A DFT-Based Descriptor to Predict the Water Vapor Corrosion Resistance of Rare-Earth Monosilicates.

Rare-earth monosilicates are used as environmental barrier coatings (EBCs) due to their excellent water vapor corrosion resistance. However, existing experimental studies on the water vapor corrosion behavior of rare-earth monosilicates are discrepant and even contradictory. Previous theoretical investigations on water vapor corrosion resistance mainly focus on a Mulliken analysis of Si-O bonds in the monosilicates. In this study, the structural and electronic properties of rare-earth monosilicates have been studied by density functional theory (DFT) calculations, and a descriptor correlated to the corrosion resistance has been developed. The maximum isosurface value of the valence band maximum (VBMFmax) can be used to predict the water vapor corrosion resistance of RE2SiO5. The results show that RE2SiO5 with a smaller VBMFmax may have better water vapor corrosion resistance.

1. Introduction

Rare-earth (RE) silicates are promising candidates for environmental barrier coatings (EBCs) due to their exceptional high-temperature durability, chemical compatibility and water vapor corrosion resistance [1]. Rare-earth monosilicates, RE2SiO5, have two types of monoclinic crystalline structures: RE2SiO5 with a space group of P21/c are called X1 phase when the ionic radius of RE elements (RE = La~Gd) is larger, while the X2 phase with a C2/c space group forms by the elements from Tb to Lu [2]. The water vapor corrosion behaviors and mechanisms may be different between the two phases.

Recently, many experimental studies have been carried out regarding the water vapor corrosion resistance of RE2SiO5 as EBCs. Wang et al. [3] found that X2-RE2SiO5 are more stable than X1-RE2SiO5 in high-temperature water steam. Nasiri et al. [4] investigated the water vapor corrosion resistance of RE2SiO5 (RE = Y, Gd, Er, Yb and Lu) in air with 90% water, and found that their water vapor resistance has the following order: Y2SiO5 > Er2SiO5 > Yb2SiO5 > Lu2SiO5 > Gd2SiO5. Klemm et al. [5] studied the water vapor corrosion resistance of Y2SiO5 and Sc2SiO5, indicating that Y2SiO5 exhibited better water vapor corrosion resistance. Unfortunately, the existing experimental studies on the water vapor corrosion behavior of rare-earth monosilicates may be discrepant or even contradictory due to the different experimental conditions [6]. It is worth pointing out that the water vapor corrosion resistance of rare-earth monosilicates can also be evaluated by theoretical calculations. For example, Han et al. [7] studied the water vapor corrosion resistance of X2-RE2SiO5 (RE = Lu, Yb, Tm, Er, Ho, Dy, Y and Sc) using first-principles calculations. They concluded that the water vapor corrosion resistance of X2-RE2SiO5 demonstrated the following order: Sc2SiO5 > Dy2SiO5 > Y2SiO5 > Ho2SiO5 > Er2SiO5 > Yb2SiO5 > Tm2SiO5 > Lu2SiO5, which shows some disagreement with the experimental findings [3,5,6]. Therefore, it is still a challenge to provide a precise order of the water vapor corrosion resistance of RE2SiO5.

In previous theoretical studies [7,8], researchers mainly focused on the Si-O bonds instead of RE-O bonds of rare-earth silicates to compare their water vapor corrosion resistances. However, the [REOx] polyhedron is less rigid than the [SiO4] tetrahedral, and is easier to collapse and react with water molecules. In this work, we used density functional theory (DFT) calculations to investigate the water vapor corrosion resistance of RE2SiO5 through RE-O bonds. By comparing the structural and electronic properties of RE2SiO5, we have developed a descriptor, i.e., the maximum isosurface value of the valence band maximum (VBMFmax), to predict their water vapor corrosion resistances.

2. Materials and Methods

All DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP) [9]. The projector augmented-wave (PAW) method and plane-wave basis sets are used [10,11]. The Perdew–Burke–Ernzerhof (PBE) potential is adopted to treat exchange–correlation interactions at the generalized gradient approximation (GGA) level [12]. The cut-off energy for the plane-wave basis was set to 520 eV throughout the present study. The k-point sampling of the Brillouin zone is based on the Monkhorst–Pack method [13]. A 3 × 4 × 4 k-point grid and a 2 × 5 × 3 k-point grid were used for X1-RE2SiO5 and X2-RE2SiO5, respectively. The crystal structures were completely optimized by the lattice parameters and internal atomic coordinates until the total energy difference and the forces on atoms were less than 1.0 × 10−6 eV and 0.01 eV/Å, respectively. Visualizations of all the structures were performed using VESTA [14].

3. Results and Discussion

3.1. Crystal Structure of RE2SiO5

The calculated lattice parameters of RE2SiO5 and the experimental data are compared in Table 1, and the 1% disagreement suggests that the optimized structures are reasonable. The crystal structures of X1- and X2-RE2SiO5 are shown in Figure 1a,b. The unit cell of RE2SiO5 contains 32 atoms, including two different RE sites (labeled as RE1 and RE2), one Si site and five different O sites (labeled as O1–O5). The four O positions of O1–O4 form a Si-centered tetrahedron [SiO4], while O5 atoms only loosely bond with rare-earth atoms [2]. The difference between X1-RE2SiO5 and X2-RE2SiO5 lies in the coordination number of rare-earth atoms, ranging from nine to seven and seven to six [2]. Figure 1c shows the energy difference between the X1 phase and X2 phase for the same RE2SiO5. The increasing energy difference indicates that the structural stability of the X1 phase decreases with the increasing ionic radius of RE atoms; RE elements tend to more often form X2-RE2SiO5 with an increase in the ionic radius of RE atoms [15].

Table 1

Experimental and calculated lattice parameters of X1- and X2-RE2SiO5.

	Method	a (Å)	b (Å)	c (Å)	β (°)	Volume (Å3)
La2SiO5	Expt. [16]Calc.	9.33209.3564	7.50887.7155	7.03327.0168	108.6790109.0060	466.8700478.9250
Pr2SiO5	Expt. [17]Calc.	9.25309.3420	7.30107.5586	6.93406.9548	108.1500108.7720	445.1000464.9780
Nd2SiO5	Expt. [18]Calc.	9.22959.3039	7.28487.4606	6.87446.9006	108.1990108.5470	439.0800454.1070
Sm2SiO5	Expt. [17]Calc.	9.16109.2362	7.11207.2989	6.82106.8096	107.5100108.1510	424.4000436.2150
Eu2SiO5	Expt. [17]Calc.	9.14209.1706	7.05407.2362	6.79006.7107	107.5300107.7030	417.9000424.2390
Gd2SiO5	Expt. [19]Calc.	9.12009.1758	7.06007.0566	6.73006.7732	107.5800107.2030	413.0900419.0640
Tb2SiO5	Expt.Calc.	14.366014.5834	6.69766.8319	10.363310.5585	122.2190122.1380	843.5900890.7910
Dy2SiO5	Expt. [17]Calc.	14.380014.5296	6.74006.8106	10.420010.5085	122.0000122.1140	856.5000880.7640
Ho2SiO5	Expt. [17]Calc.	14.350014.4802	6.71006.7785	10.370010.4563	122.2000122.0950	843.0000869.4740
Er2SiO5	Expt. [20]Calc.	14.366014.4344	6.69766.7503	10.363310.4101	122.2190122.1120	843.5900859.1420
Tm2SiO5	Expt. [17]Calc.	14.302014.3815	6.66206.7197	10.313010.3633	122.2100122.0910	828.5000848.4790
Lu2SiO5	Expt. [21]Calc.	14.277414.2753	6.63986.6687	10.246510.2827	122.2240121.9780	821.7400830.3420
Y2SiO5	Expt.Calc.	14.564314.5111	6.83546.8113	10.557010.5122	122.1320122.0870	889.9930880.3030
Sc2SiO5	Expt.Calc.	13.863613.7566	6.48386.4896	9.912010.0833	121.5360120.8350	759.3900772.9450

Figure 1

The crystal structure of RE2SiO5: (a) X1-RE2SiO5 and (b) X2-RE2SiO5. Si tetrahedra, RE polyhedra and O atoms are colored by blue, green and red, respectively. (c) The energy difference between the X1 phase and X2 phase for the same RE2SiO5.

When exposed to water-vapor-containing environments, RE2SiO5 will suffer from rapid recession, eventually generating Si(OH)4 and RE(OH)3 gas [3,6]. Generally, the [REOx] polyhedron is less rigid than the [SiO4] tetrahedral, and the RE-O bonds tend to show different bonding properties for different rare-earth monosilicates. As shown in Figure 2, we found that the radial distribution functions, g(r), of Si-O bonds remained unchanged, while the distribution of RE-O bonds changed remarkably in both X1- and X2-RE2SiO5. Therefore, the difference in the water vapor corrosion resistance should be closely related to the changing RE-O bonds and their electronic structures.

Figure 2

Radial distribution functions, g(r), of Si-O bonds and RE-O bonds in (a) X1-RE2SiO5 and (b) X2-RE2SiO5 compounds.

3.2. The Valence Band Maximum (VBM) of RE2SiO5

Chemical reactivity can be related to the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) characteristics in molecules, while in bulk materials it can be described by the valence band maximum (VBM) and the conduction band minimum (CBM) [22]. Previously, we [23] investigated the hydration sensitivity of triclinic tricalcium silicate by a combination of DFT calculations and molecular dynamics. We found that the long-term reaction with water molecules is controlled by the proton transport of silicate, and can be intrinsically related to the valence band maximum of the bulk solid. Similarly, for the corrosion behaviors induced by water vapor, the valance band maximum (VBM) of the bulk solid could be used as a descriptor to estimate the water-related corrosion resistance.

Figure 3 shows the partial charge density at the VBM of X1-RE2SiO5. The partial charge density at the VBM only exists at the sites of O atoms, suggesting that O atoms would experience an electrophilic attack. Interestingly, the charge densities distributions of X1-RE2SiO5 are almost unchanged for RE = La, Pr, Nd and Sm, and are mainly located around O5 atoms. However, Gd2SiO5 shows a completely different profile, where the charge densities are mainly located around O1–O4 atoms. O5 atoms bond with RE much more loosely when compared with the O1–O4 atoms bonding with Si atoms [2]. This may suggest that Gd2SiO5 is much more stable when reacting with water vapor, indicating that Gd2SiO5 has better water vapor corrosion resistance. The localization of the valence band maximum in RE2SiO5 can be related to the water vapor corrosion resistance, and the maximum isosurface value of the valence band maximum (VBMFmax) can be used to describe the electronic localization of RE2SiO5 [23]. As listed in Table 2, the VBMFmax of Gd2SiO5 is much smaller than that of other X1-RE2SiO5 (RE = La, Pr, Nd, Sm and Eu). More specifically, the VBMFmax of X1-RE2SiO5 ranks as Pr2SiO5 > La2SiO5 > Nd2SiO5 > Sm2SiO5 > Eu2SiO5 > Gd2SiO5. Such a decreasing VBMFmax value corresponds with an increasing water vapor corrosion resistance, implying that Gd2SiO5 has the best water vapor corrosion resistance among X1-RE2SiO5.

Figure 3

The valence band maximum (VBM) of X1-RE2SiO5. (a) X1-RE2SiO5 (RE = La, Pr, Nd and Sm). (b) Eu2SiO5. (c) Gd2SiO5. Si atoms (blue) and O atoms (red) are shown. RE atoms (RE = La, Pr, Nd and Sm) are presented by green, Eu is presented by fuchsia and Gd is presented by purple. The isosurface level is set at 0.005 e/Å.

Table 2

The maximum isosurface value of the valence band maximum (VBMFmax) of X1-RE2SiO5.

	La2SiO5	Pr2SiO5	Nd2SiO5	Sm2SiO5	Eu2SiO5	Gd2SiO5
VBMFmax(e/Å3)	0.098	0.099	0.097	0.094	0.060	0.053

For the X2-RE2SiO5 (RE = Tb, Dy, Ho, Er, Tm, Lu, Sc and Y) compounds, their VBMFmax is also analyzed, as shown in Figure 4. It is worth pointing out that the charge densities distributions of X2-RE2SiO5 are almost unchanged for RE = Tb, Dy, Ho, Er, Tm, Lu and Y. However, Sc2SiO5 shows a slightly different profile, where the charge densities around O atoms are a little more than those of other X2-RE2SiO5. This could imply that Sc2SiO5 is less stable when reacting with water vapor, indicating that Sc2SiO5 has worse water vapor corrosion resistance. Both Y2SiO5 and Er2SiO5 have a smaller value of the VBMFmax than that of Gd2SiO5, indicating that Gd2SiO5 has worse water vapor corrosion resistance. This is in agreement with the experimental outcomes of Wang et al. [3]. On the basis of the trend in Figure 3c, Y2SiO5 has better water vapor corrosion resistance than Sc2SiO5, which is consistent with what Klemm et al. concluded [5]. The decreasing order of RE2SiO5 (RE = Y, Er and Lu) in our results may also provide an explanation for the experimental results conducted by Nasiri et al. [4]. Additionally, we can conclude that the water vapor corrosion resistance of X2-RE2SiO5 has the following order: Tb2SiO5 > Dy2SiO5 > Y2SiO5 > Ho2SiO5 > Er2SiO5 > Tm2SiO5 > Lu2SiO5 > Sc2SiO5.

Figure 4

The valence band maximum (VBM) of X2-RE2SiO5. (a) X2-RE2SiO5 (RE = Tb, Dy, Ho, Er, Tm, Lu and Y). (b) Sc2SiO5. Si atoms (blue) and O atoms (red) are shown. RE atoms (RE = Tb, Dy, Ho, Er, Tm, Lu and Y) are presented by green and Sc is presented by light purple. The isosurface level is set at 0.001e/Å. (c) The maximum isosurface value of the valence band maximum (VBMFmax) of X2-RE2SiO5 (RE = Tb, Dy, Ho, Er, Tm, Lu, Sc and Y).

4. Conclusions

The water vapor corrosion resistance of RE2SiO5 (RE = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu, Sc and Y) was studied based on DFT calculations. A DFT-based descriptor, the maximum isosurface value of the valence band maximum (VBMFmax), was developed to predict the corrosion resistance for both X1- and X2-RE2SiO5. According to the proposed descriptor, it was found that Gd2SiO5 had the best water vapor corrosion resistance in X1-RE2SiO5 and that the water vapor corrosion resistance of X2-RE2SiO5 has the following order: Tb2SiO5 > Dy2SiO5 > Y2SiO5 > Ho2SiO5 > Er2SiO5 > Tm2SiO5 > Lu2SiO5 > Sc2SiO5.