Synthesis, mechanical and thermal properties of a

Available online at www.sciencedirect.com

ScienceDirect Journal of the European Ceramic Society 35 (2015) 3641–3650

Synthesis, mechanical and thermal properties of a damage tolerant ceramic: ␤-Lu2Si2O7 Zhilin Tian a,b , Liya Zheng a , Jingyang Wang a,∗ a

High-performance Ceramics Division, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 110016 Shenyang, China b University of Chinese Academy of Sciences, Beijing 100049, China Received 15 January 2015; received in revised form 28 April 2015; accepted 3 May 2015 Available online 21 May 2015

Abstract ␤-Lu2 Si2 O7 is a promising candidate in the third generation of environmental barrier coating (EBC) materials for silicon-based ceramics due to its excellent high temperature environmental durability. However, the high temperature thermal and mechanical properties of ␤-Lu2 Si2 O7 are seldom reported, which hinders the design and evaluation of its EBC applications. In this paper, pure and dense ␤-Lu2 Si2 O7 sample was successfully fabricated and its mechanical properties, including Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, flexural strength, fracture toughness and hardness were investigated. The ball indentation test reveals that the main deformation mechanisms of ␤-Lu2 Si2 O7 at room temperature are deformation twinning and dislocation glide, which indicate that ␤-Lu2 Si2 O7 is a damage tolerant ceramic. In addition, the thermal expansion coefficient and thermal shock resistance were measured at high temperatures. ␤-Lu2 Si2 O7 possesses excellent high temperature elastic stiffness up to 1470 ◦ C, and the critical temperature difference for thermal shock resistance is 270 K. © 2015 Elsevier Ltd. All rights reserved. Keywords: Rare-earth silicate; Processing; Mechanical property; Thermal property; EBC

1. Introduction Silicon-based ceramics such as SiC, Si3 N4 and SiC-matrix composites are promising structural materials for high temperature applications due to their good mechanical properties and excellent oxidation resistance in dry air. However, when exposed to combustion environments containing water vapor, siliconbased ceramics are oxidized and corroded due to volatilization of gaseous silicon hydroxide [1]. To solve this problem, an EBC is needed to protect the host material. Recent works suggested that ␤-Lu2 Si2 O7 EBC could survive at 1300 ◦ C for 500 h in a high velocity steam jet environment. Meanwhile, the silicon nitride substrate was well protected from corrosion and oxidation [2]. However, cracks frequently appear in ␤-Lu2 Si2 O7 coating during thermal cycles, which leads to the failure of the protection. Prediction or evaluation of the thermal stress level requires the

∗

Corresponding author. Tel.: +86 024 23971762. E-mail address: [email protected] (J. Wang).

http://dx.doi.org/10.1016/j.jeurceramsoc.2015.05.007 0955-2219/© 2015 Elsevier Ltd. All rights reserved.

knowledge of the mismatch of thermal and mechanical properties between certain substrates and the ␤-Lu2 Si2 O7 coating. Therefore, to get a better understanding of its performance and make optimization for EBC applications, it is necessary to obtain the relevant properties of ␤-Lu2 Si2 O7 from room to high temperature. ␤-Lu2 Si2 O7 is also recognized as an important intergranular phase at the grain boundary of Si3 N4 when Lu2 O3 is used as a sintering aid. It also has a great effect on the mechanical properties of Si3 N4 . Several studies have demonstrated that the high temperature strength and oxidation resistance of Si3 N4 are correlated with the radius of the rare earth (RE) cation in the oxide additives, for example as the smaller the RE cation is, the better the properties of the silicon nitride is [3,4]. Choi and Lee [4] showed that Y2 O3 , Lu2 O3 and Sc2 O3 , among all lanthanide oxides, imparted the highest flexural strength value to Si3 N4 . However, the thermal and mechanical properties of ␤-Lu2 Si2 O7 are rarely reported so far, which is of critical importance for understanding how to improve the mechanical properties of Si3 N4 and enhance the reliability of EBCs.

3642

Z. Tian et al. / Journal of the European Ceramic Society 35 (2015) 3641–3650

Previous studies have reported the luminescent properties [5] and water vapor corrosion of ␤-Lu2 Si2 O7 [6]. Besides these primitive experimental data, many thermal and mechanical properties, especially those at elevated temperature, are still lacking. In this paper, pure and dense ␤-Lu2 Si2 O7 was fabricated by a two-step method, and its mechanical and thermal properties were comprehensively investigated from room to high temperature. Meanwhile, the equilibrium lattice configurations and elastic constants were calculated by DFT calculations, and both 3D directional dependent and temperature dependent Young’s modulus were characterized in some detail. In addition, thermal expansion coefficient was measured up to 1473 K, and the critical temperature difference for thermal shock resistance of ␤-Lu2 Si2 O7 was also investigated further. The investigation on the bulk ␤-Lu2 Si2 O7 samples provides some critical intrinsic thermal and mechanical properties which cannot be obtained from studying the ␤-Lu2 Si2 O7 coating material. The obtained basic thermal and mechanical properties satisfy the requirements of materials used for silicon-based ceramic coatings. Furthermore, they can provide some instructions on the design and optimization of ␤-Lu2 Si2 O7 as an EBC for silicon-based ceramics.

2. Theoretical calculation methods and experimental procedure

According to the Voigt approximation, the bulk and shear modulus are expressed as BV =

1 2 (c11 + c22 + c33 ) + (c12 + c13 + c23 ) 9 9

GV =

1 (c11 + c22 + c33 − c12 − c13 − c23 ) 15 1 + (c44 + c55 + c66 ) 5

(2)

According to the Reuss approximation, the bulk and shear modulus are expressed as BR = GR =

1 (s11 + s22 + s33 ) + 2 (s12 + s13 + s23 )

1 4 (s11 + s22 + s33 ) − 4 (s12 + s13 + s23 ) + 3 (s44 + s55 + s66 )

(3) (4)

The Voigt and Reuss approximations represent the upper and lower limits of the true polycrystalline modulus. Hill proposed the arithmetic mean values of the Voigt’s and Reuss’s modulus by BH =

1 (BR + BV ) 2

(5)

GH =

1 (GR + GV ) 2

(6)

2.1. Theoretical calculation method Theoretical investigations were accomplished using the CASTEP [7] code, in which the plane-wave pseudopotential total energy calculation was employed. The plane-wave energy cutoff and the Brillouin zone sampling were fixed at 450 eV and 3 × 3 × 3 special k-point meshes, respectively. Interactions of electrons with ion cores were represented by the Vanderbilt-type ultrasoft pseudopotential for Lu, Si and O atoms [8]. The electronic exchange-correlation energy was treated according to the localized density approximation (LDA) [9]. The crystal structures were fully optimized by independently modifying lattice parameters and internal atomic coordinates. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimization scheme [10] was used to minimize the total energy and interatomic forces. The elastic constants were determined from linear fits of the stresses as functions of applied homogeneous elastic strains [11]. We applied a set of given homogeneous deformations with finite values and calculated the generated stresses after optimizing the internal degrees of freedom. The criteria for convergences in geometry optimization were selected as: the difference in total energy within 1 × 10−6 eV/atom, the ionic Hellmann–Feynman forces within 0.002 eV/Å and the ˚ maximum ionic displacement within 1 × 10−4 A. ␤-Lu2 Si2 O7 crystallizes in the C2/m space group and has 13 independent elastic constants. For each strain pattern, six amplitudes ε, three positive and three negative, were applied with |ε| within 0.5%. The polycrystalline bulk modulus B, shear modulus G, and Young’s modulus E were determined according to the Voigt, Reuss, and Hill approximations [12–14].

(1)

The Young’s modulus E can be calculated using the Hill’s shear and bulk modulus: E=

9GH BH 3BH + GH

(7)

Thus, υl and υs are longitudinal and shear sound velocities, respectively, which can be deduced from the shear modulus GH and bulk modulus BH by BH + 4GH /3 υl = (8) ρ GH 1/2 (9) υs = ρ The average sound velocity υm is calculated by 1/3 3(υs υl )3 υm = 2υl 3 + υs 3

(10)

Using the average sound velocity υm , Debye temperature Θ is obtained by [15]: h 3n NA ρ 1/3 (11) υm Θ= kB 4π M where h is Planck constant, kB is Boltzmann’s constant, n is the number of atoms in the primitive cell, NA is Avogadro’s number, ρ is the density, and M is the molecular weight. Based on the elastic constants, the directional dependence of Young’s modulus (for monoclinic crystals) in 3D representation


can be given by [16]: 1 = l14 s11 + 2l12 l22 s12 + 2l12 l32 s13 + 2l13 l3 s15 + l24 s22 E + 2l22 l32 s23 + 2l1 l22 l3 s25 + l34 s33 + 2l1 l33 s35 + l22 l32 s44 + 2l1 l22 l3 s46 + l12 l32 s55 + l12 l22 s66

(12)

where sij are the elastic compliance constants that can be obtained through an inversion of the elastic constants matrix (sij = cij −1 ). l1 , l2 and l3 are the directional cosines to the x-, yand z-axes, respectively. 2.2. Sample preparation Bulk ␤-Lu2 Si2 O7 sample was prepared by two steps. First, pure Lu2 SiO5 powder was synthesized by commercially available powders of Lu2 O3 (Rear-Chem. Hi-Tech. Co. Ltd., Huizhou, China) and SiO2 (Sinopharm Chemical Reagent Co. Ltd., Shanghai, China) with a mole ratio of Lu2 O3 to SiO2 of 1:1. The powders were mixed by wet ball milling for 24 h in a Si3 N4 jar, using Si3 N4 balls and ethanol as media. The obtained slip was dried at 60 ◦ C for 24 h, and then passed through a 120 mesh sieve to get the desired powders. Pressureless sintering was used to synthesize pure Lu2 SiO5 powder at 1550 ◦ C for 1 h. Dense ␤-Lu2 Si2 O7 ceramic was fabricated by mixing pure Lu2 SiO5 powder and SiO2 powder with a mole ratio of Lu2 SiO5 to SiO2 of 1:1. After ball milling for 24 h and drying, the powders were placed in a BN-coated graphite mold with a diameter of 50 mm. The hot pressing was done in a furnace using graphite as heating element at 1850 ◦ C with a heating rate of 10 ◦ C/min for 1 h under the pressure of 30 MPa in a flowing argon atmosphere. The density of as-synthesized samples was determined by the Archimedes method. The phase compositions of the samples were identified using an X-ray diffractometer (XRD) with CuKα radiation (D/max-2400, Rigaku, Tokyo, Japan). Microstructures were observed with SUPRA 35 SEM (LEO, Oberkochen, Germany). 2.3. Measurements of mechanical properties The dynamic Young’s modulus and internal friction were evaluated by the impulse excitation technique using samples with the dimension of 3 mm × 15 mm × 40 mm. The samples were measured in a graphite furnace HTVP 1750 ◦ C (IMCE, Diepenbeek, Belgium) at a heating rate of 4 ◦ C/min in an Ar atmosphere. The vibration signal captured by a laser vibrometer was analyzed with the resonance frequency and damping analyzer. The Young’s modulus was calculated from the flexural resonant frequency, ff , according to ASTME 1876-97: L3 mff 2 T1 (13) E = 0.9465 w t3 where E is the dynamic elastic modulus in Pa, m is the mass of the specimen in kg, ff is the fundamental flexural resonant frequency in Hz; and w, L and t are the width, length and thickness of the specimen, respectively, in meters. T1 is a correction factor,

3643

depending on the Poisson’s ratio v and the thickness/length ratio t/L. The internal friction Q−1 corresponding to the flexural vibration mode was calculated by Q−1 = k/πff , where k is the exponential decay parameter of the amplitude of the flexural vibration component. The bulk modulus of ␤-Lu2 Si2 O7 was evaluated from the relationship between Young’s modulus E and shear modulus G, B=

GE 3(3G − E)

(14)

Bending strength was measured with the dimension of 3 mm × 4 mm × 36 mm and the tests were performed in a universal testing machine (CMT4204, SANS, Shenzhen, China). A three-point bending method with a crosshead speed of 0.5 mm/min was used. Three samples were measured and the testing surface of the sample was polished with a diamond paste of 1.5 ␮m to minimize the machining flaws before the bending test. Fracture toughness was measured using a single-edge notched beam (SENB) method. The notches were introduced by diamond coated wheel slotting. The inner and outer spans of the four-point bending test were 10 mm and 30 mm, respectively, and the crosshead speed was 0.05 mm/min. Three samples were used in fracture toughness measurements. The Vickers microhardness was measured at loads of 5, 10, 30 and 50 N with a dwell time of 15 s. To explore the mechanism of damage tolerance of ␤-Lu2 Si2 O7 , the Hertzian contact test was performed at room temperature. Bulk ␤-Lu2 Si2 O7 samples with dimensions of about 3 mm × 4 mm × 4 mm were indented by a spherical Si3 N4 indenter with a diameter of 8 mm with a crosshead speed of 0.05 mm/min at room temperature. TEM samples were prepared from regions surrounding indentations by polishing back to the indented surface and ion-milling at 4.0 kV. The samples were observed using a 200 kV Tecnai G2 F20 TEM (FEI, Eindhoven, The Netherlands). 2.4. Measurements of thermal properties The average linear thermal expansion coefficient was obtained from the temperature dependent changes of the length of the specimen from room temperature to 1473 K in air by using a vertical high temperature optical dilatometer (ODHT, Modena, Italy). The dimension of the sample was 3 mm × 4 mm × 14 mm. Thermal shock resistance tests were performed by holding rectangular specimens of dimensions 3 mm × 4 mm × 36 mm in a chamber furnace maintained at the desired temperatures for 10 min allowing for temperature equilibration, followed by quenching in a water container at a temperature of 298 K. The samples were then dried before subjecting them to residual strength tests. The strengths of the quenched samples were measured by a three-point bending method on a universal mechanical testing machine and three samples were used for each quenching temperature. The crosshead speed was 0.5 mm/min. The critical temperature difference (Tc ) that was used as a quantitative index of thermal shock resistance was determined from the plot of residual strength vs. test temperature, being the temperature at which a 30% average residual strength drop occurred. To

3644


Table 1 Calculated and experimental lattice parameters of ␤-Lu2 Si2 O7 . Lattice constants

Expt.

Calc.

a (Å) b (Å) c (Å) β (o ) ρ (g/cm3 )

6.762 8.835 4.711 101.99 6.25

6.772 8.888 4.710 101.57 6.20

highlight the cracks in the sample after thermal shock, the sample was soaked in blue ink for 24 h and then used for observation. 3. Results and discussion 3.1. Theoretical elastic stiffness To investigate basic properties, the equilibrium crystal structure of ␤-Lu2 Si2 O7 was first computed. Table 1 compares the optimized lattice parameters with experimental data [17]. The calculated lattice parameters deviate from the experimental data by less than 0.5%, demonstrating the high reliability of present DFT calculations. The crystal structure of ␤-Lu2 Si2 O7 showed in Fig. 1(a) can be described as a close hexagonal packing of the oxygens with Lu3+ cations in octahedral holes and Si in tetrahedral holes in alternating parallel layers (0 0 1). The Si2 O7 group shows a Si O Si bond angle of 180◦ , and the SiO4 tetrahedron shows a very low degree of distortion compared to other disilicate configurations. There are three types of oxygen: the first one (O1) is bridging oxygen between the two silicon ions of the Si2 O7 group to which lutetium atoms are not bonded. The other two oxygen ions (O2 and O3) are terminal oxygen of the Si2 O7 group and they are involved in bonding with lutetium atoms [18]. Wang et al. [19] investigated the low shear resistance of ␥-Y2 Si2 O7 and found that it originated from the inhomogeneous strength of its chemical bonds. The Y O bond is weaker and readily stretches and shrinks; and Si O bond is stronger

and more rigid. The relatively softer YO6 octahedron positively accommodates shear deformation by structural distortion, while the Si2 O7 pyrosilicate unit is more resistant to deformation. Moreover, Zhou et al. [20] calculated the Mulliken population of ␤-Yb2 Si2 O7 which also indicated strong Si O bonds and weak Yb-O bonds. Similarly to ␥-Y2 Si2 O7 and ␤-Yb2 Si2 O7 , ␤-Lu2 Si2 O7 consists of REO6 octahedrons and Si2 O7 pyrosilicate units. Therefore, in ␤-Lu2 Si2 O7 , the Lu O bond should be weaker than the Si O bond. The inhomogeneous strength of chemical bonds may endow ␤-Lu2 Si2 O7 with novel damage tolerance as well. It is well established that anisotropic chemical bonding is reflected by the anisotropy of Young’s modulus [20]. To reveal the anisotropy of chemical bonding and the resulting anisotropic elastic stiffness, elastic constants are listed in Table 2 together with those of ␤-Yb2 Si2 O7 20 and ␥-Y2 Si2 O7 19 for comparison. The elastic stiffness of a solid determines its response to applied elastic strain and provides information about bonding characteristics. The elastic constants representing stiffness against uniaxial strains, c11 , c22 , and c33 of ␤-Lu2 Si2 O7 , ␤-Yb2 Si2 O7 and ␥-Y2 Si2 O7 are high, whereas those which correspond to shear deformation, c44 , c55 , c66 , are relatively low. The elastic constant c11 is larger than c22 and c33 for ␤-Lu2 Si2 O7 , which originates from the stronger chemical bond in the [1 0 0] direction than those in [0 1 0] and [0 0 1] directions [21]. The crystallographic information of ␤-Lu2 Si2 O7 shows that the strong Si O Si bridges mainly align along the [1 0 0] direction. The elastic constants for ␤-Yb2 Si2 O7 show the same trend due to their similar crystal structures. But for ␥-Y2 Si2 O7 , c22 is much larger than c33 and c11 . Also, the crystal structure of ␥-Y2 Si2 O7 (Fig. 1(b)) shows that the strong Si O Si bridges are predominantly along the [0 1 0] direction. Directional representation of the elastic modulus is an effective method of describing the details of elastic anisotropy. It visually demonstrates the variation feature of elastic modulus along different crystallographic directions. Derived from the elastic constants matrix and Eq. (12), the directional Young’s

Fig. 1. Crystal structures of (a) ␤-Lu2 Si2 O7 and (b) ␥-Y2 Si2 O7 . The arrows show how the ␤ phase might transform to ␥ phase.


3645

Table 2 Elastic constants cij (in GPa) of ␤-Lu2 Si2 O7 , ␤-Yb2 Si2 O7 and ␥-Y2 Si2 O7 . Compounds

c11

c22

c33

c44

c55

c66

c12

c13

c15

c23

c25

c35

c46

␤-Lu2 Si2 O7 ␤-Yb2 Si2 O7 20 ␥-Y2 Si2 O7 19

298 256 196

215 209 287

210 188 214

77 73 73

107 103 107

74 67 85

119 104 123

135 116 118

−24 −10 6

118 108 104

42 43 −19

−9 −2 29

28 24 −34

modulus was calculated and the results are presented in Fig. 2(a). In the 3D profile, an isotropic material would exhibit a spherical shape of elastic modulus, and the deviation from that spherical shape indicates the anisotropic character. The obtained directional dependence of Young’s modulus of ␤-Lu2 Si2 O7 obviously deviates from sphericity which indicates an obvious anisotropic elasticity. Fig. 2(b–d) show the planar projections of Young’s modulus of ␤-Lu2 Si2 O7 on (1 0 0), (0 1 0) and (0 0 1) atomic planes, which provide more details about the directional dependences of Young’s modulus. As Fig. 2(b) shows, the Young’s modulus on the (1 0 0) atomic plane shows weaker anisotropy than those on other planes. The anisotropic elastic stiffness of ␤Lu2 Si2 O7 is mainly attributed to the heterogeneity of chemical bonds [20]. 3.2. Preparation of pure and dense sample Anisotropic elastic stiffness is predicted in the above section. To verify the theoretical results, bulk ␤-Lu2 Si2 O7 samples

were prepared by a two-step method. The main reasons are: first, the Lu2 O3 and SiO2 powders react very slowly and, therefore, it is difficult to achieve stoichiometric phase equilibrium especially when the material is prepared by a solid reaction method. This issue has been encountered during the preparation of other rare earth disilicates. For instance, Monteverde et al. reported that 13 mol% excess silica was needed for the preparation of RE2 Si2 O7 (RE = rare earth) single phases [22]. Similarly, a sintering aid (LiYO2 ) was needed in the synthesis of ␥-Y2 Si2 O7 to enhance the mass transfer [23]. Second, the phase region for ␤Lu2 Si2 O7 is quite narrow in Lu2 O3 -SiO2 system, which means that stoichiometry should be strictly satisfied in order to synthesize single phase ␤-Lu2 Si2 O7 . However, it is difficult to precisely control the stoichiometry in the experiment, and the competitive reactions of forming Lu2 SiO5 and ␤-Lu2 Si2 O7 compounds occur simultaneously. Therefore, in this work, pure Lu2 SiO5 and SiO2 powders were used as starting materials, which can avoid the competitive reaction of forming the Lu2 SiO5 impurity phase. The XRD pattern (Fig. 3) and SEM image (Fig. 4) demonstrate

Fig. 2. Directional Young’s modulus of ␤-Lu2 Si2 O7 : (a) in 3-D scenario; (b) on (1 0 0); (c) on (0 1 0); and (d) on (0 0 1) atomic planes.

3646

Z. Tian et al. / Journal of the European Ceramic Society 35 (2015) 3641–3650 Table 3 Comparisons of experimental room temperature mechanical properties of ␤Lu2 Si2 O7 , ␤-Yb2 Si2 O7 and ␥-Y2 Si2 O7 .

Fig. 3. X-ray diffraction pattern of hot pressed ␤-Lu2 Si2 O7 .

that the two-step method is an effective way to prepare single phase ␤-Lu2 Si2 O7 samples. Fig. 3 shows the XRD pattern of the as-prepared ␤-Lu2 Si2 O7 sample, and it is seen that it is nearly phase pure (compared with JCPDS card No. 35-0326) without detectable impurity phases. Fig. 4 shows the morphology of ␤Lu2 Si2 O7 sample after thermal etching at 1300 ◦ C for 30 min in atmosphere. Most grains are equiaxial with sizes from 5 ␮m to 30 ␮m. The density of sample is 6.25 g/cm3 , which is about 100% of the theoretical density. 3.3. Mechanical properties The measured mechanical properties at room temperature are listed in Table 3. It can been seen that the calculated Young’s modulus (178 GPa), shear modulus (68 GPa), bulk modulus (160 GPa) and Poisson’s ratio (0.315) are close to the experimental results. In addition, the elastic stiffness of ␤-Lu2 Si2 O7 is higher than that of ␥-Y2 Si2 O7 and ␤-Yb2 Si2 O7 , which may be caused by the stronger bond of Lu O than Y O. Cation field strength (CFS) can be used to represent bond strengths of rare earth silicates. Hampshire proposed that the CFS can be calculated by: CFS = Zc /rc 2 , where Zc is ionic charge of the cation and rc is ionic radius of cation [24,25]. The ionic radius of the lanthanides decreases with increasing atomic number

Fig. 4. Microstructure of thermal etched surface of ␤-Lu2 Si2 O7 .

Properties

␤-Lu2 Si2 O7

␤-Yb2 Si2 O7 20

␥-Y2 Si2 O7 23

Young’s modulus (GPa) Bulk modulus (GPa) Shear modulus (GPa) Poisson’s ratio Vickers hardness (GPa) Flexural strength (MPa) Fracture toughness (MPa m1/2 ) Debye temperature (K)

178 ± 2 153 ± 2 68 ± 1 0.306 7 ± 0.3 168 ± 10 2.6 ± 0.2 473

168 141 65 0.300 7.3 ± 0.2 159 ± 5 2.76 ± 0.22 461

155 ± 3 112 61 0.270 6.2 ± 0.1 135 ± 4 2.0 ± 0.5 618

because of the lanthanide contraction. As a result, the effective force attracting anions (i.e. the CFS) increases. Using the ˚ Yb3+ (0.868 A) ˚ and Lu3+ (0.861 A), ˚ ionic radius of Y3+ (0.9 A), ˚ −2 , we obtained the CFS of Y, Yb and Lu, which are 3.704 A ˚ −2 , respectively. This suggests that the ˚ −2 and 4.047 A 3.980 A bonding strength of Lu O is stronger than that of Y O and Yb O. Beyond the elastic stiffness, the flexural strength and fracture toughness are of significant importance for ceramics when used as structural materials. The flexural strength of ␤Lu2 Si2 O7 is only a little higher than that of ␤-Yb2 Si2 O7 , but about 33 MPa higher than that of ␥-Y2 Si2 O7 . As with the flexural strength, ␤-Lu2 Si2 O7 and ␤-Yb2 Si2 O7 have similar fracture toughnesses which are higher than that of ␥-Y2 Si2 O7 . Moreover, the Debye temperature of ␥-Y2 Si2 O7 is much higher than those of the two ␤-type rare silicates. Fig. 5 shows the Vickers hardness of ␤-Lu2 Si2 O7 as a function of indentation loads. Vickers hardness depends on the applied load and asymptotically approaches a value about 7.0 ± 0.3 GPa at high loads. The Vickers hardness of ␤-Lu2 Si2 O7 is close to the isostructural ␤-Yb2 Si2 O7 but higher than ␥-Y2 Si2 O7 . Moreover, ␥-Y2 Si2 O7 and ␤-Yb2 Si2 O7 were recognized as damage tolerant ceramics in previous works, and their damage tolerance originated from the inhomogeneous strength of chemical bonds and low shear deformation resistance [19,20]. Actually, both ␥ and ␤ phases consist of corner sharing Si2 O7 double tetrahedra and RE atoms, and one can transform to the other by shuffling of the RE atoms and movement or rotation of

Fig. 5. Vickers hardness ␤-Lu2 Si2 O7 as a function of indentation loads.


3647

Fig. 6. TEM micrographs of indented ␤-Lu2 Si2 O7 : (a) bright image of the deformation twinning of ␤-Lu2 Si2 O7 ; (b) HRTEM image of deformation twinning of ␤-Lu2 Si2 O7 ; (c) corresponding FFT of (b).

the double tetrahedral [26]. Consequently, ␤-Lu2 Si2 O7 might be a damage tolerant ceramic as well. Good damage tolerance can endow ␤-Lu2 Si2 O7 with improved reliability, and thus prolong the lifespan when used as EBC. General methods to evaluate damage tolerance of a material include a nonlinear stress-strain relation [27], a slow decrease of residual strength at different indentation loads [28], and an interlocking microstructure [29]. In addition to these phenomenal descriptions of damage tolerance, there are some parameters such as G/B [30], Hv /E31 and KIC /σ [32], which can qualitatively illustrate the damage tolerance of the materials. In fracture mechanics, the ratio of Vickers hardness and Young’s modulus (Hv /E) emerges as an important parameter for elastic–plastic contacts. Hv and E quantify the loading half-cycle and the unloading half-cycle, respectively [31]. Lawn et al. showed that the radius of the indentation contact area varied with Hv /E, which determined whether a body behaves elastically (brittle), elastic–plastically, or plastically (ductile) [33]. Addtionally, the ratio of bulk modulus to shear modulus (G/B) can be used to assess the brittle or ductile behavior for a solid [30]. A lower G/B value denotes better ductility, and a critical value of G/B = 0.57 is suggested to distinguish the ductile and brittle materials [34]. In addtion, the ratio of fracture toughness to bending strength determines the inherent crack size which is related to damage tolerance. The ductile materials tend to have lower values of Hv /E and G/B, but a higher value of KIC /σ than brittle ones. Therefore, Hv /E, G/B and KIC /σ can be taken as useful indicators of the damage tolerance of materials. The values of Hv /E, G/B, and KIC /σ of ␤-Lu2 Si2 O7 and some damage tolerant ceramics are shown in Table 4 [20,23]. The Hv /E value for ␤-Lu2 Si2 O7 is lower than those of ␥-Y2 Si2 O7 and ␤-Yb2 Si2 O7 , and is close to that of the machinable ceramic LaPO4 . Moreover, the G/B value of ␤-Lu2 Si2 O7 is the lowest among all the ceramics listed in Table 4 and it is lower than 0.57, suggesting the less brittle characteristic of ␤-Lu2 Si2 O7 . In addition, the KIC /σ value of ␤-Lu2 Si2 O7 (0.015) is similar to that of ␥-Y2 Si2 O7 and higher than that of LaPO4 .

To validate the damage tolerance of ␤-Lu2 Si2 O7 , a Hertzian contact test was performed at room temperature. TEM observations were conducted for the investigation of deformation mechanisms, and a large number of twinning were found in the deformed ␤-Lu2 Si2 O7 sample. Fig. 6(a) illustrates the typical lamellar twinning. The representative high resolution transmission electron microscopy (HRTEM) image of deformation twinning in ␤-Lu2 Si2 O7 (Fig. 6b) and the fast Fourier transform (FFT) of the HRTEM image (Fig. 6c), demonstrate that it is (1 1 0) twin. The investigation on the microhardness of single crystal ␤-Lu2 Si2 O7 by Pidol et al. [35] showed that the minimum hardness is along the [1 1 0] and [1 −1 0] directions. This result suggests that (1 1 0) and (1 −1 0) planes are easy slip atomic planes. Twinning is an important deformation mechanism in low symmetry materials which possess few slip systems at room temperature, and imparts quasi-plasticity to complex oxides. Beyond that, parallel dislocations were also found in the deformed ␤-Lu2 Si2 O7 sample. Fig. 7 clearly shows active dislocation glide. Dislocations are often created in pairs and pile up against the grain boundaries. It is well known that the brittle nature of a typical ceramic limits plastic deformation through dislocation glide and deformation twinning at room temperature; the present results have confirmed the quasi-plasticity and damage tolerance of ␤-Lu2 Si2 O7 by mechanisms of deformation twinning and dislocation glide. 3.4. Thermal properties In addition to the mechanical properties, the thermal expansion, temperature dependent Young’s modulus and thermal

Table 4 Comparisons of ratio of Hv /E, G/B and KIC /σ of some damage tolerant ceramics.

Hv /E G/B KIC /σ

␤-Lu2 Si2 O7

LaPO4 23

␥-Y2 Si2 O7 23

␤-Yb2 Si2 O7 20

0.039 0.44 0.015

0.037 0.53 0.010

0.040 0.51 0.015

0.043 0.46 0.017

Fig. 7. TEM micrographs of dislocations in indented ␤-Lu2 Si2 O7 sample.

3648


Fig. 8. Thermal expansion coefficient of polycrystalline ␤-Lu2 Si2 O7 .

shock resistance are of critical importance for EBC materials. Thermal expansion of polycrystalline ␤-Lu2 Si2 O7 measured by an optical dilatometer is shown in Fig. 8. It can be seen that the length of ␤-Lu2 Si2 O7 sample expands linearly with increasing temperature. Since the as-sintered sample has no preferable orientation, an isotropic average thermal expansion of ␤-Lu2 Si2 O7 bulk materials is observed. The average linear thermal expansion coefficient (TEC) was determined in terms of the slope of thermal expansion vs. temperature during heating process and the linear TEC for ␤-Lu2 Si2 O7 is (5.48 ± 0.01) × 10−6 K−1 . The linear TEC of rare earth disilicates is slightly modified by the RE3+ ionic radius but strongly depends on different polymorphs. It can be explained by considering the two types of bonds present in a rare-earth silicate structure, namely, Si O and RE O bonds. Previous investigations have indicated that the Si O mean coefficient of thermal expansion is about ∼ 0 K−1 [36]. Therefore, ␤-Lu2 Si2 O7 mainly expands along the REO6 polyhedral chains. In addition, Hazen et al. [37] found that the thermal expansion coefficients of different RE2 Si2 O7 polymorphs were mainly determined by the cation charge and the cation coordination. Thus, due to the same cation charge and coordination, the linear thermal expansion coefficient of ␤-Lu2 Si2 O7 is close to that of the isostructural ␤-Sc2 Si2 O7 (5.4 × 10−6 K−1 ) [36]. The thermal expansion coefficient is a very important parameter for the selection of EBC materials. For instance, the mismatch of the linear TEC between the substrate and EBC has a negative effect on its performance because of coating cracking and spalling due to a high thermal stress. The thermal expansion coefficient of ␤-Lu2 Si2 O7 is close to that of SiC and SiC/SiC CMC (4.5 − 5.5 × 10−6 K−1 ) [6], which produces a small magnitude of residual thermal stress and renders it a promising candidate for EBC. When used as EBC material, ␤-Lu2 Si2 O7 can maintain its phase stability without phase transformation during heating or cooling processes. The temperature dependent dynamic Young’s modulus provides information about when the elastic stiffness abruptly decreases and softens, which is helpful for design and selection of the coating material. The temperature dependences of the dynamic Young’s modulus and internal friction of ␤-Lu2 Si2 O7 are shown in Fig. 9. The Young’s modulus of

Fig. 9. Dynamic Young’s modulus and internal friction of ␤-Lu2 Si2 O7 at different temperatures.

␤-Lu2 Si2 O7 decreases slowly and almost linearly with increasing temperature up to about 1400 ◦ C, and it is 147 GPa at 1470 ◦ C, which is about 83% of that at room temperature. Fig. 9 suggests that ␤-Lu2 Si2 O7 has an excellent retention of high temperature elastic stiffness. Beyond 1400 ◦ C, Young’s modulus decreases quickly which indicates obvious softening of ␤-Lu2 Si2 O7 . However, the Young’s modulus cannot be measured at the temperature above 1470 ◦ C, because the noise is too high to resolve the resonance frequency of the sample. Wachtman et al. [38] proposed an empirical formula for the temperature dependence of Young’s modulus: T0 E = E0 − A × T × exp − (15) T in which E0 is the Young’s modulus at 0 K, T is the absolute temperature and A is the parameter depending on the material and relates to Grüneisen parameter. The Young’s moduli below 1300 ◦ C were fitted by Eq. (15) (dash-dotted line in Fig. 9), and the result yields E = 176 − 0.02218 × T × exp (−494/T ). Extrapolated E0 is equal to 176 GPa, which is close to the theoretical Young’s modulus, 178 GPa, from DFT calculation. To determine the experimental Debye temperature, the longitudinal υl and shear υs sound velocities are calculated using the fitted Young’s modulus E0 , experimental Poisson’s ratio ν, and theoretical density ρ0 [39]: (1 − ν) E0 υl = (16) ρ0 (1 + ν) (1 − 2ν) E0 1 υs = (17) ρ0 2 (1 + ν) Thereafter, experimental Debye temperature is obtained by Eqs. (10) and (11). The experimental Debye temperature is 470 K, which is very close to the theoretical value, 473 K, from DFT calculation. In addition to the temperature dependent Young’s modulus, the critical temperature at which the deformation mechanism is generally changed can be determined in Fig. 9. Internal friction remains low magnitude from room temperature up to 1300 ◦ C,


3649

Table 5 Comparisons of thermal shock resistance of ␤-Lu2 Si2 O7 and some structural ceramics.

Thermal shock resistance (K)

Fig. 10. Residual strength of ␤-Lu2 Si2 O7 after thermal shock at different temperatures.

and increases exponentially thereafter. The internal friction data, which is also referred to as the mechanical loss spectrum, can be used to obtain the brittle to ductile transition temperature (BDTT) of ceramics. Kardashev [40] suggested that the exponential increase of internal friction corresponded exactly to the BDTT. Using linear fits of the internal friction data at various temperature ranges, the BDTT is found to be about 1320 ◦ C. Damping mechanisms are positive factors for improving toughness in hard and brittle materials. It also accounts for the ability of the material to dissipate locally a part of the vibration energy and hence to improve toughness by crack propagation blunting. The temperature above the BDTT can supply sufficient strain tolerance which can extend the life of EBC. Thermal shock resistance is a significant parameter for the evaluation of performance of EBC materials. Sensitivity of EBC materials to thermal shock originates from the internal mechanical stresses induced by temperature gradients, and the highly brittle nature of typical ceramics. Thermal shock resistance can be determined using the method suggested by Hasselmann [41]. Test pieces were quenched by dropping them from high temperature to room temperature environments. The strength retention of the samples was measured after the abrupt quenching. Fig. 10 shows the residual strength of ␤-Lu2 Si2 O7 as a function of quenching temperature. It can be seen that below about 500 K, the strength does not decrease significantly. Above 500 K, the residual strength decreases slowly when stress is generated by temperature difference between the interior and the surface of a test piece and crack initiation may occur during quenching. The residual strength drops sharply within a narrow temperature range. Around 600 K, residual strength rapidly decreases when thermal stress exceeds strength and fracturing occurs. When samples were quenched from higher temperatures, the residual strength maintains at low value and cracks propagation can be observed near the surface after thermal shock (inset in Fig. 10). The thermal shock resistance parameter is “figures of merit” that should help for the ranking and selection of materials for engineering design involving thermal stress fracture. It can be obtained according to the definition of critical temperature difference (Tc ), which is the temperature difference between the

␤-Lu2 Si2 O7

Al2 O3 23

SiC

ZrO2

Si3 N4

Sialons

270

150

300

500

500

510

furnace and the ambient temperature of water bath when there is a 30% strength drop occurred after quenching. Fig. 10 indicates the critical temperature difference Tc to be about 270 K. The thermal shock resistance of some engineering ceramics are listed in Table 5 [42]. It is seen that the thermal shock resistance of ␤-Lu2 Si2 O7 is higher than dense Al2 O3 and close to SiC. Once again, this result highlights ␤-Lu2 Si2 O7 for its potential application as protective EBC for Si-based ceramics and composites. 4. Conclusions Pure and dense ␤-Lu2 Si2 O7 was successfully synthesized by two steps using a hot pressing sintering method. The mechanical properties including Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio, flexural strength, fracture toughness and Vickers hardness were reported for the first time. The inhomogeneous chemical bonds result in its anisotropic elastic stiffness. TEM observation of the Hertzian contact test sample suggests that deformation twinning and dislocation glide are the main plastic deformation mechanisms at room temperature, which endow ␤-Lu2 Si2 O7 with the novel damage tolerance. Meanwhile, ␤-Lu2 Si2 O7 possesses good high temperature mechanical properties, its Young’s modulus maintains a high value up to 1470 ◦ C (with only a 17% degradation) and the BDTT of ␤-Lu2 Si2 O7 is determined at about 1320 ◦ C according to the exponential increment of internal friction data. The TEC of ␤-Lu2 Si2 O7 is measured to be (5.48 ± 0.01) × 10−6 K−1 , which is closed to that of silicon-based ceramics and composites. Moreover, the critical temperature difference Tc of ␤-Lu2 Si2 O7 under thermal shock is 270 K, which ensures its tolerance to a rapid temperature change in the harsh environment. The present work shed light on ␤-Lu2 Si2 O7 for its competitive applications as an advanced EBC candidate. Acknowledgements The authors gratefully acknowledge Thomas Hills who assisted in revising the manuscript. This work was supported by the National Natural Science Foundation of China under Grant Nos. 51032006 and 51372252. References [1] Hong ZL, Cheng LF, Zhang LT, Wang YG. Water vapor corrosion behavior of scandium silicates at 1400 ◦ C. J Am Ceram Soc 2009;92:193–6. [2] Ueno S, Ohji T, Lin HT. Recession behavior of a silicon nitride with multilayered environmental barrier coating system. Ceram Int 2007;33:859–62.

3650


[3] Hong ZL, Yoshida H, Ikuhara Y, Sakuma T, Nishimura T, Mitomo M. The effect of additives on sintering behavior and strength retention in silicon nitride with RE-disilicate. J Eur Ceram Soc 2002;22:527–34. [4] Choi HJ, Lee JG, Kim YW. High temperature strength and oxidation behaviour of hot-pressed silicon nitride-disilicate ceramics. J Mater Sci 1997;32:1937–42. [5] Ohashi H, Albab MD, Becerro AI, Chain P, Escudero A. Structural study of the Lu2 Si2 O7 –Sc2 Si2 O7 system. J Phys Chem Solid 2006;68: 464–9. [6] Lee KN, Fox DS, Bansal NP. Rare earth silicate environmental barrier coatings for SiC/SiC composites and Si3 N4 ceramics. J Eur Ceram Soc 2005;25:1705–15. [7] Segall MD, Lindan Philip JD, Probert MJ, Pickard CJ, Hasnip PJ, Clark SJ, et al. First-principles simulation: ideas, illustrations and the CASTEP code. J Phys: Condens Matter 2002;14:2717–44. [8] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B: Condens Matter 1990;41:7892–5. [9] Ceperley DM, Alder BJ. Ground state of the electron gas by a stochastic method. Phys Rev Lett 1980;45:566–9. [10] Pfrommer BG, Côté M, Louie SG, Cohen ML. Relaxation of crystals with the quasi-Newton method. J Comput Phys 1997;131:233–40. [11] Milman V, Warren MC. Elasticity of hexagonal BeO. J Phys: Condens Matter 2001;13:241–51. [12] Voigt W. Lehrbuch der Kristallphysik. Leipzig: Taubner; 1928. [13] Reuss A. Berechnung del Fliessgrenze von Mischkristallen aufgrund der Plasti- zitätbedingung für Einkristalle. Z Angew Math Mech 1929;9: 49–58. [14] Hill R. The elastic behavior of a crystalline aggregate. Proc Phys Soc London Sect A 1952;65:349–54. [15] Clarke DR. Materials selection guidelines for low thermal conductivity thermal barrier coatings. Surf Coat Technol 2003;163:67–74. [16] Nye JF. Physical properties of crystals: their representation by tensors and matrices. New York, NY: Oxford University Press; 1985. [17] Soetebier F, Urland W. Crystal structure of lutetium disilicate, Lu2 Si2 O7 . Z Kristallogr NCS 2002;217:22. [18] Pidol L, Harari AK, Viana B, Ferrand B, Dorenbos P, Haas JTM, et al. Scintillation properties of Lu2 Si2 O7 :Ce3+ , a fast and efficient scintillator crystal. J Phys: Condens Matter 2003;15:2091–102. [19] Wang JY, Zhou YC, Lin ZJ. Mechanical properties and atomistic deformation mechanism of ␥-Y2 Si2 O7 from first-principles investigations. Acta Mater 2007;55:6019–26. [20] Zhou YC, Zhao C, Wang F, Sun YJ, Zheng LY, Wang XH. Theoretical prediction and experimental investigation on the thermal and mechanical properties of bulk ␤-Yb2 Si2 O7 . J Am Ceram Soc 2013;96:3891–900. [21] Feng J, Xiao B, Zhou R, Pan W. Anisotropy in elasticity and thermal conductivity of monazite-type REPO4 (RE = La, Ce, Nd, Sm, Eu and Gd) from first-principles calculations. Acta Mater 2013;61:7364–83. [22] Ueno S, Jayaseelan DD, Ohji T. Water vapor corrosion behavior of lutetium silicates at high temperature. Ceram Int 2006;32:451–5.

[23] Sun ZQ, Zhou YC, Wang JY, Li MS. ␥-Y2 Si2 O7 , a machinable silicate ceramic: mechanical properties and machinability. J Am Ceram Soc 2007;90:2535–41. [24] Becher PF, Hampshire S, Pomeroy MJ, Hoffmann MJ, Lance MJ, Satet RL. An overview of the structure and properties of silicon-based oxynitride glasses. Int J Appl Glass Sci 2011;2:63–83. [25] Choi HJ, Kim GH, Lee JG, Kim YW. Refined continuum model on the behavior of intergranular films in silicon nitride ceramic. J Am Ceram Soc 2000;83:2821–7. [26] MacLaren I, Richter G. Structure and possible origins of stacking faults in gamma-yttrium disilicate. Philos Mag 2009;89:169–81. [27] Suzuki A, Baba H. Assessment of damage tolerance and reliability for ceramics. J Soc Mater Sci 2001;50:290–6. [28] Sun ZQ, Wang JY, Li MS, Zhou YC. Mechanical properties and damage tolerance of Y2 SiO5 . J Eur Ceram Soc 2008;28:2895–901. [29] Shen ZJ, Zhao Z, Peng H, Nygren M. Formation of tough interlocking microstructures in silicon nitride ceramics by dynamic ripening. Nature 2002;417:266–9. [30] Music D, Schneider JM. Elastic properties of MFe3 N (M = Ni, Pd, Pt) studied by ab initio calculations. Appl Phys Lett 2006;88:031914. [31] Lawn B. Fracture of brittle solids. Cambridge: Cambridge University Press; 1993. [32] Bao YW, Hu CF, Zhou YC. Damage tolerance of nanolayer grained ceramics and quantitative estimation. Mater Sci Technol 2006;22:227–30. [33] Quinn JB, Quinn GD. Indentation brittleness of ceramics: a fresh approach. J Mater Sci 1997;32:4331–46. [34] Jiang X, Zhao J, Jiang X. Correlation between hardness and elastic moduli of the covalent crystals. Comput Mater Sci 2011;50:2287–90. [35] Pidol L, Harari AK, Viana B, Basset G, Calvat C, Chambaz B, et al. Czochralski growth and physical properties of cerium-doped lutetium pyrosilicate scintillators Ce3+ :Lu2 Si2 O7 . J Cryst Growth 2005;275:899–904. [36] Fernández-Carrión AJ, Allix M, Becerro AI. Thermal expansion of rareearth pyrosilicates. J Am Ceram Soc 2013;96:2298–305. [37] Hazen RM, Prewitt CT. Effects of temperature and pressure on interatomic distances in oxygen-based minerals. Am Miner 1977;62:309–15. [38] Wachtman Jr JB, Tefft WE, Lam Jr DG, Apstein CS. Exponential temperature dependence of Young’s modulus for several oxides. Phys Rev 1961;122:1754–9. [39] Bruls RJ, Hintzen HT, With Gde Metselaar R. The temperature dependence of the Young’s modulus of MgSiN2 , AlN and Si3 N4 . J Eur Ceram Soc 2001;21:263–8. [40] Kardashev BK, Nefagin AS, Ermolaev GN, Leont’eva-Smirnova MV, Potapenko MM, Chernov VM. Internal friction and brittle–ductile transition in structural materials. Tech Phys Lett 2006;32:799–801. [41] Hasselman DPH. Unified theory of thermal shock fracture initiation and crack propagation in brittle ceramics. J Am Ceram Soc 1969;52:600–4. [42] Ashby MF, Jones DRH. Engineering materials 2. 4th ed. Boston, MA: Butterworth–Heinemann; 2013.