Adjusting the correlation between the oxidation resistance and mechanical properties of Pt-based thermal barrier coating

Vacuum 172 (2020) 109067

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Adjusting the correlation between the oxidation resistance and mechanical properties of Pt-based thermal barrier coating Yong Pan a, *, Delin Pu a, Yanlin Jia b, c, ** a

School of Materials Science and Engineering, Southwest Petroleum University, Chengdu, 610500, China College of Materials Science and Engineering, Central South University, Changsha, 410083, China c College of Materials Science and Engineering, Beijing University of Technology, 100 Ping Le Yuan, Chaoyang District, Beijing, 100124, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Thermal barrier coating Oxidation resistance Mechanical properties First-principles calculations

Although PtAl is an attractive thermal barrier coating (TBC), the key problem is to adjust the correlation between the oxidation resistance and mechanical properties. Here, we apply the first-principle calculations to investigate the oxidation mechanism of PtAl coating and explore the influence of alloying elements(Y, Cr and Si) on the oxidation resistance of PtAl coating. We further study the influence of Cr concentration on the elastic modulus and brittle-or-ductile behavior of PtAl. It is found that O prefers to occupy the center of Pt tetrahedron. Compared to Y-dopant, Cr-dopant and Si-dopant enhance the oxidation resistance of PtAl coating because the charge interaction of Cr–O and Si–O is stronger than that of the Al–O atoms. In particular, the Cr element effectively improves the shear deformation resistance and elastic stiffness of PtAl. With increasing Cr concentration, the formation of Cr–Al bond enhances the elastic stiffness and shear deformation resistance of PtAl. Therefore, our results predict that Cr is a useful element to improve the overall performance of PtAl thermal barrier coating.

1. Introduction For the advanced aerospace gas turbines, turbine blade and rocket engines, a major challenge is how to adjust the balance between the oxidation resistance and mechanical properties of advanced hightemperature structural materials [1–7]. Over the last years, the search for high melting point and high strength material is regarded as the key issue for the applications of high-temperature structural materials [8–15]. Under high-temperature environment, however, the harmful influence of O on the alloy or compound severely hinders the further development of the future high-temperature materials because O in alloy or compound destroys the cohesive force among atoms and then results in “pest oxidation” [16–20]. In particular, if we focus on the improvement of the mechanical properties, the oxidation resistance of high-temperature materials becomes worse, and vice versa [21]. Therefore, we hope that we can explore these high-temperature mate­ rials with overall performance to meet the requirement of a complex environment such as high melting-point, high strength and oxidation resistance etc. Naturally, the oxidation resistance of high-temperature materials mainly depends on the antioxidation elements (Cr, Al, Y an Si etc)

because the formation of oxides (Cr2O3, Al2O3, Y2O3 and SiO2) effec­ tively enhances the oxidation resistance of high-temperature materials under high-temperature environment [22–26]. However, the improve­ ment of mechanical properties of high-temperature material is related to the transition metal [27,28]. To improve the balance between the oxidation resistance and mechanical properties, therefore, it is necessary to search for the suitable transition metals (Cr and Y) to improve the oxidation resistance and mechanical properties of high-temperature materials. Recently, Pt–Al compounds are attractive thermal barrier coatings (TBC) because of their excellent thermodynamically stable, high melting-point and good mechanical properties etc [29–33]. In partic­ ular, B2-phase PtAl coating has grown interesting due to the symmet­ rical Pt–Al bonds. For its mechanical properties, our work has shown that the calculated bulk modulus and Young’s modulus of B2-phase PtAl are 188 GPa and 218 GPa, respectively, which are larger than that of the conventional NiAl alloy [34,35]. The fracture stress (FS) of PtAl coating increases with increasing temperature. When the temperature is up to 750 � C, the fracture stress of PtAl coating is 292 MPa [36]. Note that PtAl coating is more thermodynamically stable than that of the other Pt–Al compounds [37,38]. For its oxidation resistance, Odusote and Cornish

* Corresponding author. ** Corresponding author. College of Materials Science and Engineering, Central South University, Changsha, 410083, China. E-mail addresses: [email protected] (Y. Pan), [email protected] (Y. Jia). https://doi.org/10.1016/j.vacuum.2019.109067 Received 16 September 2019; Received in revised form 6 November 2019; Accepted 7 November 2019 Available online 12 November 2019 0042-207X/© 2019 Elsevier Ltd. All rights reserved.

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alloying elements and PtAl, the 2s22p4, 3s23p2, 3s23p1, 5d96s1, 3p63d54s1 and 4d15s2 were considered for O, Si, Al, Pt, Cr and Y, respectively. The interactions between the ions and electrons were adopted by the ultra­ soft pseudopentional [49,50]. A plane-wave basis set with a cutoff en­ ergy of 400 eV was used. The integration in the Brillouin zone was performed by the k point generated with 8 � 8 � 8 for oxidized PtAl and alloyed PtAl, respectively. All atomic positions and internal coordinates of oxidized PtAl and alloyed PtAl were relaxed during the process of structural optimization [51]. 3. Results and discussion Essentially, the oxidation behavior of thermal barrier coating is determined by the three factors such as (1) interaction between O and PtAl, (2) the atomic configuration near the O atom and (3) interstice radius. For B2-cubic structure, it is easy to absorb O due to large in­ terstice radius and the thermal activation energy under hightemperature. It is well known that the first-principle calculation is an effective tool to insight into the oxidation mechanism and mechanical properties of high-temperature materials [52–54]. To reveal the oxida­ tion mechanism, the oxidation mechanism of PtAl is estimated by the first-principle calculation. The capacity of oxidation behavior of O-doped PtAl is measured by the O-doped formation energy(Ead) [55], which is given by:

Fig. 1. Structural model of oxidized PtAl. Here, we consider two O doped sites: O occupies the center of Al tetrahedron, which defined as the O(1) site, and O occupies the center of Pt tetrahedron which defined as the O(2) site.

have pointed out that the formation of α-Al2O3 particle effectively im­ proves the oxidation resistance of PtAl coating [39,40]. However, the oxidation mechanism of PtAl coating is entirely unclear. In particular, to meet the requirement of future aerospace and automotive applications, a great challenge is to enhance its mechanical properties with ensuring excellent oxidation resistance. To solve above these problems, here, we use the first-principle calculation to study the oxidation mechanism of PtAl coating. Two O doped sites are considered. To improve its oxidation resistance, we further explore the influence of alloying elements on the oxidation resistance of PtAl coating. Three antioxidation elements: Cr, Y and Si are considered. To reveal the nature of oxidation resistance, the structure and chemical bonding of PtAl with doping of alloying elements are discussed. Based on the result of the oxidation mechanism, we further investigate the influence of Cr concentration on the mechanical prop­ erties of PtAl coating. Our work shows that Cr-dopant not only improves the oxidation resistance but also enhances the elastic stiffness and shear deformation resistance of PtAl coating. As mentioned above, our work opens up a new clue to adjust and improve the balance between the oxidation resistance and mechanical properties of PtAl coating.

(1)

Ead(O) ¼ Etot(PtAl–O)-Etot(PtAl)-μ(O)

where Etot(PtAl–O), Etot(PtAl) and μ(O) are the total energy of O-doped PtAl, the parent PtAl and chemical potential of O, respectively. To explore the influence of alloying elements on the oxidation resistance of PtAl, we should firstly study the structural stability of PtAl with doping of alloying elements. The stability of doped element is estimated by the impurity formation energy(ΔEf) [56–58]: ΔEf ¼ EAl→TM PtAl

EPtAl þ μAl

(2)

μTM

where EAl→TM and EPtAl are the total energy of PtAl with doping of PtAl alloying elements(TM) and the parent PtAl. μAl and μTM are the chemical potential of Al and TM elements, respectively. To explore the oxidation mechanism, Table 1 lists the calculated lattice parameters, volume, O-doped formation energy (Ead) and bond length of oxidized PtAl coating. Here, the calculated lattice parameter of PtAl is in good agreement with the other theoretical result [44]. From Table 1, it is concluded that PtAl is oxidized because the calculated doped formation energy of oxidized PtAl coating is smaller than zero. In particular, the calculated doped formation energy of O(2) site ( 5.802 eV) is smaller than that of the O(1) site ( 5.729 eV), indicating that O occupies the center of Pt tetrahedron is more thermodynamically stable than that of the O occupies the center of Al tetrahedron. Naturally, the capacity of oxidation behavior is related to the structural configuration and the charge interaction between O and PtAl. Firstly, the introduction of O results in volume expansion of PtAl because the calculated volume of O-doped PtAl is larger than that of the PtAl. The difference is attributed to the position of O due to the charge interaction between O and the PtAl coating. Secondly, the O occupied O(1) site leads to lattice expansion of PtAl along the b-axis. However, O occupied O(2) site leads to lattice expansion of PtAl along the a-axis and c-axis. The variation of lattice parameter is determined by the localized hy­ bridization between O, Al tetrahedron and Pt tetrahedron. From Fig. 1,

2. Theoretical methods B2-phase noble metal aluminide is a cubic structure (Pm-3m, No. 221) [41–43], which is easy to absorb O. To study the oxidation mechanism, we firstly consider its structural feature. The lattice parameter of PtAl is a ¼ 3.090 Å [44]. The calculated lattice parameter of unit-cell is a ¼ 3.088 Å, which is in good agreement with the other theoretical results [44]. Following, we built 2 � 2 � 2 supercell model to treat the interaction between O and PtAl. Here, we design two O doped sites: O(1) site which is surrounded by the Al tetrahedron and O(2) site which is surrounded by the Pt tetrahedron. The oxidation model of PtAl is shown in Fig. 1. Here, the oxidation mechanism of PtAl and the mechanical proper­ ties of Cr-doped PtAl were calculated by using the first-principle calculation, as implemented in the CASTEP code [45,46]. The ex­ change correlation function of oxidized PtAl and Cr-doped PtAl was treated by the generalized gradient approximation(GGA) with PBE functional [47,48]. To treat the charge interaction among the O,

Table 1 Calculated lattice parameters, (Å), volume, V(Å3), O-doped formation energy, Ead(O) (eV) and bond length (Å) of oxidized PtAl coating. Type

Method

a

PtAl O(1) site O(2) site

Cal Cal Cal

6.176 5.776 6.516

b 7.420 5.879

c

V

5.776 6.516

235.6 247.6 249.6

2

Ead(O) 5.729 5.802

Pt–Al

Al–O

Pt–O

2.674 2.509 2.552

2.021 1.688

2.340 2.570

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Fig. 2. Calculated density of state for (a) the parent PtAl, (b) O(1) site and (c) O(2) site, respectively. Table 2 Calculated lattice parameters, (Å), volume, V(Å3), impurity formation energy, ΔEf (eV), O-doped formation energy Ead(O) (eV) and bond length (Å) of TM-doped PtAl. Type

Method

a

PtAl Y-dopant Y-dopant-oxide Cr-dopant Cr-dopant-oxide Si-dopant Si-dopant-oxide

Cal Cal Cal Cal Cal Cal Cal

6.176 6.326 6.352 6.174 6.503 6.169 6.557

b 6.326 6.635 6.174 5.893 6.169 5.802

c

V

6.326 6.352 6.174 6.503 6.169 6.557

235.6 253.1 267.7 235.3 249.2 234.8 249.5

when O locates at the center of Al tetrahedron (O(1) site), the intro­ duction of O improves the charge interaction between Pt and O. How­ ever, O occupied O(2) site enhances the charge interaction between Al and O. This result is demonstrated by the electronic structure and bond length. Fig. 2 shows the calculated density of state of the parent PtAl, O(1) site and O(2) site, respectively. It is clear that there is an obvious localized hybridization between Pt-5d state and Al-3p state near the Fermi level. The structural stability of PtAl is attributed to the formation of Pt–Al bond. Here, the calculated bond length of Pt–Al bond is 2.674 Å, which is in good agreement with the other theoretical result [35]. When PtAl is oxidized, O leads to band shift from the low energy region to the Fermi level. As a result, the introduction of O improves the localized hybridization between Pt and Al. Compared with the O(1) site and the parent PtAl coating, the calculated bond length of Pt–Al bond for O(1) site is 2.511 Å, which is smaller than that of the corresponding bond of the parent PtAl bond. Importantly, we also observe the localized hybridization between O and PtAl. From Table 1, the calculated bond length of Pt–O bond for O(1) site (2.340 Å) is shorter than that of the O (2) site (2.570 Å). However, the calculated bond length of Al–O bond for O(2) site (1.688 Å) is shorter than that of the O(1) site (2.021 Å). The variation of bond demonstrates that the oxidation behavior of O(2) site is stronger than that of the O(1) site. In particular, we find the Al2O3

ΔEf 0.196 3.572 0.143

Ead(O)

TM-O

Al–O

Pt–O

5.275

2.204

1.672

2.564

5.915

1.693

1.699

2.569

6.356

1.603

1.706

2.621

because the calculated bond length of Al–O bond is in good agreement with other theoretical result (1.780 Å) [59]. This is why PtAl shows better oxidation resistance due to the formation of Al–O bond. For thermal barrier coatings, the improvement of oxidation resis­ tance is still a big challenge for their high-temperature applications. As we know, alloying addition (Cr, Y and Si etc) is an effective method to improve the oxidation resistance of high-temperature materials [60–62]. Hence, we further study the influence of alloying elements (Cr, Y and Si) on the antioxidation of PtAl. To explore the alloying effect, we must consider two aspects: the stability of alloying addition and the capacity of oxidation behavior. Here, the stability of alloying addition is measured by the impurity formation energy (ΔEf) [63]. Importantly, the capacity of oxidation behavior is estimated by the O-doped formation energy (Ead(O)). Therefore, we consider the O occupied the center of Pt tetrahedron. Table 2 lists the calculated lattice parameters, volume, impurity formation energy, O-doped formation energy and bond length of Ydoped, Cr-doped and Si-doped PtAl. It is clear that the calculated im­ purity formation energy of Cr-dopant and Si-dopant is smaller than zero. On the contrary, the calculated impurity formation energy of Y-dopant is larger than zero. Therefore, it is concluded that Cr-dopant and Si-dopant are thermodynamically stable. We further note that the calculated im­ purity formation energy of Cr-dopant is much smaller than that of the Si-

Fig. 3. Density of state for (a) Y-doped PtAl, (b) Cr-doped PtAl and (c) Si-doped PtAl, respectively. 3

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Fig. 4. Density of state for (a) Y-dopant, (b) Cr-dopant and (c) Si-dopant, respectively.

dopant. In other words, Cr-dopant is more thermodynamically stable than that of the Si-dopant. Essentially, the stability of doped element is related to the structural configuration and electronic interaction between the alloying elements and PtAl. From Table 2, Y-dopant leads to lattice expansion and volume expansion of the parent PtAl. On the contrary, Cr-dopant and Si-dopant give rise to lattice and volume shrinkages of the parent PtAl. Although the variation of lattice parameter is related to the atomic radius, these results also indirectly demonstrate that Cr-dopant and Si-dopant improve the localized hybridization between alloying and PtAl coating. To understand the nature of alloying, Fig. 3 shows the calculated density of state of Y-dopant, Cr-dopant and Si-dopant, respectively. Compared with Figs. 2(a) and Figure 3(a), it is observed that the Ydopant results in band shift from the valence band to the conduction band. In particular, the main peak of Y element locates at the high en­ ergy region. Although there is the localized hybridization among the Y4d state, Al-3p state, Al-3s state ad Pt-5d state, the main peak (Y-4d state) above the Fermi level forms the Y–Pt antibonding state. Here, the calculated value of Mulliken population and bond length of Y–Pt bond is 0.41 and 2.892 Å, respectively. There is well explained why the Ydopant is thermodynamically unstable. However, the electronic contribution of Cr-dopant and Si-dopant is different from the Y-dopant. From Fig. 3, the DOS profile of Cr-dopant is contributed by the Cr-3d state, Al-3s state, Al-3p state and Pt-5d state, respectively. However, the sharp peak of Cr element just locates at the Fermi level. Compared to the Y-dopant, the antibonding state of Crdopant is obviously weaker than that of the Y-dopant. Here, the calcu­ lated Mulliken population and bond length of Cr–Pt bond is 0.05 and 2.673 Å, respectively. Namely, Cr-dopant improves the localized hy­ bridization between Cr and Pt. For Si-dopant, the DOS profile is composed of Si-3p state, Al-3s state, Al-3p state and Pt-5d state, respectively. Compared to Y-dopant and Cr-

dopant, the main peak of Si element locates at the valence band region. As a result, the strong charge interaction forms the Cr–Pt bond. The calculated Mulliken population and bond length of Si–Pt bond is 0.26 and 2.636 Å, respectively. As mentioned above, this is why Cr-dopant and Si-dopant are thermodynamically stables in comparison to the Ydopant. Following, we study the influence of alloying elements (Y, Cr and Si) on the oxidation resistance of PtAl. As listed in Table 2, the calculated value of O-doped formation energy of alloyed doped PtAl is smaller than zero. In particular, the calculated O-doped formation energy of Crdopant and Si-dopant is smaller than that of O(2) site ( 5.802 eV), indicating that alloying elements of Cr and Si improve the oxidation resistance of PtAl. Here, we note that the calculated O-doped formation energy of Si-dopant is 6.356 eV, which is smaller than that of Crdopant and Y-dopant. Therefore, it is concluded that Si is benefit to enhance the oxidation resistance in comparison to other alloying elements. Similarity, the capacity of oxidation resistance is demonstrated by both the structural configuration and electronic interaction between the alloying elements and PtAl coating. It can be seen that the Y-dopant results in lattice expansion of PtAl along the a-axis, b-axis and c-axis. However, Cr-dopant and Si-dopant lead to lattice expansion of PtAl along a-axis and c-axis. On the contrary, Cr-dopant and Si-dopant result in lattice shrinkage of PtAl along the b-axis. We suggest that the decreasing of b-axis improves the localized hybridization between the alloying elements and PtAl. The variation of lattice parameter is demonstrated by the electronic structure and chemical bonding. Fig. 4 shows the calculated density of state of oxidized Y-doped, Crdoped and Si-doped PtAl, respectively. When O is introduced, it is found that the O takes part in localized hybridization between O and TMdoped PtAl. The formation of Y–O bond, Cr–O bond and Si–O bond is attributed to the charge interaction of Y–O atoms, Cr–O atoms and Si–O

Fig. 5. Charge density along (001) plane for (a) Y-dopant, (b) Cr-dopant and (c) Si-dopant, respectively. 4

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atoms, respectively. Owing to the choice of alloying element, the introduction of O results in band shift. For Y-doped system, the alloying element Y improves the localized hybridization between O and Al below the Fermi level. As a result, Y-doped system forms the strong Al–O bond. Interestingly, Cr-dopant and Si-dopant give rise to band shift (Al and Pt) from the valence band to the conduction band. In other words, Crdopant and Si-dopant enhance the localized hybridization between alloying elements and O. Therefore, alloying elements of Cr and Si improve the oxidation resistance of PtAl. The variation of the electronic contribution is further demonstrated by the charge density. To reveal the nature of chemical bonding, Fig. 5 shows the calculated contour plots of the charge density distribution of oxidized TM-doped PtAl coating. It is found that the formation of Al–O bond, Pt–O bond and TM-O bond derives from the Al–O atoms, Pt–O atoms and TM-O atoms, respectively. However, the marked different is attributed to the chemical bonding. From Fig. 5, the calculated bond length of Y–O bond, Cr–O bond and Si–O bond is 2.204 Å for Y-dopant, 1.693 Å for Cr-dopant and 1.603 Å for Si-dopant, respectively. Importantly, the alloying element Y weakens the localized hybridization between Y and O, and enhances the electronic interaction between Al and O. This result is demonstrated by the Y–O bond and Al–O bond. Here, the calculated bond length of Y–O bond is larger than that of the Al–O bond. In particular, the calculated bond length of Al–O bond for Y-dopant (1.672 Å) is shorter than the corresponding bond of O(2) site (1.688 Å). These results indicate that the bond strength of Y–O bond is weaker than that of Al–O bond. This is why Y element does not improve the oxidation resistance of PtAl. However, the alloying elements of Cr and Si improve the localized hybridization between alloying elements (Cr and Si) and O, and then weaken the electronic interaction between Al and O. Compared with Figs. 4 and 5, the calculated bond length of TM-O (TM ¼ Cr and Si) is shorter than the corresponding Al–O bond. In particular, the calculated bond length of Al–O bond for Cr-dopant and Si-dopant is longer than the corresponding Al–O bond for O(2) site. In other words, the bond strength of Cr–O bond and Si–O bond is stronger than that of the Al–O bond. This is why alloying elements of Cr and Si improve the oxidation resistance of PtAl coating. The equation of oxidation capacity is seen by equations (3) and (4). Cr þ Al2O3→Cr2O3þAl

(3)

3Siþ2Al2O3→3SiO2þ4Al

(4)

Fig. 6. Calculated doped formation energy (ΔEf) of PtAl as a function of Cr concentration.

Fig. 7. Calculated elastic modulus of PtAl coating as a function of Cr concentration.

For high-temperature materials, the mechanical properties play a crucial role in high-temperature applications. Besides the oxidation resistance, therefore, we should further examine the mechanical prop­ erties. As mentioned above, we find that alloying elements of Cr and Si are beneficial for improving the oxidation resistance of PtAl. Consid­ ering the d-orbit effect, we investigate the influence of Cr concentration on the mechanical properties of PtAl. Here, we should consider two aspects: (1) the stability of Cr-dopant and (2) the correlation between Cr concentration and the mechanical properties. The stability of Cr-dopant is measured by the doped formation energy (ΔEf) [56]. Here, the mechanical properties of Cr-doped PtAl coating are esti­ mated by both the elastic modulus and brittle-or-ductile behavior [64, 65]. Furthermore, the elastic modulus (bulk modulus (B), shear modulus (G) and Young’s modulus (E)) are calculated by the elastic constants(Cij) [66,67]. Here, the elastic constants of all compounds are calculated by the stress-strain method. Here, the bulk modulus and shear modulus of Cr-doped PtAl are calculated by the Voigt-Reuss-Hill(VRH) approxima­ tion [68–70]. In addition, the brittle-or-ductile of Cr-doped PtAl is examined by the Pugh rule [71–73]. If B/G < 1.75, a solid shows the brittleness. On the contrary, If B/G > 1.75, a material exhibits ductility. To study the influence of Cr concentration on the mechanical prop­ erties, we consider five Cr concentrations: 0, 3.123 at%, 6.25 at%, 12.5 at% and 25 at%, respectively. Fig. 6 shows the calculated doped formation energy of Cr-doped PtAl as a function of Cr concentration. It

can be seen that the Cr-doped PtAl coating is a thermodynamically stable because the calculated doped formation energy of Cr-doped PtAl is smaller than zero. It is found that there is a convex hull at x ¼ 6.25 at %. The calculated doped formation of Cr-doped PtAl at x ¼ 6.25 at % is 0.91 eV, which is smaller than that of the other Cr doped concentra­ tion. Hence, the convex hull indicates that Cr-doped PtAl at x ¼ 6.25 at% is more thermodynamically stable than that of the other Cr-doped concentrations. From above analysis, it is concluded that Cr element is stability in PtAl coating. Therefore, we further investigate the effect of Cr concen­ tration on the elastic modulus and brittle-or-ductile behavior of PtAl coating. Fig. 7 shows the calculated elastic modulus of PtAl coating as a function of Cr concentration. The calculated bulk modulus of Cr-doped PtAl increases when x<3.125%. However, the calculated bulk modulus of Cr-doped PtAl decreases when x>3.125%. According to the first-principles calculations, the increasing of bulk modulus is that the low concentration of Cr improves the localized hybridization between Pt and Al, and then enhances the bond strength of Pt–Al bond. With increasing Cr element, the Cr–Al bond plays an important role in Crdoped PtAl coating. This is why the bulk modulus of Cr-doped PtAl (x>3.125%) is smaller than the parent PtAl coating. This result is demonstrated by the charge density (see Fig. 10). In addition, we find that the shear modulus and Young’s modulus of Cr-doped PtAl increases 5

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Cr is introduced, the DOS profile of Cr-doped PtAl is composed of Cr-3d state, Pt-5d state, Al-3s state and Al-3p state. In particular, the strong localized hybridization between Cr and Al (below the Fermi level) forms the strong Cr–Al bond, which enhances the deformation of PtAl. With increasing Cr concentration, the main peaks of Cr-3d state and Al-3p state occur shift from the low energy region to the Fermi level. As a result, the band shift improves the localized hybridization between Cr3d state and Al-3p state. Therefore, it is concluded that the Cr-d state plays an important role in mechanical properties of PtAl coating. To reveal the nature of the mechanical properties, Fig. 10 displays the charge density distributed of Cr-doped PtAl. Five Cr concentrations are considered. For parent PtAl, the charge interaction between Pt and Al forms the directional Pt–Al bond, which is the origin of mechanical properties for PtAl. When Cr element is introduced, it is found that the charge interaction between Cr and Al forms the directional Cr–Al bond, which can improve the mechanical properties of PtAl. With increasing Cr concentration, the localized hybridization between Cr and Al be­ comes strong, which is demonstrated by the chemical bonding. As shown in Fig. 10, we find that the bond length of Cr–Al bond for high concentration of Cr is shorter than that of low concentration of Cr. This is why the Cr element effectively improves the mechanical properties of PtAl.

Fig. 8. Calculated B/G ratio of PtAl as a function of Cr concentration.

gradually with increasing Cr concentration. Therefore, Cr-dopant can effectively improve the shear deformation resistance and elastic stiffness of PtAl coating. As mentioned above, we predict that Cr element not only improves the oxidation resistance of PtAl coating, but also enhances the elastic properties of PtAl coating. To study the influence Cr concentration on the brittle-or-ductile behavior of PtAl coating, Fig. 8 shows the calculated B/G ratio of PtAl as a function of Cr concentration. It can be seen that the calculated B/G ratio is 4.41 for the parent PtAl, 3.47 for 3.125 at% Cr, 3.36 for 6.25 at% Cr, 3 for 12.5 at% Cr and 1.62 for 25 at% Cr, respectively. Obviously, the calculated B/G ratio of PtAl decreases gradually with Cr concentration. Moreover, Cr-doped PtAl coating exhibits ductile behavior when x < 12.5 at%. However, Cr-doped PtAl coating shows the brittle behavior when x > 25 at%. Therefore, it is necessary to select appro­ priate Cr concentration to adjust the overall performances of PtAl coating. To reveal the nature of mechanical properties, Fig. 9 shows the density of state of Cr-doped PtAl as a function of Cr concentration. When

4. Conclusions To solve the balance between the oxidation resistance and mechan­ ical properties, we use the first-principles calculations to study the oxidation mechanism of PtAl thermal barrier coating and explore the influence of alloying elements (Y, Cr and Si) on the oxidation resistance of PtAl. Based on the oxidation affect, we further investigate the effect of Cr concentration on the elastic properties and brittle-or-ductile behavior of PtAl. To examine the oxidation affect, we consider two O-doped sites: O(1) site (O occupied Al tetrahedron) and O(2) site(O occupied Pt tet­ rahedron), respectively. To study the influence of Cr element on the mechanical properties, we select five Cr concentrations: 0, 3.125 at%,

Fig. 9. Calculated density of state of Cr-doped PtAl as a function of Cr concentration. (a) the parent PtAl, (b) Cr concentration at 3.125 at%, (c) Cr concentration at 6.25 at%, (d) Cr concentration at 12.5 at%,(e) Cr concentration at 25 at%, respectively. 6

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Fig. 10. Calculated charge density of Cr-doped PtAl as a function of Cr concentration. (a) the parent PtAl, (b) Cr concentration at 3.125 at%, (c) Cr concentration at 6.25 at%, (d) Cr concentration at 12.5 at%,(e) Cr concentration at 25 at%, respectively.

References

6.25 at%, 12.5 at% and 25 at%, respectively. The results show that O prefers to occupy O(2) site because the calculated O-doped formation energy of O(2) site ( 5.802 eV) is smaller than that of the O(1) site ( 5.729 eV). Furthermore, Y-dopant is a thermodynamically unstable, in contrary to Cr-dopant and Si-dopant are thermodynamically stable. The calculated electronic structure shows that Y-dopant weakens the localized hybridization between Y and O, and enhances the electronic interaction between Al and O. However, Crdopant and Si-dopant improve the localized hybridization between alloying elements (Cr and Si) and O, and then weaken the electronic interaction between Al and O. Therefore, we can conclude that Cr and Si can effectively improve the oxidation resistance of PtAl. In particular, the calculated shear modulus and Young’s modulus of Cr-doped PtAl coating increase gradually with increasing Cr concentration. The calculated electronic structure reveals that the improvement of me­ chanical properties is attributed to the strong localized hybridization between Cr and Al. With increasing Cr concentration, the localized hy­ bridization of Cr–Al atoms becomes strong.

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Declaration of competing interest The authors declare no conflict of interest. Acknowledgments This work is supported by the State Key Laboratory of Advanced Technology for Comprehensive Utilization of Platinum Metals (Grant No. SKL-SPM-201816) and National Natural Science Foundation of China(Grant No. 51274170). We acknowledge the great help from Dr. Y. Zheng and R. Pan. 7

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Vacuum 172 (2020) 109067

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