Elastic Moduli and Mechanical Properties of Mo₅SiB₂ Single Crystals in the Mo-Si-B System

Abstract

With outstanding high-temperature properties, the intermetallic Mo₅SiB₂ alloy is regarded as an extremely competitive ultra-temperature structural material. The maximum Young’s modulus of 398.0 GPa for single Mo₅SiB₂ crystals was found to be at the vertex of the [010] direction, while the minimum value of 264.0 GPa was found in the [001] direction. For hardness, the maximum value was 451.7 HV after compression at 1200 °C in the radial direction, while the maximum hardness was 437.2 HV at 1300 °C in the axial direction of {111}<110>, showing obvious anisotropy. Under compression, the flow stresses rapidly increased and then decreased with the increase in strain, corresponding to the two different stages of work hardening and softening. An EBSD test showed that the grain orientation remained the same at different rates, but the texture was different. After high-temperature compression, the crystal underwent plastic deformation, dislocations slipped along the slip plane, and the grain rotated, so the grain texture changed from {111}<110> to {001}<110>.

1. Introduction

Due to its extremely high melting point, outstanding high-temperature mechanical properties, and good oxidation resistance, the refractory molybdenum silicides have become a hot research topic in the field of high-temperature structural materials [1,2,3,4,5,6] and will be used as the key material for the high-temperature parts of military and civil aviation engines and gas turbines [7,8].

The current research work mainly focuses on two hot phase regions (Mo₅SiB₂ + Mo₅Si₃ + Mo₃Si and Moss + Mo₅SiB₂ + Mo₃Si) in the Mo-Si-B ternary system phase diagram (Mo_ss is the solid solution of Si and B atoms in α-Mo). Of these two three-phase zone alloys, the former has the better high-temperature strength and creep resistance [9,10]. In addition, the alloy in the three-phase zone also has a good room-temperature fracture toughness due to the toughening effect of Moss [11]. However, since Mo starts to oxidize at 300 °C and MoO₃ starts to volatilize at 500 °C, the oxidation resistance of this alloy is reduced to different degrees [12]. The latter has more outstanding oxidation resistance and high-temperature creep resistance but a lower fracture toughness at room temperature [13].

The Mo₅SiB₂ phase plays a very important role in the high-temperature properties of these two three-phase regions due to its outstanding high-temperature strength, high-temperature creep resistance, and oxidation resistance [10,14,15]. For example, the steady-state creep rate of a single Mo₅SiB₂ crystal oriented at [021] is only 10⁻⁸–10⁻⁹ s⁻¹ at 1500 °C [16,17]. The Mo₅SiB₂ phase is a body-centered tetra (D81, tI32, I4/mcm) crystal structure, where Mo_I occupies position 4c, Mo_п occupies position 16l, the Si atom occupies position 4c, and the B atom occupies position 8h (see Figure 1), which such a crystal structure leading to a very high melting point for Mo₅SiB₂ (~2200 °C) [18]. Since the density (8.864 g/cm³) is relatively low, the Mo₅SiB₂ phase itself is considered to be a potential new generation of ultra-high-temperature structural materials.

Although much research has been devoted to the two three-phase regions, few studies have been conducted on the single Mo₅SiB₂ phase, mainly because the Mo₅SiB₂ phase has the characteristics of a high melting point (~2200 °C), high hardness (HV~17.8 GPa), and low fracture toughness (3.2 MPa·m^1/2) at room temperature [19], which brings great difficulties to the preparation of Mo₅SiB₂ and the determination of its mechanical properties. At present, most studies on Mo₅SiB₂ phase alloys have focused on the crystal structure and defects of the polycrystalline state [20,21,22], phase stability [23,24], elastic modulus [25], physical properties [25], and antioxidant properties [26], while systematic studies on their mechanical properties are lacking. In aprevious study of a polycrystalline Mo₅SiB₂ phase alloy, our research group found [27,28,29] that the Mo₅SiB₂ phase underwent a brittle–ductile transition in a wide temperature range (1000–1200 °C) and had an abnormal yield stress temperature effect similar to that of other intermetallic compounds. However, the public references cannot explain the Mo₅SiB₂ phase’s anisotropy plastic deformation behavior, the brittle–ductile transition temperature’s wide range, and the yield stress of the abnormal phenomenon such as the temperature effect. Therefore, in this paper, we took the monocrystalline Mo₅SiB₂ phase alloy as the research object, obtained its specific crystal direction, and established the relationship between the anisotropy of its macroscopic mechanical properties and the evolution of its microscopic dislocation structure during deformation.

2. Experiment Procedures

In a simulation experiment, the Mo₅SiB₂ cell model was constructed by using the Castep module of Materials Studio software. The GGA-PBE method was used to calculate the electronic structure and elastic parameters of the model on the basis of geometric structure optimization. The Brillouin zone K point of the model was set to 4 × 4 × 2, and the cut-off energy was 290 eV. The convergence condition of the geometric structure optimization was set as follows: The precision of plane wave energy was set to 1.0 × 10⁻⁵ eV/Atom, the energy on each atom was not more than 0.03 eV/atom, the tolerance offset was 1.0 × 10⁻⁴ nm, the internal stress was not more than 0.05 GPa, and the force per unit distance was no more than 3 × 10⁻³ eV/nm.

The raw materials used in this work were 99.9 wt.% Mo, 99.999 wt.% Si and 99.99 wt.% B. The Mo₅SiB₂ polycrystalline alloy was prepared via argon arc melting before being water-cooled in a copper mold with a diameter of 20 mm. The casting was homogenized after vacuum annealing at 1400 °C for 10 h. The single Mo₅SiB₂ crystals were prepared with the helical crystal selection method using an electron beam suspension zone and directional melting and solidification technology. Small crystals with different orientations were directly cut as seed crystals, and the single crystals were prepared with the seed crystal method. The single crystal samples were processed into dimensions of Φ5 mm × 10 mm via wire cutting to serve as compression samples. High-temperature compression tests were conducted at a constant displacement rate in a vacuum at a temperature range of 110–1400 °C and a strain-rate regime of 10⁻² to 10⁻³ s⁻¹. The microhardnessand nanohardness of single crystal and polycrystalline Mo₅SiB₂ were measured and compared. The applied load used for the nanoindentation tests was 100 mN, and that of the microhardness test was 200 g. The indenter of the microhardness tester was a diamond cone with a top angle of 120°. The EBSD method was used to determine the crystal orientation transition during tensile deformation. The microstructure of the samples was characterized before and after deformation with optical, scanning (SEM), and transmission electron microscopy (TEM).

3. Results and Discussion

3.1. Elastic Modulus and Shear Modulus Simulation

The elastic stiffness matrix c_ij and compliance matrix s_ij of the Mo₅SiB₂ single crystals were obtained via first principles calculations [30].

$$c_{ij}=\left[\begin{array}{cccccc}461.65280& 154.14490& 177.85275& 0& 0& 0\\ 154.14490& 461.65280& 177.85275& 0& 0& 0\\ 177.85275& 177.85275& 366.72895& 0& 0& 0\\ 0& 0& 0& 163.82995& 0& 0\\ 0& 0& 0& 0& 163.82995& 0\\ 0& 0& 0& 0& 0& 137.67965\end{array}\right]$$

(1)

$$s_{ij}=\left[\begin{array}{cccccc}0.0027539& -0.0004980& -0.0010940& 0& 0& 0\\ -0.0004980& 0.0027539& -0.0010940& 0& 0& 0\\ 177.85275& 177.85275& 366.72895& 0& 0& 0\\ 0& 0& 0& 0.0061039& 0& 0\\ 0& 0& 0& 0& 0.0061039& 0\\ 0& 0& 0& 0& 0& 0.0072632\end{array}\right]$$

(2)

Figure 2 shows each vector l in a rectangular coordinate system. l₁, l₂, and l₃ are the direction cosines of <100>, <010>, and <001>, respectively. Here, θ is the angle between vector l and the z-axis and φ is the angle between the projection of vector l onto the xy plane and the x-axis. Each vector on the shear plane perpendicular to l along the end of vector l is denoted as m, and χ is the angle between vector m and the secant line (the secant line formed by the projection of the extension line of vector l on the xy plane and the shear plane). Accordingly, the flexibility matrix s_ij was used to obtain the elastic modulus of the Mo₅SiB₂ single crystals in each direction in the spatial lattice.

$$\begin{array}{ll}1/E=& S_{11}{l}_1^4+2S_{12}{(l_1{l}_2)}^2+2S_{13}{(l_1{l}_3)}^2+2S_{14}(l_2{l}_3{l}_1^2)+2S_{15}(l_3{l}_1^3)+2S_{16}(l_2{l}_1^3)\\ & +S_{22}{l}_2^4+2S_{23}{(l_2{l}_3)}^2+2S_{24}(l_3{l}_2^3)+2S_{25}(l_1{l}_3{l}_2^2)+2S_{26}(l_1{l}_2^3)\\ & +S_{33}{l}_3^4+2S_{34}(l_2{l}_3^3)+2S_{35}(l_1{l}_3^3)+2S_{36}(l_1{l}_2{l}_3^2)\\ & +S_{44}{(l_2{l}_3)}^2+2S_{45}(l_1{l}_2{l}_3^2)+2S_{46}(l_1{l}_3{l}_2^2)\\ & +S_{55}{(l_1{l}_3)}^2+2S_{56}(l_2{l}_3{l}_1^2)\\ & +S_{66}{(l_1{l}_2)}^2\end{array}$$

(3)

where

$$l=\left(\begin{array}{c}\sin \theta \cos \varphi \\ \sin \theta \sin \varphi \\ \cos \theta \end{array}\right)$$

(4)

$$m=\left(\begin{array}{c}\cos \theta \cos \varphi \cos \chi -\sin \varphi \sin \chi \\ \cos \theta \sin \varphi \cos \chi +\cos \varphi \sin \chi \\ -\sin \theta \cos \chi \end{array}\right)$$

(5)

A three-dimensional diagram of the elastic modulus of the Mo₅SiB₂ single crystalsis shown in Figure 3a. The isosurface of the elastic modulus was projected onto the crystal plane (001), as shown in Figure 3b. The maximum Young’s modulus of the Mo₅SiB₂ single crystals was obtained at the vertex of the crystal direction of [010], with E_max = 398.0 GPa. The minimum value was obtained in the crystal direction of [001], with E_min = 264.0 GPa.

The shear modulus of the Mo₅SiB₂ single crystals in each direction in the lattice was related to l vector and m vector, and the shear modulus G in any direction in space was expressed as follows [30].

$$\begin{array}{ll}1/G=& 4\left[S_{11}{\left(l_1{m}_1\right)}^2+S_{22}{\left(l_2{m}_2\right)}^2+S_{33}{\left(l_3{m}_3\right)}^2\right]\\ & +S_{44}{\left(l_2{m}_3+l_3{m}_2\right)}^2+S_{55}{\left(l_1{m}_3+l_3{m}_1\right)}^2+S_{66}{\left(l_1{m}_2+l_2{m}_1\right)}^2\\ & +8\left[S_{12}\left(l_1{l}_2{m}_1{m}_2\right)+S_{13}\left(l_1{l}_3{m}_1{m}_3\right)+S_{23}\left(l_2{l}_3{m}_2{m}_3\right)\right]\\ & +4l_1{m}_1\left[S_{14}\left(l_2{m}_3+l_3{m}_2\right)+S_{15}\left(l_1{m}_3+l_3{m}_1\right)+S_{16}\left(l_1{m}_2+l_2{m}_1\right)\right]\\ & +4l_2{m}_2\left[S_{24}\left(l_2{m}_3+l_3{m}_2\right)+S_{25}\left(l_1{m}_3+l_3{m}_1\right)+S_{26}\left(l_1{m}_2+l_2{m}_1\right)\right]\\ & +4l_3{m}_3\left[S_{34}\left(l_2{m}_3+l_3{m}_2\right)+S_{35}\left(l_1{m}_3+l_3{m}_1\right)+S_{36}\left(l_1{m}_2+l_2{m}_1\right)\right]\\ & +2S_{45}\left(l_2{m}_3+l_3{m}_2\right)\left(l_1{m}_3+l_3{m}_1\right)\\ & +2S_{46}\left(l_2{m}_3+l_3{m}_2\right)\left(l_1{m}_2+l_2{m}_1\right)\\ & +2S_{56}\left(l_1{m}_3+l_3{m}_1\right)\left(l_1{m}_2+l_2{m}_1\right)\end{array}$$

(6)

The shear and elastic moduli of the Mo₅SiB₂ single crystals on the crystal plane (100) along different crystal orientations are shown in Figure 4. The maximum shear modulus of the Mo₅SiB₂ single crystals was calculated at the vertex of the crystal orientation [$\overline{1}$10], with G_max = 163.8 GPa. The minimum value was calculated at the vertex of the crystal orientation [100], with G_min = 112.1 GPa.

3.2. Mechanical Properties of Mo₅SiB₂ Single Crystals

Figure 5 shows the true stress–strain curves of the [021] oriented Mo₅SiB₂ single crystals at different temperatures and strain rates. At the beginning of the experiment, all flow stresses rapidly increased with the increase in strain, which was due to the rapid increase in dislocation density during deformation (see Figure 6). At 1200 °C, a large amount of dislocation appeared with the increase in strain, and the dislocation density significantly increased when the deformation temperature further increased to 1300 °C. The interaction between dislocations hindered the further movement of the other dislocations, resulting in a work hardening phenomenon. However, when the deformation temperature increased to 1400 °C, the dislocation density was reduced to a very low level, leading to a softening effect. The strain rate also had an important effect on the dislocation motion. At 1200 °C and 1300 °C, the density of the specimens deformed at a strain rate of 0.01 s⁻¹ was higher than that of the specimens deformed at a strain rate of 0.001 s⁻¹, which is consistent with the stress–strain curves of the Mo₅SiB₂ single crystals shown in Figure 5.

By comparing the Mo₅SiB₂ single crystals prepared in this word with the macromorphologies of other metals after compression, it was found that the macromorphologies of the Mo₅SiB₂ single crystals with all temperatures and compression rates after compression at high temperature were not “drum” but showed a symmetric “s-shape” deformation whose direction was consistent and had obvious macro-anisotropy (see Figure 6a). In order to further explore the changes of the material microstructure before and after compression deformation, the microhardness of different grain orientations was tested, and the results are shown in Figure 7. The microhardness at 1100 °C was 392.1 HV in the radial direction and 429.1 HV in the axial direction. With the increase in compression temperature, the microhardness first increased and then decreased. The process of material deformation at high temperatures is affected by many factors, and pure Mo₅SiB₂ single crystals with a single orientation were prepared in this study, which could have effectively eliminated the uncertainty factors of grain size and direction. It can be seen from the microhardness test that the maximum hardness was 451.7 HV at 1200 °C in the radial direction, while the maximum hardness was 437.2 HV at 1300 °C in the axial direction of {111}<110>, showing obvious anisotropy.

Figure 7 shows the microhardness and nanoindentation test results of the monocrystalline and polycrystalline Mo₅SiB₂ alloys. Under the same test conditions, the microhardness of the <110> direction (radial) reached 442.1 HV, which was about 10% higher than that of the <211> (axial) direction and 20% higher than that of the polycrystalline Mo₅SiB₂. Nanoindentation test results showed that the elastic modulus of the polycrystalline Mo₅SiB₂ with the same composition was 390.3 GPa. However, the value of single crystals in the axial direction was only 241.7 GPa, but the nanohardness of the single crystal Mo₅SiB₂ was similar to that of the monocrystal Mo₅SiB₂, which fully reflects that the existence of a grain boundary hindered the occurrence of plastic deformation. The single crystal in the <110> orientation avoided the influence of grain boundary defects, leading to the consistency of strength and toughness.

The samples with the highest compression strength at 1200 °C were selected for an EBSD test. It was found that the grain orientation remained the same under different rates but the texture microstructure was different. From the EBSD results of the compressed materials shown in Figure 8, it can be clearly seen that after high-temperature compression, the Mo₅SiB₂ crystals underwent plastic deformation and slipped along the slip plane while the grain rotated, so the texture changed from {111}<110> to {001}<110>.

4. Conclusions

For Mo₅SiB₂ single crystals, the maximum Young’s modulus of 398.0 GPa was calculated at the vertex of the [010] direction, while the minimum value of 264.0 GPa was calculated in the [001] direction. For hardness, the maximum value was 451.7 HV after compression at 1200 °C in the radial direction, while the maximum hardness was 437.2 HV at 1300 °C in the axial direction of {111}<110>, showing obvious anisotropy. Under compression, the flow stresses rapidly increased and then decreased with the increase in strain, corresponding to the two different stages of work hardening and softening. An EBSD test showed that the grain orientation remained the same at different rates, but the texture was different. After high-temperature compression, the crystal underwent plastic deformation, dislocations slipped along the slip plane, and the grain rotated, so the grain texture changed from {111}<110> to {001}<110>.