PHYSICAL REVIEW B 86, 014114 (2012)

Experimental evidence for the structural models of Re2N and Re2C from micro-Raman spectroscopy

Alexandra Friedrich* and Bjorn WinklerGeowissenschaften, Goethe-Universitat, Altenhoferallee 1, D-60438 Frankfurt am Main, Germany

Keith RefsonRutherford-Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom

Victor MilmanAccelrys, 334 Science Park, Cambridge CB4 0WN, United Kingdom

(Received 13 January 2012; published 27 July 2012)

The vibrational properties of the high-pressure, high-temperature phases of hexagonal Re2N rhenium nitrideand Re2C rhenium carbide are reported from micro-Raman spectroscopy at ambient and high pressure and fromtheoretical calculations based on density functional theory. These data confirm the structural model of Re2Nproposed recently. The ambiguity of the location of the carbon position in Re2C is resolved. We show that thestructures of Re2N and Re2C are isotypic, with the N and C atoms occupying the same trigonal prismatic voidsin the hexagonal stacking of Re atoms. The effect of pressure on vibrational properties is investigated, and modeGruneisen parameters of the Raman-active modes are found to be between 1.1 and 1.6 for both Re2N and Re2C.

DOI: 10.1103/PhysRevB.86.014114 PACS number(s): 61.50.Ks, 63.20.−e, 78.30.−j

I. INTRODUCTION

Transition-metal carbides and nitrides are a large andcomplex group of industrially relevant refractory compounds,which are, for example, used as abrasives or “ultrahigh-temperature ceramics” as they often have a high melting pointin combination with a very low compressibility and high hard-ness. In recent years there has been a rapidly growing interestin synthesizing new transition-metal nitrides and carbides athigh-pressure, high-temperature conditions. Their structure-property relations have been studied extensively,1,2 although anumber of fundamental questions remain unanswered.

For the heavy transition-metal nitrides and carbides thelocation of the light nitrogen or carbon atoms in the crystalstructure is often problematic. This has led to some ambiguityin the case of rhenium carbide. Hexagonal rhenium carbide(P 63/mmc, a = 2.8403 A, c = 9.8543 A) was reported for thefirst time from high-pressure, high-temperature syntheses atp > 6 GPa and T = 1073 K.3,4 A monocarbide compositionwith a γ ′-MoC-type structure and the rhenium atoms on Wyck-off position 4(f ) in a hexagonal AABB stacking sequencealong the c axis was proposed. A few years ago we synthesizedthis phase at 12–67 GPa and 1000–3800 K.5,6 However, weproposed a different composition close to Re2C as supportedby the results of quantum-mechanical calculations based ondensity functional theory (DFT). The carbon positions wereproposed to occupy Wyckoff position 2(b) at 0, 0, 1/4 ina trigonal prismatic coordination of rhenium atoms betweenthe AA and BB layers (Fig. 1, left). Recently, Zhao et al.7

synthesized Re2C0.924 at 2–6 GPa and 1073–1873 K andproposed yet another structural model that differs from theearlier suggestion by Juarez-Arellano et al.5 They put forwardthe anti-ReB2-type structure with carbon occupying Wyckoffposition 2(c) at 1/3, 2/3, 1/4 on another trigonal prismaticallycoordinated site between the AA and BB layers based on theirtheoretical calculations (Fig. 1, right).

Nearly at the same time we have synthesized novel rheniumnitrides, Re3N and Re2N, at 13–31 GPa and T > 1700 K.8

The crystal structure of Re2N was described in space groupP 63/mmc [a = 2.83(5) A, c = 9.88(1) A] with the rheniumatoms on Wyckoff position 4(f ) as in the case of Re2C.Independent of Zhao et al.7 the nitrogen atoms were located onWyckoff position 2(d) at 2/3, 1/3, 1/4 using DFT modeling.8

The structure is of the anti-MoS2 type (Fig. 1, right). Indeed,the ReB2 structure is of the MoS2 type, and the structuralmodel proposed for Re2C by Zhao et al.7 is equivalent to thatproposed for Re2N by Friedrich et al.,8 with the exception of atranslation of the origin by c/2. This would suggest isotypismof Re2C and Re2N.

Very recently, Deligoz et al.9 have reported vibrationalproperties of Re2N from first-principles calculations basedon our structural model. Vibrational spectroscopy offers aninvaluable complementary tool in resolving crystal structures.In the present paper vibrational properties of Re2N and Re2Care determined using micro-Raman spectroscopy at ambientand high pressures up to 18.5(2) and 30.7(1) GPa, respectively.In addition quantum-mechanical calculations of the phononfrequencies were performed for both compounds with differentstructural models. The combination of experimental datareported below with our theoretical results and those byDeligoz et al.9 finally presents an unambiguous resolution ofthe crystal structures of Re2N and Re2C with respect to theirN/C atom positions.

II. EXPERIMENTAL DETAILS

The micro-Raman measurements were carried out onpolycrystalline samples from our earlier high-pressure, high-temperature synthesis studies by reaction of the elements in thelaser-heated diamond-anvil cell.6,8 One sample each of Re2Nand Re2C was synthesized at about 20(1) GPa and 2000 K and40(1) GPa and 2000 K, respectively. The samples had beencharacterized by x-ray diffraction, and details can be foundin our earlier studies.6,8 It was found by x-ray diffraction thatRe2C contains a small amount of Re, which has not reacted,

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FRIEDRICH, WINKLER, REFSON, AND MILMAN PHYSICAL REVIEW B 86, 014114 (2012)

FIG. 1. (Color online) Crystal structure of (left) Re2C(P 63/mmc) after Juarez-Arellano et al.5 and (right) of Re2N andRe2C of anti-MoS2-type after Friedrich et al.8 and Zhao et al.7 Notethe different carbon positions in the projection along [001].

and Re2N forms a mixture with Re3N, the phase, which isstable at lower pressures and high temperature. The thin sampleplates with maximum dimensions of about 70 μm were recov-ered at ambient conditions, removed from the gasket hole, andput on a glass plate for the Raman-spectroscopic measurementsat ambient conditions. Most of the NaCl or Al2O3 thermalinsulation was removed, and only the main phases and smallruby chips, which had served for pressure determination via theruby-fluorescence method,10 were present. The samples werethen reloaded in Boehler-Almax-type diamond-anvil cells11

with neon as the pressure-transmitting medium and ruby grainsfor the measurements at high pressure.

Micro-Raman measurements were performed on the sam-ples in 180◦ reflection geometry with a Renishaw Ramanspectrometer (RM-1000) equipped with a Nd/YAG laser(532 nm, 200-mW output power). The system was calibratedusing the band at 519 cm−1 of a silicon wafer.12 Uncertaintiesof the measurements are about 1 cm−1. At ambient conditions a50× objective lens was employed, while for the high-pressuremeasurements a 20× objective lens with a long workingdistance was employed. In order to avoid any damage ofthe sample by the laser radiation, only about 10% of the fulllaser power was applied at ambient conditions and up to 33%at high pressures. The spectra were recorded in the spectralrange from 100 to 4000 cm−1 (10-s exposure time) and inthe limited range of 100 to 900 cm−1 (180–1800-s exposuretimes) where the lattice vibrations were observed. Ramanspectra in the vicinity of ruby grains were determined by thestrong fluorescence background of ruby. At ambient conditionstwo-dimensional Raman maps were recorded across thesamples in 5–8-μm steps in order to allow characterizationof phase distributions. Raman spectra were recorded in stepsof about 1–3 GPa at increasing pressure up to 18.5(2) and30.7(1) GPa for Re2N and Re2C, respectively. The Raman

bands were fitted to pseudo-Voigt functions using the programDATLAB.13

III. COMPUTATIONAL DETAILS

Two sets of DFT calculations were performed using theCASTEP code.14 This code is an implementation of Kohn-ShamDFT based on a plane-wave basis set in conjunction withpseudopotentials. The plane-wave cutoff was set to energiesranging from 330 to 600 eV. All pseudopotentials wereultrasoft.15 One set of calculations was done by employingthe PBE-GGA exchange-correlation functional,16 while in asecond set the PBESOL-GGA functional for solids17 wasemployed. The rhenium pseudopotential is characterized bya core radius of 2.1 a.u., and the 5s and 5p semicore stateswere treated as valence states. The nitrogen pseudopotentialhad a core radius of 1.5 a.u. The Brillouin-zone integralswere performed using Monkhorst-Pack grids18 with spacingsbetween grid points of less than 0.03 A−1. Full geometryoptimizations were performed so that forces were convergedto less than 0.007 eV/A and the stress residual was convergedto 0.02–0.150 GPa. Phonons were computed by the finite-displacement technique.19

IV. RESULTS AND DISCUSSION

The lattice dynamics of Re2N was reported in Deligozet al.9 applying the structural model proposed by ourgroup.8 According to group theory, hexagonal Re2N has fourRaman-active modes �Ra = 2E2g + 1A1g + 1E1g . TypicalRaman spectra of Re2N and Re2C are shown in Fig. 2. Threeof the four Raman-active modes could be detected for Re2N inthe experiment (Table I). The experimentally measured Ramanshifts coincide within 4% with the Raman shifts calculated forthe Raman-active vibrational modes of Re2N by Deligoz et al.9

using ab initio modeling, which is an excellent agreement.In order to unambiguously confirm this structural modelwith nitrogen on Wyckoff position 2(d), which was proposedby Friedrich et al.8 for Re2N, we calculated the phononfrequencies of the vibrational modes for both model systemsof Re2N, with the nitrogen atoms occupying Wyckoff position2(b) as in Juarez-Arellano et al.5 for Re2C and position 2(d)as in Friedrich et al.8 for Re2N and in Zhao et al.7 for Re2C.

FIG. 2. (Color online) Raman spectra of Re2N and Re2C atambient conditions.

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TABLE I. Raman-active phonon frequencies (cm−1) of Re2N and Re2C at the � point from experiment and from DFT.

Compound

Re2N Re2N (Ref. 9) Re2N Re2N Re2N Re2C Re2C Re2N (Ref. 9) Re2N Re2C Re2C Re2C

Method Exp DFT DFT DFT DFT Exp DFT DFT Exp Exp Exp DFTPBE PBESOL PBESOL PBE PBESOL PBE PBESOL

N position 2(d) 2(d) 2(b) 2(b) 2(d) 2(d) 2(d)Pressure (GPa) 0.0001 0 0 0 0 0.0001 0 20 18.5(2) 19.6(2) 30.7(1) 30E2g 128 131 146 93 76 124 133 143 135 132 136 143E2g 169 162 184 95 77 175 182 176 181 187 194 197A1g 271 282 285 237 239 278 275 309 293 302 313 307E1g 507 436 443 452 585 564 560 630 653 627

A comparison of the calculated modes with the experimentallymeasured Raman modes clearly shows the good agreementfor our structural model [nitrogen on position 2(d)], while themodel with nitrogen on position 2(b) results in a significantvariation of the Raman shifts of the vibrational modes,especially for the E2g modes at low frequencies (Table I).

For Re2C four Raman-active modes were measured. Threeof the modes can be compared to the three modes measuredfor Re2N. They are close to each other, with the E2g modeat 124 cm−1 at a few lower wave numbers and the E2g

and A1g modes shifted up to 7 cm−1 higher with respect toRe2N. Hence, it is evident that the crystal structure of Re2C isisotypic to that of Re2N. This is further confirmed by theexcellent agreement of our calculated phonon frequencieswith the experimentally measured Raman shifts (Table I).With these data the controversy of the crystal structure ofRe2C with respect to its carbon position is solved and clearlyconfirms the structural model proposed by Zhao et al.7 Further,no additional Raman bands which could be attributed toRe2N or Re2C and could indicate the presence of N2 entitieswithin the crystal structure were observed. This confirms thatnitrogen dissociates during synthesis, similar to the synthesisof Re3N8 and η-Ta2N3,20 but in contrast to the other knowntransition-metal nitrides of period VI elements with higheratomic numbers, i.e., OsN2,21 IrN2,21,22 and PtN2,22,23 whereN2 entities are present.

The small differences in the Raman shifts between Re2Nand Re2C are attributed to the substitution of nitrogen bycarbon. According to Deligoz et al.,9 all Raman-active �-pointphonon modes of Re2N include atomic vibrations of both Reand N atoms except for the A1g mode at 271 cm−1, whichincludes atomic vibrations only from N atoms while Re atomsdo not vibrate. The A1g mode of Re2C vibrates at slightlyhigher frequency of 278 cm−1, which is in agreement withthe slightly lower mass of carbon with respect to nitrogen.Due to the observed increasing shifts between the modes ofRe2N and Re2C at increasing wave number, it is proposedthat the difference is even larger for the E1g vibrational modeat the highest wave number (i.e., 585 cm−1 for Re2C). Thisis unambiguously confirmed by our DFT calculation, whichresults in 564 cm−1 for the E1g mode of Re2C compared to436 cm−1 (this DFT study) or 507 cm−1 by Deligoz et al.9 forRe2N (Table I). The significant difference can be explainedby the different bond populations of the equally long Re-Nand Re-C bonds as obtained from DFT. The Re-C bond shows

a larger bond population (1.03) than the Re-N bond (0.76),and hence it has a more covalent character. This makes theRe-C bond stronger compared to the Re-N bond, leading tovibrations at higher energies. The Raman bands of Re2N andRe2C at frequencies below 400 cm−1 are seen as sharp spectrallines with a width that increases from about 4 to 9 cm−1 withRaman shift, similar to the linewidths of the Raman modesof Re3N.24 The Re2C Raman mode at 585 cm−1 is slightlybroader, with a linewidth of about 15 cm−1. The linewidthsdo not change within the measurement accuracy at pressureincrease.

There is only one Raman-active vibrational mode at zerowave vector for pure rhenium (hcp lattice),25 i.e., the E2g modeat 121 cm−1. The Raman shift of the band at 121–128 cm−1

is similar for Re, Re3N, Re2N, and Re2C. This is consistentwith the structural models of these phases, which are allderived from the hcp structure of rhenium by a differentstacking sequence of the layers of rhenium atoms, i.e., AB

in Re, ABB in Re3N, and AABB in Re2N and Re2C.A comprehensive overview on possible compositions andstructural arrangements of interstitial and lamellar rhenium

FIG. 3. Frequency shifts of the vibrational modes and fits of linearregression to the experimental data (solid symbols, solid lines) ofRe2C (diamonds) and Re2N (triangles) and theoretical data (opensymbols, dashed lines) of Re2N from Deligoz et al.9 and Re2C fromthis study.

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TABLE II. Pressure dependence of the Raman shifts dνi/dp and mode Gruneisen parameters γi for Re2N and Re2C as obtained fromexperiment and theory. Mode Gruneisen parameters were calculated considering B0 = 401(10) GPa for Re2N (Ref. 8) and B0 = 405(30) GPafor Re2C (Ref. 6).

dνi/dp γi

Mode Re2N (Ref. 9) Re2N Re2C Re2Ca Re2N (Ref. 9) Re2N Re2C Re2Ca

E2g 0.60 0.370 0.368 0.33 1.84(4) 1.16(3) 1.20(9) 1.00(7)E2g 0.70 0.575 0.569 0.50 1.73(4) 1.36(3) 1.32(10) 1.11(8)A1g 1.35 1.098 1.082 1.07 1.92(5) 1.62(4) 1.58(11) 1.58(11)E1g 2.65 2.168 2.10 2.10(5) 1.50(11) 1.51(12)

aDFT, PBESOL, this study.

nitrides has been given most recently by Soto et al.,26 whoconfirmed the higher stability of the lamellar structures and thepreference of the trigonal prismatic site for nitrogen locationwithin the rhenium matrix as observed for Re3N and Re2Nby first-principles calculations. The subsequent nitridiationof rhenium leads to a shift of the rhenium mode to higherwave numbers. The highest wave number is observed forRe2N. A two-dimensional mapping across the surface ofpart of the Re2C sample showed the presence of varyingamounts of rhenium in addition to Re2C. This is in agreementwith the results of earlier powder x-ray diffraction of thissample.6 The presence of unreacted rhenium is due to theinhomogeneous distribution and contact between the rheniumfoil and graphite powder within the salt-filled chamber of thediamond-anvil cell during synthesis. The phase distribution ofRe and Re2C within the sample was not further quantifieddue to the overlap of the E2g Raman mode of rhenium(121 cm−1; Ref. 25) with the E2g mode of Re2C at 124 cm−1. Inaddition, only the surface of the opaque sample is contributingto the Raman signal. In contrast, maps across the main partsof both surfaces of the plate-like Re2N sample showed onlythe presence of Re2N, not Raman signals of pure rheniumor of Re3N,24 which has Raman-active modes at 123, 133,237, and 476 cm−1. This is astonishing as earlier powderx-ray diffraction and Laue micro x-ray diffraction experimentsof the same sample clearly showed a mixture of Re2N andRe3N and their phase distribution within the sample.8 Thiscan only be interpreted by the difference of the penetrationdepth of the x-ray beam and the laser beam into the sample.It is assumed that the surface, which was in homogeneouscontact with the surrounding nitrogen during synthesis, wasfully nitridized during laser heating, forming Re2N, whilethe inner parts of the sample partly remained Re3N. Thiscould be a consequence of the temperature gradients within thesample during laser heating and of limited nitrogen diffusioninto the sample.

The pressure-induced shifts of the vibrational modesconfirm the mechanical stabilities of Re2N and Re2C up to18.5(2) GPa and 30.7(1), respectively (Fig. 3). The modeGruneisen parameter γ was calculated for each vibrationalmode i according to γi = B0(dνi/dp)/νi0, where B0 is the bulkmodulus at zero pressure (GPa), ν is the frequency (cm−1), p isthe pressure (GPa), and νi0 is the frequency of the vibrationalmode i at ambient pressure (cm−1). The values for B0 were401(10) GPa and 405(30) GPa for Re2N (Ref. 8) and Re2C,6

respectively. The mode Gruneisen parameters are between

1.1 and 1.6 for the Raman-active modes of both Re2N andRe2C (Table II). They coincide for the individual modes ofRe2N and Re2C within the standard deviations, which wereobtained from the uncertainties of the bulk moduli. This furtherconfirms the isotypism of Re2N and Re2C crystal structures.The mode Gruneisen parameters are in a similar range tothose reported for the Raman-active modes of pure rhenium(1.8 for the E2g mode; Ref. 25) and for Re3N (1.2–1.85).24

The mode Gruneisen parameters obtained from the calculateddata of Re2N by Deligoz et al.9 using the experimentallydetermined bulk modulus are slightly larger, with valuesin the range of 1.7–2.1, while those of Re2C from DFTcalculations (1.0–1.6) are similar to the experimental values(Table II).

V. SUMMARY AND CONCLUSION

With this study we could demonstrate the power of thecombination of experiment and ab initio modeling to solve thecrystal structures of very tiny samples, which contain bothlight and heavy elements, synthesized at extreme pressureand temperature conditions in the diamond-anvil cell. Thestructural model for Re2N as obtained from x-ray diffrac-tion and density functional theory8 was finally confirmedby studying the vibrational properties at ambient and highpressure by a comparison of the measured Raman spectrum ofRe2N with the calculated Raman-active modes. It was foundthat Re2C is isotypic to Re2N and both C and N atoms arelocated on Wyckoff position 2(c) [or 2(d), depending on thechoice of origin of the unit cell]. The isotypism of the twocompounds is further indicated by the strong similarity oftheir mode Gruneisen parameters. This confirms the structuralmodel by Zhao et al.7 for Re2C and by Friedrich et al.8 forRe2N.

ACKNOWLEDGMENTS

Financial support from the DFG, Germany, within SPP1236(Projects No. FR-2491/2-1 and No. WI-1232) and fromGoethe-Universitat via the FOKUS program (A.F.) is grate-fully acknowledged. Part of the CASTEP calculations wereperformed at the STFC E-Science facility. We thank theSPP1236 for the use of the central high-pressure facility and A.Woodland (Frankfurt) for access to the Raman spectrometer.

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