Study on water vapor corrosion resistance of rare earth monosilicates RE2SiO5 (RE = Lu, Yb, Tm, Er, Ho, Dy, Y, and Sc) from first-principles calculations.

Corrosion resistance of rare earth monosilicates (RE2SiO5, RE = Lu, Yb, Tm, Er, Ho, Dy, Y, and Sc) in water vapor has been studied using the first-principles calculations. The results show that the water vapor corrosion resistance of RE2SiO5 demonstrates the following order: Sc2SiO5 > Dy2SiO5 > Y2SiO5 > Ho2SiO5 > Er2SiO5 > Yb2SiO5 > Tm2SiO5 > Lu2SiO5. To further improve their water vapor resistance, a doping strategy has been employed for the first time. Two scenarios have been investigated: one is a half mole proportion of substitution of various rare earth elements for Yb in the Yb2SiO5 lattice; the other is a half mole fraction substitution of rare earth elements in RE2SiO5 (RE = Lu, Yb, Er and Y) by scandium. It is unveiled that the water vapor resistance of YbScSiO5 and YScSiO5 has been greatly improved in contrast to other rare earth monosilicates. The current study provides guidelines for the selection of environmental barrier coatings with a better water vapor corrosion resistance.

Introduction

The silicon-based non-oxide ceramic materials, as hot section components of aero-engines, suffer from rapid recession at a high temperature combustion environment owing to water vapor corrosion [1, 2, 3]. As a result, environmental barrier coatings (EBCs) are usually mandatory to be applied on those substrates to prevent them from reacting with water vapor, thereby alleviating such rapid recession problems [4, 5, 6, 7]. Recently rare earth monosilicates (RE2SiO5) are proposed as one of the most promising EBC topcoat materials due to their excellent properties for EBC applications [8, 9, 10].

For an EBC topcoat, good water vapor corrosion resistance is a prerequisite. However, regarding the water vapor resistance property of different rare earth monosilicates, there are contradictions in different literature. For instance, K.N. Lee et al. [8] shows that the water vapor resistance of RE2SiO5 has the following order: Yb2SiO5 > Er2SiO5 > Y2SiO5 > Lu2SiO5. While, Ref. [11] unveils a slightly different trend, with Yb2SiO5 and Lu2SiO5 possessing best and poorest water vapor resistance but indicating that Y2SiO5 has better water vapor resistance than Er2SiO5. In addition, as these experimental results were tested in an alumina tube, it is reported that the alumina contamination can probably change water vapor corrosion resistance of RE2SiO5 [12]. However, as the working conditions of EBCs are alumina free, the above testing results cannot probably represent the genuine water vapor corrosion resistance of rare earth monosilicates in combustion environment of gas turbines that is normally free of alumina species. Therefore, these data on water vapor corrosion resistance are required to test in an atmosphere that is similar to combustion environments and free of alumina species. Unfortunately, experimentally it is difficult to conduct water vapor corrosion resistance tests without introducing alumina at such a high temperature, as there are rare water vapor inert media that is suitable to conduct such experiments.

Alternatively, these water vapor corrosion resistance data can be obtained by theoretical calculations. The first-principle calculations have been proven to be a powerful tool to predict the properties of compounds with identical crystalline structure but various elements. For instance, the water vapor corrosion resistance of RE2Si2O7 with the same crystal structure could be reflected by the strength of Si-O bonds [13]. It is worth pointing out that, a stronger Si-O bond is usually reflected by a higher Mulliken population, given Si-O bonds in an identical crystallographic environment. In addition, the water vapor resistance of 0.75BaO 0.25SrO Al2O3 2SiO2 (BSAS) with a hexagonal crystal structure had also been predicted by the strength of Si-O bonds and the calculated results were in good agreement with the experimental data [14]. These all studies suggest the feasibility of a computational method for comparing water vapor corrosion resistance of different materials with the same crystal structure.

Therefore, in the current work, in order to unveil RE2SiO5 with best water vapor corrosion resistance, the strength of Si-O bonds (or Mulliken population) in RE2SiO5 is calculated by first-principles. Apparently, RE2SiO5 have the identical crystalline structure, and thus the Si-O bond strength can be a reflection of their water vapor corrosion resistance. Further, motivated by a possible improvement of water vapor corrosion resistance by doping strategy, we employ different rare earth elements (Lu, Er, Y and Sc) to substitute a half proportion of Yb in Yb2SiO5. In addition, as YbScSiO5 exhibits a larger value of Mulliken population, i.e. better water vapor corrosion resistance, the Sc element is then used to substitute 50% of rare earth elements in A2SiO5 (A = Lu, Er and Y). Finally, we rank all RE2SiO5 currently investigated on water vapor corrosion resistance, which might provide some beneficial guidelines for the selection of EBC topcoats with a better water vapor corrosion resistance.

Methods

The first principles calculations were carried out by using CASTEP code [15]. The plane wave basis was employed under periodic boundary conditions. The kinetic energy cutoff was set to 450 eV for expanding Bloch waves in the reciprocal space. For the energy integrations, a discretized 2 × 3 × 4 k sampling grid was applied in the first irreducible Brillouin zone based on Monkhorst-Pack method [16]. For the exchange correlation energy, polarized local density approximation (LDA) was used [17]. The crystal structures were fully optimized by independently modifying lattice parameters and internal atomic coordinates. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimization scheme [18] was employed to minimize the total energy and interatomic forces. For the pseudo-atoms, the ultra-soft type pseudopotentials were applied for RE, Si, and O atoms to account the electrostatic interactions between valence electrons and the ionic core. The criteria for convergence in geometry optimization were selected as follows: the difference in total energy within 1 × 10−6 eV/atom, the ionic Hellmann–Feynman forces within 0.002 eV/Å, the maximum stress within 0.01 GPa and the maximum ionic displacement within 1 × 10−4 Å. After geometric optimization, the Mulliken bond populations were analyzed. The distance cut-off for bond populations was 3.0 Å.

Result and discussion

Table 1 illustrates experimental and calculated lattice parameters of the optimized RE2SiO5 (RE = Lu, Yb, Tm, Er, Ho, Dy, Y, and Sc). The calculated lattice parameters deviate from the experimental data by around 1.05% for a, 1.43% for b, and 1.34% for c, respectively, suggesting that the current optimized structures are reasonable. The crystal structures of RE2SiO5 are shown in Fig. 1. The unit cell of RE2SiO5 contains 32 atoms, which occupy 8 different crystallographic sites including two different RE3+ sites (labeled as RE1 and RE2), one Si site and five O sites (labeled as O1–O5). Four oxygen (O1–O4) atoms form a Si-centered distorted tetrahedron SiO4, whilst O5, without any Si atom as its nearest neighbor, is loosely bonded to four rare earth cations, forming a distorted polyhedron REO6 and REO7. Hence, the RE2SiO5 consists of SiO4 tetrahedra, REO6 and REO7 polyhedra [19]. When exposed to water vapor environment at high temperature, SiO4 is subjected to water vapor attacking. As for the Si-O bond in the same environment, the higher Mulliken population represents stronger Si-O bond. Given a compound possessing a higher Mulliken population of Si-O bonds, it tends to give a better water vapor corrosion resistance, owing to the fact that those SiO4 polyhedra with a higher Mulliken population of Si-O bonds are more difficult to be completely corroded. According to Fig. 4 or Table 2, Sc2SiO5 has the highest value of Mulliken population than other rare earth monosilicates, indicating that Sc2SiO5 possesses the best water vapor corrosion resistance. Moreover, the water vapor resistance of RE2SiO5 has the following order: Sc2SiO5 > Dy2SiO5 > Y2SiO5 > Ho2SiO5 > Er2SiO5 > Yb2SiO5 > Tm2SiO5 > Lu2SiO5. Except for Lu2SiO5, other rare earth monosilicates have rather close Mulliken population, suggesting that they have close water vapor resistance. Lu2SiO5 exhibits the lowest value of Mulliken population, even much lower than the average value of Mulliken population, suggesting that the water vapor corrosion resistance of Lu2SiO5 is much weaker than that of other rare earth monosilicates. As the Lu2SiO5 has a smaller ionic radius than silicon-based non-oxide ceramic materials, the Lu-O bond will be shorter. On the other hand, the volume of Lu2SiO5 is the same as other rare earth monosilicates (as shown in Table 1). Thus, the Si-O bond needs to become longer to remain the volume and consequently mulliken population of Si-O bond in Lu2SiO5 becomes the lowest.

Table 1

Experimental and calculated lattice parameters of RE2SiO5, YbBSiO5 (B = Lu, Er, Y, Sc) and AScSiO5 (A = Lu, Er, Y).

	Method	a (Å)	b (Å)	c (Å)	β (°)	V (Å3)
Lu2SiO5	Expt. [19]	14.254 (9)	10.241 (8)	6.641 (7)	122.20 (8)	819.3 (10)
	Calc.	14.3509	10.2609	6.6322	122.511	823.566
Yb2SiO5	Expt. [19]	14.28 (1)	10.28 (1)	6.653 (5)	122.2 (1)	824.0 (7)
	Calc.	14.1935	10.0753	6.5739	122.134	796.028
Tm2SiO5	Expt. [19]	14.302 (9)	10.313 (9)	6.662 (6)	122.21 (9)	828.5 (9)
	Calc.	14.1607	10.1037	6.5541	122.113	806.709
Er2SiO5	Expt. [19]	14.32 (2)	10.35 (2)	6.69 (1)	122.3 (3)	836.7 (41)
	Calc.	14.1717	10.1761	6.5822	122.189	803.295
Ho2SiO5	Expt. [19]	14.35 (2)	10.37 (2)	6.71 (1)	122.2 (3)	843.0 (38)
	Calc.	14.1961	10.14563	6.5792	122.101	802.632
Dy2SiO5	Expt. [19]	14.382 (2)	10.42 (2)	6.74 (1)	122.0 (3)	856.5 (72)
	Calc.	14.2331	10.1645	6.5833	122.113	806.709
Y2SiO5	Expt. [20]	14.371 (3)	10.388 (3)	6.710 (4)	122.17 (4)	848 (1)
	Calc.	14.2556	10.2188	6.5854	122.309	810.801
Sc2SiO5	Expt. [21]	13.679 (1)	9.967 (1)	6.4257 (6)	121.12 (1)	750.0
	Calc.	13.6452	9.6243	6.3202	121.848	705.042
YbLuSiO5	Calc.	14.2672	10.1342	6.6640	122.142	815.844
YbErSiO5	Calc.	14.3747	10.2637	6.6607	122.143	832.071
YbYSiO5	Calc.	14.1806	10.1410	6.6063	122.143	832.071
YbScSiO5	Calc.	13.6904	10.2753	6.6009	120.635	798.964
LuScSiO5	Calc.	13.6993	10.1693	6.5320	120.729	782.221
ErScSiO5	Calc.	13.9797	10.0158	6.6000	121.812	785.308
YScSiO5	Calc.	13.6695	10.3210	6.6145	120.510	803.976

Fig. 1

The crystal structures of RE2SiO5 and SiO4 polyhedron.

Fig. 4

Mulliken bond populations of Si–O bonds in RE2SiO5, YbBSiO5 (B = Lu, Er, Y and Sc) and AScSiO5 (A = Lu, Er and Y).

Table 2

Mulliken bond populations, bond length and density of Mulliken Population (Mulliken bond populations/bond-length) of Si–O bonds in RE2SiO5, YbBSiO5 (B = Lu, Er, Y, Sc) and AScSiO5 (A = Lu, Er, Y).

	Si–O bond population	Si–O bond length (Å)	Density of Si–O bond Population (/Å)
Lu2SiO5	0.5233	1.6246	0.3221
Yb2SiO5	0.5609	1.6237	0.3454
Tm2SiO5	0.562	1.6233	0.3462
Er2SiO5	0.564	1.6216	0.3478
Ho2SiO5	0.5633	1.6219	0.3473
Dy2SiO5	0.5664	1.6216	0.3493
Y2SiO5	0.5652	1.6216	0.3485
Sc2SiO5	0.5696	1.6187	0.3519
YbLuSiO5	0.5413	1.6211	0.3339
YbErSiO5	0.5206	1.6311	0.3192
YbYSiO5	0.5522	1.6295	0.3389
YbScSiO5	0.5719	1.6172	0.3536
LuScSiO5	0.5626	1.6185	0.3476
ErScSiO5	0.5487	1.6279	0.3371
YScSiO5	0.5801	1.6177	0.3586

As our primary concern is the bonding strength of Si-O bonds in RE2SiO5, which directly relates to the water vapor corrosion resistance of a rare earth monosilicate, it appears that there exists another strategy to tailor the Si-O bonding length (or strength) in a fixed RE2SiO5. As already mentioned, the RE2SiO5 consists of SiO4 tetrahedra, REO6 and REO7 polyhedra. Due to the chemical property similarity of the lanthanide elements, it is easy to introduce a second lanthanide element in the RE2SiO5 lattice. The introduction of a second rare earth element, i.e. doping, can potentially alter the size of REO6 and REO7 polyhedra, which can result in an opposite change of SiO4 tetrahedra, thereby causing the corresponding Si-O bond length (or bond strength) change. In the current study, Yb2SiO5 is selected as the ‘matrix’ compound and a half proportion of Yb in Yb2SiO5 is substituted by a second rare earth element, such as Lu, Er, Y and Sc. Fig. 2 shows the optimized structure of YbBSiO5 (B = Lu, Er, Y and Sc). As discussed, RE3+ has two crystallographic sites, RE1 and RE2, in the RE2SiO5 lattice. It is found that Yb in the RE2 sites has been replaced by a second rare earth element B (B = Lu, Er, Y and Sc). The results suggest that the substitution of Sc for Yb in Yb2SiO5 can dramatically improve the water vapor corrosion resistance and the Mulliken population value of YbScSiO5 exceeds the highest value of all undoped rare earth monosilicates. However, the substitution of the other three rare earth elements, i.e. Lu, Er and Y, for Yb in Yb2SiO5 reduces the water vapor resistance.

Fig. 2

The optimized crystal structures of RE2SiO5, YbBSiO5 (B = Lu, Er, Y and Sc) and AScSiO5 (A = Lu, Er and Y).

Further, regarding the dramatic improvement of the Mulliken population by the substitution of Sc for Yb in Yb2SiO5, a half mole fraction substitution of Sc for various ‘matrix’ rare earth monosilicate compounds, A2SiO5 (A = Lu, Er and Y), has been investigated. As shown in Fig. 2, the RE2 sites in A2SiO5 (A = Lu, Er and Y) are occupied by Sc. As illustrated in Fig. 3, the values of Mulliken population of RScSiO5 (R = Lu, Yb and Y) have been improved by at least 10%. In particular, the Mulliken population of YScSiO5 has been dramatically improved, which perhaps has the best water vapor resistance in all rare earth silicates currently investigated.

Fig. 3

Bond length of Si–O bonds in RE2SiO5, YbBSiO5 (B = Lu, Er, Y and Sc) and AScSiO5 (A = Lu, Er and Y).

The half mole fraction substitution of Sc for R in R2SiO5 (R = Lu, Yb and Y) improves water vapor resistance, whereas the half mole fraction substitution of Sc for Er in Er2SiO5 reduces water vapor resistance. This can be accounted for in the context of the crystal lattice energy. Due to a smaller radius of Sc3+, when a half proportion of rare earth elements in R2SiO5 (R = Lu, Yb and Y) are substituted by Sc, the doped rare earth monosilicate crystals will contract in order to reduce the system energy. As a result, Si-O bonds in RScSiO5 (R = Lu, Yb and Y) will become shorter than R2SiO5 (R = Lu, Yb and Y) as shown in Fig. 3, leading to an increase of Mulliken population. According to Table 1, the volume of ErScSiO5 crystal structure is smaller than that of Er2SiO5. However, as the volume contraction of ErScSiO5 can probably be realized by shortening Er-O or Sc-O bonds, the Si-O bonds can even become longer so as to reduce the system energy of ErScSiO5. Thus, as shown in Figs. 3 and 4, Si-O bonds in ErScSiO5 become longer than these in Er2SiO5 and Mulliken population of Si-O bonds in ErScSiO5 correspondingly decreased, suggesting that water vapor resistance of ErScSiO5 decreases. In brief, when the substitution of Sc for Er in ErScSiO5 occurred, water vapor resistance of ErScSiO5 became weaker to reduce crystal lattice energy. By contrast, water vapor resistance of RScSiO5 (R = Lu, Yb and Y) became stronger to reduce crystal lattice energy.

Density of Mulliken bond populations of Si–O bonds has also been performed to compare water vapor resistance of rare earth monosilicates. Density of Mulliken bond populations represents Mulliken bond population/bond-length. The calculated data are displayed in Table 2 and Fig. 5. Obviously, the trend of water vapor resistance is essentially the same as results from Mulliken bond populations in Fig. 4. However, there are two differences in water vapor resistance. The new order is: Sc2SiO5 > Dy2SiO5 > Y2SiO5 > Er2SiO5 > Ho2SiO5 > Tm2SiO5 > Yb2SiO5 > Lu2SiO5. In the previous order, water vapor resistance of Er2SiO5 and Ho2SiO5 is similar and Er2SiO5 is closely following Ho2SiO5. Whereas, the current results reveal that water vapor resistance of Er2SiO5 and Ho2SiO5 is still similar but Ho2SiO5 is closely following Er2SiO5. Likewise, water vapor resistance of Tm2SiO5 and Yb2SiO5 has changed and Yb2SiO5 is currently following closely Tm2SiO5 according to density of Mulliken bond populations of Si–O bonds in RE2SiO5. The trend of water vapor resistance of other rare earth silicates is in good agreement with that from Mulliken bond populations.

Fig. 5

Density of Mulliken bond populations of Si–O bonds in RE2SiO5, YbBSiO5 (B = Lu, Er, Y, Sc) and AScSiO5 (A = Lu, Er, Y).

Conclusion

The water vapor resistance of RE2SiO5 (RE = Lu, Yb, Tm, Er, Ho, Dy, Y, and Sc) has been studied using first-principles calculations. By comparing the Mulliken population of Si–O bonds, it is found that the currently investigated rare earth monosilicates except Lu2SiO5 have similar water vapor corrosion resistance. Lu2SiO5 shows much lower water vapor resistance. In addition, a doping strategy of RE2SiO5 by a second rare earth element on the RE site has been employed for the first time to seek a compound with better water vapor corrosion resistance. Two series of calculations have been carried out: the first is using different rare earth element dopants, i.e. Lu, Er, Y and Sc, to substitute a half mole proportion of Yb in the Yb2SiO5 lattice; the second is using Sc as a dopant to substitute a half mole proportion of rare earth elements in different rare earth monosilicates, i.e. Lu2SiO5, Er2SiO5 and Y2SiO5. The results show that the Sc substitution of Yb2SiO5 can greatly improve its water vapor resistance, whereas the substitution of Lu, Er and Y for Yb in Yb2SiO5 is not beneficial to the water vapor resistance. Further, the Sc substitution for Y in Y2SiO5 can noticeably improve its water vapor corrosion resistance. Indeed, the solid solution of ScYSiO5 exhibits the best water vapor resistance of all rare earth monosilicates currently investigated. The current study ranks water vapor resistance of common rare earth monosilicates and suggests the doping on the RE site could possibly further improve its water vapor resistance, which provides guidelines for the selection of environmental barrier coating topcoat materials with water vapor corrosion resistance.

Declarations

Author contribution statement

Jing Han: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Yanfei Wang: Conceived and designed the experiments; Wrote the paper.

Rongjun Liu: Conceived and designed the experiments.

Di Jiang: Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.

Funding statement

This work was supported by the National Science Foundation of China under the contract 51502342, Research Funding of National University of Defense Technology under the contract ZK17-03-57 and Hunan Provincial Natural Science Foundation of China under the contract 2018JJ1029.

Competing interest statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.