# Iron melting curve from ab initio molecular dynamics calculations

Audrey CampBell  School for Engineering of Matter, Transport, and Energy,
Arizona State University, Tempe, Arizona 85285, USA  Sang-Heon Shim  School of
Earth and Space Exploration, Arizona State University, Tempe, Arizona 85285,
USA  Qi-Jun Hong<EMAIL_ADDRESS>School for Engineering of Matter,
Transport, and Energy, Arizona State University, Tempe, Arizona 85285, USA

###### Abstract

We calculate the melting curve of iron from ambient pressure to 350 GPa, based
on density functional theory (DFT) molecular dynamics simulations. We discover
that the DFT melting curve is significantly higher than the current consensus
from the previous diamond anvil cell (DAC) experiment. We investigate into the
discrepancy and discover that carbon contamination is a possible cause of the
lower melting temperatures from DAC. Further experimental investigation is
required to resolve the discrepancy.

melting temperature, density functional theory, molecular dynamics

###### pacs:

2

##  I  Introduction

The solid inner core of the Earth’s core is composed of almost pure Iron,
while the liquid outer core is believed to be mostly Iron with some trace
light elements. The boundary between the two cores is of particular interest
to the scientific community as a way to define the temperature of the Earth’s
core. Since the two regions of the Earth’s core share a boundary they must be
in equilibrium at that boundary. This allows us to make assumptions about the
equilibrium conditions and makes it possible to computationally determine the
temperature of the core at this boundary. In the past others have preformed
physical shock tests to simulate the pressure that would be present at the
Earths core and have estimated the melting temperature of the Earth’s core
through extrapolation to around 6100-6300K Experimental_1; Experimental_2;
Experimental_3.

In addition to the physical experiments multiple other researchers have
attempted to computationally find the melting temperature of the Earth’s core
comp_1; comp_2; comp_3; comp_4. Computational experiments have placed the
melting temperature for Iron at the Earths core to be around 6,700-7000K,
which is noticeably higher then most of the experimental research. Computation
results suggest that the melting temperature of the Earth’s core is above the
temperature reported by most physical experiments including those provided by
Anzelli et al. Experimental_1 in 2013. This discrepancy between the
experimental results and the computational results leaves the actual melting
temperature of the Earth’s core in question. This discrepancy is in part
because of the extreme conditions under which the Earth’s cores exist.

The Earths Core exists at high pressures and temperatures which results in the
unique behavior of Fe. This is due to the pressure, which is estimated to be
around 350 gigapascals with a temperature which is suspected to be equal to
the melting temperature of iron at 350GPa. This complies with the knowledge
that the outer core is liquid, thus implying that the temperature is around at
or around the melting temperature of iron. The inner core though, is solid, as
stated previously, this leads to question of what is the temperature of the
inner core. To answer this question it is imperative that explore the melting
behavior of iron at increasing pressures.

##  II methods

To calculate melting temperatures of Fe metals and FeCx under extreme
temperature and pressure conditions, we use an efficient extension of the
coexistence method Hong2013 and its implementation and automation in the
SLUSCHI code Hong2016, based on density functional theory (DFT) molecular
dynamics (MD) simulations. In this approach, we manage to reduce the cell size
down to approximately 100 atoms, which drastically reduces computational cost.
This highly efficient method makes it possible to perform, directly from first
principles, dozens of expensive melting point calculations of iron, which
would otherwise be extremely expensive, especially considering the large
number of various pressure conditions, as well as in the FeCx system to study
the impact from carbon contamination. Our method runs solid-liquid coexisting
simulations on small-size systems, and the melting temperatures are rigorously
inferred based on statistical analysis of the fluctuations and probability
distributions of the solid and liquid phases Hong2013; Hong2016, as
illustrated in Fig. 1. The accuracy (typically with an error smaller than 100
K), robustness, and efficiency of the method have been demonstrated in a range
of materials HfCN2015; Hong2015; Ta_EOS2015; Kapush2017; Hong2018; Hong2019;
Ushakov2019; Fyhrie2019; Hong2021. The reader may refer to Ref. Hong2013;
Hong2016 for detailed derivation, validation and examples.

Figure 1: An illustration of how the small-size coexistence method is
implemented in practice. At 330GPa and a trial temperature of 7500 K, we
launch eight MD duplicates of 252 Fe atoms in periodic cells with 50-50 solid-
liquid coexistence. These eight MD duplicates end in four solids and four
liquids. The outcome distribution is evident based on both the structures and
the energies (a liquid has a disordered structure and a relatively higher
energy). Thus $T=7500$ K, $n=8$ and $k=4$. Performing simulations at various
temperatures enables us to collect a set of vectors (T, n, and k), based on
which we then infer the melting temperature and its uncertainty based on
maximum likelihood estimation. Details of the small-size coexistence method
and the SLUSCHI package are available at Ref. Hong2013; Hong2016.

DFT calculations were performed by the Vienna Ab initio Simulation Package
(VASP) VASP, with the projector-augmented-wave (PAW) PAW implementation and
the generalized gradient approximation (GGA) for exchange correlation energy,
in the form known as Perdew, Burke, and Ernzerhof (PBE) PBE. Since the
simulations were performed at high pressure and high temperature conditions,
we used accurate pseudopotentials where the semi-core $p$ states were treated
as valence states. The electronic temperature is accounted for by imposing a
Fermi distribution of the electrons on the energy level density of states, so
it is consistent with the ionic temperature. We list in Table 1 the cell size
of the melting point calculations. Our earlier study suggests that cell size
needs to be approximately 10 Å to control finite-size error Hong2013;
Hong2016. Thus we enforce this requirement in the construction of the
supercells, which generates system sizes ranging from 168 to 252 atoms,
depending on the pressure condition, as higher pressure compresses more atoms
into the periodic $\sim 10\times 10\times 10\text{ \AA}^{3}$ cell, thus
rendering the calculations considerably more expensive than those at ambient
pressure. The planewave energy cutoff is set to the default value (normal
precision) of the pseudopotential during the MD simulations, and it is further
increased to the high-precision value during the correction for the Pulay
stress Francis1990. MD step size is adjusted during the simulations by SLUSCHI
to balance accuracy and efficiency, varying from 1.8 fs at ambient pressure
and relatively low temperature to 0.5 fs at above 300 GPa and 7000 K.

DFT MD techniques are utilized to simulate atomic movements and trajectories.
Specifically, MD simulations are carried out under constant number of atoms,
pressure and temperature condition ($NPT$, isothermal-isobaric ensemble). Here
the thermostat is conducted under the Nosé-Hoover chain formalism Nose1984;
Nose1984-2; Hoover1985; Martyna1992. The barostat is realized by adjusting
volume every 80 steps according to average pressure. Although this does not
formally generate an isobaric ensemble, this approach has been shown to
provide an effective way to change volume smoothly and to avoid the unphysical
large oscillation caused by commonly used barostats in small cells Hong2013.

##  III Results and discussion

###  III.1 Melting temperatures

Figure 2: Melting temperature of iron from ambient to 350 GPa. Red symbols are
DFT PBE melting temperature in this work. The blue line is from DAC experiment
in Ref. Experimental_1. The green dots are computational melting temperatures
from Refs. comp_1; comp_4. The black dots are based on the experimental work
of shock measurement in Ref. Experimental_3. Our DFT melting temperatures
deviate from DAC measurements in Ref. Experimental_1 as the pressure is
increased. However, adding approximately 1 at. % of carbon, FeC0.01,
significantly reduces the melting temperature to values consistent with Ref.
Experimental_1 at high pressures.  Figure 3: Computational melting temperature
based on DFT versus experiments. Error bars of 100 K were plotted as red dash
lines for eye guide. Plotted are materials at ambient pressure that meet the
requirements that (1) I have studied the materials using the method, and that
(2) there exist experimental values to compare with. The GGA-PBE functional is
employed unless elaborated in the label. PBE tends to underestimate melting
temperature, most likely due to its under-binding nature. PBE-HSE often
provides lower and upper boundaries of the melting temperature.

Based on our approach of direct DFT simulations, we calculate the melting
temperatures of iron under various pressure conditions, ranging from ambient
pressure to 350 GPa, which is slightly higher than the Earth’s inner-core
boundary pressure of 330 GPa. We then generate the melting curve and solid-
liquid phase diagram of Fe, as shown in Fig. 2 and Table 1. High-pressure Fe
undergoes a phase transition from FCC ($\gamma$ phase) to HCP ($\epsilon$
phase) at approximately 90 GPa. Our approach, the small-size coexistence
method Hong2013 and the SLUSCHI package Hong2016, has the built-in ability to
identify the correct structure of the solid because the structure with the
lowest Gibbs free energy can easily nucleate at the solid-liquid interface
even if the wrong solid structure was initially assumed. We then launch a
fresh SLUSCHI calculation with the correct crystal structure, which will lead
to a higher melting temperature than that from the wrong structure, because
the most stable phase has the lowest free energy and the highest relative
stability (with respect to liquid), i.e., melting temperature, compared to
other less stable phases. For example, the DFT melting temperature of FCC is
higher than that of BCC at 50 GPa, as shown in Table 1, suggesting FCC is the
stable phase.

While in good agreement with other computational work from DFT comp_1; comp_4,
our simulations indicate that the melting temperature of Fe at the Earth’s
core pressure condition is significantly higher than previous experimental
values, as shown in Fig. 2. At 330 GPa, our calculated DFT melting temperature
is at least 600 K higher than the extrapolated experimental value in Ref.
Experimental_1, while, without experimental extrapolation at 150 and 200 GPa,
the DFT melting temperature is still higher by at least 300 K.

The observation strongly contradicts a general trend, that PBE melting
temperature often serves as the lower boundary, which we found from DFT
melting temperature calculations. Based on our study on dozens of materials of
various types Hong2022_CMS, it is demonstrated that PBE calculations
underestimate melting temperature in practice, with the PBE melting
temperatures often lower than the experimental values, as shown in Fig. 3. DFT
functional error is responsible for the underestimation. It is a well-known
issue that GGA underestimates bond strength Perdew2008. Since there are more
and stronger bonds in the solid phase than in the liquid, the bonding energies
of the solid phase are underestimated by a more significant amount than those
of the liquid phase, thus rendering the solid phase relatively unstable. An
unstable solid phase therefore results in an early melting, i.e., a lower
melting temperature. In practice, we can employ a different density
functional, e.g., a correction from the local density approximation (LDA) or
the Heyd-Scuseria-Ernzerhof (HSE) functional HSE, which always increases the
melting temperature and often leads to an overestimate, since LDA
overestimates bonding. Thus, PBE simulation and LDA/HSE correction can serve
as the melting temperature’s lower and upper boundaries. The same relation
among PBE, LDA, and experiment is also observed in DFT calculations by other
researchers Zhu2020, using a different method, the free energy approach, for
melting temperature calculation.

This conflict, that DFT PBE melting temperature is typically a lower boundary
but the calculated iron melting curve in this work is significantly higher
than the DAC experiment, motivates us to find the root cause of the
discrepancy. On the one hand, DFT calculations can be inaccurate, which may
lead to an overestimation of melting temperatures. On the other hand,
experimental measurements can have significant errors due to extremely
challenging and reactive temperature and pressure conditions, resulting in
issues such as sample contamination and temperature gradient.

###  III.2 Carbon contamination

We investigate the impact of carbon contamination on melting temperature. DAC
measurement was performed with the Fe samples in contact with the diamond,
which raises the possibility of the samples being inevitably contaminated by
carbon under extreme temperature and pressure conditions. We simulate the
carbon contamination effect by adding a very small amount of carbon to iron,
approximately 1 atomic %. We find that, even with only a small amount of
carbon, melting temperature is significantly reduced by approximately 200 K,
from 4029 to 3790 K at 100 GPa and from 4769 to 4570 K at 150 GPa. With carbon
contamination, the melting temperature of FeC0.01 agrees more closely with the
DAC experiment, significantly narrowing the discrepancy, as shown in Fig. 2.
This observation suggests that carbon contamination can be a possible reason
responsible for the discrepancy between DAC experiment and DFT computation at
high pressures. As a result, at the earth’s inner-core boundary, the melting
temperature of pure iron may be significantly higher than our current
consensus. At a higher pressure of 200 GPa, the change in temperature is
drastic, from 5563 to 4549 K by more than 1000 K, suggesting a profound impact
of carbon contamination as pressure increases.

###  III.3 DFT accuracy

We systematically study the impact on melting temperature from DFT variables,
including Brillouin Zone (BZ) sampling, exchange-correlation functional, and
pseudopotential versions.

We study the impact of BZ sampling by comparing different k-points (the gamma
point vs. a special k-point) in melting temperature calculations. Thanks to
the high temperatures, which broaden the Fermi distribution of electrons, the
calculations become less sensitive to BZ sampling. Hence as shown in Table 1,
the difference is smaller than 100 K in melting temperature regardless of the
pressure condition, which suggests it is sufficient to use the Baldereschi
special k-point $(1/4,1/4,1/4)$ Baldereschi73 for all the calculations. Our
previous experience shows that the special “mean-value” k-point generally
gives a better melting temperature than the gamma point. One possible reason
is that the special k-point better captures the average kinetic energy of the
plane waves inside the BZ Baldereschi73.

To examine the impact of different density functionals, we perform two
additional calculations with the LDA functional at 330GPa and compare them
with the PBE functional we employ throughout this study. As shown in Table 1,
the difference is slight, less than 3% of the melting temperature and
$2\sigma$ ($\sigma$ is the standard error). This observation indicates that
the melting temperature calculations are not sensitive to the choice of
density functionals. Thus relying on the PBE functional generates accurate DFT
melting temperatures for the materials system.

We find significant differences between the two pseudopotentials provided by
VASP, i.e., the one built in the year of 2000 (marked as version “Fe_pv
06Sep2000”) and the latest one built in 2007 (marked as version “Fe_pv
02Aug2007” and recommended by the VASP developers). The melting temperature
difference grows as pressure increases, from less than 100 K below 150 GPa, to
more than 500 K at 330 GPa. At the earth’s inner core boundary, the
“06Sep2000” pseudopotential predicts a melting temperature of $6821\pm 88$ K,
which lies in the range of several previous independent computations, e.g.,
$6700\pm 600$ based on the free energy method and PAW GGA functional Alfe99 ,
$6390\pm 100$ K based on the coexistence method and PAW PW91 functional
comp_1, and $6900\pm 400$ K based on the free energy method and quantum Monte
Carlo (QMC) comp_4. In contrast, the “02Aug2007” version suggests a melting
temperature of $7384\pm 94$ K, significantly higher than the range but still
barely overlaps with the uncertainty boundary. Regardless of the approaches,
all computational values are considerably higher than the extrapolated
experimental melting temperature of 6200 K based on DAC measurement. At
ambient pressure, both versions generate melting temperatures that agree well
with the experimental value for the BCC $\delta$ phase. Both pseudopotentials
mistakenly suggest that the $\gamma$ phase is more stable, with its melting
temperature higher than that of the $\delta$ phase, but the error from the
“02Aug2007” version, at approximately 100 K, is significantly smaller.

##  IV Conclusions

We calculate the DFT melting curve of iron from ambient pressure to 350 GPa,
employing the small-size coexistence method and the SLUSCHI package. The
melting curve is significantly higher than the previous DAC experiment. We
investigate into the discrepancy and discover that carbon contamination is a
possible cause of the lower melting temperatures from DAC. The DFT computation
suggests that iron melting temperatures are higher than the current consensus
and thus further experimental investigation is urgently needed to resolve the
discrepancy.

Table 1: Melting temperature calculations and their detailed settings Calc. | Systems | MT (K) | Pseudopotentials | radius | $N^{b}$ | kmesh | $\sum{n}^{c}$ | CPU | Daysd
---|---|---|---|---|---|---|---|---|---
ID | (Å) | Hours
Melting curve (ambient to 350 GPa) |  |  |  |  |  |  |
1 | FCC Fe 1 atm | 1928 $\pm$ 34 | Fe_pv 02Aug2007 | 10.3 | 180 | (1/4,1/4,1/4) | 25 | 43,686 | 32
2 | BCC Fe 1 atm | 1828 $\pm$ 27 | Fe_pv 02Aug2007 | 10.2 | 172 | (1/4,1/4,1/4) | 25 | 40,960 | 24
3 | FCC Fe 50 GPa* | 3120 $\pm$ 44 | Fe_pv 02Aug2007 | 9.4 | 192 | (1/4,1/4,1/4) | 43 | 164,630 | 155
4 | BCC Fe 50 GPa* | 2502 $\pm$ 32 | Fe_pv 02Aug2007 | 9.5 | 192 | (1/4,1/4,1/4) | 36 | 88,689 | 155
5 | HCP Fe 100 GPa | 4019 $\pm$ 57 | Fe_pv 02Aug2007 | 9.8 | 192 | (1/4,1/4,1/4) | 49 | 55,883 | 31
6 | HCP Fe 150 GPa | 4739 $\pm$ 59 | Fe_pv 02Aug2007 | 9.6 | 192 | (1/4,1/4,1/4) | 22 | 78,754 | 40
7 | HCP Fe 200 GPa | 5563 $\pm$ 71 | Fe_pv 02Aug2007 | 9.6 | 228 | (1/4,1/4,1/4) | 37 | 277,071 | 124
8 | HCP Fe 250 GPa | 6324 $\pm$ 60 | Fe_pv 02Aug2007 | 9.5 | 228 | (1/4,1/4,1/4) | 20 | 118,762 | 79
9 | HCP Fe 300 GPa | 7036 $\pm$ 80 | Fe_pv 02Aug2007 | 9.3 | 228 | (1/4,1/4,1/4) | 62 | 421,906 | 142
10 | HCP Fe 330 GPa | 7385 $\pm$ 94 | Fe_pv 02Aug2007 | 9.8 | 252 | (1/4,1/4,1/4) | 45 | 290,600 | 153
11 | HCP Fe 350 GPa | 7626 $\pm$ 89 | Fe_pv 02Aug2007 | 9.7 | 252 | (1/4,1/4,1/4) | 25 | 173,786 | 120
Carbon impurity |  |  |  |  |  |  |  |
12 | HCP FeC0.01 100 GPaf | 3780 $\pm$ 99 | Fe_pv 06Sep2000 | 9.9 | 192 | (1/4,1/4,1/4) | 36 | 124,676 | 82
20 | HCP Fe 100 GPa | 4029 $\pm$ 102 | Fe_pv 06Sep2000 | 9.9 | 192 | (1/4,1/4,1/4) | 30 | 144,284 | 84
13 | HCP FeC0.01 150 GPae | 4400 $\pm$ 71 | Fe_pv 06Sep2000 | 9.7 | 194 | (1/4,1/4,1/4) | 27 | 170,974 | 69
14 | HCP FeC0.01 150 GPaf | 4570 $\pm$ 82 | Fe_pv 06Sep2000 | 9.7 | 192 | (1/4,1/4,1/4) | 30 | 89,363 | 50
21 | HCP Fe 150 GPa | 4769 $\pm$ 89 | Fe_pv 06Sep2000 | 9.8 | 192 | (1/4,1/4,1/4) | 24 | 128,780 | 53
15 | HCP FeC0.01 150 GPaf *** | 4471 $\pm$ 55 | Fe_pv 02Aug2007 | 9.7 | 192 | (1/4,1/4,1/4) | 30 | 89,363 | 50
6 | HCP Fe 150 GPa | 4739 $\pm$ 59 | Fe_pv 02Aug2007 | 9.6 | 192 | (1/4,1/4,1/4) | 22 | 78,754 | 40
16 | HCP FeC0.01 200 GPaf | 4549 $\pm$ 79 | Fe_pv 06Sep2000 | 9.4 | 192 | (1/4,1/4,1/4) | 23 | 110,254 | 54
22 | HCP Fe 200 GPa *** | 5563 $\pm$ 71 | Fe_pv 06Sep2000 | 9.6 | 228 | (1/4,1/4,1/4) | 37 | 277,071 | 124
Pseudopotential version |  |  |  |  |  |  |  |
17 | FCC Fe 1 atm*** | 2098 $\pm$ 41 | Fe_pv 06Sep2000 | 10.0 | 192 | (1/4,1/4,1/4) | 21 | 79,650 | 39
1 | FCC Fe 1 atm | 1928 $\pm$ 34 | Fe_pv 02Aug2007 | 10.3 | 180 | (1/4,1/4,1/4) | 25 | 43,686 | 32
18 | BCC Fe 1 atm | 1779 $\pm$ 24 | Fe_pv 06Sep2000 | 9.7 | 168 | (1/4,1/4,1/4) | 21 | 427,292 | 210
19 | BCC Fe 1 atm | 1764 $\pm$ 27 | Fe_pv 06Sep2000 | 9.6 | 168 | (1/4,1/4,1/4) | 20 | 221,046 | 113
2 | BCC Fe 1 atm | 1828 $\pm$ 27 | Fe_pv 02Aug2007 | 10.2 | 172 | (1/4,1/4,1/4) | 25 | 40,960 | 24
20 | HCP Fe 100 GPa | 4029 $\pm$ 102 | Fe_pv 06Sep2000 | 9.9 | 192 | (1/4,1/4,1/4) | 30 | 144,284 | 84
5 | HCP Fe 100 GPa | 4019 $\pm$ 57 | Fe_pv 02Aug2007 | 9.8 | 192 | (1/4,1/4,1/4) | 49 | 55,883 | 31
21 | HCP Fe 150 GPa | 4769 $\pm$ 89 | Fe_pv 06Sep2000 | 9.8 | 192 | (1/4,1/4,1/4) | 24 | 128,780 | 53
6 | HCP Fe 150 GPa | 4739 $\pm$ 59 | Fe_pv 02Aug2007 | 9.6 | 192 | (1/4,1/4,1/4) | 22 | 78,754 | 40
22 | HCP Fe 200 GPa*** | 5500 $\pm$ 49 | Fe_pv 06Sep2000 | 9.9 | 252 | (0,0,0) | 63 | 258,642 | 160
7 | HCP Fe 200 GPa | 5563 $\pm$ 71 | Fe_pv 02Aug2007 | 9.6 | 228 | (1/4,1/4,1/4) | 37 | 277,071 | 124
?? | HCP Fe 330 GPa *** | 6821 $\pm$ 88 | Fe_pv 06Sep2000 | 9.9 | 252 | (1/4,1/4,1/4) | 63 | 258,642 | 160
10 | HCP Fe 330 GPa | 7385 $\pm$ 94 | Fe_pv 02Aug2007 | 9.8 | 252 | (1/4,1/4,1/4) | 45 | 290,600 | 153
24 | HCP Fe 330 GPa | 7218 $\pm$ 84 | Fe_sv 23Jul2007 | 9.7 | 252 | (1/4,1/4,1/4) | 24 | 152,575 | 69
k-points and BZ sampling |  |  |  |  |  |  |  |
25 | FCC Fe 1 atm | 2151 $\pm$ 38 | Fe_pv 06Sep2000 | 10.0 | 192 | (0,0,0) | 21 | 79,650 | 39
17 | FCC Fe 1 atm*** | 2098 $\pm$ 41 | Fe_pv 06Sep2000 | 10.0 | 192 | (1/4,1/4,1/4) | 21 | 79,650 | 39
26 | HCP Fe 100 GPa | 4002 $\pm$ 117 | Fe_pv 06Sep2000 | 9.6 | 180 | (0,0,0) | 21 | 42,328 | 25
20 | HCP Fe 100 GPa | 4029 $\pm$ 102 | Fe_pv 06Sep2000 | 9.9 | 192 | (1/4,1/4,1/4) | 30 | 144,284 | 84
27 | HCP Fe 150 GPa | 4713 $\pm$ 79 | Fe_pv 06Sep2000 | 9.7 | 192 | (0,0,0) | 25 | 44,313 | 15
21 | HCP Fe 150 GPa | 4769 $\pm$ 89 | Fe_pv 06Sep2000 | 9.8 | 192 | (1/4,1/4,1/4) | 24 | 128,780 | 53
28 | HCP Fe 235 GPa | 5763 $\pm$ 56 | Fe_pv 06Sep2000 | 9.6 | 228 | (0,0,0) | 25 | 115,141 | 73
23 | HCP Fe 330 GPa | 6759 $\pm$ 49 | Fe_pv 06Sep2000 | 9.9 | 252 | (0,0,0) | 63 | 258,642 | 160
?? | HCP Fe 330 GPa *** | 6821 $\pm$ 88 | Fe_pv 06Sep2000 | 9.9 | 252 | (1/4,1/4,1/4) | 63 | 258,642 | 160
Density functional, LDA vs. PBE |  |  |  |  |  |  |  |
29 | HCP Fe 330 GPa | 7216 $\pm$ 88 | Fe_pv_LDA 02Aug2007 | 9.8 | 252 | (1/4,1/4,1/4) | 33 | 88,496 | 34
10 | HCP Fe 330 GPa | 7385 $\pm$ 94 | Fe_pv 02Aug2007 | 9.8 | 252 | (1/4,1/4,1/4) | 45 | 290,600 | 153
30 | HCP Fe 330 GPa*** | 7160 $\pm$ 60 | Fe_sv_LDA 23Jul2007 | 9.7 | 252 | (1/4,1/4,1/4) | 25 | 289,428 | 47
24 | HCP Fe 330 GPa | 7218 $\pm$ 84 | Fe_sv 23Jul2007 | 9.7 | 252 | (1/4,1/4,1/4) | 24 | 152,575 | 69