High-temperature structural applications require material with a high melting point, high strength, superior oxidation resistance, and excellent creep behavior at elevated temperatures. This was demonstrated in a number of studies that showed that refractory metal silicide appears to be more attractive because of their superior physical and chemical properties. Nickel aluminides, titanium aluminides, and transition metal disilicides have been intensively investigated.^[1–3] Refractory transition-metal silicide has been amply investigated so far, which can effectively improve the performance, such as the gas turbine engine in a power generation system:^[4] even a minor increase in the efficiency of an engine can result in a significant decrease in fuel cost and reduction in harmful emissions.^[5] Among the refractory metal silicides, the silicide in the Mo–Si system shows a promising potential because Mo has a lower density than other refractory metals, and Mo does not embrittle with the increases of oxygen and nitrogen contamination. In the Mo–Si system, there are three intermetallic phases, i.e., C11_b-structured MoSi₂, D8_m–structured Mo₅Si₃, and A15-structured Mo₃Si. The MoSi₂ and Mo₅Si₃ have been studied extensively in the last several decades as promising ultra-high structural materials because of their high melting temperatures (2303 K, 2018 K), relatively low densities (6.24 g/cm³, 8.19 g/cm³), high thermal conductivities, thermodynamic compatibilities, excellent oxidation resistances at high temperatures, and low temperature plastic deformabilities.^[6,7] However, each of MoSi₂ and Mo₅Si₃ exhibits the phenomena of poor fracture toughness, poor creep strength at high temperatures, and accelerating oxidation in 450 °C–550 °C, so that there are great difficulties with industrial applications. In order to remedy these drawbacks, extensive efforts have been made to form composite MoSi₂-based alloys. MoSi₂ is a brittle intermetallic and silicide ceramic with significant potential as the matrix phase of advanced high temperature structural composites. Meyer et al.^[8] suggested that the Mo₅Si₃ controls the creep rate of the Si–Mo system. Recent study confirmed that the eutectic MoSi₂ and Mo₅Si₃ composite can significantly modify the creep strength of the MoSi₂.^[9,10] Binary compound of silicon and molybdenum is the second nickel-based super alloy of a new class of highly competitive high-temperature structural materials, so they were widely used in MoSi₂-based, Mo₅Si₃-based alloys.^[11,12]

It has been reported that MoSi₂ has a body-centered-tetragonal C11_b structure of the space group I4/mmm (139). There is a strong covalent bond between Si atoms aligned along the c-axis in MoSi₂. Mo₅Si₃ belongs to the space group I4/mcm (140) with a body-centered tetragonal lattice (tI32).^[13] The bulk modulus is an important engineering design parameter for material. In 1990, the elastic constant of MoSi₂ was calculated from the velocity of ultrasonic waves which was measured by using a simple pulse-echo method by Morihiko et al.^[14] The bulk modulus B₀ of polycrystalline material is estimated from the following equations:

In this paper, we investigate the compression behaviors of MoSi₂ and Mo₅Si₃, and determine the equation of state (EOS) under high pressure. In addition, the compression behaviors of materials are analyzed mainly at pressures up to 41.1 GPa. Here, we for the first time report on the MoSi₂ and Mo₅Si₃ study of molybdenum silicide in DAC by using in-situ high-pressure ADXRD with synchrotron radiation.

The experimental samples were purchased commercially from Qinhuangdao Eno Material, of which the content of MoSi₂ was 98% and the rest was Mo₅Si₃. Because the strengths of MoSi₂ and Mo₅Si₃ are equivalent and the interaction between the specimens can be ignored under high pressure, we can analyze the compressibilities of the two samples in the same experiment. The initial materials were characterized by x-ray diffraction (XRD, model DX-2500, Dandong, China) using a Cu- radiation source with λ = 1.5404 Å to check the crystal structure, purity and morphology. Figure 1 shows the power XRD pattern of the starting specimen. In situ high pressure ADXRD measurements on powder were performed at room temperature by using a synchrotron x-ray source (λ = 0.6199 Å) of the 4W2 high-pressure station of the Beijing Synchrotron Radiation Facility (BSRF, Beijing). The DAC where there is a pair of beveled diamond anvils ( culet) and the stainless steel (T301) gasket of about in thickness. A -diameter hole drilled in the center of the gasket is used as a sample chamber in this experiment. The sample was pre-compressed with a separate pair of diamond anvils and located in the hole in the gasket. Methanol-methanol mixture (4:1) was used as the pressure-transmitting medium to provide relative hydrostatic pressure. By the ruby fluorescence method, the pressure was determined during such an experiment.^[18,19] The spot size of the x-ray beam was focused into a size of approximately . In-situ powder diffraction data were recorded by using a two-dimensional (2D) imaging plate detector for further analysis. Then, the Bragg diffraction rings were converted into a series of one-dimensional (1D) intensity versus diffraction angle 2θ patterns by using the FIT2D program. It allows for detector calibration and integration of powder diffraction data scanning from the 2D detector to 1D 2θ by using a CeO₂ calibration material from NIST.^[20] Finally, the diffraction patterns were indexed and refined with the GSAS program packages.

Fig. 1.

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	Fig. 1. The x-ray diffraction patterns of the initial specimen under normal pressure and room temperature. The five-pointed star represents the diffraction peak of MoSi2 and the rhombus represents the diffraction peak of Mo5Si3.

Figure 2 shows the spectrum ADXRD patterns of the initial powder under high pressure up to 41.1 GPa. From this figure we can see fifteen diffraction peaks, i.e., peaks (0 0 2), (0 1 0), (1 1 0), (1 0 3), (1 1 2), (2 0 0) for MoSi₂ and peaks (2 1 1), (3 1 0), (0 0 2), (4 0 0), (3 2 1), (2 0 2), (4 2 0), (4 1 1), (6 2 0) for Mo₅Si₃. Since the peak (1 1 2) for MoSi₂ and peaks (4 0 0), (2 0 2), (6 2 0) for Mo₅Si₃ are too low, they are not taken into account when calculating the unit cell parameters. Compared with peaks of MoSi₂ and Mo₅Si_3, the peak of Mo₅Si₃ is weak, but it does not affect the data analysis. With increasing pressure, all the reflections (diffraction peaks) shift toward higher 2θ angle monotonically, and become generally broadened and weakened, indicating a pressure-induced reduction of the d-spacing and thus the unit cell volume. However, these diffraction peaks are unrelated to each other in the entire compression process. These phenomena suggest that MoSi₂ and Mo₅Si₃ maintain their crystal structures but with reduced crystallinity. When the pressure reaches a maximum value of 41.1 GPa in this work, no new peaks are observed, so we are able to conclude that no phase transition occurs in the whole compression process.

Fig. 2.

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Fig. 2. (color online) X-ray diffraction patterns (λ = 0.6199 Å) of the sample under various pressures at room temperature. The five-pointed star represents the diffraction peak of MoSi2 and the rhombus represents the diffraction peak of Mo5Si3. (a) The diffraction patterns of MoSi2 and Mo5Si3 upon compression to the highest pressure of 41.1 GPa. (b) Rietveld refinement pattrens of the specimen about 4.9 GPa. Red line: calculated curve, black short lines: Bragg position, forks type: experimental curve, blue lines: difference curve.

Figure 3 shows the pressure evolutions of the unit-cell parameters for MoSi₂ and Mo₅Si₃, where the line is the fit to data. In the range of experimental error allowed, the unit-cell volume decreases with increasing pressure. The pressure-volume curves for MoSi₂ and Mo₅Si₃ are fitted to the best Birch–Murnaghan EOS^[21,22]

Fig. 3.

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	Fig. 3. (color online) Plots of normalized unit cell volume versus pressure for MoSi2 (solid red circle) and Mo5Si3 (solid black square). The black and red solid lines represent the best fits of Birch–Murnaghan EOS.

The data listed in Table 1 are the constants for Mo, Si, MoSi₂, and Mo₅Si₃. It is found from Table 1 that the bulk modulus of the silicon-molybdenum compound is between the bulk moduli of Mo and Si, i.e., the bulk modulus of molybdenum (273 GPa) is the highest, and that the silicon (97.9 GPa) is the lowest. The bulk modulus of Mo₅Si₃ (308.4 (7.6) GPa) is slightly larger than the bulk modulus of MoSi₂ (222.1 (2.1) GPa). The discrepancies between the bulk moduli of MoSi₂ and Mo₅Si₃ may be explained partially by the fact that the differences in the structure among their crystals lead to differences in their bulk modulus. The cell volume of Mo₅Si₃ is more than 5.6 times as big as MoSi₂. However, the bulk modulus of MoSi₂ is smaller than that of Mo₅Si₃. It is well known that the interatomic bonding strength of the -Si-Mo-Si- chain is stronger than that of the -Mo-Mo- and -Si-Si- chain. In the structure of Mo₅Si₃ contained are a lot of -Si-Mo-Si- chains so that its bulk modulus is relatively high.

Table 1.

Table 1.

Table 1. Values of structure parameters (a, b, c), bulk modulus (B0), pressure derivative (), and elastic constants (C11, C33) of the Mo–Si system, compared with previous results of Mo, Si, Mo5Si3, and MoSi2. . Materials a, b/Å c/Å /GPa /GPa /GPa /GPa Ref. Mo 273 [25], [26] Si 97.9 [27]–[29] MoSi2 3.206 7.848 210.2 417 514.5 [23] 3.175 7.886 222.1 (2.1) 4 This work Mo5Si3 9.648 4.903 242 (Hill approximation) 446 390 [24] 9.687 4.881 308.4 (7.6) 0.7 (0.1) This work

Table 1. Values of structure parameters (a, b, c), bulk modulus (B0), pressure derivative (), and elastic constants (C11, C33) of the Mo–Si system, compared with previous results of Mo, Si, Mo5Si3, and MoSi2. .

The compression behaviors of the unit cell axes of MoSi₂ and Mo₅Si₃ are shown in Fig. 4 and Table 1. We made a least-squares fitting on axis, and the fitting results yield

Fig. 4.

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	Fig. 4. (color online) Plots of cell parameter ratio ( and ) versus pressure for MoSi2 (a) and Mo5Si3 (b). Both a- and c-lattice constants show a gentle decrease upon compression.

MoSi₂:

Mo₅Si₃:

Figure 4 shows the compressive behaviors in the a-axis and the c-axis directions for both materials. However, the anisotropy of MoSi₂ is more distinct than that of Mo₅Si₃. In general, the compressibility of the material is described by the elastic constants. The elastic constants C₁₁, C₂₂, and C₃₃ represent respectively the compressibilities in the a, b, and c directions.^[30] Previous studies reported that the ) direction of the MoSi₂ is easier to compress than the ), and the compressibilities of Mo₅Si₃ and MoSi₂ are just opposite, its compressibility in the ) direction is much stronger than the ). For MoSi₂, with ; however, for Mo₅Si₃, with .^[31] It is essential to consider the crystal structures of MoSi₂ and Mo₅Si₃ in order to analyze the respective anisotropic behavior.

The schematic views of MoSi₂ (a) and Mo₅Si₃ (b) are shown in Fig. 5. The crystal structure of MoSi₂ can be simply described as the accumulation of Mo and Si atoms along the c-axis. The crystal structure can be described simply as ABA’BA-type structure as shown in Fig. 5(a). In the B (silicon atoms) layer, the Si atoms of the MoSi₂ material are not only arranged on the a–b plane, but also form an angle with respect to the a–b plane; thus, the specially puckered B layers structure may enhance incompressibility in the c direction. In addition, the directional electronic repulsion between the silicon atoms and molybdenum atoms aligned along the c-axis can reduce the pressure induced compression in the c direction. However, unlike the Mo atom, the four Si atoms in the A (molybdenum atoms) layer are in the same plane and the layer has only one Si atom. Owing to the fact that the weak metallic bond between atoms of molybdenum is the significantly important framework, the compressibility along the a-axis is strengthened. Compared with the MoSi₂, Mo₅Si₃ has the extremely complex unit cell structure as shown in Fig. 5(b), in which a-lattice parameter is larger than c-lattice parameter and no close-packed planes exist. Mo and Si of atoms are alternately arranged in each unit cell. We speculate that it is this particular structure that leads to Mo₅Si₃ with less anisotropy, linear compressions in the a-axis and the c-axis almost simultaneously. However, the a-axis is more likely to be compressed from the overall point of view.

Fig. 5.

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	Fig. 5. (color online) Schematic crystal structures of MoSi2 (a) and Mo5Si3 (b). Gray solid spheres represent Mo atoms and blue solid balls are Si atoms.

In this work, the structural stabilities and compressive behaviors of MoSi₂ and Mo₅Si₃ materials under static compression are studied by using a synchrotron radiation ADXRD technique in a DAC for the first time. MoSi₂ and Mo₅Si₃ are found to have a stable tetragonal structure with a maximum pressure of 41.1 GPa. The third-order Birch–Murnaghan equation is used to obtain MoSi₂ and Mo₅Si₃ of the bulk modulus B₀ values of 222.1 (2.1) GPa, 308.4 (7.6) GPa and the values of their pressure derivative of 4 and 0.7 (0.1). As the pressure increases, the unit cell volumes of MoSi₂ and Mo₅Si₃ are gradually reduced. The MoSi₂ c-axis compression rate is significantly smaller than the a-axis, but for Mo₅Si₃ the a-axis is less than c-axis, which reveals the anisotropies of both materials are determined by the structure of the material itself. Our study thus contributes to the design of new high temperature refractory composite materials through providing a practical guideline by considering multiple combined factors that may influence their performances in Mo–Si systems.