First-principles study of a new structure and oxidation mechanism of Pt₃Zr

Abstract

Zirconia (ZrO₂)–metal interfaces are interesting for solid oxide fuel cells. Although the oxidation of Pt₃Zr provides a new route for the formation of ZrO₂–Pt interfaces, the crystal structure of Pt₃Zr remains controversial and the oxidation mechanism of Pt₃Zr is unclear. To solve these problems, we use first-principles calculations to explore the crystal structure of Pt₃Zr. We demonstrate a stable structure of Pt₃Zr based on phonon dispersion. Importantly, two new Pt₃Zr structures, Ti₃Pt-type (Pm3̄m) and Fe₃Al-type (Fm3̄m), are predicted. To study the oxidation mechanism, two possible doped models are considered. The calculated results show that the O atom prefers to occupy the tetrahedral interstitial site (TI) in comparison to the octahedral interstitial site (OI). We find that the oxidizing capacity of the Fe₃Al-type cubic structure is stronger than that of other structures. In particular, we predict that Pt₃Zr exhibits better oxidation capacity in comparison to other metals because of the strong localized hybridization between Zr and O.

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1. Introduction

Zirconia (ZrO₂)–metal interfaces have widely used in solid oxide fuel cells (SOFCs), heterogeneous catalysis, gas sensors, etc.^1–9 Although ZrO₂ shows excellent chemical and thermal stabilities, the poor electrical conductivity hinders the application because of the requirement of sensitive probing techniques.^10,11 To solve this problem, an effective method is to oxidize Zr on an appropriate metal substrate. However, Zr deposited on a metal substrate should meet three conditions: oxygen reduction reaction (ORR), growth of the oxide layer and better catalytic activity of the metal substrate. In particular, the ORR clearly confirms the degree of oxidation between Zr and the metal substrate. Therefore, high ORR catalytic activity strongly depends on the d-state of the transition metal.^12–14

Platinum-group-metals are important catalysts because of their excellent chemical and physical properties.^15–18 In particular, Pt is a fascinating catalyst because it effectively promotes the process of ORR.^19–21 Recently, the oxidation behavior of Pt₃Zr (0001) surface was studied by the experiment and first-principles calculations.²² They found that the weak localized hybridization between Pt and Zr is beneficial to oxidation of Zr metal. Note that the metal addition will accelerate the growth of ZrO₂ film on the Pt₃Zr (0001) surface.²³ Therefore, structural configuration plays a crucial role in ORR and the formation of ZrO₂–Pt interface. Unfortunately, the crystal structure of Pt₃Zr remains controversial. Earlier work suggested that Pt₃Zr is a Au₃Cu-type cubic structure.^24,25 On the contrary, Stalick et al. found that Pt₃Zr belongs to a Ni₃Ti-type hexagonal structure,²⁶ which is different from the previous viewpoint. As a result, the nature of oxidation mechanism of Pt₃Zr is unclear.

To explore the catalytic activity of Pt₃Zr and improve the formation of ZrO₂–Pt interface, in our works, we investigate the crystal structure and oxidation mechanism of Pt₃Zr by using the first-principles calculations. According to the structural feature, we predict two possible cubic structures. Importantly, the structural stability of Pt₃Zr is estimated by the formation enthalpy and phonon dispersion. To examine the oxidation mechanism and oxidation capacity of Pt₃Zr, we calculate and compare the oxygen doped formation energy between O-doped Pt₃Zr and many metals. In particular, we examine the possible adsorption site of Pt₃Zr. Finally, we predict that Pt₃Zr shows better oxidation capacity in comparison to many metals.

2. Model and methods

To explore the oxidation mechanism, we firstly study the crystal structure of Pt₃Zr. To our knowledge, one is that Pt₃Zr is a Ni₃Ti-type hexagonal structure with space group of P6₃/mmc. The lattice parameters of hexagonal structure are a = 5.653 Å and c = 9.347 Å, respectively.²⁴ Another is that Pt₃Zr belongs to the Au₃Cu-type cubic structure with space group of Pm3̄m, and the lattice parameter is a = 4.051 Å.²⁶ In comparison to hexagonal structure, we suggest that Pt₃Zr with cubic structure can promote the oxidation of Pt₃Zr because of the localized hybridization between oxygen and Pt₃Zr. Therefore, we further design two possible structures: Ti₃Pt-type with cubic structure and Fe₃Al-type with cubic structure, respectively. The structural models of Pt₃Zr are shown in Fig. 1.

Fig. 1 Structural model of Pt₃Zr, (a) Ni₃Ti-type with hexagonal structure, (b) Au₃Cu-type with cubic structure, (c) Ti₃Pt-type with cubic structure and (d) Fe₃Al-type with cubic structure, respectively.

In this paper, the total energy, structural information, electronic structure and chemical bonding of Pt₃Zr and O-doped Pt₃Zr were calculated by using the first-principles calculations, as implemented in the CASTEP code.²⁷ The exchange–correlation-functional was calculated by using the generalized gradient approximation (GGA) within PW91 functional.^28,29 To treat the interaction between electrons and the ions, the atomic configurations of O, Pt and Zr were 2s²2p⁴, 5p⁶5d⁹6s¹ and 4p⁶4d²5s², respectively. Based on the convergence test, the plane-wave basis set for electron wave function with cutoff energy of 400 eV was used. The k-point grids of 10 × 10 × 5 for Ni₃Ti-type structure, 12 × 12 × 12 for Au₃Cu-type structure, 10 × 10 × 10 for Ti₃Pt-type structure, 11 × 11 × 11 for Fe₃Al-type structure, 14 × 14 × 8 for Zr and 17 × 17 × 17 for Pt were treated, respectively. To examine the dynamically stable, the phonon calculation was carried out by using the supercell method within the PHONON code.³⁰

3. Results and discussions

3.1 Structural prediction

The structural stability of Pt₃Zr is measured by the formation enthalpy and phonon dispersion, respectively. The equation of formation enthalpy (ΔH) is given by:

ΔH = E_Pt3Zr − 3E_Pt − E_Zr (1)

where E_Pt3Zr, E_Pt and E_Zr are the total energy of Pt₃Zr, isolated Pt atom and isolated Zr atom, respectively.

Table 1 lists the calculated lattice parameters, density, and formation enthalpy of Pt₃Zr with four structures. It can be seen that these structures are thermodynamically stable at the ground state because the calculated formation enthalpy of these structures is smaller than zero. Our predicted two structures (Ti₃Pt-type and Fe₃Al-type) are also thermodynamically stable. Importantly, the calculated formation enthalpy of Ni₃Ti-type structure is −8.188 eV per atom, which is smaller than that of Au₃Cu-type structure. The slight difference implies that external condition is easy to result in phase transition from Ni₃Ti-type structure to Au₃Cu-type structure. This result is similar to the Fairbank's viewpoint.²⁴

Table 1 Calculated equilibrium lattice parameters, a-axis and c-axis (Å), density, ρ (g cm⁻³) and formation enthalpy, ΔH (eV per atom) of Pt₃Zr

Structure	Method	a	c	ρ	ΔH
Ni3Ti-type	GGA	5.742	9.398	16.75	−8.188
	Exp^24	5.653	9.347
Au3Cu-type	GGA	4.061		17.77	−8.178
	Theo^25	3.980
	Exp^26	4.051
Ti3Pt-type	GGA	5.198		16.00	−7.918
Fe3Al-type	GGA	6.513		16.26	−7.871

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In addition to thermodynamically stable, the dynamically stable of Pt₃Zr should examine follow. To study the dynamically stable, Fig. 2 displays the calculated phonon dispersion curves of Pt₃Zr with four structures. It is clear that Pt₃Zr with Ni₃Ti-type structure is a dynamically unstable because the imaginary phonon frequency is observed in this structure. However, we find that there is no imaginary phonon frequency in Au₃Cu-type structure, indicating that this structure is a dynamically stable at the ground state. Based on the first-principles calculations, we demonstrate the Stalick's viewpoint. Importantly, we predict two new Pt₃Zr structures (Ti₃Pt-type and Fe₃Al-type) because no imaginary phonon frequencies are found in these structures.

Fig. 2 Calculated phonon dispersion curves of Pt₃Zr, (a) Ni₃Ti-type structure, (b) Au₃Cu-type structure, (c) Ti₃Pt-type structure and (d) Fe₃Al-type structure, respectively.

To further insight into the nature of dynamically stable, Fig. 3 shows the calculated phonon density of state (PhDOS) of Pt₃Zr with four structures. It can be seen that negative frequencies are found in Ni₃Ti-type structure, indicating that this structure is a mechanically unstable at the ground state. The calculated PhDOS profile reveals that the mechanically unstable of Ni₃Ti-type is attributed to the vibration of Pt atom at low frequency region. However, Au₃Cu-type, Ti₃Pt-type and Fe₃Al-type structures are mechanically stable because no negative frequencies are observed in these structures. In particular, the whole low frequency model of Au₃Cu-type structure derives from the vibration of Pt atom and Zr atom. With increasing frequency, Zr's vibration plays an important role in thermodynamic properties. Therefore, it is concluded that the structural stability of Pt₃Zr is markedly influenced by Pt–Zr bond.

Fig. 3 Phonon density of state of Pt₃Zr, (a) Ni₃Ti-type structure, (b) Au₃Cu-type structure, (c) Ti₃Pt-type structure and (d) Fe₃Al-type structure, respectively.

To further reveal the structural stability, the structural information of Pt₃Zr is discussed. As listed in Table 1, the calculated lattice parameters of Ni₃Ti-type structure (space group: P6₃/mmc, no: 194) are a = 5.742 Å and c = 9.398 Å, which are in good agreement with the experimental data.²⁴ In this structure (see Fig. 1(a)), the alternative Pt layer and Pt–Zr layer can be viewed along the c-axis. In particular, each Zr atom is surrounded by 4 Pt atoms at Pt–Zr layer. Therefore, Pt–Zr bond (2.601 Å) can improve the structural stability of Pt₃Zr with Ni₃Ti-type structure. However, the cohesive force between layers is determined by the bond strength of Pt–Pt bond and part of Pt–Zr bond. In other words, Pt–Pt and Pt–Zr bonds play a key role in structural stability. The calculated bond length of Pt–Pt and Pt–Zr bonds is 2.924 Å and 2.968 Å, respectively.

For Au₃Cu-type structure (see Fig. 1(b)), the calculated lattice parameter is a = 4.061 Å, which is in excellent agreement with the experimental data and theoretical results.^25,26 Note that the symmetrical Pt–Zr bonds effectively improve it's structural stability. The calculated bond length of Pt–Zr bond is 2.871 Å, which is similar to the previous theoretical result.³¹ Note that the bond length of Pt–Zr bond of Au₃Cu-type structure is slightly smaller than the corresponding bond for Ni₃Ti-type structure, indicating that the structural feature of the former can obviously improve the structural stability in comparison to the latter. Thus, we should consider the cubic structure to oxidize Zr.

The calculated lattice parameter of Ti₃Pt-type and Fe₃Al-type structures is a = 5.198 Å and a = 6.513 Å, respectively. From Fig. 1, Ti₃Pt-type structure is similar to Nb₃Si-type structure. In comparison to Au₃Cu-type structure, Pt atom in Ti₃Pt-type structure occurs migration from (0.50, 0, 0.50) site to (0.25, 0, 0.50) site. As a result, the variation of atomic position changes the localized hybridization between Pt and Zr, which forms two different Pt–Zr bonds. The calculated bond length of Pt–Zr bond is 2.599 Å and 2.906 Å, respectively. In particular, the atomic configuration can provide a large number of interstitial sites to adsorb oxygen. In addition, we find that the calculated lattice parameter of Ti₃Pt-type and Fe₃Al-type structures is larger than that of Au₃Cu-type structure.

For Fe₃Al-type structure, Pt atom migrates from (0.50, 0, 0.50) site to (0.25, 0.25, 0.25) site. Each Pt atom is surrounded by 4 Zr atoms and 8 Pt atoms. The calculated bond length of Pt–Zr bond is 2.820 Å. Importantly, the network Pt–Zr bonds can improve the structural stability of Pt₃Zr.

To reveal the nature of chemical bonding, Fig. 4 shows the calculated density of state (DOS) of Pt₃Zr with four structures. We can see that the DOS profile of Pt₃Zr is composed of Pt-5d state and Zr-4d state. The strong localized hybridization between Pt and Zr forms the Pt–Zr bond. It is worth noticing that the DOS profile of Ni₃Ti-type structure is similar to Au₃Cu-type structure. From Fig. 4, there is a deep valley near Fermi level (E_F), which separates the bonding state and antibonding state. For Ti₃Pt-type and Fe₃Al-type structures, however, the Zr-PDOS profile right shifts from E_F to high energy region. That is to say, Pt's migration weakens the localized hybridization between Pt and Zr. As a result, Pt–Pt bond plays an important role in structural stability, particularly for catalytic properties.

Fig. 4 Total and partial density of state (DOS) of Pt₃Zr, (a) Ni₃Ti-type structure, (b) Au₃Cu-type structure, (c) Ti₃Pt-type structure and (d) Fe₃Al-type structure, respectively.

3.2 Oxidation mechanism

We suggest that the formation of ZrO₂–Pt interface strongly depends on the interaction between Pt₃Zr and O atom. To examine the formation of ZrO₂–Pt interface, we calculate the oxygen doped formation energy of O-doped Pt₃Zr. In particular, we discuss and analyze the chemical bonding of O-doped Pt₃Zr to reveal the formation of ZrO₂–Pt interface. It must be mentioned that the formation of ZrO₂ film is related to the interstice radius of Pt₃Zr, which is determined by the atomic configuration of Pt₃Zr. Therefore, it is necessary to insight into the oxidation mechanism of Pt₃Zr.

According to the first-principles calculations, we consider the oxidation behavior of three stable Pt₃Zr structures: Au₃Cu-type, Ti₃Pt-type and Fe₃Al-type, respectively. To reveal the oxidation mechanism, we design the possible interstice models: tetrahedral interstice site (TI) and octahedral interstice site (OI), respectively. Oxygen mechanism of Pt₃Zr is measured by the oxygen doped formation energy (E_ad), which is given by:

where and E_Pt3Zr are the total energy of O-doped Pt₃Zr and parent Pt₃Zr at the ground state, respectively. μ_O is the chemical potential of O atom. Generally, the negative oxygen doped formation energy indicates the thermodynamically stable at the ground state.

To explore the catalytic activity of Pt₃Zr, we calculate and compare the capacity of oxygen between Pt₃Zr and many metals. Firstly, we explore the oxidation mechanism of Pt₃Zr. From Fig. 1, Au₃Cu-type is a typical cubic structure. Therefore, we design two possible occupied sites: TI site and OI site, respectively. However, the structural feature of Ti₃Pt-type structure is more complex than that of Au₃Cu-type structure. According to the structural feature, we design two different OI sites and one TI site. Although the doped model of Fe₃Al-type structure is similar to Au₃Cu-type structure, the atomic interaction of the former is stronger than the latter. That is to say, Fe₃Al-type structure is easily to adsorb a large number of oxygen.

Fig. 5 shows the calculated oxygen doped formation energy of O-doped Pt₃Zr and many metals. We can conclude that TI model is more thermodynamically stable than that of OI model because the calculated oxygen doped formation energy of the former is lower than the latter. This discrepancy is attributed to the localized hybridization between O and Zr. For Pt₃Zr, TI site can effectively improve the charge interaction between Zr and O, which forms the Zr–O bond. In particular, O atom prefers to occupy the TI site of Fe₃Al-type structure in comparison to other structures. Therefore, we can adjust the crystal structure of Pt₃Zr to promote the formation of ZrO₂. In particular, the calculated oxygen doped formation energy of Fe₃Al-type with TI site is about −9.029 eV, which is smaller than that of other structures. This result indicates that Pt₃Zr with Fe₃Al-type structure shows the better catalytic activity in comparison to other structures. This reason is attributed to the atomic configuration of Pt₃Zr.

Fig. 5 Calculated oxygen adsorption energy of O-doped Pt₃Zr at tetrahedral interstice site (TI) and octahedral interstice site (OI), together with many metals.

As we know, many metals such as Pt, Cu, Ni and Co etc. are important parts of solid oxide fuel cells.^32–35 To estimate the catalytic activity of Pt₃Zr, we compare the oxygen doped formation energy between Pt₃Zr and many metals. As shown in Fig. 5, the calculated oxygen doped formation energy of metal Zr is −10.068 eV, which is smaller than that of Pt₃Zr. This result indicates that metal Zr shows better oxidation capacity in comparison to Pt₃Zr. This is why ZrO₂ has been widely investigated over the last years. Importantly, although the oxygen doped formation energy of Pt₃Zr is larger than that of metal Zr, the oxygen doped formation energy of Pt₃Zr is smaller than that of other metals (see Fig. 5). The calculated electronic structure shows that the better oxidation capacity of Pt₃Zr derives from the strong localized hybridization between O and metal Zr. As mentioned above, we can predict that Pt₃Zr is expected to have better catalytic activity in comparison to other metals.

To reveal the nature of the oxidation mechanism, we further analyze the chemical bonding of O-doped Pt₃Zr. The first-principle calculations show that the bond length of Zr–O bond for Au₃Cu-type structure and Ti₃Pt-type structure is 2.026 Å and 2.014 Å, respectively, which are smaller than the corresponding Zr–O bond (2.05 Å) of ZrO₂.^36,37 However, the calculated bond length of Zr–O bond of Fe₃Al-type structure is 2.076 Å, which is close to the bond length of Zr–O bond for ZrO₂. On the other hand, the calculated electronic localization density shows that there is a strong localized hybridization between Pt and O for Au₃Cu-type structure. The calculated bond length of Pt–O bond is 2.117 Å. However, Pt–O antibonding state in Ti₃Pt-type and Fe₃Al-type structures is found. In other words, Ti₃Pt-type and Fe₃Al-type structures are beneficial to the formation of ZrO₂. The oxidation mechanism of Pt₃Zr with three structures is shown in Fig. 6. As mentioned above, we predict that Pt₃Zr with Fe₃Al-type structure is beneficial to the formation of ZrO₂.

Fig. 6 Oxygen adsorption mechanism of Pt₃Zr, (a) Au₃Cu-type structure, (b) Ti₃Pt-type structure and (c) Fe₃Al-type structure, respectively.

To gain insight the nature of oxidation behavior, Fig. 7 shows the calculated DOS of O-doped Pt₃Zr with three structures. We observe that the DOS profile of Pt₃Zr is mainly contributed by Pt-5d state and Zr-4d state. The strong localized hybridization between Pt and Zr forms the Pt–Zr bond. However, oxygen addition can improve the charge equilibrium between Pt and Zr. As shown in Fig. 7, we can see that the charge interaction between O and Zr forms the Zr–O bond, which demonstrates the existence of Zr–O bond.

Fig. 7 Total and partial density of state (DOS) of O-doped Pt₃Zr, (a) Au₃Cu-type structure, (b) Ti₃Pt-type structure and (c) Fe₃Al-type structure, respectively.

4. Conclusions

In summary, we apply first-principles calculations to study the crystal structure and oxidation mechanism of Pt₃Zr. To explore the stable structure, we calculate the formation enthalpy, phonon dispersion, lattice parameters and electronic structure of Pt₃Zr. In addition, we predict two possible new Pt₃Zr structures: Ti₃Pt-type (space group: Pm3̄m, no. 223) and Fe₃Al-type (space group: Fm3̄m, no. 225). To investigate the oxidation mechanism, we calculate the oxygen doped formation energy and chemical bonding of O-doped Pt₃Zr. In particular, we compare the oxygen doped formation energy of Pt₃Zr and many metals.

The calculated results show that although Pt₃Zr with hexagonal structure is more thermodynamically stable than that of cubic structure, hexagonal structure is a dynamically unstable at the ground state. The calculated oxygen doped formation energy of TI site is smaller than that of OI site. The calculated oxygen doped formation energy of Pt₃Zr with Fe₃Al-type structure is smaller than that of other structures. The calculated chemical bonding shows that Pt₃Zr with Fe₃Al-type structure is easy to form the ZrO₂ because of the formation of Zr–O bond. In particular, the calculated oxygen doped formation energy of Fe₃Al-type with TI site is smaller than that of other metals, indicating that Pt₃Zr shows the good catalytic activity in comparison to metals.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by grants from the Sichuan Provincial Colleges’ Sate Key Laboratory of Oil and Gas Reservoir Project (X151517KCL36) and the national natural science foundation of China (No. 51267007). We acknowledge the help from Lady Yun Zheng.

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