Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
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Structural and Physical Properties of ZrSi2 under High Pressure: Experimental Study and First-Principles Calculations Haihua Chen,†,∥ Hao Liang,†,‡ Fang Peng,*,‡ Huishan Li,† Bin Wang,† Xinxin Xia,‡ Xiaodong Li,§ Pei Wang,∥,⊥ and Liping Wang*,∥,⊥ †
Department of Basic Education, Qinghai University, Xining 810016, P. R. China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, P. R. China § Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, P. R. China ∥ High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Las Vegas, Nevada 89154, United States ⊥ Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology, Shenzhen 518055, P. R. China
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‡
ABSTRACT: Zirconium disilicide (ZrSi2) has been investigated experimentally and theoretically for its structural and physical properties at high pressures. In situ compression experiments demonstrate that at low pressure, ZrSi2 adopts the C49 structure (space group Cmcm), which persists up to 54.5 GPa at room temperature, and the unit cell of ZrSi2 along b-axis is at least twice as compressible as along a- and c-axis. A bulk modulus of 170.0 ± 0.7 GPa (K′0 = 4) is derived from the compression experiment employing methanol−ethanol mixture as the pressure-transmitting medium. Diffraction line-width analysis suggests a yield strength of about 3.0 GPa for ZrSi2 under high pressures at room temperature. The first-principles calculations mostly agree with the experimental results, such as mechanical and dynamic stability and elastic anisotropy (Kc > Ka ≫ Kb). However, predicted axial modulus Kb by modeling is significantly smaller than the experimentally determined value, resulting in a sizable discrepancy between experimental (170.0 GPa) and theoretical (121.0 GPa) bulk moduli.
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INTRODUCTION
Transition-metal disilicides have been proposed as potential effective additives for ZrB2-based ceramics.6,9 Indeed, with MoSi2 as additive, ZrB2-based composites were successfully densified at 1750−1800 °C.10 With a melting point (∼1620 °C)11 much lower than that of MoSi2 (∼2030 °C),12 ZrSi2 quickly became a candidate additive to substitute MoSi2 and was subsequently employed (∼20 vol %) in the pressureless sintering of dense ZrB2 composites at 1650 °C.13 More recent studies have further shown the effectiveness of ZrSi2 as an additive in improving the sinterability, lowering the sintering temperature, and reinforcing the oxidation resistance of UHTC. 4,6,9 These studies demonstrate the increasing importance of ZrSi2 in manufacturing, and it is imperative to investigate how it performs physically, chemically, and
Zirconium disilicide (ZrSi2) as a new disilicide additive of transition metals for ceramic sintering with relatively low density, high creep strength, and excellent stability at high temperatures has attracted great research interests in electronic, aerospace, medical, and many other fields.1−3 It is known that sintering of ultrahigh-temperature ceramics (UHTC) such as ZrB2 and HfB2 requires extreme conditions.4 For instance, it is difficult to achieve the near-fully dense single-phase ZrB2 ceramics at temperatures below 2100 °C owing to the covalent bonds and low self-diffusivity.5,6 To lower the required high temperature, metal nitride additives such as ZrN and AlN have to be added to pure ZrB2 powder.7,8 However, a temperature of about 1900 °C is still needed.6 It is therefore desirable to develop new additives to further decrease the sintering temperatures that are currently necessary for UHTCs. © XXXX American Chemical Society
Received: September 10, 2018
A
DOI: 10.1021/acs.inorgchem.8b02559 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 1. (a) XRD pattern at ambient condition, an SEM image (upper-right inset), and schematics of crystal structure (lower left inset) of the starting ZrSi2. (b) Synchrotron ADXD patterns at room temperature and different pressures (NPTM). dimensional signals to conventional intensity-2θ diffraction patterns20 from which the lattice parameters and full widths at half-maximum of diffraction lines were obtained. The yield strength of ZrSi2 was analyzed by the line width analysis method (LWAM), which has been described elsewhere.21−23 Primary sources causing the broadening of diffraction lines during compression are grain-size reduction and microscopic deviatoric strain ε.23,24 Once ε is known, microscopic deviatoric stress υ can be determined as ε × E, where E is the aggregate Young’s modulus.21−24 When polycrystalline sample starts to deform plastically, υ is equal to yield strength Y (υ = εE = Y).25 The following diffraction lines of ZrSi2, which were detected under high pressure, were used for LWAM analysis: (020), (110), (021), (130), (111), (131), and (080). In some cases, the (110) and (130) reflections were left out due to their low signal-to-noise ratios. The first-principles calculations were carried out using Vienna ab initio simulation package.26,27 The generalized gradient approximation (GGA) using the Perdew−Burke−Ernzerhof functional was first employed as the exchange correlation potential.28,29 The plane-wave basis sets and projector-augmented wave method30 were used with 4d25s2 and 3s23p2 as valence electrons for Zr and Si, respectively. An energy cutoff of 800 eV and appropriate Monkhorst−Pack k-meshes were selected for all enthalpy calculations to converge to less than 1 meV/atom. Simulation was also performed using the local density approximation (LDA) as the exchange correlation function with appropriate parameters.31,32 The elastic constants were obtained from the stress tensor in the presence of a small strain.33 The bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio were calculated with the Voigt−Reuss−Hill method.34 The phonon dispersion curves were computed by a supercell approach as in the Phonopy program.35
constitutively in different conditions (e.g., varying temperature and/or pressure) to improve its functionality. There have been a few studies to date on ZrSi2, which has an orthorhombic structure (space group CmCm) at ambient conditions.5 The structure and the thermal expansion at high temperatures were examined via X-ray diffraction (XRD) method.1,14 Plastic deformation behavior of bulk and singlecrystal ZrSi2 was investigated at ambient pressure.14,15 The bulk modulus was estimated via cold compression in a cubic press with energy-dispersive synchrotron X-ray diffraction as the probe.16 More recently, various properties of ZrSi2 at high pressure and temperature have been predicted through the first-principles calculation.17 There is generally a lack of experimental investigations of deformational properties of ZrSi2 at high pressures that are important to materials science and other cross disciplinaries.18 In this work, high-pressure experiments were carried out using diamond anvil cell (DAC) and synchrotron angle-dispersive X-ray diffraction (ADXD) to determine the equation of state (EOS), elastic properties, and yield strength of ZrSi2. The experimental study is further supplemented by the first-principles calculations.
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EXPERIMENTAL AND THEORETICAL METHODS
The ZrSi2 powder (99.9%) purchased from Alfa Aesar as the starting material was first characterized by XRD (λ = 1.5404 Å) and field emission scanning electron microscopy (SEM) of its crystal structure, micromorphology, and purity. A symmetric DAC with a culet size of 300 μm was used to generate high pressures. In situ experiment without pressure-transmitting medium (referred to as NPTM hereafter) was performed at 16BM-D of the High Pressure Collaborative Access Team (HPCAT), Advanced Photon Source (APS), Argonne National Laboratory (ANL). The ZrSi2 powder was packed into the center hole (130 μm in diameter) of the Re gasket, which was pre-indented to about 30 μm thickness at ∼25 GPa and then laser-cut through the middle of the indentation for the sample chamber. A 5 μm ruby sphere was used as the pressure marker19 and a positional reference during ADXD measurement. The incident X-ray beam with wavelength 0.4133 Å was focused to approximately 5 μm × 7 μm. In situ experiment with methanol−ethanol mixture (4:1) as the pressure-transmitting medium (referred to as MEM hereafter) was carried out at Beamline 4W2 of the Beijing Synchrotron Radiation Facility (BSRF) with the incident X-ray beam having a wavelength of 0.6199 Å. The sample chamber is 80 μm in diameter at the center of a stainless steel (T301) gasket pre-indented to ∼20 μm thickness at ∼18 GPa. Diffraction patterns were collected using MAR-345 detectors that were calibrated by a CeO2 standard at the beginning of all the experiments. The Fit2D software was used to convert two-
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RESULTS AND DISCUSSION Figure 1a displays an XRD pattern and an SEM image of the starting ZrSi2, confirming its orthorhombic structure (i.e., each zirconium atom is coordinated by eight silicon atoms; lower left inset). The refined lattice parameters at ambient conditions are a = 3.696 Å, b = 14.751 Å, and c = 3.665 Å, yielding a unitcell volume of 199.83 Å3. These values agree with previous results17 and our theoretical calculation (GGA), but differ significantly from those by LDA method, as shown in Table 1. The average grain size of about 1.0 μm for the starting sample was estimated from SEM images. No significant amount of impurity was found in the powder. In Situ Synchrotron ADXD Experiments. Figure 1b shows the typical diffraction patterns for ZrSi2 under high pressures up to 54.5 GPa from the NPTM experiment, suggesting that the orthorhombic structure persisted to the B
DOI: 10.1021/acs.inorgchem.8b02559 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry Table 1. Summary of the Lattice Parameters a, b, c (Å), Unit-Cell Volume V (Å3), Bulk Modulus K0 (GPa), and Pressure Derivative K′0 in Present Work and Other Studiesa method
a
b
c
V
K0
I II GGA LDA ref 16 ref 17
3.696 3.690 3.701 3.655
14.751 14.750 14.849 14.509
3.665 3.664 3.675 3.633
199.8 199.4 202.0 192.6
3.706
14.735
3.672
201.0
182.0 170.0 121.0 142.0 114.8 120.6
common practice in EOS study in multi-anvil press is to anneal the sample at high temperatures to minimize the stress.36 Due to limited pressure range in the early experiment (0−7 GPa), the determination of the bulk modulus of ZrSi2 could be complicated by significant stresses in the sample during compression (see next section). Lastly, we cannot rule out that the discrepancy in the bulk modulus is due to the inherent differences in the starting materials. It has been shown that Si vacancies can significantly affect the structure and physical properties of metal disilicide.37,38 When compared to some of the neighboring transition-metal disilicides, ZrSi2 has a bulk modulus close to that of VSi2,39,40 larger than that of TiSi2,40 but smaller than that of NbSi2, TaSi2,41 and MoSi2.42 Yield Stress and Strength. The line-width analysis for MEM and NPTM experiments yielded nearly identical results (Figure 3). The deviatoric stress in ZrSi2 in both experiments
K′0 4 4 4 4 3.9
a
I and II represent the NPTM and MEM experiment, respectively.
highest pressure at room temperature (i.e., no structural phase transition). Pressure (P)−volume (V) data sets (Figure 2)
Figure 2. Experimental and theoretical (GGA) P−V data for ZrSi2. The solid curve is the BM-EOS fit to the combined data of NPTM (blue) and MEM (red).
Figure 3. Relationships between the microscopic deviatoric stress in ZrSi2 and pressure in NPTM and MEM.
were fitted to the third-order Birch−Murnaghan equation of state (BM-EOS)25 with K′0 = 4, yielding bulk moduli of K0 = 170.0 ± 0.7 and 182.0 ± 0.8 GPa for MEM and NPTM, respectively. An average bulk modulus of 176.0 ± 0.5 was obtained from the combined P−V data of both experiments (Figure 2). The axial variations with pressure in MEM can be described by the following quadratic relationships a /a0 = 1 − 1.26 × 10−3P + 2.19 × 10−6P 2
(1)
b/b0 = 1 − 1.51 × 10−3P − 1.09 × 10−5P 2
(2)
c /c0 = 1 − 1.48 × 10−3P + 9.34 × 10−6P 2
(3)
increased linearly with pressure between 0 and 10 GPa and remained at steady-state value during further increases in pressure, indicating the plastic deformation of the samples in both experiments starting from 10 GPa. The average deviatoric stress of 2.9 GPa in the plastic deformation region is taken as the yield stress or yield strength for ZrSi2. This value is also equivalent to the macroscopic differential stress under pressures greater than 10 GPa.24,25 The yield strength of ZrSi2 is significantly higher than those obtained at ambient pressure and high temperatures,14 but much lower than that of SiC (13.6 GPa)43 and Al2O3 (12.0 GPa).44 It is commonly noticed that DAC experiments without pressure-transmitting medium tend to yield greater bulk moduli than those obtained under hydrostatic condition. The effect caused by differential stress on the determination of bulk modulus of ZrSi2 in NPTM can be estimated based on the yield strength of ZrSi2 obtained above. When incident X-ray beam is parallel to the principal stress axis (σ3) as in DAC experiments in this work, X-ray diffractions recorded by detectors primarily correspond to stress axes σ1 and σ2 (σ1 = σ2).25 If the sample was plastically deforming during compression, the differential stress withheld by ZrSi2 must be equal to its yield strength (Y), i.e., σ3 − σ1 = Y. The true pressure is then close to σ1 = σ2 = P − Y/3, where P is the average pressure determined from the ruby scale: P = (σ1 + σ2 + σ3)/3 = (2σ1 + σ3)/3 = σ1 + Y/3. The correction to pressures greater than 10 GPa in NPTM is ∼1 GPa. A BM-EOS fit to these data points yielded K = 177 ± 1 GPa (K′0 = 4), a
where a, b, and c are the lattice parameters at P (GPa) and a0, b0, and c0 the parameters at ambient condition. By applying BM-EOS (K′0 = 4) to the normalized axial variations with respect to pressure, axial moduli of Ka = 748 ± 2 GPa, Kb = 423 ± 5 GPa, and Kc = 811 ± 14 GPa were obtained. Hence, the unit cell of ZrSi2 along the b-axis is nearly twice as compressible as along the a- and c-axis, consistent with the layered structure of ZrSi2 (Figure 1a, inset). It is apparent that the bulk moduli presented here for ZrSi2 are significantly larger than those in literature,14,16 though it seems that the earlier values were derived from single experiment using a cubic apparatus in combination with energy-dispersive synchrotron radiations.16 Neither P−V data nor K′0 was reported in both studies. Furthermore, the data were collected upon the cold compression, during which it is known the sample often experiences differential stresses. A C
DOI: 10.1021/acs.inorgchem.8b02559 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry Table 2. Elastic Constants of ZrSi2 (Cij in GPa) at Two Pressures (P in GPa) P
C11
C22
C33
C44
C55
C66
C12
C13
C23
0 55
223 435
169 368
255 489
99 210
128 261
106 207
86 185
97 260
72 131
decrease of 5 GPa compared to uncorrected result and close to the average value obtained from the global fitting. That is, the differential stress has a relatively small effect on the bulk modulus of ZrSi2 due to sufficient pressure range used in the current study. First-Principles Calculations. The elastic constants (Cij) of ZrSi2 were calculated at 0 K and 0−60 GPa from the stress− strain relationship.28 The results for 0 and 55 GPa are listed in Table 2. The Cij values at both pressures satisfy the criteria for mechanical stability of a CmCm phase having an orthorhombic structure,17 thus confirming the stability of ZrSi2 at the experimental conditions. Phonon dispersion has also been calculated for ZrSi2 at 0 and 55 GPa (Figure 4). Lack of any
G = 92.3 + 1.5P
(5)
E = 226.2 + 3.7P
(6)
where K, G, and E are the bulk, shear, and Young’s modulus, respectively, and P is the pressure in GPa. Simulation with LDA yielded a larger bulk modulus (Table 1). As the bulk and shear moduli measure the resistance to fracture and plastic deformation, respectively, K/G can be used to indicate the ductility of materials. The K/G ratio for ZrSi2 is 1.40 at 0 GPa, lower than the critical value of 1.75, suggesting that ZrSi2 is brittle at ambient conditions.45 The calculated linear bulk moduli are Ka = 676 GPa, Kb = 294 GPa, and Kc = 746 GPa. The theoretical anisotropy, i.e., Kc > Ka ≫ Kb, agrees with the experimental result, though two values for Kb differ by 130 GPa (Table 3). It is predicted that ZrSi2 is even more compressible Table 3. Bulk Moduli along the Orthorhombic Crystallographic Axes a, b, and c (Ka, Kb, and Kc in GPa), Density ρ, and Poisson’s Ratio ν for ZrSi2
Figure 4. Phonon dispersion curves of ZrSi2 at (a) 0 GPa and (b) 55 GPa.
method
Ka
Kb
Kc
ρ
ν
GGA exp.
675.5 748.5
293.9 423.6
745.8 811.3
4.86 4.89
0.22
along b-axis than experimentally determined in this study. Defects such as Si vacancies in the starting sample could contribute to this difference.37,38 Low Kb value results totally in the discrepancy between experimental and theoretical bulk moduli as Kc and Ka agree well (within 10%). Further studies are needed to clarify the large difference in Kb.
imaginary modes in the Brillouin zone at both pressures confirms the dynamic stability of ZrSi2 within the experimental conditions, consistent with the observations. The aggregate bulk, shear, and Young’s moduli for ZrSi2 have been calculated from the theoretical Cijs,34 shown in Figure 5. The results are in excellent agreement with previous first-principles calculation (GGA), though a different routine was used in the earlier study.17 They can be described by the following equations (4) K = 121.0 + 2.5P
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CONCLUSIONS In summary, in situ compression experiments using DAC and synchrotron ADXD and first-principles calculations have been carried out to study the structural and deformational properties of ZrSi2 at high pressures. A bulk modulus of K0 = 170.0 ± 0.7 GPa (K′0 = 4), which is significantly larger than the theoretical value of 121.0 ± 0.1 GPa, was derived for ZrSi2 from the experiment with pressure-transmitting medium. The discrepancy could be due to the presence of defects (e.g., Si vacancies) in the sample. A strong elastic anisotropy is demonstrated for ZrSi2 as b-axis is at least twice as compressible as a- and c-axes. The calculated ratio of bulk and shear moduli (K/G) is 1.40 at 0 GPa, indicating ZrSi2 is brittle at ambient condition. Transition from elastic to plastic deformation was observed for ZrSi2 at 10 GPa, and a yield strength of ∼3 GPa was determined. Finally, the aggregate bulk modulus (K), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν) were obtained, which are essential parameters for materials when their rigidity is to be analyzed.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (F.P.). *E-mail:
[email protected] and
[email protected] (L.W.).
Figure 5. Aggregate moduli calculated from theoretical Cijs. Experimental bulk moduli are also plotted for comparison. Lines are linear fits to the data. D
DOI: 10.1021/acs.inorgchem.8b02559 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
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ORCID
Hao Liang: 0000-0002-4965-4705 Xiaodong Li: 0000-0002-2290-1198 Pei Wang: 0000-0002-0423-9639 Liping Wang: 0000-0002-6137-3113 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS H.C. wishes to express sincere thanks to the University of Nevada Las Vegas (UNLV) for its hospitality. This work is supported by the National Natural Science Foundation of China (Grant No. 11604175) and the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Cooperative Agreement #DE-NA0001982. The nonhydrostatic compression experiment was performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory (ANL). HPCAT operations are supported by DOENNSA under Award No. DE-NA0001974 and DOE-BES under Award No. DE-FG02-99ER45775, with partial instrumentation funding by NSF. APS is supported by DOE-BES, under Contract No. DE-AC02-06CH11357. The hydrostatic compression experiment was carried out at Beamline 4W2 of the Beijing Synchrotron Radiation Facility (BSRF), which is supported by Chinese Academy of Sciences (Grant Nos. KJCX2-SW-N03 and KJCX2-SW-N20).
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REFERENCES
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DOI: 10.1021/acs.inorgchem.8b02559 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
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DOI: 10.1021/acs.inorgchem.8b02559 Inorg. Chem. XXXX, XXX, XXX−XXX
