subsequently annealed under argon atmosphere at 400°C in an aluminum foil or at 500°C in a tantalum foil. The compositions of the alloys and the LPSO types were verified by X-ray diffraction (XRD). Examples of patterns obtained are shown in supplementary materials.

Scanning Electron Microscopy (SEM) observations were made using a TESCAN VEGA3 SB and SERON TECHNOLOGY microscopes equipped with back scattered electron detectors (hereafter referred to as BSE mode). Furthermore, the elemental composition of the surface was analyzed using an energy dispersive X-ray (EDXS) detector. The phase proportion was estimated by analyzing SEM images with ImageJ software. For SEM analysis, the bulk samples were mechanically polished up to 4000 grit SiC paper with absolute ethanol as lubricant until a mirror surface was obtained.

The reaction of magnesium with water (hydrolysis) considered in this study is:

Mg + 2H 2 O = Mg(OH) 2 + H 2 (2)
Hydrolysis reactions were carried out in a closed 100 mL three-neck round bottom flask connected to a burette that dips in a beaker of water. The experimental setup was previously described in ref [START_REF] Pighin | Nanostructured Mg for hydrogen production by hydrolysis obtained by MgH2 milling and dehydriding[END_REF]. Water from the beaker is initially sucked up into the burette. Then, the dihydrogen (H 2 ) produced during the experiment induces water displacement back to the beaker and a balance connected to a computer records the mass variation, allowing to follow in real time the hydrogen generation. Bulk samples were filed and about 30 mg of material were taken to react with 20 mL of simulated seawater solution (i.e. 35 g/L NaCl). The powders obtained from filing were relatively gross shavings with a flat face and a ribbed one. Their dimensions ranged from tens to hundreds of micrometers. SEM micrographs of the particles can be consulted in supplementary materials. The solution was rapidly stirred with a magnetic bar and during the whole experiment the temperature was kept at a constant value of 25°C. After measurement, 1 mL of 2.4 M HCl was added to complete the hydrolysis process and thereby generate the maximum H 2 amount the sample could release. The yield of reaction was calculated from this amount of H 2 . The curve fitting was done with Simulink-Matlab software.

Hydrolysis

The alloys tested can be divided in two groups based on the shape of their hydrolysis curve. ). These alloys present hydrolysis curves with sigmoidal shape (Figure 1B). The estimated α-Mg proportions are respectively: 27, 41, 50, 73 and 92%, again with an error of 3%.

It has been evidenced in other works that galvanic coupling occurs between LPSO and α-Mg phases, increasing corrosion rate of the latter [START_REF] Liu | Role of the LPSO structure in the improvement of corrosion resistance of Mg-Gd-Zn-Zr alloys[END_REF][START_REF] Li | Effect of volume fraction of LPSO phases on corrosion and mechanical properties of Mg-Zn-Y alloys[END_REF][START_REF] Han | The Anodic Role of Ni-Containing LPSO Phases During the Microgalvanic Corrosion of Mg 98 Gd 1.5 Ni 0.5 Alloy[END_REF]. In particular, previous work on the present alloys confirmed that during hydrolysis reaction, α-Mg reacts prior to LPSO phase [START_REF] Legrée | Hydrogen generation by hydrolysis reaction using magnesium alloys with long period stacking ordered structure[END_REF]. Therefore, it is noteworthy that the rapidly reacting alloys (first group) are mainly composed of LPSO while α-Mg richer alloys belong to the sigmoidal curve group. BSE micrographs of figure 2 illustrate the microstructural and phase proportion differences between the two groups. The clear regions are LPSO phase and the dark ones are α-Mg. In the first group (figure 2A), little α-Mg amounts are surrounded by LPSO and react quickly. In the second (figure 2B), larger amounts of α-Mg are less subjected to galvanic coupling. This microstructural effect on corrosion has been evidenced on other Mg alloys by Alasmar et al [START_REF] Alasmar | Hydrogen generation from Mg-NdNiMg 15 composites by hydrolysis reaction[END_REF]. Hancock and Sharp proposed a method for comparing solid-state reactions kinetics based on nucleation and growth processes [START_REF] Hancock | Method of Comparing Solid-State Kinetic Data and Its Application to the Decomposition of Kaolinite, Brucite, and BaCO3[END_REF][START_REF] Sharp | Equations, Numerical Data for Some Commonly Used Solid State Reaction[END_REF]. It consists in plotting ln(-ln(1-y)) as a function of ln(t), as y and t denote the reaction fraction and the time respectively :

ln(t) = ln(-ln(1-y)) (2)
The resulting curve has an ordinate at the origin equal to ln(k) which is relative to nucleation and growth kinetics and exhibits linear shape of slope n dictated by the reaction mechanism. This method impose data linearization without taking into account extreme values that are often corrupted (e.g.

t=0 not defined exactly). The reactions that can be distinguished are diffusion controlled mechanism (0.54< n <0.62), phase boundary controlled mechanism (1.07< n <1.11) and Avrami equations (n=1, 2,

3). In order to examine what value of n each compound would show; this method was applied to our hydrolysis data between 15 and 50% of reaction and the parameters obtained are listed in table 1.

The values of n obtained ranged from about 1 to 2 and tend to be bigger as the α-Mg amount in the alloy is higher. Figure 3 shows that value of n is directly proportional to α-Mg proportion.

Extrapolation to α-Mg = 0% gives a n value of 0.87 which is in good agreement with the n value of 0.82 exhibited by our unique "pure" LPSO compound. Alloys with a major part of LPSO have n values close to 1 meaning that they can whether be described by phase boundary controlled kinetic or one dimensional growth. As the interpretation of n values is not trivial, first order kinetic (n=1) is a good compromise for modeling LPSO reaction as it has minimalistic assumptions (kinetic depends only on a constant factor and the reactant concentration). Note that first order reaction is the particular case of Avrami equation when n=1. According to figure 3, the bigger the α-Mg inclusions in the alloy, the closer to 2 is the value of n. This indicates that α-Mg is consumed by propagation of a twodimensional interface. These interpretations are coherent with SEM surface observation of alloys

Kinetic model

The presence of two phases and three alloyed elements combined with all their different interactions with the solution (OH -, H + , Cl -…) results in numerous possible underlying mechanisms involved. For this reason, building a straightforward model based on fundamental mechanisms seems out of reach. The approach chosen is rather based on "available reactant" consumed, with an expression for each contribution (LPSO and α-Mg phases). The aim is to develop a model that can fit accurately the whole range of H 2 generation kinetics data of alloys with different microstructures and chemical compositions. Although several models has been considered and tested to describe the hydrolysis reaction (e.g. contracting volume, Jander ,…), the model presented hereafter has been chosen based on its good ability to fit the data as well as its non-dependency on geometrical factor.

According to the preliminary observations exposed in section 3, H 2 generation from LPSO is modeled with a first order law. The sigmoidal curves obtained from α-Mg reacting prior to LPSO can be modeled with a logistic function. Functions of such kind describe the evolution of a population (here Mg(OH) 2 ) toward a fixed upper limit (Mg amount in the sample). Combination of these two expressions (first order and logistic) to model hydrolysis kinetic of dual phase alloys is an attempt to account separately for LPSO and α-Mg contributions to global H 2 generation. Hydrogen fraction generated (α) as a function of time (t) is expressed as follows:

In these relations, α1 and α2 are first order and logistic contributions respectively, parameters a1 and a2 are relative to the proportion of LPSO and α-Mg respectively, k1 and k2 are the reaction kinetic parameters of LPSO and α-Mg respectively and b is a positive real number defining the inflection point of the logistic function. A last term is subtracted in order to impose .

The first group of alloys shows initial reactions driven by LPSO kinetic because Mg inclusions are small and rapidly consumed. First order component accounts for it (Eq. ( 3)). It also integrates the α-Mg inclusions at the surface that react quickly under strong galvanic coupling influence. As the LPSO is consumed, the inner α-Mg inclusions (initially not in contact with the solution) appear and react with a delay. This delay corresponds to the duration of surrounding LPSO consumption and is traduced by the initial flat stage of the logistic function. Thus, the logistic function (Eq. ( 4)) accounts for the reaction of Mg with less or even no coupling (as LPSO is partly or fully consumed) that occurs at the end of the reaction. The second group of alloys presents initial reaction driven by α-Mg under galvanic influence that is described by the logistic function (Eq. ( 4)). Simultaneously the reaction of the LPSO starts. It is still described with first order equation (Eq. ( 3)) but its kinetic is much slower due to anodic protection effect of surrounding α-Mg.

where ym i and y i are values at point i for model and data respectively and n is the number of data points. Error values as well as model parameters are summarized in table 2. Error values are all around 5.10 -3 meaning that the fitting is satisfying and homogeneous among the different alloys. Only Mg 87.5 Ni 5.5 Y 7 has a higher error of 1.3.10 -2 . This higher error is due to fitting with only first order function and remains very satisfying.

Modelling results

An interesting correlation is observed on figure 6 between the α-Mg fraction the model gives (parameter a2) and the one measured by SEM. Perfect equality between SEM estimation and proportion parameter is not expected since the model assumes equal yield for the two phases.

Previous work on these materials showed that after hydrolysis some LPSO phase remained while Mg phase was consumed completely [START_REF] Legrée | Hydrogen generation by hydrolysis reaction using magnesium alloys with long period stacking ordered structure[END_REF]. Furthermore, SEM estimation is a volumic fraction while a1 and a2 parameters are molar fractions (relative to produced H 2 ). Alloys with phase ratio close to 50% ). These comparisons show the strong reliability of the model in describing accurately hydrolysis kinetics of various alloys. Additionally, all parameters obtained are completely coherent with the nature of the alloys fitted.

Conclusion

The model described in this work showed a good ability to fit the data of a large number of alloys [START_REF] Fanfoni | The Johnson-Mehl-Avrami-Kolmogorov model: A brief review[END_REF]. In addition, parameters were coherent with independent physico-chemical analyses led on the materials. Its originality relies on considering the two phases as independently reacting

First group

Second group materials whose measure is superimposed. As galvanic coupling imposes a material to react preferentially, it is possible to deduce which phase influence early and late reaction. This model is advantageous for several reasons:

i) It allows to fit reactions kinetics that are too complex to use a model based on fundamental steps.

ii) Parameters involved have simple physical meaning (phase proportion and kinetics).

iii) The whole data range is fitted with very good accuracy. iv) Sole information required is knowing which phase reacts preferentially.

v) Distinction of the different phases contributions is possible with a rather good accuracy.

vi) Applicability to a wide variety of two-phase alloys.

The limit of the model is the arbitrary distinction between two time constants. Obviously, each contribution may overlap the other, especially at interface. This is why knowing proportions of each phase is a good way to verify consistency of the model and impose pertinent constraints while refining the parameters. If the phase proportions are known, the corresponding parameters can be fixed. Furthermore, it is better if the reaction order of the nobler phase alone is known as it can be hidden by the reaction of the less noble one. The purpose of this method relies more on distinguishing reaction kinetics of the alloy components than highlighting corrosion mechanisms.

Alloys studied here involve fusion and annealing of Mg with rare earth and transition elements, which represent a quite expensive manufacturing both economically and energetically speaking.

Although they offer very efficient hydrogen generation (high yield and kinetics), end-of use alloy scraps would probably be preferable for application [START_REF] Uan | Generation of hydrogen from magnesium alloy scraps catalyzed by platinum-coated titanium net in NaCl aqueous solution[END_REF][START_REF] Uan | Producing hydrogen in an aqueous NaCl solution by the hydrolysis of metallic couples of low-grade magnesium scrap and noble metal net[END_REF][START_REF] Bacha | Effect of ball milling strategy (milling device for scaling-up) on the hydrolysis performance of Mg alloy waste[END_REF]. The strength of this model being its applicability to any binary alloy, its adaptation to commercial alloys scraps undergoing galvanic coupling is underway.

Figure 1 :

 1 Figure 1: Hydrolysis reaction in 35 g/L NaCl solution for A) alloys with rapid kinetics and B) alloys with sigmoidal kinetics.

Figure 2 :

 2 Figure 2: BSE-SEM micrographs of A) Mg 91 N 4 Sm 5 (first group) and B) Mg 97 NiY 2 (second group). Clear and dark regions are LPSO and α-Mg phases respectively.

Figure 3 :

 3 Figure 3: Dependency of linearization slope determined between 15 and 50% of reaction on α-Mg proportion in the alloy.

Figure 5

 5 illustrates the curve fitting of Mg 91 Ni 4 Gd 5 (1 st group) and Mg 97 NiY 2 (2 nd group) and details first order (LPSO) and sigmoidal (Mg) contributions. This figure also demonstrates that the model is able to fit the data properly. The error criterion minimized for data fitting is:

Figure 5 :

 5 Figure 5: Hydrolysis curves and model fitting of A) Mg 91 Ni 4 Gd 5 and B) Mg 97 NiY 2 .

(

  Mg 94 Ni 3 Y 3 , Mg 91 Cu 4 Y 5 (50h), Mg 91 Cu 4 Y 5 (10d), Mg 94 Ni 2 Y 4 ) have worst correlation compared to the others. This is because the distinction of two time constants is a simplification assumption, so that overlapping occurs between the two contributions. Indeed, all alloys with majoritarian LPSO (first group) underestimate the α-Mg fraction because first order integrates small α-Mg inclusions reacting initially. Despite these considerations, the phase proportions parameters are in good agreement with

Figure 6 :

 6 Figure 6: Comparison between α-Mg volume fractions estimated with SEM and α-Mg fraction parameters (a2) from the model.

Figure 7 :

 7 Figure 7: Kinetic parameters for LPSO (black) and α-Mg (red) phases.

  related information in[START_REF] Inoue | Correlative atom probe tomography and scanning transmission electron microscopy reveal growth sequence of LPSO phase in Mg alloy containing Al and Gd[END_REF][START_REF] Kishida | A formation criterion for Order-Disorder (OD) phases of the Long-Period Stacking Order (LPSO)-type in Mg-Al-RE (Rare Earth) Ternary Systems[END_REF][START_REF] Saal | Thermodynamic stability of Mg-based ternary long-period stacking ordered structures[END_REF][START_REF] Charbonnier | Hydrogenation Properties of Mg 83.3 Cu 7.2 Y 9.5 with Long Period Stacking Ordered Structure and Formation of Polymorphic γ-MgH 2[END_REF][START_REF] Inoue | Novel hexagonal structure and ultrahigh strength of magnesium solid solution in the Mg-Zn-Y system[END_REF][START_REF] Yokobayashi | Enrichment of Gd and Al atoms in the quadruple close packed planes and their in-plane long-range ordering in the long period stacking-ordered phase in the Mg-Al-Gd system[END_REF][START_REF] Kishida | Crystal structures of highly-ordered longperiod stacking-ordered phases with 18R, 14H and 10H-type stacking sequences in the Mg-Zn-Y system[END_REF][START_REF] Kishida | The crystal structure of the LPSO phase of the 14 H-type in the Mg-Al-Gd alloy system[END_REF]. The second group includes Mg 91 Cu 4 Y 5 (500°C, 50h, 14H+Mg), Mg 91 Cu 4 Y 5 (500°C, 10d, 14H+Mg), Mg 94 Ni 2 Y 4 (500°C, 10d, 18R+Mg), Mg 97 NiY 2 (500°C, 50h, 18R+Mg) and Mg 97 Ni 1.5 Y 1.5 (500°C, 10d, 14H+Mg

	The first group composed of Mg 87.5 Ni 5.5 Y 7 (400°C, 50h, 18R), Mg 91 Ni 4 Y 5 (500°C, 10d, 14H), Mg 91 Ni 4 Y 5
	(400°C, 10d, 18R), Mg 91 Ni 4 Gd 5 (500°C, 10d, 14H), Mg 91 Ni 4 Sm 5 (500°C, 10d, 14H) and Mg 94 Ni 3 Y 3 (500°C,
	50h, 14H) presented a rapid linear H 2 evolution with time at the initial stage of the reaction (Figure

1A). Mg 87.5 Ni 5.5 Y 7 is composed of single phase 18R LPSO while the others present, in addition to the LPSO phase, respectively 15, 12, 21, 16 and 18 % of α-Mg phase, based on BSE-SEM images analysis.

The error for these surface proportion estimations is about 3%. The reader unfamiliar with LPSO structures may find

Table 1 :

 1 Parameters values obtained by linearization of hydrolysis data between 15% and 50% of reaction. Mg 91 Ni 4 Y 5 (500°C) Mg 91 Ni 4 Y 5 (400°C) Mg 91 Ni 4 Gd 5 Mg 91 Ni 4 Sm 5 Mg 94 Ni 3 Y 3

	n	8.20.10 -1	1.08	1.10	9.85.10 -1	1.21	9.45.10 -1
	k	5.78.10 -3	1.54.10 -3	3.35.10 -3	4.61.10 -3	1.96.10 -3	5.91.10 -3
				"2 nd group"
	Alloy Mg 91 Cu 4 Y 5 (50h) Mg 91 Cu 4 Y 5 (10d)	Mg 94 Ni 2 Y 4	Mg 97 NiY 2 Mg 97 Ni 1.5 Y 1.5
	n	1.17	1.20	1.46	1.51	1.67
	k	3.01.10 -4	2.86.10 -4	9.70.10 -5	6.12.10 -5	3.29.10 -5

"1 st group" Alloy Mg 87.5 Ni 5.5 Y 7

Table 2

 2

	:
	Model
	paramet
	ers
	values
	for
	eleven
	studied
	alloys.


Kai-Chi Lo
email: kaichi.lo@mx.nthu.edu.tw

Hideyuki Murakami
email: murakami.hideyuki@nims.go.jp

Uwe Glatzel

Jien-Wei Yeh

Stéphane Gorsse

An-Chou Yeh

Elemental Effects on the Oxidation of Refractory Compositionally Complex Alloys

Keywords: Refractory alloys, Compositionally complex alloys, Oxidation

The oxidation of refractory compositionally complex alloys (RCCAs) is one of the most critical subjects for their high temperature applications. In this work, several RCCAs were systematically designed and isothermally oxidised at 1000 ˚C for up to 24 hours; the elemental effects of Al, Cr, Mo, Nb Ta, Ti, V, and Zr on the oxidation of the RCCAs were studied. It was found that Al, Cr, Ti could enhance the oxidation resistance of the RCCAs by promoting the formation of rutile-type AlTaO 4 , CrTaO 4 , and their related oxides, while Zr and V formed non-protective oxides such as Nb 2 Zr 6 O 17 , Ta 2 Zr 6 O 17 , ZrTiO 4 , and VTa 9 O 25 , resulting in severe internal oxidation.

Mo appeared to be effective in suppressing internal oxidation, but it could form non-protective MoTiTa 8 O 25 . Ta was slightly more beneficial than Nb for reducing the oxidation mass gain. This study provides insights on the elemental effects on the oxidation and guidelines for improving the oxidation resistance of RCCAs.

Introduction

The development of materials for turbine engine is crucial for reducing fossil fuel consumption and global warming, since the increase in operation temperature of turbine engine can enhance its efficiency, potential materials with higher temperature capability than that of superalloys are intensively studied. Nowadays, Ni-based superalloys are widely used in the hottest sections of a gas turbine owing to their outstanding mechanical properties and surface stability. However, the temperature capability of the Ni-based superalloys has reached its limit due to the melting point of the solvent element Ni, which is 1455 ˚C. Therefore, developing new alloys with even higher melting points than Ni-based superalloys is important. Recently, RCCAs have been proposed as potential candidates for advanced high temperature applications. By combining multiple refractory elements, such as W, Ta, Mo, Nb, etc., in similar atomic ratio, RCCAs can exhibit extraordinary strength at extremely high temperature [START_REF] Senkov | Refractory high-entropy alloys[END_REF][START_REF] Senkov | Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys[END_REF][START_REF] Senkov | Microstructure and properties of a refractory NbCrMo0.5Ta0.5TiZr alloy[END_REF][START_REF] Senkov | Effect of aluminum on the microstructure and properties of two refractory high-entropy alloys[END_REF][START_REF] Senkov | Microstructure and Properties of Aluminum-Containing Refractory High-Entropy Alloys[END_REF][START_REF] Chen | Microstructure and mechanical properties at elevated temperatures of a new Al-containing refractory high-entropy alloy Nb-Mo-Cr-Ti-Al[END_REF][START_REF] Senkov | Development of a Refractory High Entropy Superalloy[END_REF]. Although the high temperature strength of RCCAs is promising, they show poor environmental resistance in general owing to the inability to form a protective oxide scale at high temperature. While an advanced Ni-based superalloy containing Al content as low as 8.7 at% could possess excellent surface stability by forming a protective Al 2 O 3 scale [START_REF] Smialek | High-temperature oxidation[END_REF][START_REF] Huang | Oxidation behavior of a single-crystal Ni-base superalloy in air at 900, 1000 and 1100° C[END_REF][START_REF] Bensch | Modelling of High Temperature Oxidation of Alumina-Forming Single-Crystal Nickel-Base Superalloys[END_REF][START_REF] Kawagishi | Development of an oxidation-resistant high-strength sixth-generation single-crystal superalloy TMS-238[END_REF][START_REF] Pint | The use of two reactive elements to optimize oxidation performance of alumina-forming alloys[END_REF], RCCAs do not show such property even with 20 at% of Al content [START_REF] Liu | Microstructure and oxidation behavior of new refractory high entropy alloys[END_REF][START_REF] Gorr | Phase equilibria, microstructure, and high temperature oxidation resistance of novel refractory high-entropy alloys[END_REF][START_REF] Gorr | High temperature oxidation behavior of an equimolar refractory metal-based alloy 20Nb 20Mo 20Cr 20Ti 20Al with and without Si addition[END_REF][START_REF] Gorr | High-Temperature Oxidation Behavior of Refractory High-Entropy Alloys: Effect of Alloy Composition[END_REF][START_REF] Chang | Oxidation Behavior between 700 and 1300° C of Refractory TiZrNbHfTa High-Entropy Alloys Containing Aluminum[END_REF][START_REF] Müller | Effect of microalloying with silicon on high temperature oxidation resistance of novel refractory high-entropy alloy Ta-Mo-Cr-Ti-Al[END_REF][START_REF] Cao | Effects of Al and Mo on high temperature oxidation behavior of refractory high entropy alloys[END_REF][START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF][START_REF] Zhang | Oxidation response of a vacuum arc melted NbZrTiCrAl refractory high entropy alloy at 800-1200[END_REF][START_REF] Gorr | A new strategy to intrinsically protect refractory metal based alloys at ultra high temperatures[END_REF][START_REF] Lo | Oxidation behaviour of a novel refractory high entropy alloy at elevated temperatures[END_REF][START_REF] Waseem | Combinatorial synthesis and analysis of AlxTayVz-Cr20Mo20Nb20Ti20Zr10 and Al10CrMoxNbTiZr10 refractory high-entropy alloys: Oxidation behavior[END_REF][START_REF] Butler | Native oxidation resistance of Al20Nb30Ta10Ti30Zr10 refractory complex concentrated alloy (RCCA)[END_REF][START_REF] Yurchenko | Oxidation Behavior of Refractory AlNbTiVZr0.25 High-Entropy Alloy[END_REF]. One of the latest developments in enhancing the oxidation resistance of RCCAs is attributed to the formation of CrTaO 4 -based oxide scale, which has been studied at the temperature range of 900 to 1500 ˚C and up to 200 hours [START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF][START_REF] Gorr | A new strategy to intrinsically protect refractory metal based alloys at ultra high temperatures[END_REF][START_REF] Lo | Oxidation behaviour of a novel refractory high entropy alloy at elevated temperatures[END_REF][START_REF] Sheikh | Alloying effect on the oxidation behavior of a ductile Al0.5Cr0.25Nb0.5Ta0.5Ti1.5 refractory high-entropy alloy[END_REF]; the formation of continuous CrTaO 4 -based oxide scale could decrease oxidation mass gain [START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF][START_REF] Gorr | A new strategy to intrinsically protect refractory metal based alloys at ultra high temperatures[END_REF], but the substrate beneath it still shows certain degree of internal oxidation, which is not observed in the Al 2 O 3 -forming substrate [START_REF] Bensch | Modelling of High Temperature Oxidation of Alumina-Forming Single-Crystal Nickel-Base Superalloys[END_REF][START_REF] Kawagishi | Development of an oxidation-resistant high-strength sixth-generation single-crystal superalloy TMS-238[END_REF][START_REF] Litz | Selective carbide oxidation and internal nitridation of the Ni-base superalloys IN 738 LC and IN 939 in air[END_REF][START_REF] Konrad | Internal oxidation with significant contribution of oxygen diffusion through the oxide phase[END_REF][START_REF] Konrad | Determination of Oxygen Diffusion Along Nickel/Zirconia Phase Boundaries by Internal Oxidation[END_REF]. Detailed examination on the internally oxidised region in the CrTaO 4 -based-oxide-forming substrate shows strong presence of nitrides in addition to oxides [START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF][START_REF] Gorr | A new strategy to intrinsically protect refractory metal based alloys at ultra high temperatures[END_REF][START_REF] Lo | Oxidation behaviour of a novel refractory high entropy alloy at elevated temperatures[END_REF], indicating such oxide scale might not stop nitrogen intake and thus the nitridation of the substrate, which usually leads to its embrittlement [START_REF] Krupp | Selective oxidation and internal nitridation during high-temperature exposure of single-crystalline nickel-base superalloys[END_REF].

For an advanced Ni-based superalloy, the formation of a protective Al 2 O 3 scale can be achieved by means of alloying, such as adding Al, Cr, and Si [START_REF] Brady | Alloy design strategies for promoting protective oxide-scale formation[END_REF][START_REF] Pint | Oxidation resistance: One barrier to moving beyond Ni-base superalloys[END_REF][START_REF] Wang | High-temperature oxidation behavior of Ti 2 AlC in air[END_REF][START_REF] Hua | Laser shock processing effects on isothermal oxidation resistance of GH586 superalloy[END_REF]. While the alloying strategy for tuning the surface stability of Ni-based superalloys have already been well-established, the alloying effects on oxidation behaviour for RCCAs is still scarce. In this study, the oxidation behaviours of several RCCAs have been designed and analysed with respect to compositions and thermodynamic simulation. The aim of this study is to provide an understanding on the compositional effects on the oxidation of RCCAs and guidelines for designing oxidation-resistant RCCAs.

Material and methods

Alloy design

To have an overview of alloying strategy, the oxidation mass gain curves based on literature data of several representative RCCAs and a Ni-based superalloy CMSX-4 at 1000 ˚C were plotted and shown in Figure 1(a) [START_REF] Gorr | Phase equilibria, microstructure, and high temperature oxidation resistance of novel refractory high-entropy alloys[END_REF][START_REF] Gorr | High-Temperature Oxidation Behavior of Refractory High-Entropy Alloys: Effect of Alloy Composition[END_REF][START_REF] Cao | Effects of Al and Mo on high temperature oxidation behavior of refractory high entropy alloys[END_REF][START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Waseem | Combinatorial synthesis and analysis of AlxTayVz-Cr20Mo20Nb20Ti20Zr10 and Al10CrMoxNbTiZr10 refractory high-entropy alloys: Oxidation behavior[END_REF][START_REF] Butler | Native oxidation resistance of Al20Nb30Ta10Ti30Zr10 refractory complex concentrated alloy (RCCA)[END_REF][START_REF] Butler | High temperature oxidation behaviors of equimolar NbTiZrV and NbTiZrCr refractory complex concentrated alloys (RCCAs)[END_REF][START_REF] Waseem | A combinatorial approach for the synthesis and analysis of AlxCryMozNbTiZr high-entropy alloys: Oxidation behavior[END_REF][START_REF] Göbel | The isothermal-oxidation behavior of several nickel-base single-crystal superalloys with and without coatings[END_REF]. The oxidation mass gain curves of RCCAs with short testing duration [START_REF] Waseem | Combinatorial synthesis and analysis of AlxTayVz-Cr20Mo20Nb20Ti20Zr10 and Al10CrMoxNbTiZr10 refractory high-entropy alloys: Oxidation behavior[END_REF][START_REF] Waseem | A combinatorial approach for the synthesis and analysis of AlxCryMozNbTiZr high-entropy alloys: Oxidation behavior[END_REF] or microalloying [START_REF] Müller | Effect of microalloying with silicon on high temperature oxidation resistance of novel refractory high-entropy alloy Ta-Mo-Cr-Ti-Al[END_REF][START_REF] Müller | Effect of Y Additions on the Oxidation Behaviour of Novel Refractory High-Entropy Alloy NbMoCrTiAl at 1000 °C in Air[END_REF] were not included. According to composition and mass gain, these RCCAs could be divided into 3 groups: RCCAs with only Zr and other non-protective-oxide-forming elements (black lines), RCCAs with both Al and Zr (red lines), and RCCAs with Al but no Zr (blue lines).

The general trends deduced from Figure 1 Additionally, Al, Cr, Mo, V were selected since these elements are commonly used for enhancing either the oxidation resistance [START_REF] Sheikh | Accelerated oxidation in ductile refractory high-entropy alloys[END_REF][START_REF] Sheikh | Aluminizing for enhanced oxidation resistance of ductile refractory high-entropy alloys[END_REF][START_REF] Senkov | Oxidation behavior of a refractory NbCrMo0.5Ta0.5TiZr alloy[END_REF][START_REF] Lin | Effect of Al addition on mechanical properties and microstructure of refractory AlxHfNbTaTiZr alloys[END_REF] or mechanical properties [START_REF] Senkov | Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys[END_REF][START_REF] Senkov | Effect of aluminum on the microstructure and properties of two refractory high-entropy alloys[END_REF][START_REF] Senkov | Microstructure and Properties of Aluminum-Containing Refractory High-Entropy Alloys[END_REF][START_REF] Senkov | Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy[END_REF][START_REF] Juan | Enhanced mechanical properties of HfMoTaTiZr and HfMoNbTaTiZr refractory high-entropy alloys[END_REF][START_REF] Juan | Solution strengthening of ductile refractory HfMoxNbTaTiZr high-entropy alloys[END_REF][START_REF] Lin | Effect of Al addition on mechanical properties and microstructure of refractory AlxHfNbTaTiZr alloys[END_REF][START_REF] Senkov | Mechanical properties of low-density, refractory multi-principal element alloys of the Cr-Nb-Ti-V-Zr system[END_REF][START_REF] Guo | Microstructure and mechanical properties of refractory MoNbHfZrTi high-entropy alloy[END_REF] of RCCAs. New compositions that were investigated in order to elucidate elemental effects could be categorized into Group A, Group B and Group C.

Experimental procedures

The ingots of the alloys of interest shown in Figure 1(b) were prepared by arc-melting high purity elements (> 99.9 wt%) under Ti-gettered pure argon atmosphere on a water-cooled copper hearth according to their nominal compositions.

The as-cast compositions of the ingots are listed in Table 1. Each button-shaped, 20-gram ingot was flipped and re-melted 4 times to ensure the chemical homogeneity.

The ingots had shiny surfaces and showed no sign of oxidation after the melting process. The ingots were subsequently electric-discharge-machined into 6 × 5 × 5 mm blocks of specimens. The top surfaces of all specimens were ground with #1200 SiC abrasive paper prior to any subsequent tests. Isothermal oxidation was performed with a muffle furnace at 1000 ˚C for various duration. The specimens were spaced 10 mm apart from each other in an Al 2 O 3 boat crucible and positioned into the furnace after the furnace interior was heated to 1000 ˚C and furnace-cooled to ambient temperature upon reaching the desired testing duration. At least 2 specimens were used per alloy for the isothermal oxidation test to ensure the repeatability of the testing results. Here, 2-hour isothermal oxidation was mainly for observation on the cross-sectional microstructure, while 24-hour isothermal oxidation was mainly for X-ray diffraction (XRD) of the oxidised specimens, which was carried out with Bruker D2 Phaser equipped with Cu target. Goniometer scanning was performed between 2θ = 20˚ ~ 100˚ with a scanning rate of 5.7˚ per minute. The oxide scales of the specimens were either ground into fine powder (for specimens oxidised for 24 hours) or kept on the top surfaces of the specimens (for specimens oxidised for 2 hours) for XRD analysis. Thermogravimetric analysis (TGA) was also carried out in flowing dry air at 1000 ˚C for up to 2 hours with SETARAM TAG 24-18S simultaneous symmetrical thermoanalyser to investigate the oxidation kinetics of the studied RCCAs. Specimens for TGA had dimensions of 6 × 3 × 2 mm 3 with each surface ground with #1200 SiC abrasive paper. Each specimen was carefully placed in a micro Al 2 O 3 cylindrical crucible to minimize its contact with the crucible, then the crucible with specimen was hung by a Pt wire vertically. The mass gain of the specimen was recorded automatically every 0.02 minute up to 2 hours with an accuracy of 0.023 μg. Each tested TGA specimen was compared with that of isothermal oxidation tests to ensure the consistency between the results. The mass of the tested TGA specimen itself and the total mass of the tested TGA specimen with the crucible were also measured to evaluate the spallation of the specimens. The specimens were polished with 0.02 μm colloidal silica prior to metallographic observation with a JEOL-JSM 7610F scanning electron microscope (SEM) equipped with back-scattered electron (BSE) and energy-dispersive X-ray spectroscopy (EDS) detectors. Image analysis for estimating the porosity of the external oxide scale was carried out with ImageJ software by averaging the area fraction of the porosity in 3 random regions which covered over 800 μm 2 area each within the external oxide scale.

Results

Microstructures prior oxidation

According to Figure 2

Thermogravimetric analysis

Oxidation: R0 and R1 alloys (Group A)

Comparing XRD results of both R0 and R1 after 2 and 24 hours of isothermal oxidation at 1000 ˚C, all conditions appeared to render the same oxide products, 3 show both alloys were oxidised prominently in the manner of internal oxidation since the morphology and chemical profile of the metallic substrate were preserved within the oxidised region, while no obvious external oxide scale was observed. Interestingly, the scales of the oxidised regions were significantly different between these alloys:

The thickness of internal oxidation region (t IO ) was ~358 μm for R0, which was over twice as large as ~168 μm t IO of R1, Figure 4(b)(c). Cross-sectional SEM-EDS analysis revealed R2 was the least oxidized, while R1-Ti was the most affected by oxidation at 1000 ˚C, Figure 5(b)~(e) and Table 4.

Table 4

Chemical compositions (in at%) of the indicated regions in Figure 5 6(a). For R2+Cr, diffraction peaks of AlTaO 4 were pronounced under both conditions, while that of Ta 2 O 5 were only found after 2 hours of isothermal oxidation. In the case of R2+V, only the diffraction peaks from AlNbO 4 were identified after 2 hours, while that of VTa 9 O 25 and AlTaTiO 6 were detected after 24 hours of isothermal oxidation.

Cross-sectional SEM-EDS analysis showed all alloys in this group formed external oxide scale within 2 hours at 1000 ˚C, Figure 6 on the properties of these complex oxides is still strictly limited, it is important to examine and deduce the characteristics of these oxides that could be important for future alloy design.

The effects of Al, Cr, Nb, Ta, and Ti addition

Traditionally, the surface stability of an alloy can be related to the formation of a continuous and protective oxide scale [START_REF] Smialek | High-temperature oxidation[END_REF][START_REF] Brady | Alloy design strategies for promoting protective oxide-scale formation[END_REF][START_REF] Pint | Oxidation resistance: One barrier to moving beyond Ni-base superalloys[END_REF], which can be achieved by alloying with protective-oxide-forming elements or modified matrix properties, such as the oxygen solubility [START_REF] Smialek | High-temperature oxidation[END_REF][START_REF] Brady | Alloy design strategies for promoting protective oxide-scale formation[END_REF][START_REF] Wagner | Reaktionstypen bei der Oxydation von Legierungen[END_REF]. For Al and Cr, both elements are frequently added to enhance oxidation resistance, since Al 2 O 3 and Cr 2 O 3 scales have been proven to be effective barriers [START_REF] Pint | Oxidation resistance: One barrier to moving beyond Ni-base superalloys[END_REF]. However, in the present study, both protective oxide scales were not observed. Instead, rutile-type Al-and Cr-bearing complex oxides, such as AlTaO 4 and CrTaO 4 or their related oxides, were observed in most of the studied alloys.

Despite the absence of Al 2 O 3 and Cr 2 O 3 , these complex oxides seem to provide reasonable protection against oxidation, especially in the case of R2+Cr, since it formed a continuous rutile-type complex oxide scale, Figure 6 and7. The prominent peak intensity of rutile-type (Al 0.2 Nb 0.2 Ti 0.6 )O 2 for R1 also corresponded with its greatly reduced t O and oxidation mass gain comparing to R0, Figure 4(a) and 7. This observation agrees with that observed in previous literatures [START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF][START_REF] Gorr | A new strategy to intrinsically protect refractory metal based alloys at ultra high temperatures[END_REF][START_REF] Lo | Oxidation behaviour of a novel refractory high entropy alloy at elevated temperatures[END_REF], in which the formation of rutile-type CrTaO 4 -based oxide could improve the oxidation resistance of RCCAs. It is also proposed that while Cr addition could promote formation of rutile-type oxides such as CrNbO 4 and CrTaO 4 , the formation of CrTaO 4 would be more favourable than that of CrNbO 4 owing to its more negative formation free energy [START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF]. But since other factors, such as the kinetics of oxide growth and oxygen permeability of the oxide, are also essential for the formation of a protective oxide layer, whether CrTaO 4 is preferable to CrNbO 4 as the protective oxide layer requires further study to be clarified.

Interestingly, while the oxidation of R1-Nb and R1-Ta showed no noticeable difference in terms of t EO , t IO , and t O , the mass gain of R1-Nb was 2.3 mg/cm 2 lower than that of R1-Ta after isothermally oxidised at 1000 ˚C for 2 hours, Figure 3 and7.

It appears that the Ta-rich dendrite arms in R1-Nb had reduced oxygen intake, while its interdendritic regions had similar oxygen intake comparing to that of the dendrite arms and interdendritic regions of R1-Ta, Table 4. Given both RCCAs had similar t O , R1-Nb would ingest less oxygen and thus have lower oxidation mass gain than R1-Ta.

While Ta and Nb are usually considered similar in terms of their chemical properties owing to their adjacent locations in the Periodic Table, Ta was found to have more pronounced effect on reducing the oxidation mass gain of TiAl-based intermetallics at 1000 ˚C comparing to Nb by decreasing the diffusion rate of oxygen [START_REF] Vojtěch | Comparison of Nband Ta-effectiveness for improvement of the cyclic oxidation resistance of TiAl-based intermetallics[END_REF]. These observations suggest that the addition of Ta could be slightly superior to Nb in terms of oxidation resistance.

Furthermore, it appears that the formation of rutile-type oxides, including TiO 2 , AlTaO 4 , CrTaO 4 and their related oxides is generally beneficial for oxidation resistance since R1-Ti did not form rutile-type oxide and was severely oxidised within 2 hours at 1000 ˚C. While the positive effects of rutile-type oxides have been reported

previously [START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Müller | On the oxidation mechanism of refractory high entropy alloys[END_REF][START_REF] Gorr | A new strategy to intrinsically protect refractory metal based alloys at ultra high temperatures[END_REF][START_REF] Lo | Oxidation behaviour of a novel refractory high entropy alloy at elevated temperatures[END_REF][START_REF] Nilsson | The role of aluminum additions in the oxidation and wear of a TaC: C low-friction coating[END_REF][START_REF] Ren | The influence of CrTaO4 layer on the oxidation behavior of a directionally-solidified nickel-based superalloy at 850-900° C[END_REF][START_REF] Chan | Cyclic oxidation response of multiphase niobium-based alloys[END_REF][START_REF] Qu | Effects of Cr and Al on High Temperature Oxidation Resistance of Nb-Si System Intermetallics[END_REF], the origin for the formation of the rutile-type oxides remains an intriguing subject for further investigation. TiO 2 is one of the most common oxides that possesses rutile-type crystal structure; when more than 2 refractory elements are co-oxidised, Ti can also be solutioned in rutile-type complex oxides [START_REF] Lo | An oxidation resistant refractory high entropy alloy protected by CrTaO 4-based oxide[END_REF][START_REF] Lo | Oxidation behaviour of a novel refractory high entropy alloy at elevated temperatures[END_REF]. While Al and Ta can form rutile-type AlTaO 4 when their oxides react with each other [START_REF] Jasper-Toennies | Synthesis and structure of AlTaO4[END_REF], rutile-type oxide was not detected in the oxide scale of R1-Ti.

Therefore, the presence of Ti could benefit the oxidation resistance of RCCAs by promoting the formation of rutile-type oxide.

The effects of Mo addition

Since MoO 3 would sublimate at 800 ˚C and above [START_REF] Gulbransen | Oxidation of Molybdenum 550° to 1700[END_REF], the oxidation of Mo is definitely not the reason behind the reduced t O of R2+Mo. Since R2+Mo showed the thinnest t IO among all tested RCCAs in the present study, it could be postulated that the internal oxidation was suppressed due to the presence of Mo. Considering a binary alloy system M-Al, in which M is an oxygen-soluble arbitrary metal nobler than Al and Al is a dilute solute. Here, if Al 2 O 3 is thermodynamically very stable and the diffusivity of Al is significantly lower than that of oxygen, the time (t) dependency for the depth of internal oxidation (ξ) of such alloy can be described as [START_REF] Smialek | High-temperature oxidation[END_REF]:

…….. (1)
In which is the oxygen solubility of the alloy substrate. Such relationship indicates that reduced would suppress internal oxidation. Generally, the internal oxidation is not desirable for the oxidation resistance of an alloy since the protective oxide scale is formed via external oxidation. Upon the formation of a continuous external oxide scale, it could act as a barrier and retard the oxidation of the alloy.

Although the capabilities of such barrier depend on several factors, such as its integrity, gas permeability, and gas diffusivity, the formation of an external oxide scale and reduced internal oxidation are beneficial for the oxidation resistance of the alloy. Previous study suggested Mo possesses extremely low oxygen and nitrogen solubility as pure element [START_REF] Gorr | High-Temperature Oxidation Behavior of Refractory High-Entropy Alloys: Effect of Alloy Composition[END_REF] and it could improve the surface stability of TiAl-based alloys by decreasing the solubility of oxygen and nitrogen in the alloy substrate [START_REF] Shida | The effect of various ternary additives on the oxidation behavior of TiAl in high-temperature air[END_REF][START_REF] Pérez | Oxidation behaviour of a Ti-46Al-1Mo-0.2Si alloy: the effect of Mo addition and alloy microstructure[END_REF]. Consequently, the reduced internal oxidation of R2+Mo might result from the decreased caused by Mo addition. On the other hand, the external oxide scale of R2+Mo was relatively thick and full of rounded pores comparing to that of R2+Cr, indicating the former oxidised more severely than the later and might suffer from the formation and evaporation of volatile oxides, Figure 6.

The area fraction of the rounded pores was estimated to be 2.4 % according to the image analysis. Since R2+Mo contains 20 at% of Mo, it is possible that volatile oxides, such as MoO 3 , would form during the isothermal oxidation at 1000 ˚C. prevented heavy evaporation of MoO 3 by forming an external oxide scale since there was no obvious MoO 3 residue in the crucible after the oxidation test. Therefore, the oxidation mass loss caused by MoO 3 in the present study could be neglectable at least up to 2 hours of isothermal oxidation at 1000 ˚C. But considering the relatively thick oxide scale of R2+Mo comparing with that of R2+Cr, such oxide is not likely to be an efficient oxygen barrier. These could be the reasons why R2+Mo has thicker and more porous external oxide scale comparing to that of R2+Cr.

The effects of Zr and V addition

According to the oxidation behaviours of Zr-and V-bearing RCCAs, it appears that both alloying additions were detrimental since they are associated with large oxidation mass gain or t O for RCCAs, Figure 1 and7. While Zr is a common constituent in ductile RCCAs [START_REF] Senkov | Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy[END_REF][START_REF] Wu | A refractory Hf25Nb25Ti25Zr25 high-entropy alloy with excellent structural stability and tensile properties[END_REF][START_REF] Juan | Solution strengthening of ductile refractory HfMoxNbTaTiZr high-entropy alloys[END_REF][START_REF] Sheikh | Accelerated oxidation in ductile refractory high-entropy alloys[END_REF][START_REF] Senkov | Microstructure and elevated temperature properties of a refractory TaNbHfZrTi alloy[END_REF], ZrO 2 , which is a common form of Zr-related oxide, is known for its detrimental effects due to its polymorphism properties across a wide range of temperature [START_REF] Patil | Axial thermal expansion of ZrO2 and HfO2 in the range room temperature to 1400°C[END_REF][START_REF] Yoshihara | Influence of Zr Addition on Oxidation Behavior of TiAl-Based Alloys[END_REF]. However, since ZrO 2 was not detected in this work, its role on oxidation might not be so direct. Alternatively, ZrO 2 could react with other refractory oxides, such as TiO 2 and Nb 2 O 5 , to form complex refractory oxides, such as ZrTiO 4 [START_REF] Yoshihara | Influence of Zr Addition on Oxidation Behavior of TiAl-Based Alloys[END_REF][START_REF] Newnham | Crystal Structure of ZrTiO4[END_REF][START_REF] Tsai | Oxidation resistance and structural evolution of (TiVCrZrHf)N coatings[END_REF][START_REF] Kashkarov | High-temperature oxidation resistance of Ti-implanted E110 alloy[END_REF] and Nb 2 Zr 6 O 17 [START_REF] Butler | High temperature oxidation behaviors of equimolar NbTiZrV and NbTiZrCr refractory complex concentrated alloys (RCCAs)[END_REF]. Interestingly, Ta 2 Zr 6 O 17 was additionally found in the present study, presumably it was formed due to a reaction between ZrO 2 and Ta 2 O 5 . Despite there has been no literature specifically describing the properties of these Zr-related complex refractory oxides, it is not likely that these oxides are protective against oxidation since these Zr-bearing alloys show poor oxidation resistance [START_REF] Butler | High temperature oxidation behaviors of equimolar NbTiZrV and NbTiZrCr refractory complex concentrated alloys (RCCAs)[END_REF][START_REF] Yoshihara | Influence of Zr Addition on Oxidation Behavior of TiAl-Based Alloys[END_REF]. RCCAs containing Zr as main constituent could suffer from heavy internal oxidation owing to the high affinity and solubility with oxygen and nitrogen of Zr [START_REF] Gorr | Current Status of Research on the Oxidation Behavior of Refractory High Entropy Alloys[END_REF], which agrees with the observation in the present study, Figure 3 and7. On the other hand, although V has high solubility for oxygen [START_REF] Gorr | Current Status of Research on the Oxidation Behavior of Refractory High Entropy Alloys[END_REF][START_REF] Pint | The Role of Oxygen Uptake and Scale Formation on the Embrittlement of Vanadium Alloys[END_REF],

V 2 O 5 could melt and become volatile at above 690 ˚C [START_REF] Feng | Phase Equilibria of the SiO2-V2O5 system[END_REF]. In this work, the Al 2 O 3 crucible used as the container for R2+V was heavily contaminated after the 24 hours of isothermal oxidation at 1000 ˚C. Along with large pores shown in Figure 6, which were 8.2 % in area fraction within the oxide scale of R2+V, it is reasonable to assume that the formation and melting of V 2 O 5 occurred during the test. Another noticeable V-related oxide found in R2+V was the tetragonal VTa 9 O 25 , which has not been reported in the literature regarding to the oxidation of RCCAs. While its impact on the surface stability of RCCAs is unknown, it has been suggested that VTa 9 O 25 is a stable oxide at the Ta 2 O 5 -rich end of V 2 O 5 -Ta 2 O 5 quasi-binary phase diagram and it could melt at around 1800 ˚C [START_REF] Schadow | Investigations on the Quasi-binary System V2O5-Ta2O5[END_REF]. Therefore, it is likely that some of the V 2 O 5 reacted with

The characteristics of complex oxides

The other group of complex oxides identified in this work includes AlNbO 4 , TiNb 2 O 7 , and Ti 2 Nb 10 O 29 . In previous studies, these oxides were found when Nb content was high enough to reach its solubility limits in TiO 2 for TiAl-based alloys [START_REF] Chen | Oxidation of Intermetallic Alloys in Ti-Al-Nb Ternary System[END_REF][START_REF] Yoshihara | Effects of Nb addition on oxidation behavior of TiAl[END_REF] or when Nb 2 O 5 could react with Al 2 O 3 in Nb-based alloys [START_REF] Qu | Effects of Cr and Al on High Temperature Oxidation Resistance of Nb-Si System Intermetallics[END_REF][START_REF] Chen | Oxidation mechanisms of an intermetallic alloy at high temperatures[END_REF].

Interestingly, the effects of these oxide on the surface stability of the reported alloys can be either positive or negative. For TiAl-based alloys, the formation of TiNb 2 O 7 could deteriorate oxidation resistance by interrupting the Nb-doped TiO 2 scale, which could have assisted the formation of a continuous Al 2 O 3 scale [START_REF] Chen | Oxidation of Intermetallic Alloys in Ti-Al-Nb Ternary System[END_REF][START_REF] Yoshihara | Effects of Nb addition on oxidation behavior of TiAl[END_REF]; on the other hand, the formation of AlNbO 4 could enhance oxidation resistance of Nb-based alloys by increasing the integrity of the oxide scale [START_REF] Qu | Effects of Cr and Al on High Temperature Oxidation Resistance of Nb-Si System Intermetallics[END_REF]. While the role of Ti 2 Nb 10 O 29 on the surface stability has not been specifically described in the literature, it is frequently found in the oxide scale of Ti-bearing and Nb-based alloys and could decompose into TiNb 2 O 7 [START_REF] Hong | Oxidation behavior of Nb-24Ti-18Si-2Al-2Hf-4Cr and Nb-24Ti-18Si-2Al-2Hf-8Cr hypereutectic alloys at 1250 °C[END_REF][START_REF] Ventura | Oxidation Behavior of Nb-20Mo-15Si-5B-20Cr and Nb-20Mo-15Si-5B-20Ti Alloys Up To 1300°C[END_REF]. It is evident that these oxides would not be effective oxygen barriers comparing to Al 2 O 3 , Nb-doped TiO 2 , or rutile-type oxide like CrNbO 4 [START_REF] Chen | Oxidation of Intermetallic Alloys in Ti-Al-Nb Ternary System[END_REF][START_REF] Yoshihara | Effects of Nb addition on oxidation behavior of TiAl[END_REF][START_REF] Portillo | The possible application of Nb-W-Cr alloys in high-temperature air[END_REF]. Therefore, the formation of these oxides should be avoided when designing RCCAs that form protective oxide scale at high temperature, and this could be achieved by limiting Nb content in RCCAs.

Multiple complex refractory oxides have been observed instead of simple oxides, such as Al 2 O 3 and ZrO 2 , in the present study. Here, the simple oxides might react with each other and form complex oxides rather than existing independently, or the complex oxides were directly formed as the stable oxides in the studied system. In both cases, the formation free energy of the complex oxides could be more negative than that of the simple oxides. However, such data cannot be retrieved from current thermodynamic databases despite they do contain the constituents of the present alloys. This is because these databases have been developed for a particular alloy family, so each database can only accurately describe the corner region of the phase diagram containing the main element. Although thermodynamic databases dedicated to high entropy alloys has been intensively developed, they currently contain a very limited number of assessed ternaries with oxygen. Still, the TCOX11 database for In summary, the content of Al, Cr, and Ti in RCCAs could benefit the oxidation resistance by forming rutile-type complex oxides, while Zr and V contents could deteriorate surface stability by forming non-protective oxides and enhancing internal oxidation; Mo addition could greatly suppress internal oxidation of the substrate, but the formation of non-protective MoTiTa 8 O 25 might lead to reduced resistance against oxidation; Ta addition could be slightly more beneficial than Nb addition in terms of oxidation resistance owing to reduced oxygen intake of the alloy bulk. The properties and the parent alloys of the observed oxides in the present study are summarized in Table 6. The formation of oxides and their growth kinetics are heavily composition dependent, thus changing the alloying amount of each element could lead to different oxidation kinetics. These results and discussions present in this article could provide guidelines for the design of RCCA with improved oxidation resistance in the future.

  (a) indicate that the Al-bearing RCCAs have reduced oxidation mass gain, while Zr-bearing RCCAs have increased oxidation mass gain. In order to further elucidate the compositional effects of individual elements on the oxidation behaviour of RCCAs, new compositions were designed based on quasi-binary technique in this work: Al content was fixed at 20 at%, while the rest of the components were selected refractory elements combined in equi-molar ratio. The Al content was specifically controlled since it was considered the reference element for the formation of Al 2 O 3 . The deduction of compositional effects for a specific element was done by adding or removing that element from a mother composition, then comparing the results of these two alloys. Figure1(b) shows the compositions and designations of the new alloys. NbTaTiZr was the base alloy since this composition contains frequently used elements for RCCAs[START_REF] Senkov | Development of a Refractory High Entropy Superalloy[END_REF][START_REF] Senkov | Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy[END_REF][START_REF] Wu | A refractory Hf25Nb25Ti25Zr25 high-entropy alloy with excellent structural stability and tensile properties[END_REF][START_REF] Juan | Enhanced mechanical properties of HfMoTaTiZr and HfMoNbTaTiZr refractory high-entropy alloys[END_REF][START_REF] Juan | Solution strengthening of ductile refractory HfMoxNbTaTiZr high-entropy alloys[END_REF][START_REF] Sheikh | Accelerated oxidation in ductile refractory high-entropy alloys[END_REF][START_REF] Sheikh | Aluminizing for enhanced oxidation resistance of ductile refractory high-entropy alloys[END_REF].

Figure 1

 1 Figure 1 (a) The oxidation mass gain curves or the terminal oxidation mass gain of the selected RCCAs reported in the literature and (b) the flow chart for the design of the studied RCCAs in this work.

  Figure 2 (a) XRD patterns of all studied RCCAs and microstructural BSE images of the as-cast (b) R0 (c) R1 (d) R1-Nb (e) R1-Ta (f) R1-Ti (g) R2 (h) R2+Cr (i) R2+Mo (j) R2+V.

Figure 3

 3 Figure3illustrates the oxidation kinetics of the studied RCCAs at 1000 ˚C for up to 2 hours. The TGA for R1-Ti and R2+V was waived owing to heavy oxidation or contamination of these alloys that could damage the instrument. The oxidation mass gain after 2 hours of isothermal oxidation at 1000 ˚C was 33.4, 19.3, 17.0, 12.2, 5.7, 1.8, and 1.0 mg/cm 2 for R0, R1-Ta, R1-Nb, R1, R2, R2+Mo, and R2+Cr, respectively.All tested RCCAs showed no noticeable spallation, except R0 had spallation from the extruding oxide formed along the corners of the specimen. But since the metallographic observation was carried out at the flat surfaces of the specimen, such spallation is not expected to affect the observation and measurement in the following sections.

Figure 3

 3 Figure 3 Oxidation mass gain curves of the studied RCCAs measured at 1000 ˚C for 120 minutes.

Figure 4 (

 4 Figure 4(a). Based on the relative intensity of the diffraction peaks, the main oxide product for R0 was TiNb 2 O 7 , while that for R1 were (Al 0.2 Nb 0.2 Ti 0.6 )O 2 and Nb 2 Zr 6 O 17 under both oxidation condition. Ta 2 O 5 was also found in both alloys, while TiO 2 and AlNbO 4 were identified in R0 and R1, respectively.Figure 4(b)(c) and Table3 show

Figure 4

 4 Figure 4 (a) XRD patterns of R0 and R1 after 2 and 24 hours of isothermal oxidation and cross-sectional BSE images of (b) R0 and (c) R1 after 2 hours isothermal oxidation at 1000 ˚C. The red lines in (b)(c) represent t IO .

  Figure 5 (a) XRD patterns of R1-Nb, R1-Ta, R1-Ti, and R2 after 2 and 24 hours of isothermal oxidation and cross-sectional BSE images of (b) R1-Nb (c) R1-Ta (d) R1-Ti (e) R2 after 2 hours of isothermal oxidation at 1000 ˚C. The yellow line in (e) marks the thickness of external oxide scale (t EO ) while red lines in (b)~(e) mark t IO . The width of the cracks (magenta arrowheads in (c)(d)) was excluded during the thickness measurement.

  (b)~(e). Region 1, 3, 5 and 2, 4, 7 are respectively the oxidised dendrite arms and inter-dendritic regions of R1-Nb, R1-Ta, and R1-Ti, while Region 6 and 8 are respectively the oxidised inter-diffusion zone of R1-Ti and the external oxide scale of R2.

  Figure 6 (a) XRD patterns of R2+Cr, R2+Mo, and R2+V after 2 and 24 hours of isothermal oxidation and cross-sectional BSE images of (b)(c) R2+Cr (d)(e) R2+Mo (f)(g) R2+V after 2 hours of isothermal oxidation at 1000 ˚C. The yellow and red lines in (b)(d)(f) respectively mark t EO and t IO , while the magenta arrowheads in (d)~(g) indicate the pores caused by evaporation of volatile oxides in the external oxide scale.

Figure 7 t

 7 Figure 7 t EO , t IO , and t O of the studied RCCAs after 2 hours of isothermal oxidation at 1000 ˚C.

Furthermore, the tetragonal MoTiTa 8 O

 8 [START_REF] Waseem | Combinatorial synthesis and analysis of AlxTayVz-Cr20Mo20Nb20Ti20Zr10 and Al10CrMoxNbTiZr10 refractory high-entropy alloys: Oxidation behavior[END_REF] was present in the oxide scale of R2+Mo alloy. Despite its presence was mentioned in the oxidation of CrMo 0.5 NbTa 0.5 TiZr[START_REF] Senkov | Oxidation behavior of a refractory NbCrMo0.5Ta0.5TiZr alloy[END_REF],no further description regarding to its properties was discussed. In this work, the formation of MoTiTa 8 O 25 could result from a reaction among MoO 3 , TiO 2 , and Ta 2 O 5 in Ta 2 O 5 -rich environment: …….. (2) Since MoTiTa 8 O 25 is largely preserved while MoO 3 is not found in the oxide scale of R2+Mo after the isothermal oxidation at 1000 ˚C, the thermal stability of MoTiTa 8 O 25 should be superior to that of MoO 3 . It appears that MoTiTa 8 O 25

Ta 2 O

 2 5 and formed VTa 9 O 25 instead of melting away during the oxidation of R2+V at 1000 ˚C via the following reaction: …….. (3) Since VTa 9 O 25 possesses much higher melting point than that of V 2 O 5 , the formation of VTa 9 O 25 might be less harmful to the surface stability of RCCAs than that of V 2 O 5 .

  Thermo-Calc Software dedicated to the thermodynamic simulation of oxides allows the clarification to the formation of the intermediate oxide ZrTiO 4 in Ti-O-Zr bearing alloys. As shown in Figure 8, three ternary oxides adjacent to both phase fields with ZrO 2 and TiO 2 exist with different stability range. Above 1150 ˚C, the disordered ꞵ-Zr x Ti 1-x O 4 crystallizes in an orthorhombic structure. At lower temperatures, it undergoes two ordering transitions to α-ZrTiO 4 , and α'-ZrTiO 4 below 1050 ˚C. This could help explaining the presence of ZrTiO 4 in the oxide layer of some (Zr, Ti)-bearing alloys [63, 65, 66], including R1-Nb in this study.

Figure 8

 8 Figure 8 ZrO 2 -TiO 2 ternary phase diagram calculated with Thermo-Calc Software equipped with TCOX11 database.

Several

  RCCAs have been designed by systematic change in composition with respect to Al, Cr, Mo, Nb, Ta, Ti, V, Zr and subjected to isothermal oxidation for up to 24 hours at 1000 ˚C in order to examine the effects of the individual elements on oxidation. It is found that the addition of Al, Cr, and Ti could benefit the oxidation resistance by forming rutile-type complex oxides instead of their individual oxides, while the addition of Zr and V degraded the oxidation resistance by forming non-protective oxides or promoting internal oxidation. Mo addition appeared to suppress the internal oxidation, yet the formation of non-protective MoTiTa 8 O 25 might undermine the surface stability. Ta addition showed slightly reduced oxidation mass gain comparing with Nb addition owing to the reduced oxygen intake of the alloy bulk in the present study. This work has presented the effects of multiple elements on the oxidation of RCCAs and their associated oxides formation, and it may provide guidelines to design future RCCAs with enhanced oxidation resistance.

Table 1

 1 Compositions (in at%) of the studied alloy samples determined by EDS.

	Alloy	Al	Cr	Mo	Nb	Ta	Ti	V	Zr
	R0	-	-	-	24.9±0.6	27.1±1.4	22.8±1.2	-	25.3±1.2
	R1	18.0±1.1	-	-	21.0±0.0	20.1±2.1	19.3±0.2	-	22.1±1.5
	R1-Nb 19.0±0.8	-	-	-	25.6±2.3	25.7±0.5	-	29.8±1.5
	R1-Ta 18.1±0.4	-	-	27.2±0.4	-	26.4±0.5	-	28.3±0.3
	R1-Ti 19.3±0.9	-	-	24.0±0.8	24.9±0.2	-	-	31.8±0.1
	R2	21.4±1.6	-	-	26.4±0.4	27.9±0.7	24.4±0.5	-	-
	R2+Cr 19.5±0.0 19.5±0.4	-	20.2±0.1	21.4±0.4	19.5±0.3	-	-
	R2+Mo 20.1±2.9	-	20.4±1.1	19.9±0.7	20.7±0.7	19.0±0.5	-	-
	R2+V 18.7±0.4	-	-	20.9±0.3	22.2±0.4	19.0±0.2	19.2±0.1	-

Table 2

 2 Chemical compositions (in at%) of the indicated regions in Figure2(b)~(j).

	Region	Al	Cr	Mo	Nb	Ta	Ti	V	Zr
	1 (R0)	-	-	-	28.8±0.5 36.9±0.3 18.1±0.3	-	16.3±0.5
	2 (R0)	-	-	-	24.0±1.3 20.6±2.6 23.4±1.0	-	32.1±3.0
	3 (R1)	11.0±0.6	-	-	26.5±0.3 33.3±1.2 18.5±0.6	-	10.7±0.2
	4 (R1)	26.4±0.2	-	-	12.0±1.9	6.0±2.2	19.4±1.0	-	36.3±3.8
	5 (R1)	34.2±0.4	-	-	8.3±0.5	3.4±0.4	10.6±0.4	-	43.6±1.1
	6 (R1-Nb)	12.2±0.6	-	-	-	44.5±0.1 26.7±0.3	-	16.7±0.2
	7 (R1-Nb)	22.5±0.2	-	-	-	14.8±1.0 25.2±0.0	-	37.6±0.8
	8 (R1-Ta)	16.9±0.9	-	-	30.1±0.9	-	27.0±0.8	-	26.0±0.7
	9 (R1-Ta)	18.1±0.4	-	-	27.2±0.4	-	26.4±0.5	-	28.3±0.3
	10 (R1-Ti)	8.1±0.3	-	-	35.3±0.3 46.4±0.3	-	-	10.3±0.5
	11 (R1-Ti)	24.0±1.7	-	-	21.5±1.7 11.4±2.4	-	-	43.0±3.9
	12 (R1-Ti)	35.3±0.4	-	-	13.0±0.5	5.7±0.0	-	-	46.0±0.5
	13 (R2)	18.6±0.4	-	-	27.1±0.0 33.7±0.8 20.6±0.7	-	-
	14 (R2)	21.7±1.1	-	-	26.4±0.3 26.6±2.1 25.5±1.1	-	-
		19.7±0.2	-	-	20.

5±0.2 19.0±0.8 20.8±0.3 20.0±0.3 -

Table 3 Chemical

 3 Nb, R1-Ta, R1-Ti, and R2, Figure5(a). It is noteworthy that rutile-type oxides, such as AlTaO 4 , were absent in the oxide scale of R1-Ti, which was thoroughly oxidised without any metallic part left after 24 hours of isothermal oxidation at 1000 ˚C. For R1-Nb, diffraction peaks of AlTaO 4 and Ta 2 O 5 were prominent, while that of Ta 2 Zr 6 O 17 and ZrTiO 4 were also identified; for R1-Ta, TiO 2 and Nb 2 Zr 6 O 17 exhibited the highest diffraction peaks, while that of Nb 2 O 5 and AlNbO 4 were also present. For R1-Ti, Nb 2 Zr 6 O 17 was the dominant oxide since its diffraction peaks were the highest among all other detected oxides. TiO 2 and Ta 2 O 5 were found with high diffraction intensity for the oxide scale of R2, while Ti 2 Nb 10 O 29 was also observed.

	3 and 2, 4 are respectively the oxidised dendrite arms and inter-dendritic regions of
	Group A alloys.
	Region	O	Al	Nb	Ta	Ti	Zr
	1 (R0) 66.8±0.9	-	8.9±0.4	10.5±0.5	7.2±0.7	6.6±0.2
	2 (R0) 69.1±0.5	-	7.7±0.6	6.6±0.6	7.0±0.8	9.6±0.8
	3 (R1) 67.1±0.5	3.0±0.5	8.4±0.6	11.0±1.2	5.3±0.4	5.2±1.5
	4 (R1) 61.8±1.5	8.4±0.8	6.0±0.7	4.7±1.0	7.5±1.0	11.6±1.5

compositions (in at%) of the indicated regions in Figure

4

(b)(c). Region 1,

3.4 Oxidation: R1-Nb, R1-Ta, R1-Ti, and R2 alloys (Group B)

Similar to that of R0 and R1, XRD analysis suggested that oxide products appeared to be the same after 2 and 24 hours of isothermal oxidation at 1000 ˚C for R1-

Table 5

 5 Chemical compositions (in at%) of the indicated regions in Figure6(c)(e)(g).

	Region	O	Al	Cr	Mo	Nb	Ta	Ti	V
	1 (R2+Cr)	69.9±1.9 13.7±1.6 6.5±0.6	-	1.5±0.2	1.0±0.2	7.3±1.7	-
	2 (R2+Cr)	69.4±0.3 5.4±0.5	1.3±0.0	-	8.8±0.2	9.3±0.3	5.8±0.5	-
	3 (R2+Cr)	67.1±0.9 6.9±0.7	6.2±0.5	-	6.6±0.4	7.4±0.2	5.8±0.3	-
	4 (R2+Cr)	66.1±1.1 7.0±0.3	8.7±0.8	-	6.1±0.4	7.9±0.6	4.3±0.6	-
	5 (R2+Mo) 65.9±0.6 12.6±0.7	-	0.5±0.2	7.5±0.9	6.3±0.4	7.1±1.3	-
	6 (R2+Mo) 69.0±0.8 3.9±1.0	-	2.8±0.5 10.6±0.8 9.7±0.6	4.0±0.7	-
	7 (R2+V)	58.5±5.0 14.1±1.1	-	-	10.1±1.3 6.9±1.0	6.7±1.1	3.8±0.7
	8 (R2+V)	66.7±2.4 0.4±0.3	-	-	15.0±1.7 12.0±0.7 1.9±0.2	4.0±0.5
	9 (R2+V)	62.1±1.6 9.8±0.4	-	-	4.8±0.3	7.4±0.2 10.8±0.9 5.2±0.8

suppress internal oxidation but form an external oxide scale with porosity, while V addition was clearly devastating for oxidation resistance. Cr addition appeared to greatly improve oxidation resistance since R2+Cr showed the lowest oxidation mass gain and t O among all studied alloys. The oxides observed in the present study rarely possessed simple compositions, such as Al 2 O 3 and Cr 2 O 3 . Since current understanding

Table 6

 6 The constituents, crystal structures, and the parent alloys of the observed oxides in this work.

	Element Combination	Oxide	Crystal Structure	Alloy(s)
					R1
					R1-Ta
		Nb	AlNbO 4	Monoclinic	R1-Ti
					R2+Mo
	Al	Ta	AlTaO 4	Tetragonal (rutile)	R2+V R2+Cr
		Nb, Ti	(Al 0.2 Nb 0.2 Ti 0.6 )O 2 Tetragonal (rutile)	R1
					R1-Nb
		Ta, Ti	AlTaTiO 6	Tetragonal (rutile)	R2+Mo
					R2+V
	Cr	Ta	CrTaO 4	Tetragonal (rutile)	R2+Cr
	Mo	Ta, Ti	MoTiTa 8 O 25	Tetragonal	R2+Mo
	V	Ta	VTa 9 O 25	Tetragonal	R2+V
					R1
	Zr	Nb	Nb 2 Zr 6 O 17	Orthorhombic	R1-Ta
					R1-Ti

(R2+Cr)

16.1±0.0 13.4±0.1 -23.4±0.6 31.1±0.2 16.0±0.3 --16 (R2+Cr) 19.4±0.3 33.8±2.1 -15.4±0.6 15.3±0.9 16.3±1.7 --17 (R2+Cr) 24.4±1.0 13.3±2.5 -20.4±1.1 12.4±2.0 29.5±2.9 --18 (R2+Mo) 11.5±1.9 -24.8±1.0 20.6±0.2 28.8±2.1 14.3±1.2 --19 (R2+Mo) 22.3±2.1 -17.6±1.4 20.7±0.4 15.6±2.1 23.8±1.7 --20 (R2+V) 17.8±0.2 --21.0±0.2 25.5±0.7 17.4±0.5 18.4±0.3 -21 (R2+V)

Acknowledgements

This work was financially supported by the "High Entropy Materials Centre" from The Featured Areas Research Centre Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) and from the Project MOST107-2923-E-007-010-MY3, MOST109-2221-E-007-057, MOST110-2634-F-007-024, MOST110-2224-E-007-001, MOST110-2221-E-007-020-MY3 by Ministry of Science and Technology (MOST) in Taiwan. UG gratefully acknowledge the support by the Deutsche Forschungsgemeinschaft through the Priority Programme SPP 2006 "Compositionally Complex Alloys -High Entropy Alloys (CCA -HEA)". SG gratefully acknowledge the support by the CNRS through the 80 PRIME programme.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.