Equation of state and compressibility of nickel semiboride

N.V. Chandra Shekar n, M. Sekar, P.Ch. SahuCondensed Matter Physics Division, Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, India

a r t i c l e i n f o

Article history:Received 19 February 2014Accepted 7 March 2014Available online 15 March 2014

Keywords:Transition metal semiborideHigh pressurex-ray diffractionElectronic structureStructural stability

a b s t r a c t

The compound Ni2B stabilizes in tetragonal structure at NTP with space group I4/mcm (No. 140), andlattice parameters; a¼ 0.499 nm and c¼0.424 nm. The B–B bond distance is of about 0.212 nm and theB–B interaction is expected to be very small. High pressure x-ray diffraction study on this compound wascarried out up to 28 GPa. It was seen that the compound remained stable throughout out this pressurerange and the B–B distance decreased by about �4%. Electronic structure calculations were carried outusing the Full Potential Linear Augmented Plane Wave (FP-LAPW) method to understand its structuralstability with respect to pressure. It is seen that the Fermi level lies on a plateau region with very lowdensity of states, despite the compound being metallic in nature. Further, the computations at reducedvolumes revealed that the density of states at EF almost remained constant with pressure, which hasbeen attributed to its structural stability under pressure.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Metal borides occur in wide range of composition from ternarymetal rich to boron–rich structures [1]. The crystal structuresdepend strongly on the metal/boron ratio. Borides show specialfeatures such as short boron–boron contacts and formation of one,two, and three dimensional boron networks [1]. Borides withshort bond length are also important, being potential super hardmaterials [2]. Binary semi-borides are important class of borideswhich crystallize in tetragonal Cu2Al structure type with spacegroup I4/mcm (No. 141).

The electronic structures of several transition metal semi-borides were calculated by Mohn (1988) and found that thecalculated magnetic moment and the hyperfine field were inagreement with experiments [3]. The paper reports that themagnetic moment formations in iron and cobalt semiborides areinfluenced by the hybridization of the d orbital of transition metaland p orbital of boron atom [3]. However, it is surprising that thereare no experimental reports on investigation of these compoundsunder pressure. The effect of external pressure on the B–Binteraction and stability of the tetragonal structure will be inter-esting to study. In this paper we report high pressure x-raydiffraction studies on Ni2B, a Pauli paramagnet, up to a pressureof about 25 GPa. We have also tried to correlate its high pressurebehavior with its computed electronic structure.

2. Experimental details

The experiments were carried out with Ni2B powder (99% pure)procured fromM/s Alfa Aesar. The powder was characterized usingIP based mar345dtb diffractometer and the lattice parameterswere found to be a¼0.499 nm and c¼0.424 nm at ambient,which matches well with the ICDD standard values (PDF Cardno. 89-1995). The high pressure experiments were carried outusing Mao–Bell type diamond cell and a laboratory based rotatinganode x-ray source. The x-ray diffraction patterns were recordedusing an IP based mar345dtb with overall resolution of 0.001 Å.

The powder sample was loaded in a 200 mm size hole in thestainless steel gasket and Ag was used as an internal pressurecalibrant. The mixture of methanol–ethanol and water in the ratioof 16:3:1 was used as a pressure transmitting medium.

3. Computational details

The calculations were carried out by the FP-LAPW methodusing WIEN2K code [4]. The band structure and the density ofstates for Ni2B were calculated using 1984 k-points in theirreducible Brillouin zone (IBZ). The improved version of general-ized gradient approximation (GGA – PBE96) [5] was used. Theplane-waves with a cut off of RMTnKmax¼8 were used, where RMTdenotes the smallest atomic sphere radius and Kmax is themagnitude of the largest k-vector in the plane wave expansion.The k-points and the RMTnKmax were optimized by repeating thecalculations until the total energy got stabilized. Since Ni2B isa Pauli paramagnet, the calculations were carried out without spin

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Physica B

http://dx.doi.org/10.1016/j.physb.2014.03.0150921-4526/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author.E-mail address: chandru@igcar.gov.in (N.V. Chandra Shekar).

Physica B 443 (2014) 95–98

polarization and spin–orbit interaction. The position of atoms inNi2B with Al2Cu type structure (space group I4/mcm) wereoptimized and finally their positions were as follows: Ni atom at(the 8(h) point symmetry position) 0.16845219, 0.66845219 and 0;and B atom at 0, 0 and ¼, position (the 4(a) point symmetryposition). The optimized lattice parameters were taken as: a¼0.4982 nm and c¼ 0.4239 nm for the ambient structure. Thecalculations were also performed at reduced volume of 0.95,0.9 and 0.85 times V0 for the same number of k points.

4. Results and discussions

Fig. 1 shows high pressure x-ray diffraction patterns for thesample as well as the calibrant (Ag). The Bragg peaks at ambientcould be very clearly indexed to the tetragonal phase of thecompound. As a function of pressure, all the peaks broaden andshift towards higher theta as expected. There is no emergence ofany new feature to pressures as high as 28 GPa.

The c/a ratio and the relative B–B bond length as a function ofpressure are shown in Fig. 2. Although the c/a ratio decreasesmonotonically as a function of pressure, it is observed that even for

10% decrease in volume of the cell, the B–B bond length decreasesonly by about 4%. In order to have any significant interaction betweenthe boron atoms, it is believed that we have to reach much higherpressures in order to decrease B–B bond length below 0.15 nm. TheP–V curve was fitted with Birch–Murnaghan equation of state andthe bulk modulus was found to be �236.874.1 GPa with itspressure derivative fixed at 2. The value matched very well withthe calculated bulk modulus of about 240 GPa. Fig. 3 shows theexperimental and calculated compression curves. The calculated P–V

Fig. 1. High pressure x-ray diffraction patterns of Ni2B at various pressures up to28 GPa. The peaks of both sample as well as Ag (used here as pressure calibrant)can be seen. G represents gasket peak.

Fig. 2. Changes in the c/a ratio and the B–B bond distance as a function of pressurefor Ni2B.

Fig. 3. V/V0 versus P plot for Ni2B. The experimental points have been fitted withthe Birch–Murnaghan equation of state. The dotted curve is a calculated one. Thedeviation from the experiment seems to be well within the error limits..

Fig. 4. (Bottom). The total density of state for Ni2B, Ni and B. It is clear that DOS at EF isdominated by Ni. (Top) Density of states plotted at various reduced volumes for Ni2B.

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curve deviates from the experimental curve at higher pressuresand is within the error limits.

The possible reasons for the high stability of the compoundunder pressure are discussed using the results obtained fromelectronic structure calculations. Fig. 4 shows the density of states(DOS) calculated for Ni2B at ambient pressure. The result matchesvery well with the earlier work [3]. The Fermi level lies in a plateauwith very low DOS (about 9 states/eV cell). The strongly hybridizedB p and Ni d states lie about 2.2 eV below the Fermi level. At theFermi level the contribution of B is very less as compared to Ni.In the earlier calculation by Mohn (1988), the sudden flattening ofthe DOS from a seemingly rapid fall as one approached from thebonding side is not clear. In our calculation, this feature hasappeared clearly, and its implication on the behavior of the systemis important. This could in turn be the cause for relatively largestability of the system. It is known that under compression variouseffects like the broadening of bands and movement of certainbands may result in drastic changes in the DOS near EF. However,here in Ni2B it can be anticipated with certain degree of confidencethat nothing drastic is likely to happen in the region of EF becauseof the plateau in the total DOS. In one of our earlier report onf electron based compounds, the behavior of density of states nearEF and the location of the f band has been correlated to theinherent stability of the systems [6].

In order to further confirm our speculation and look atpossible changes occurring in the electronic structure under

compression, the computations were carried out at reducedvolumes of 0.95V0, 0.90V0 and 0.85V0. Fig. 4 (inset) shows thedensity of states plotted at various reduced volumes for Ni2B. Asthe volume decreases, the overall shape of the DOS near theFermi level remains the same. The minima at the Fermi level as afunction of pressure certainly have direct implication on thestability of the crystal structure.

In Fig. 5, the band dispersion curves are plotted close to Fermienergy for 0.95V0, 0.90V0 and 0.85V0 respectively. The compoundshows metallic nature and the d bands of Ni dominate near theFermi level as seen also in the density of states plots. It is ofinterest to note that the band pinned to Fermi level between the Hdirections in the Brillouin zone remained so even at the highestcompression (pressure). In conclusion, there is no significantchange in the band dispersion curves and the DOS at EF asa function of pressure reduced volume up to 85%.

Fig. 6 shows the electron density plotted with center at (½½½)and diagonal corners are having coordinates (00½) and rightbottom (100) for Ni2B. The dark circles represent Ni atoms andlighter ones B atoms. The low charge density seen in the inter-stitial region is indicative of poor metallicity. This is also evidentfrom the low density of states at normal pressure. The degree ofcovalency seen in the electron density plot between Ni–Bdecreases as a function of compression. As evident from the plots,even at very high compression, there is hardly any change in thenature of bonding between boron atoms.

Fig. 5. Band dispersion curves plotted close to Fermi energy for Ni2B at various reduced volumes of 0.95V0, 0.90V0 and 0.85V0 respectively.

Fig. 6. The electron density plotted with center at (½½½) and diagonal corners are having coordinates (00½) and right bottom (100) for Ni2B at various reduced volumes.

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5. Conclusions

In conclusion, high pressure x-ray diffraction studies of Ni2Bshowed its tetragonal structure to be stable up to 28 GPa. The B–Bbond distance decreased by about �4% at 28 GPa, which is stilllarge for any significant B–B interaction. The structural stability ofthe compound is linked to a stable plateau region in the DOS at theFermi level. The density of states at EF is very low despite thecompound being metallic in nature.

Acknowledgments

The authors thank members of High Pressure Physics Sectionfor showing their interest in the work. They also thank IGCARManagement for support.

References

[1] T. Lundstrom, Structure, defects and properties of some refractory borides, PureAppl. Chem. 57 (1985) 1383–1390.

[2] A.L. Ivanovskii, Mechanical and electronic properties of diborides of transition3d–5d metals from first principles: toward search of novel ultra-incompressibleand superhard materials, Prog. Mater. Sci. 57 (2000) 184–228.

[3] P. Mohn, The calculated electronic and magnetic properties of the tetragonaltransition-metal semi-borides, J. Phys. C Solid State Phys. 21 (1988) 2841–2851.

[4] Blaha P., Schwarz K., MadsenG K.H., Kvasnicka D.,Luitz J. WIEN2K: ViennaUniversity of technology, Wein, Austria, 2001; isbn:3-9501031-1-1-2.

[5] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation madesimple, Phys. Rev. Lett. 77 (1996) 3865–3868.

[6] N.V. Chandra Shekar, V. Kathirvel, P.Ch. Sahu, Structural stability, phasetransformations and band-tuning of actinide and rare earth based intermetal-lics under high pressure: a perspective, Indian J. Phys. 84 (2010) 485–499.

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