Elastic, magnetic and electronic properties of iridium phosphide Ir2P

Cubic (space group: Fmm) iridium phosphide, Ir2P, has been synthesized at high pressure and high temperature. Angle-dispersive synchrotron X-ray diffraction measurements on Ir2P powder using a diamond-anvil cell at room temperature and high pressures (up to 40.6 GPa) yielded a bulk modulus of B0 = 306(6) GPa and its pressure derivative B0′ = 6.4(5). Such a high bulk modulus attributed to the short and strongly covalent Ir-P bonds as revealed by first – principles calculations and three-dimensionally distributed [IrP4] tetrahedron network. Indentation testing on a well–sintered polycrystalline sample yielded the hardness of 11.8(4) GPa. Relatively low shear modulus of ~64 GPa from theoretical calculations suggests a complicated overall bonding in Ir2P with metallic, ionic, and covalent characteristics. In addition, a spin glass behavior is indicated by magnetic susceptibility measurements.


Results and Discussion
At ambient conditions, Ir 2 P adopts a CaF 2 -type structure with a space group of Fm3m [32][33][34][35] . As shown in Fig. 1a, each iridium atom is surrounded by four phosphor atoms and [IrP 4 ] tetrahedrons are edge -sharing and form a 3D network. The refined cation-anion bond length is 2.40 Å and the cation-cation bond length is 2.77 Å.
To study the phase stability and compressibility of cubic Ir 2 P, synchrotron powder x-ray diffraction experiment was performed in a symmetric diamond anvil cell (DAC) up to 40.6 GPa at room temperature. Figure 1b shows the representative diffraction patterns as a function of pressure. A small amount of metal Ir impurity was detected in the diffraction patterns. No pressure-induced phase transition was observed, suggesting the cubic Ir 2 P is stable in the pressure range of investigation under experimental conditions. By fitting the compression data to a second and third-order Birch-Murnaghan equations of state (BM-EoS), we obtained bulk modulus Figure 1. (a) The crystal structure of cubic Ir 2 P; (b) at room temperature, representative high-pressure x-ray diffraction patterns of Ir 2 P synthesized at 15 GPa/1800 °C; (c) the volume-pressure data fitted to the 3 rd order BM-EoS from experiment and calculation. Filled circles represent the experimental data points; The solid line is the EoS fit to experimental data; The dash and dash-dot lines represent the results from LDA and GGA, respectively. Error bars for all experimental data points are smaller than the size of the symbols.
Scientific RepoRts | 6:21787 | DOI: 10.1038/srep21787 B 0 = 334(2) GPa with B 0 ′ = 4 (fixed), and B 0 = 306(6) GPa and B 0 ′ = 6.4(5), respectively. Bulk modulus values from first -principles calculations (see Methods), B 0 = 320 GPa with B 0 ′ = 5.0 from generalized gradient approximation (GGA) and B 0 = 342 GPa with B 0 ′ = 5.0 from local density approximation (LDA) ( Table 1), are consistent with the experimental results. Iridium is the second least compressible noble metal (next only to osmium) 37 . The short Ir-P bonds and presence of Ir atoms having a high density of valence electrons play key roles in limiting the lattice compression (i.e., high bulk modulus) since it is extremely difficult to shorten the distances among these atoms due to the rapidly increasing repulsive forces 9 .
Vickers hardness measurements were carried out on the polished surface of chunky Ir 2 P samples. Figure 2 shows the dependence of hardness on loading force. A hardness of 11.8 (4) GPa under a loading force of 9.8 N suggests Ir 2 P is considerably harder than hardened steel and some monoborides such as OsB (10.6 GPa) and RuB (8 GPa) ( Table 1) 4 and comparable to some ceramics (e.g., ZrO 2 ) 38 and WC-Co alloys in the hard regime. The hardness of Ir 2 P is also similar to that of Re 2 P (Table 1) 21 .
Magnetic susceptibility measurements for Ir 2 P were performed in the temperature range of 2-300 K under a magnetic field of 1 T. Figure 3 shows the temperature dependent susceptibility. The kink at ~50 K in susceptibility revealed the possible transition of magnetic state. Moreover, the violation of Curie-Weiss law and the negative Curie-Weiss temperature (inset of Fig. 3) indicated that the spin glass behavior existed in an antiferromagnetic interaction background.
To correlate the chemical bonding and mechanical properties, we have performed first -principles calculations based on the density functional theory (DFT) using the CASTEP code with a PBE and CA-PZ  exchange-correlation functional form of the GGA and LDA, respectively 39 . As shown in the calculated band structure at ambient conditions (Fig. 4a), the valence band maxima cross Fermi level and meet with the conduction band maxima between the G and X points. The overlap of valence and conduction bands indicates a metallic state for the band structure of Ir 2 P, consistent with the previous results 31,32,36 . In order to further understand the properties of Ir 2 P, the total and partial electronic densities of state (DOS) were also calculated and are shown in Fig. 4b. The Ir 5d and P 3p states of Ir 2 P dominate the DOS at the Fermi level, and the P 3s electrons basically lie at the bottom of valence band. The P 3p and Ir 5d orbitals having major contributions to total DOS reveal a strong hybridization between Ir d and P p orbitals. The finite DOS at the Fermi level indicates metallic behavior of Ir 2 P, consistent with the calculated band structure. The electronic localization function (ELF) based on the Hartree-Fock pair probability of parallel spin electron was calculated to visualize different types of bonding in solids 40 . As shown in Fig. 5a, the polar covalent bonding interactions between Ir and P are evident as the ELF maxima are strongly biased towards the P atoms. The yellow-colored electron configuration indicates a substantial accumulation of electronic charge density within the voids of crystal structure. Figure 5b clearly displays metalloid covalent bonding feature. The relatively high ELF values along Ir-P bonds mirror its covalent feature while the low ELFs between Ir ions correspond to the metallic bonding. The polar metal-metalloid (M-P) covalent bonds of short distance (2.40 Å) should result in relatively incompressible tetrahedra, which form a 3D-network through edge-sharing that further enhances Ir 2 P's ability to resist compression. Moreover, the interlaced Ir-Ir metallic bonds as in metal Ir are difficult to be shortened under pressure. All these factors play a positive role for the high incompressibility of Ir 2 P. On the other hand, the weak Ir-Ir metallic bonds make the structure susceptible to shear deformation under stress, resulting in the relatively low shear modulus ( Table 1) and hardness of Ir 2 P shown in Fig. 2.

Conclusions
In summary, we synthesized cubic Ir 2 P at high pressure and high temperature (HPHT). In the pressure range of 0 to 40.6 GPa, Ir 2 P has a high bulk modulus of B 0 = 306(6) GPa with B 0 ′ = 6.4 (5). It has a Vickers hardness of 11.8(4) GPa under a loading force of 9.8 N. These results are in consistence with the first -principles calculations that suggest the strong polar covalent bonding between Ir and P atoms leads to the incompressibility of Ir 2 P. The metallic Ir bilayers are presumably responsible for the weakest paths under shear deformation. The temperature-dependent molar susceptibility indicates the spin glass behavior in an antiferromagnetic interaction background in Ir 2 P.

Methods summary
HPHT synthesis. Ir 2 P was synthesized using a mixture of Ir powder (purity 99.9%) and red phosphorus powder (purity 99.999%) with a molar ratio of Ir : P = 2 : 1 under high pressure/temperature conditions. The syntheses were carried out in a two-stage multi-anvil apparatus based on a DS 6 × 8 MN cubic press 41,42 and a Walker-type multianvil press at Arizona State University 43 . The 14/8 sample assembly, consisting of a 14 mm (edge length) MgO octahedron, a ZrO 2 thermal insulator and a Ta heater, was compressed by eight cubic WC anvils, each with 8-mm corner truncation (edge-length). Pressures were estimated based on the calibration established by phase transitions in ZnTe, ZnS, and GaAs at room temperature, and temperatures were measured in-situ with a Pt6%Rh-Pt30%Rh or Re5%W-Re25%W thermocouple. The samples were first compressed to targeted load, and then heated with a rate of about 100 °C /min to desired temperature and hold for 30 min. The pressure was released after the temperature was quenched to room temperature. The recovered cylindrical samples have a diameter of ~3 mm and a height of ~3 mm.
Characterization methods. The recovered samples were characterized by x-ray diffraction with Cu Kα radiation source. High-pressure in-situ powder x-ray diffraction experiments were performed using a symmetric   diamond anvil cell (DAC) with a culet size of 300 μ m at 16-IDB of the High Pressure Collaborative Access Team (HPCAT), Advanced Photon Source (APS), Argonne National Laboratory (ANL). The Ir 2 P powders were loaded into a pre-indented gasket (steel) hole in diameter 170 μ m. A few ruby balls were also loaded in the sample chamber to serve as the internal pressure standard 44 . Neon was used as pressure-transmitting medium to improve hydrostatic pressure conditions for the sample. The incident x-ray beam of wavelength 0.3738 Å was focused to approximately 5 μ m × 7 μ m. The distance between image plate and sample is 182 mm. The 2D patterns of intensity versus 2θ were obtained by using the FIT2D software 45 . Vickers hardness was measured on a well -sintered polycrystalline sample under different loads of 25, 50, 100, 200, 300, 500, and 1000 g by using a Micromet-2103 hardness tester (Buehler, USA). Under each applied load, the measurement was performed with a dwelling time of 15 s, and was repeated 5-10 times to obtain statistically improved averages. The low temperature magnetic susceptibility measurements were performed in a Quantum Design superconducting quantum interference device (SQUID) an external field of 1 T.

Computation details.
First -principles calculations based on density functional theory (DFT) were performed in the CASTEP code with a PBE and CA-PZ exchange-correlation functional form of the GGA and LDA, respectively 39 . The plane-wave cut-off energy was 500 eV, and the Brillouin-zone sampling was performed with the Monkhorst-Pack grid with a k-points sampling of 7 × 7 × 7. The 5d 7 6s 2 and 3s 2 3p 3 were taken as valence electron for Ir and P atoms, respectively. Broyden-Fletcher-Goldfarb-Shanno (BFGS) scheme was considered as the minimization algorithm 46 . The bulk modulus, shear modulus, Young's modulus, and Poisson's ratio were estimated by using the Voigt-Reuss-Hill approximation 47 .