We report the partial phonon densities of states (DOS) of iron sulfide, a possible component of the rocky planet's core, measured by the Fe-57 nuclear resonant inelastic x-ray scattering and calculate the total phonon DOS under pressure. From the phonon DOS, we drive thermodynamic parameters. A comparison of the observed and estimated compressibilities makes it clear that there is a large pure electronic contribution in the observed compressibility in the metallic state. Our results present the observation of thermodynamic parameters of iron sulfide with the low-spin state of an Fe2+ ion at the high density, which is similar to the condition of the Martian core

Alfe, D

Alp, EE

Kamimura, T

Kobayashi, H

Sturhahn, W

Zhao, JY

English

UCL Discovery

Phonon Density of States and Compression Behavior in Iron Sulﬁde under PressureHisao Kobayashi*Graduate School of Material Science, University of Hyogo, 3-2-1 Koto Hyogo 678-1297, Japanand Department of Physics, Tohoku University, Sendai, 980-8578, JapanTakashi KamimuraDepartment of Physics, Tohoku University, Sendai, 980-8578, JapanDario Alfe `Department of Earth Sciences and Department of Physics and Astronomy, University of College London,London WC1E 6BT, United KingdomWolfgang Sturhahn, Jiyong Zhao, and Esen E. AlpExperimental Facilities Division, Argonne National Laboratory, Argonne, Illinois 60439, USA(Received 23 March 2004; published 4 November 2004)We report the partial phonon densities of states (DOS) of iron sulﬁde, a possible component of therocky planet’s core, measured by the 57Fe nuclear resonant inelastic x-ray scattering and calculate thetotal phonon DOS under pressure. From the phonon DOS, we drive thermodynamic parameters. Acomparison of the observed and estimated compressibilities makes it clear that there is a large pureelectronic contribution in the observed compressibility in the metallic state. Our results present theobservation of thermodynamic parameters of iron sulﬁde with the low-spin state of an Fe2  ion at thehigh density, which is similar to the condition of the Martian core.DOI: 10.1103/PhysRevLett.93.195503 PACS numbers: 63.20.–e, 71.30.+h, 76.80.+y, 91.60.GfIron sulﬁde, FeS, has been attracting attention in geo-sciences as well as condensed matter physics. The crys-tallographic properties of FeS have been investigatedextensively at high pressures and/or high temperaturesby x-ray diffraction measurements [1–5] because it isbelieved to be a component of the core of rocky planetssuch as Earth and Mars. Although the pressure vs tem-perature phase diagram has been contradictory, FeSundergoes two successive ﬁrst-order phase transitions atroom temperature, from the troilite (P  62c) to a MnP-type(Pnma) structure at 3.5 GPa and then to a monoclinicstructure at 6.5 GPawith about 7% volume reduction.Thecompressibilities in those three phases were measured tobe 13.6, 17.5, and 7:8   10 3 GPa 1, respectively. Thethermodynamic properties under pressure are essentialfor understanding the core materials of the planets.However, there is no experimental knowledge of thelattice dynamics in FeS under pressure. Phonon disper-sion relations and phonon densities of states (DOS) char-acterize the thermodynamic properties of the materials.At ambient conditions, FeS is an antiferromagneticsemiconductor with TN   589 K and belongs to thecharge-transfer regime [6,7], where an electron correla-tion plays an important role. Electrical resistivity mea-surements of FeS under pressure [8] show that thesemiconductor-metal and metal-semiconductor transi-tions occur at 3.5 and 6.5 GPa, respectively, correspond-ing to the structural phase transitions at roomtemperature. The energy gap in the semiconductor statebelow 3.5 GPa is caused by the electronic correlation,while the gap opens up between the nonbonding andantibonding bands in the semiconductor above 6.5 GPa.These phase transitions cause simultaneous changes inthe electronic and structural properties. Therefore, weneed to investigate the phonon properties of FeS in eachphase and around these phase transitions from both thegeophysics and condensed matter physical points of view.A new method based on nuclear resonant inelastic x-rayscattering (NRIXS) was introduced to measure partialphonon DOS in samples containing suitable Mo ¨ssbauernuclei [9,10]. Recently, this technique was successfullyapplied to measure the phonon DOS of "-Fe under pres-sure [11,12].In this Letter, we have applied this new method toextract the partial phonon DOS of FeS under pressureand then calculated the total phonon DOS. It is found thatthe phonon DOS of FeS is modiﬁed by the pressure-induced phase transitions, and we derive the pressuredependence of thermodynamic parameters from thesephonon DOS. In these thermodynamic parameters, thepressure dependence of a force constant is determined byHund’s rules of Fe2  ion in FeS. We evaluate the pureelectronic contribution in the compressibility of the me-tallic state.The polycrystalline samples enriched with 50 at.%57Fe were prepared by a method described elsewhere[8]. The obtained samples were conﬁrmed to be in thesingle phase by x-ray diffraction and have a stoichiomet-ric composition within the experimental accuracy.Experiments under high pressure were performed onVOLUME 93, NUMBER 19 PHYSICAL REVIEW LETTERS week ending5 NOVEMBER 2004195503-1 0031-9007=04=93(19)=195503(4)$22.50  2004 The American Physical Society 195503-13-ID beam line at the Advanced Photon Source, ArgonneNational Laboratory using a special diamond anvil cell(DAC) up to 12 GPa [12]. The pulsed synchrotron radia-tion was monochromatized with 2 meV resolution by ahigh-resolution monochromator [13] and then focused ona 5   5  m2 area of the sample in the DAC by twoorthogonal Kirkpatrick-Baez mirrors. The 57Fe NRIXSspectra were measured by tuning the highly monochrom-atized beam in an energy range of about  100 meV.Under high pressure, the powder samples were loadedwith ruby crystals into a sample cavity of a 0.15 mmdiameter in a 0.2 mm thick Be metal gasket. The use ofFluorinert as the pressure-transmitting medium ensuredquasihydrostatic conditions. Pressure was calibrated bymeasuring the wavelength shift of the R1 luminescenceline of the ruby crystal.We have also measured the delay-time spectra of 57Fe coherent nuclear forward scatteringin FeS under pressure to monitor the phase transitions[14].Figure 1 shows typical NRIXS spectra, which consistof large center peaks originating from elastic scatteringand sidebands resulting from inelastic scattering with theannihilation and creation of phonons. The resolution issufﬁcient to resolve the modiﬁcation of inelastic compo-nents in the observed spectra by the structural phasetransitions as shown in Fig. 1. The inelastic componentsin the spectra extract lead to the partial phonon DOSassuming a harmonic lattice model [15]. The extractedpartial phonon DOSare shown in Fig. 2. At 1.5 GPa in thesemiconductor with the troilite structure, there are twopeaks at 12 and 18 meVin the phonon DOS which proba-bly originate from the transverse and longitudinal acous-tic phonon branches. Furthermore, the highest-energypeak at 37 meV is probably caused by the optical phononbranches. At 4.0 GPa in the metallic state with the MnP-type structure, there exists a strong peak at 20 meVwith ashoulder around 10 meV in the phonon DOS. The spec-trum of phonon DOS at 9.5 GPa is shifted to higherenergy because of the large volume reduction at6.5 GPa. Since there are three different Fe sites in thisunit cell [5], the spectrum has a more complicated struc-ture than in the other two phases.Ab initio calculations based on density-functional the-ory (DFT) in the generalized-gradient approximationwere performed to determine the total phonon DOS ofFeS at the same pressures using the projector augmentedwave approach. Calculations were performed using theVASP code [16]. We calculated the force constant matrixand then the phonon frequencies of FeS with the threestructures using our implementation of the small dis-placement method [17]. It was found that the troilitestructure is unstable in the present calculation. SinceFeS in the troilite structure is the semiconductor due toelectron correlation, it is possible that this instability isdue to the well known inaccurate DFT description ofFIG. 1. Typical NRIXS spectra at 1.5, 4.0, and 9.5 GPa. Thecircles with error bars indicate the observed spectra and thesolid lines represent the calculated inelastic components. Thedash-dotted lines show the single phonon contribution subspec-tra and other two lines show two and multiphonon contributionsubspectra.FIG. 2. Phonon DOS of FeS. The circles with error barsrepresent the partial phonon DOS extracted from NRIXSspectra at 1.5, 4.0, and 9.5 GPa. The dash-dotted and solidlines indicate the calculated total and partial phonon DOS,respectively. The partial phonon DOS is the measured Fephonon DOS, and the total theoretical phonon DOS is thesum of Fe and S. The calculated Fe phonon DOS agreesreasonably well both in terms of energy scale, as well asabsolute magnitude.VOLUME 93, NUMBER 19 PHYSICAL REVIEW LETTERS week ending5 NOVEMBER 2004195503-2 195503-2strongly correlated systems. We used supercells contain-ing 128 and 24 atoms for the MnP-type and the mono-clinic structures, respectively. The calculated phononDOS spectra are shown in Fig. 2. The phonon modesrelated to S atoms are mainly above 30 meV , althoughthe projection of the total phonon DOS onto S atoms isnever zero even at the low energy region.The largest peakin each calculated partial phonon DOS qualitatively cor-responds to that in the extracted partial phonon DOSwithin the experimental resolution. In the MnP-typephase, the calculated phonon DOS in the region fromthe peak to about  10 meV is enhanced over the mea-surement. This discrepancy originates in the differencebetween the experimental and the predicted volume andis reduced in the monoclinic phase.We extract thermodynamic parameters by integrationof phonon DOS with various energy weights and meanforce constant from the experimentally measured phononexcitation probability, based on normalization sum rulesas given by Lipkin [18] and Sturhahn et al. [10]. Above3.5 GPa, the pressure dependences of the Fe componentsin these calculated thermodynamic parameters qualita-tively agree with those obtained from the extractedpartial phonon DOS as seen Fig. 3. These pressure de-pendences obtained from the experimental results showno discontinuity at 3.5 GPa although about a 2 orderdecrease of magnitude in electrical resistivity was ob-served [8]. On the other hand, all thermodynamic pa-rameters show distinct steplike features around 6.5 GPa.First, we discuss the pressure dependence of the meanforce constant (D). In an ionic crystal, a short-rangerepulsive force determines the interatomic force constant.This short-range repulsive force arises from the chargedistributions and Hund’s rules of atoms. In a simplemetal, there also exist interactions connecting a largenumber of ions in addition to this force because of anonlocal electron ion potential. The measurement of57Fe Mo ¨ssbauer spectra was carried out under pressure[19]. It was found that the pressure dependence of thecenter shift changes signiﬁcantly at 6.5 GPa. This resultindicated a substantial change of the 3d-electron conﬁgu-ration on the Fe ion at the second phase transition.Recently a Mo ¨ssbauer study showed a nonmagnetic quad-rupole spectrum down to 5 K at 12 GPa and x-ray emis-sion experiments observed a pressure-induced reductionof the satellite amplitude in these spectra around 6.3 GPa[20,21]. These results strongly suggest the second phasetransition is high spin to low spin (HS-LS) in the Fe2 ion. Consequently, the distinct change in the pressuredependence of DoFe around 6.5 GPa is caused by the HS-LS transition. Since DcS is larger than DcFe above 3.5 GPa,the repulsive force range of the S atom exceeds the ﬁrstnearest neighbor distance. The atomic radius of the S2 ion is about twice as large as that of the Fe2  ion and iscomparable to half the S-S bond length in the threephases. The short-range repulsive force that acts on theS atom originates from second nearest neighbor S atomsas well as from ﬁrst nearest neighbor Fe atoms.Therefore,DFe andDS are mainly given by the short-range repulsiveforce both in the semiconductor and metallic states inwhich the electronic structure is highly correlated. Nosigniﬁcant anomaly is observed in the pressure depen-dence of DoFe at 3.5 GPaSecond, we discuss the relation between D and thecompressibility ( V). The compressibility splits into twoparts, one stemming from the interatomic force ( fc)an dthe other one resulting from electronic contribution ( e)which is the key parameter to describe the metal-insulator transition and the metallic state near the insu-lator phase [22]. In the homogeneous electron gas,  e isdeﬁned as e  1n2@n@ ; (1)where n denotes electron density and   denotes chemicalpotential. In the case where the short-range repulsiveforce acts between near neighbors [23],  fc is expressedby1 fc/M      va3 pXiDi2; (2)FIG. 3. Variation of the thermodynamical parameters esti-mated from the phonon DOS as a function of pressure:(a) mean force constant (D) (b) entropy at constant volume(Sv) and (c) speciﬁc heat at constant volume (cv). The circleswith error bars represent DoFe, Sv,a n dcv evaluated from theextracted partial phonon DOS. The solid and dash-dotted linesin (a) indicate the calculated D for the Fe and S atoms,respectively. The broken and solid lines in (b) and (c) indicateSv and cv estimated from the calculated total and partialphonon DOS, respectively.VOLUME 93, NUMBER 19 PHYSICAL REVIEW LETTERS week ending5 NOVEMBER 2004195503-3 195503-3where va is the volume of a polyhedra, M is a constantdetermined by the geometry of the polyhedra, and iindicates an atom in the polyhedra. Thus  fc is directlyrelated to D.In the monoclinic phase, two of three different Fe siteshave S atom coordination similar to the MnP structurealthough the structure is a more complicated one [5].Even though we cannot estimate the exact value of Min FeS, we assume in Eq. (2) that M in the monoclinicphase is the same as in the MnP-type phase. Furthermoreva can be replaced by a volume of the chemical unit in thephases. Thus we evaluate the  V= fc ratios to be 0.68 and0.50 for the MnP-type and the monoclinic phases, re-spectively, using DcFe and DcS. Since DoFe shows no dis-continuity at 3.5 GPa, we assume DFe and DS in thetroilite phase equal to those in the MnP-type phase. Theratio of the troilite phase is evaluated to be 0.46.This ratiois in good agreement with that of the monoclinic phase inspite of the large difference in  V. Thus, this large dif-ference originates from the interatomic force determinedby the 3d-electron conﬁguration of the Fe atoms in FeS,rather than electron correlations. Furthermore, the ratioin the metallic phase is much larger than those in thesemiconductor phases. Since the electron-hole excitationwith inﬁnitely small energy occurs in a metallic state, the e value is usually ﬁnite. On the other hand,  e can beneglected in a semiconductor state because the electronDOS vanishes at the Fermi energy. Consequently thelarger  V value in the metallic state is provided by apurely electronic contribution which is estimated to beabout 40% of  V. Therefore, this discontinuous change of e characterizes the phase transition at 3.5 GPa.Finally, the density of FeS in the monoclinic phase atroom temperature is comparable to that of FeS with ahexagonal NiAs-type structure at the conditions of theMartian core, and recent x-ray diffraction measurementindicates the monoclinic phase is stable up to 1225 K at35 GPa [24]. Since the value of c=a in the NiAs-typephase shows an abrupt change at 6 GPa and decreasesbelow the ideal c=a ratio of the hexagonal closed-packedstructure [3], it is strongly suggested that the electronicstate of the Fe atom in FeS is the low-spin one at theconditions of the Martian core. The vibrational parts ofthe thermodynamic properties are not free of the3d-electronic conﬁguration. Therefore, our thermody-namic data of FeS in the monoclinic phase give rise to afundamental knowledge of physical states and a struc-tural model of the Martian core.We thank Dr. G. Shen and the GSE-CARS staff at theAPS for their help with pressure calibration and Dr. H.-K.Mao of Carnegie Institute of Washington for providingdrawings of their modiﬁed DAC. The work at Argonne issupported by U.S. DOE, BES Materials Science, underContract No. W-31-109-ENG-38. H.K. acknowledges thesupport by the Japanese Ministry of Education, Culture,Sports, Science and Technology, Grant-in-Aid forScientiﬁc Research (c), 15540319. D. A. acknowledgessupport fromtheRoyalSocietyandthe LeverhulmeTrust.*Electronic address: kobayash@sci.u-hyogo.ac.jp[1] H. E. King, Jr. and C.T. Prewitt, Acta Crystallogr. Sect. B38, 1877 (1982).[2] T. Kamimura, M. Sato, H. Takahashi, N. Mo ˆri, H.Yoshida, and T. Kaneko, J. Magn. Magn. Mater. 104–107, 255 (1992).[3] Y. Fei, C.T. Prewitt, H.K. Mao, and C. M. Bertka,Science 268, 1892 (1995).[4] K. Kusaba,Y. Syono, T. Kikegawa, and O. Shimomura, J.Phys. Chem. Solids 58, 241 (1997).[5] R.J. Nelmes, M.I. McMahon, S. A. Belmonte, and J. B.Parise, Phys. Rev. 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Phonon density of states and compression behavior in iron sulfide under pressure

We report the partial phonon densities of states (DOS) of iron sulfide, a possible component of the rocky planet's core, measured by the (57)Fe nuclear resonant inelastic x-ray scattering and calculate the total phonon DOS under pressure. From the phonon DOS, we drive thermodynamic parameters. A comparison of the observed and estimated compressibilities makes it clear that there is a large pure electronic contribution in the observed compressibility in the metallic state. Our results present the observation of thermodynamic parameters of iron sulfide with the low-spin state of an Fe(2+) ion at the high density, which is similar to the condition of the Martian core

Phonon density of states and compression behavior in iron sulfide under pressure

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