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 57Fe 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.
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ABSTRACT: In this paper, we report ab initio calculations of the vibrational and structural properties of ZnAl2O4 and ZnGa2O4 spinel structures. The calculated vibrational modes at zero pressure, at the Γ point and the complete phonon spectrum of both compounds are presented. Also, we report our findings for the high-pressure structureHigh Pressure Research 12/2009; 29:573-577. · 0.93 Impact Factor
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ABSTRACT: Static and dynamic structural properties of CuFeS2 under high pressure were investigated by x-ray diffraction and Fe57 nuclear resonant inelastic scattering. Using x-ray diffraction, we obtained evidence that a pressure-induced amorphization occurs at about 6.3GPa , which represents a metal-insulator transition. Although partial phonon densities of states extracted from Fe57 nuclear resonant inelastic scattering spectra are similar in the two phases, the derived thermodynamical parameters show anomaly at the transition. The results of extracted partial phonon densities of states and ab initio phonon calculations indicate that this pressure-induced amorphization is caused by anomalous pressure dependences of the lower optical phonon branches and the initial slopes of the transverse acoustic phonon branches.Physical review. B, Condensed matter 10/2007; 76(13). · 3.66 Impact Factor
- American Mineralogist 11/2006; 91:1941-1944. · 2.06 Impact Factor
Phonon Density of States and Compression Behavior in Iron Sulfide under Pressure
Graduate School of Material Science, University of Hyogo, 3-2-1 Koto Hyogo 678-1297, Japan
and Department of Physics, Tohoku University, Sendai, 980-8578, Japan
Department of Physics, Tohoku University, Sendai, 980-8578, Japan
Dario Alfe `
Department of Earth Sciences and Department of Physics and Astronomy, University of College London,
London WC1E 6BT, United Kingdom
Wolfgang Sturhahn, Jiyong Zhao, and Esen E. Alp
Experimental 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 the
rocky planet’s core, measured by the57Fe 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.
DOI: 10.1103/PhysRevLett.93.195503PACS numbers: 63.20.–e, 71.30.+h, 76.80.+y, 91.60.Gf
Iron sulfide, FeS, has been attracting attention in geo-
sciences as well as condensed matter physics. The crys-
tallographic properties of FeS have been investigated
extensively at high pressures and/or high temperatures
by x-ray diffraction measurements [1–5] because it is
believed to be a component of the core of rocky planets
such as Earth and Mars. Although the pressure vs tem-
perature 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 GPawith about 7% volume reduction.The
compressibilities in those three phases were measured to
be 13.6, 17.5, and 7:8 ? 10?3GPa?1, 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 disper-
sion relations and phonon densities of states (DOS) char-
acterize the thermodynamic properties of the materials.
At ambient conditions, FeS is an antiferromagnetic
semiconductor with TN? 589 K and belongs to the
charge-transfer regime [6,7], where an electron correla-
tion plays an important role. Electrical resistivity mea-
surements of FeS under pressure  show that the
semiconductor-metal and metal-semiconductor transi-
tions occur at 3.5 and 6.5 GPa, respectively, correspond-
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 Mo ¨ssbauer
nuclei [9,10]. Recently, this technique was successfully
applied to measure the phonon DOS of "-Fe under pres-
In this Letter, we have applied this new method to
extract the partial phonon DOS of FeS under pressure
and then calculated the total phonon DOS. It is found that
the phonon DOS of FeS is modified by the pressure-
induced phase transitions, and we derive the pressure
dependence of thermodynamic parameters from these
phonon DOS. In these thermodynamic parameters, the
pressure dependence of a force constant is determined by
Hund’s rules of Fe2?ion in FeS. We evaluate the pure
electronic contribution in the compressibility of the me-
The polycrystalline samples enriched with 50 at.%
57Fe were prepared by a method described elsewhere
. The obtained samples were confirmed to be in the
single phase by x-ray diffraction and have a stoichiomet-
ric composition within the experimental accuracy.
Experiments under high pressure were performed on
VOLUME 93, NUMBER 19
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2004 The American Physical Society195503-1
3-ID beam line at the Advanced Photon Source, Argonne
National Laboratory using a special diamond anvil cell
(DAC) up to 12 GPa . The pulsed synchrotron radia-
tion was monochromatized with 2 meV resolution by a
high-resolution monochromator  and then focused on
a 5 ? 5 ?m2area of the sample in the DAC by two
orthogonal Kirkpatrick-Baez mirrors. The57Fe NRIXS
spectra were measured by tuning the highly monochrom-
atized beam in an energy range of about ?100 meV.
Under high pressure, the powder samples were loaded
with ruby crystals into a sample cavity of a 0.15 mm
diameter in a 0.2 mm thick Be metal gasket. The use of
Fluorinert as the pressure-transmitting medium ensured
quasihydrostatic conditions. Pressure was calibrated by
measuring the wavelength shift of the R1luminescence
line of the ruby crystal.We have also measured the delay-
time spectra of57Fe coherent nuclear forward scattering
in FeS under pressure to monitor the phase transitions
Figure 1 shows typical NRIXS spectra, which consist
of large center peaks originating from elastic scattering
and sidebands resulting from inelastic scattering with the
annihilation and creation of phonons. The resolution is
sufficient to resolve the modification of inelastic compo-
nents in the observed spectra by the structural phase
transitions as shown in Fig. 1. The inelastic components
in the spectra extract lead to the partial phonon DOS
assuming a harmonic lattice model . The extracted
partial phonon DOSare shown in Fig. 2. At 1.5 GPa in the
semiconductor with the troilite structure, there are two
peaks at 12 and 18 meVin the phonon DOS which proba-
bly originate from the transverse and longitudinal acous-
tic phonon branches. Furthermore, the highest-energy
peak at 37 meV is probably caused by the optical phonon
branches. At 4.0 GPa in the metallic state with the MnP-
type structure, there exists a strong peak at 20 meVwith a
shoulder around 10 meV in the phonon DOS. The spec-
trum of phonon DOS at 9.5 GPa is shifted to higher
energy because of the large volume reduction at
6.5 GPa. Since there are three different Fe sites in this
unit cell , 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 approximation
were performed to determine the total phonon DOS of
FeS at the same pressures using the projector augmented
wave approach. Calculations were performed using the
VASP code . We calculated the force constant matrix
and then the phonon frequencies of FeS with the three
structures using our implementation of the small dis-
placement method . It was found that the troilite
structure is unstable in the present calculation. Since
FeS in the troilite structure is the semiconductor due to
electron correlation, it is possible that this instability is
due to the well known inaccurate DFT description of
circles with error bars indicate the observed spectra and the
solid lines represent the calculated inelastic components. The
dash-dotted lines show the single phonon contribution subspec-
tra and other two lines show two and multiphonon contribution
Typical NRIXS spectra at 1.5, 4.0, and 9.5 GPa. The
represent the partial phonon DOS extracted from NRIXS
spectra at 1.5, 4.0, and 9.5 GPa. The dash-dotted and solid
lines indicate the calculated total and partial phonon DOS,
respectively. The partial phonon DOS is the measured Fe
phonon DOS, and the total theoretical phonon DOS is the
sum of Fe and S. The calculated Fe phonon DOS agrees
reasonably well both in terms of energy scale, as well as
Phonon DOS of FeS. The circles with error bars
VOLUME 93, NUMBER 19
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strongly correlated systems. We used supercells contain-
ing 128 and 24 atoms for the MnP-type and the mono-
clinic structures, respectively. The calculated phonon
DOS spectra are shown in Fig. 2. The phonon modes
related to S atoms are mainly above 30 meV , although
the projection of the total phonon DOS onto S atoms is
never zero even at the low energy region.The largest peak
in each calculated partial phonon DOS qualitatively cor-
responds to that in the extracted partial phonon DOS
within the experimental resolution. In the MnP-type
phase, the calculated phonon DOS in the region from
the peak to about ?10 meV is enhanced over the mea-
surement. This discrepancy originates in the difference
between the experimental and the predicted volume and
is reduced in the monoclinic phase.
We extract thermodynamic parameters by integration
of phonon DOS with various energy weights and mean
force constant from the experimentally measured phonon
excitation probability, based on normalization sum rules
as given by Lipkin  and Sturhahn et al. . Above
3.5 GPa, the pressure dependences of the Fe components
in these calculated thermodynamic parameters qualita-
tively agree with those obtained from the extracted
partial phonon DOS as seen Fig. 3. These pressure de-
pendences obtained from the experimental results show
no discontinuity at 3.5 GPa although about a 2 order
decrease of magnitude in electrical resistivity was ob-
served . On the other hand, all thermodynamic pa-
rameters show distinct steplike features around 6.5 GPa.
First, we discuss the pressure dependence of the mean
force constant (D). In an ionic crystal, a short-range
repulsive force determines the interatomic force constant.
This short-range repulsive force arises from the charge
distributions and Hund’s rules of atoms. In a simple
metal, there also exist interactions connecting a large
number of ions in addition to this force because of a
nonlocal electron ion potential. The measurement of
57Fe Mo ¨ssbauer spectra was carried out under pressure
. It was found that the pressure dependence of the
center shift changes significantly at 6.5 GPa. This result
indicated 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 reduction
of the satellite amplitude in these spectra around 6.3 GPa
[20,21]. These results strongly suggest the second phase
transition is high spin to low spin (HS-LS) in the Fe2?
ion. Consequently, the distinct change in the pressure
dependence of Do
LS transition. Since Dc
the repulsive force range of the S atom exceeds the first
nearest neighbor distance. The atomic radius of the S2?
ion is about twice as large as that of the Fe2?ion and is
comparable to half the S-S bond length in the three
phases. The short-range repulsive force that acts on the
Fearound 6.5 GPa is caused by the HS-
Sis larger than Dc
Feabove 3.5 GPa,
S atom originates from second nearest neighbor S atoms
as well as from first nearest neighbor Fe atoms.Therefore,
DFeand DSare mainly given by the short-range repulsive
force both in the semiconductor and metallic states in
which the electronic structure is highly correlated. No
significant anomaly is observed in the pressure depen-
dence of Do
Second, we discuss the relation between D and the
compressibility (?V). The compressibility splits into two
parts, one stemming from the interatomic force (?fc) and
the 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 . In the homogeneous electron gas, ?eis
Feat 3.5 GPa
where n denotes electron density and ? denotes chemical
potential. In the case where the short-range repulsive
force acts between near neighbors , ?fcis expressed
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 circles
with error bars represent Do
extracted partial phonon DOS. The solid and dash-dotted lines
in (a) indicate the calculated D for the Fe and S atoms,
respectively. The broken and solid lines in (b) and (c) indicate
Svand cvestimated from the calculated total and partial
phonon DOS, respectively.
Fe, Sv, and cvevaluated from the
VOLUME 93, NUMBER 19
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where vais the volume of a polyhedra, M is a constant
determined by the geometry of the polyhedra, and i
indicates an atom in the polyhedra. Thus ?fcis directly
related to D.
In the monoclinic phase, two of three different Fe sites
have S atom coordination similar to the MnP structure
although the structure is a more complicated one .
Even though we cannot estimate the exact value of M
in FeS, we assume in Eq. (2) that M in the monoclinic
phase is the same as in the MnP-type phase. Furthermore
vacan be replaced by a volume of the chemical unit in the
phases. Thus we evaluate the ?V=?fcratios to be 0.68 and
0.50 for the MnP-type and the monoclinic phases, re-
spectively, using Dc
continuity at 3.5 GPa, we assume DFeand DSin the
troilite phase equal to those in the MnP-type phase. The
ratio of the troilite phase is evaluated to be 0.46.This ratio
is in good agreement with that of the monoclinic phase in
spite of the large difference in ?V. Thus, this large dif-
ference originates from the interatomic force determined
by the 3d-electron configuration of the Fe atoms in FeS,
rather than electron correlations. Furthermore, the ratio
in the metallic phase is much larger than those in the
semiconductor phases. Since the electron-hole excitation
with infinitely small energy occurs in a metallic state, the
?evalue is usually finite. On the other hand, ?ecan be
neglected in a semiconductor state because the electron
DOS vanishes at the Fermi energy. Consequently the
larger ?Vvalue in the metallic state is provided by a
purely electronic contribution which is estimated to be
about 40% of ?V. Therefore, this discontinuous change of
?echaracterizes the phase transition at 3.5 GPa.
Finally, the density of FeS in the monoclinic phase at
room temperature is comparable to that of FeS with a
hexagonal NiAs-type structure at the conditions of the
Martian core, and recent x-ray diffraction measurement
indicates the monoclinic phase is stable up to 1225 K at
35 GPa . Since the value of c=a in the NiAs-type
phase shows an abrupt change at 6 GPa and decreases
below the ideal c=a ratio of the hexagonal closed-packed
structure , it is strongly suggested that the electronic
state of the Fe atom in FeS is the low-spin one at the
conditions of the Martian core. The vibrational parts of
the thermodynamic properties are not free of the
3d-electronic configuration. Therefore, our thermody-
namic data of FeS in the monoclinic phase give rise to a
fundamental knowledge of physical states and a struc-
tural model of the Martian core.
We thank Dr. G. Shen and the GSE-CARS staff at the
APS for their help with pressure calibration and Dr. H.-K.
Mao of Carnegie Institute of Washington for providing
drawings of their modified DAC. The work at Argonne is
supported by U.S. DOE, BES Materials Science, under
Contract No. W-31-109-ENG-38. H.K. acknowledges the
support by the Japanese Ministry of Education, Culture,
Sports, Science and Technology, Grant-in-Aid for
S. Since Do
Feshows no dis-
Scientific Research (c), 15540319. D. A. acknowledges
support fromtheRoyalSocietyandthe LeverhulmeTrust.
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