OsN2: Crystal structure and electronic properties

APPLIED PHYSICS LETTERS 90, 011909 共2007兲 OsN2: Crystal structure and electronic properties Javier A. Montoyaa兲 INFM/Democritos National Simulation Center, via Beirut 2-4, 34014 Trieste, Italy and SISSA-International School for Advanced Studies, via Beirut 2-4, 34014 Trieste, Italy Alexander D. Hernandez The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy Chrystèle Sanloup Université Pierre et Marie Curie, case 110, 4 place Jussieu, 75252 Paris Cedex 05, France and Institut de Physique du Globe de Paris, case 89, 4 place Jussieu, 75252 Paris Cedex 05, France Eugene Gregoryanz Institut de Minéralogie et de Physique des Milieux Condensés, 4 Place Jussieu, 75252 Paris Cedex 05, France; School of Physics, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom; and Centre for Science at Extreme Conditions, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom Sandro Scandolo INFM/Democritos National Simulation Center, via Beirut 2-4, 34014 Trieste, Italy and The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy 共Received 26 September 2006; accepted 4 December 2006; published online 4 January 2007兲 Osmium nitride belongs to a family of nitrides synthesized recently at high pressures from their parent elements. Here we show, based on first-principles calculations, that the crystal structure of osmium nitride is isostructural to marcasite. Excellent agreement is obtained between the authors’ results and x-ray, Raman, and compressibility measurements. In the OsN2 marcasite structure single-bonded N2 units occupy the interstitial sites of the Os close-packed lattice, giving rise to a metallic compound. A comparison between the formation energies of OsN2 and PtN2 explains the similar thermodynamic conditions of formation reported experimentally for the two compounds. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2430631兴 A family of late transition metal nitrides has been recently synthesized starting from their constituent elements, Pt, Ir, and Os, and nitrogen.1–3 The compounds have been obtained by subjecting the parent metal to extreme conditions of pressure and temperature, in a nitrogen embedding medium, in a diamond-anvil cell. Interest in these compounds resides in their large bulk modulus, which might suggest superhard mechanical properties. High-pressure x-ray diffraction experiments on the three compounds give bulk moduli of 372 GPa 共platinum nitride兲,1 432 GPa 共iridium nitride兲, and 358 GPa 共osmium nitride兲, respectively.2 Despite intense experimental and theoretical efforts over the last two years, the crystal structure of these compounds is only known in the case of platinum nitride.4,5 X-ray diffraction measurements were able to clarify for all compounds the nature of the sublattice of the transition metal atoms, but due to the large atomic-number ratio between the metal and nitrogen, x-ray diffraction is unable to provide insight into the internal position of the nitrogen atoms nor into the stoichiometry of the compound. The metal sublattice has been reported to be face-centered cubic in the case of Pt nitride,4 orthorhombic in Os nitride, and rhombohedral in Ir nitride.2 Among a number of theoretical structures proposed in the last two years for platinum nitride, ab initio calculations show that the crystal structure with the lowest energy is isostructural to pyrite 共thus with stoichiometry Pt: N = 1 : 2兲.4,5 Calculated Raman spectra and diffraction patterns for PtN2 pyrite agree very well with experiments. Nitrogen atoms in pyrite PtN2 pair up to form single-bonded dinitrogen units 共N2兲 which fill the octahedral holes of the fcc Pt sublattice. The crystal structure of Ir and Os nitrides is not yet known. The similarity between the Raman spectra of PtN2 and Ir nitride, particularly in the frequency region of the single-bonded N2 stretching, suggests that Ir nitride could also be composed of dinitrogen units located in the interstitial holes of the rhombohedral Ir sublattice. The picture is, however, much less clear in the case of osmium nitride, where no Raman peaks have been observed,2 presumably due to the metallic character of the compound. In this work we compare the structural and mechanical data obtained from ab initio calculations with the experimental data of Ref. 2, and conclude that the crystal structure of Os nitride is isostructural to that of marcasite, a known polymorph of FeS2 structurally similar to pyrite. Therefore, dinitrogen units similar to those found in PtN2 are also present in OsN2. TABLE I. Equilibrium lattice parameters 共 in Å兲 and zero-pressure bulk modulus 共in GPa兲 and its pressure derivative 共B⬘兲 obtained from fitting calculated energies over a range of volumes with a second order BirchMurnaghan equation of state. Formation energies ⌬E are relative to Os+ N2. a Expt. Marcasite 共Calc.兲 Pyrite 共Calc.兲 Os Expt.b Os Calc. a b c B , B⬘ ⌬E 共eV兲 2.714 2.70 4.85 3.03 3.05 4.910 4.93 4.102 4.13 358,4.67 359,4.28 339,3.85 411,4.0 411,4.3 ¯ 1.15 2.15 ¯ ¯ a a兲 Electronic mail: [email protected] Reference 2. Reference 6. b 0003-6951/2007/90共1兲/011909/3/$23.00 90, 011909-1 © 2007 American Institute of Physics Downloaded 10 Jan 2007 to 129.215.196.72. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp 011909-2 Montoya et al. Appl. Phys. Lett. 90, 011909 共2007兲 FIG. 1. 共Color online兲 Marcasite structure of OsN2, space group Pnnm. Osmium atoms 共gray兲 form an orthorhombic lattice, and dinitrogen 共N2兲 units 共light blue兲 occupy the cavities of the Os lattice. The calculated N – N distance at ambient pressure is 1.427 Å. The Rietveld fit using the Pnnm space group is in excellent agreement with experiments, red crosses: data at ambient pressure 共␭ = 0.4237 Å兲; green line: Rietveld fit; black ticks: OsN2 peaks; red ticks: Os peaks. The most intense Os peaks are cut off. Calculations7 were performed within density functional theory using a Perdew-Burke-Ernzerhoff exchange correlation functional8 and a plane wave basis set for the electronic wave functions with a kinetic energy cutoff of 70 Ry. A pseudopotential description of the ion-electron interaction9 was used, with osmium’s 5s and 5p semicore electrons included in the valence. Brillouin zone integration was found to be converged with a uniform grid of 9 ⫻ 9 ⫻ 9 points 共corresponding to 205 points in the irreducible zone of the marcasite structure兲. The marcasite structure has the space group Pnnm, with osmium atoms on the Wyckoff sites 2a 关共0,0,0兲 and 共1 / 2 , 1 / 2 , 1 / 2兲兴 and nitrogen atoms on the site 4g 关共x , y兲兴, with two internal parameters x and y. Structural relaxations were thus performed by relaxing the nitrogen positions, while osmium atoms are fixed by symmetry. The calculated properties 共equilibrium volume, lattice parameters, and bulk modulus兲 of OsN2 marcasite are reported in Table I and agree very well with experiment. The calculated nitrogen internal parameters at 0 GPa are x = 0.127 51 and y = 0.403 86. A Rietveld refinement 共Fig. 1兲 of the observed diffraction pattern using the Pnnm space group shows that the marcasite structure is fully consistent with the x-ray data. The theoretical formation energy of marcasite OsN2, calculated as a difference between the ab initio total energies of OsN2 and those of Os metal and molecular N2 in the ⑀ structure at zero pressure, is found to be positive 共1.15 eV兲, indicating that the compound is in principle thermodynamically unstable towards decomposition into its constituent elements, at zero pressure. It is interesting to remark that the formation energy of PtN2 was also found to be positive, but larger than the one found here for OsN2.4 This indicates a lower propensity to dissociate back into the constituent elements in the case of OsN2, with respect to PtN2, which is consistent with the experimental observation that much larger quantities of OsN2 than PtN2 have been found in the samples recovered at ambient pressure. From the calculated energies as a function of volume, at T = 0 K, we extracted the pressure dependence of the enthalpies shown in Fig. 2. Upon application of pressure the formation energy of OsN2 marcasite decreases and eventually vanishes at 23 GPa 关Fig. 2共a兲兴 above which the compound becomes more stable than its constituents, at least at low temperature. This is consistent with the experimental finding that the compound can be synthesized only when pressure reaches 50 GPa. We also notice that the enthalpy of a hypothetical OsN2 compound with the pyrite structure is significantly higher than that of OsN2 marcasite at all calculated pressures 共up to 200 GPa兲. A more appropriate comparison of the theoretical predictions with the reported conditions for the synthesis of the compound 共50 GPa, 2000 K兲 would require a calculation of its finite-temperature Gibbs free energy of formation, which is beyond the scope of this work. We remark, however, that at the conditions of synthesis, nitrogen is likely to be in the liquid state. An extrapolation of the melting curve of nitrogen measured up to 18 GPa,10 in fact, gives 1500– 1750 K for the melting temperature at 50 GPa,2 which is below the reaction temperature. Assuming that differences between the vibrational contributions to the free energy are negligible for the solid phases and using for the excess free energy of the liquid the empirical expression derived by Kroll based on thermochemical data,11 we obtain at 50 GPa a reaction temperature of 2100 K, in good agreement with the experimental value. We thus conclude that the synthesis of the compound is likely to occur at, or close to, the thermodynamic boundary. In an attempt to rationalize the experimental observation that the synthesis conditions of the three nitrides are nearly FIG. 2. 共Color online兲 共a兲 Enthalpy vs pressure for OsN2 pyrite, OsN2 marcasite, and their constituents at T = 0. 共b兲 Same as in 共a兲 for PtN2 pyrite. Downloaded 10 Jan 2007 to 129.215.196.72. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp 011909-3 Appl. Phys. Lett. 90, 011909 共2007兲 Montoya et al. FIG. 3. 共Color online兲 Electronic bands of marcasite OsN2 at ambient pressure along high symmetry lines together with the corresponding density of states and its projection onto the constituent atoms. The Fermi energy is set to zero. identical,2 we report in Fig. 2共b兲 the enthalpy of formation for pyrite PtN2 共a similar comparison with Ir nitride is not possible as its structure is not yet known兲. Interestingly, even though the zero-temperature calculated transition pressure is slightly lower than the one found for OsN2, the zerotemperature formation energy of PtN2 at 50 GPa is very similar to that of OsN2 共⬃−1.3 eV兲. Under the assumption discussed above that finite-temperature corrections to the free energy can be approximated by simply considering the excess free energy of liquid nitrogen, then it appears that the thermodynamical boundaries for the high-temperature synthesis of OsN2 and PtN2 are likely to be very close, in agreement with the experimental findings. We finally comment on the electronic structure of OsN2 marcasite. Our band structure calculations 共Fig. 3兲 show that, contrary to PtN2 which is known to be an insulator,4 OsN2 marcasite has a metallic character, which is in agreement with the experimentally observed absence of first-order Raman peaks for this compound. Os belongs, like Pt, to the last row of the transition metal series and has two electrons less than Pt, so an insulating character would be compatible with electron counting arguments. In order to understand why OsN2 is a metal it is interesting to consider a hypothetical OsN2 compound with the pyrite structure. In a simplified picture in which the density of electronic states 共DOS兲 only depends on the crystal structure and not on the electron filling, the electronic structure of pyrite OsN2 can be obtained from that of pyrite PtN2 by removing eight electrons 共the unit cell of pyrite contains 4 f.u.兲, which corresponds to the Fermi level indicated by the red line in Fig. 4共c兲, which would imply a metallic character also for this hypothetical compound. The ab initio DOS of OsN2 pyrite 关Fig. 4共b兲兴 confirms that the reasoning is correct. The gap at a filling of 80 electrons/cell 共eight electrons above the Fermi level兲 is still present, and the Fermi level lies in a region of finite density of states. However, the OsN2 pyrite DOS has a very high density of states at the Fermi level, which is typically FIG. 4. 共Color online兲 Density of electronic states and its integral for 共a兲 OsN2 marcasite, 共b兲 OsN2 pyrite, and 共c兲 PtN2 pyrite. The Fermi energy is set to zero. associated with an instability of the electronic structure, leading either to magnetism or to structural distorsions. The marcasite structure, with its simple structural connection to pyrite, can be seen as a way for the system to relieve the electronic instability found in the pyrite structure. OsN2 marcasite 关Fig. 4共a兲兴 shows, in fact, a much lower density of states at the Fermi level, which explains its lower energy with respect to OsN2 pyrite. The OsN2 structure in Fig. 1 was generated with A. Kokalj’s XCRYSDEN package 共http://www.xcrysden.org/兲. The authors acknowledge useful discussions with R. Rousseau, G. Profeta, A. Oganov, and A. Young. This work was partially supported by INFM through “Progetti di calcolo parallelo.” 1 E. Gregoryanz, C. Sanloup, M. Somayazulu, J. Badro, G. Fiquet, H.-K. Mao, and R. J. Hemley, Nat. Mater. 3, 294 共2004兲. A. F. Young, C. Sanloup, E. Gregoryanz, S. Scandolo, R. J. Hemley, and H.-K. Mao, Phys. Rev. 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