Phonon Density of States and Compression Behavior in Iron Sulfide under Pressure

Abstract

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. DOI: 10.1103/PhysRevLett.93.195503 PACS numbers: 63.20.-e, 71.30.+h, 76.80.+y, 91.60.Gf Iron sulfide, FeS, has been attracting attention in geosciences as well as condensed matter physics. The crystallographic properties of FeS have been investigated extensively at high pressures and/or high temperatures by x-ray diffraction measurements [1][2][3][4][5] because it is believed to be a component of the core of rocky planets such as Earth and Mars. Although the pressure vs temperature phase diagram has been contradictory, FeS undergoes two successive first-order phase transitions at room temperature, from the troilite (P 62c) to a MnP-type (Pnma) structure at 3.5 GPa and then to a monoclinic structure at 6.5 GPa with about 7% volume reduction. The compressibilities in those three phases were measured to be 13.6, 17.5, and 7:8 10 ÿ3 GPa ÿ1 , respectively. The thermodynamic properties under pressure are essential for understanding the core materials of the planets. However, there is no experimental knowledge of the lattice dynamics in FeS under pressure. Phonon dispersion relations and phonon densities of states (DOS) characterize the thermodynamic properties of the materials.At ambient conditions, FeS is an antiferromagnetic semiconductor with T N 589 K and belongs to the charge-transfer regime [6,7], where an electron correlation plays an important role. Electrical resistivity measurements of FeS under pressure [8] show that the semiconductor-metal and metal-semiconductor transitions occur at 3.5 and 6.5 GPa, respectively, corresponding to the structural phase transitions at room temperature. The energy gap in the semiconductor state below 3.5 GPa is caused by the electronic correlation, while the gap opens up between the nonbonding and antibonding bands in the semiconductor above 6.5 GPa. These phase transitions cause simultaneous changes in the electronic and structural properties. Therefore, we need to investigate the phonon properties of FeS in each phase and around these phase transitions from both the geophysics and condensed matter physical points of view. A new method based on nuclear resonant inelastic x-ray scattering (NRIXS) was introduced to measure partial phonon DOS in samples containing suitable Mössbauer nuclei [9,10]. Recently, this technique was successfully applied to measure the phonon DOS of "-Fe under pressure [11,12].In this Lette...

Equilibrium iron isotope fractionation factors of minerals: Reevaluation from the data of nuclear inelastic resonant X-ray scattering and Mössbauer spectroscopy

“…The INRXS spectrum for troilite published recently by Kobayashi et al (2004) is presented in Fig. 9.…”

“…Error bars for pyrite and marcasite reflect uncertainties in Mö ssbauer temperatures: 598 ± 12 K for pyrite and 516 ± 26 K for marcasite. The PDOS of troilite from INRXS synchrotron radiation experiments(Kobayashi et al, 2004). The temperature dependence of the iron b-factors for troilite (FeS) and Fe 3 S. The iron b-factors for pyrite, hematite and siderite are presented for comparison.…”

Geophysical applications of nuclear resonant spectroscopy

“…NRIXS signals originate from particular resonant nuclei only, and this complete isotope selec tivity is truly unique among techniques for the study of lattice vibrations. For example, materials surrounding the sample that do not contain resonant nuclei produce no unwanted background, and this feature now permits experiments under extreme pressuretemperature conditions that were impossible before (Lubbers et al, 2000a;Mao et al, 2001Mao et al, , 2004bStruzhkin et al, 2001;Lin et al, 2003Lin et al, , 2004aLin et al, , 2004bLin et al, , 2005bShen et al, 2004;Papandrew et al, 2004;Kobayashi et al, 2004;Zhao et al, 2004). Details on the scattering mechanisms and methodology for NRJXS and SMS have been published elsewhere Sturhahn, 2004).…”

High-pressure studies with x-rays using diamond anvil cells

“…From the low-energy region of each phonon DOS, Debye sound velocity can be derived. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Phonon DOS has been determined for a number of iron compounds and alloys: FeO [519,520], FeS [521], Fe-Ni [522], Fe-Si alloys [287,522], FeH [523], Fe3S [524], Fe3C [525][526][527], Fe2O3 [528], (Mg,Fe)O [497], and (Mg,Fe)SiO3 enstatite [529]. For nanocrystalline Fe, large distortions were found in its phonon DOS [530], showing a lifetime broadening at high energies and an enhancement in its phonon DOS at energies below 15 meV.…”

“…Examples of sound velocity determination using NRIXS include: Fe [63,297,517,518], FeO [519,520], FeS [521], Fe-Ni [522], Fe-Si alloys [287,522], FeH [523], Fe3S [524], Fe3C [525][526][527], Fe2O3 [528], and (Mg,Fe)O [497]. The Debye parabola is best constrained at the low-energy limit, and a resolution of better than 2 meV is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 therefore essential in NRIXS for approaching that limit.…”