The high-pressure behavior of diamantane was investigated using angle-dispersive synchrotron x-ray diffraction (XRD) and Raman spectroscopy in diamond anvil cells. Our experiments revealed that the structural transitions in diamantane were extremely sensitive to deviatoric stress. Under non-hydrostatic conditions, diamantane underwent a cubic (space group Pa3) to a monoclinic phase transition at below 0.15 GPa, the lowest pressure we were able to measure. Upon further compression to 3.5 GPa, this monoclinic phase transformed into another high-pressure monoclinic phase which persisted to 32 GPa, the highest pressure studied in our experiments. However, under more hydrostatic conditions using silicone oil as a pressure medium, the transition pressure to the first high-pressure monoclinic phase was elevated to 7–10 GPa, which coincided with the hydrostatic limit of silicone oil. In another experiment using helium as a pressure medium, no phase transitions were observed to the highest pressure we reached (13 GPa). In addition, large hysteresis and sluggish transition kinetics were observed upon decompression. Over the pressure range where phase transitions were confirmed by XRD, only continuous changes in the Raman spectra were observed. This suggests that these phase transitions are associated with unit cell distortions and modifications in molecular packing rather than the formation of new carbon-carbon bonds under pressure.

Carbon based nanomaterials are of broad interest due to their unique properties and potential applications. Diamondoids are cage hydrocarbons with sp3 hybridized carbon atoms and structures similar to subunits of diamond lattices.1,2 They can be distilled from crude oil and display some of the unique properties of diamond.3,4 These molecules, especially the higher diamondoids,5,6 can form a variety of shapes from rods, disks to screws, making them ideal building blocks for a wide range of applications in nanotechnology.7,8 For example, the exceptional electronic properties of higher diamondoid monolayers have attracted attention in using these unique materials as functional elements to regulate energy flow at the nanoscale.9,10

Diamantane, C14H20, also called congressane, is the second member of the diamondoid family and is composed of two face-fused adamantane cages. It was first synthesized and characterized in 1965.11 At ambient pressure and room temperature, diamantane has a cubic structure (space group Pa3) with each unit cell containing four molecules. Some of its many applications are in polymers, advanced materials, and as a potential anti-tumor agent.1 Owing to its diamondoid structure, diamantane possesses many physical characteristics similar to adamantane, including rigidity, lipophilicity, low strain energy, etc. However, diamantane also differs significantly from adamantane. For example, the diamantane skeleton possesses two different types of tertiary C–H bonds (apical and medial).

Currently there have only been a limited number of studies on the high-pressure properties of these newly distilled carbon forms, with only adamantane12,13 and [121] tetramantane14 having been investigated. High-pressure x-ray diffraction (XRD) experiments on adamantane have been conducted at room-temperature where a phase transition from an orientationally disordered phase to an ordered tetragonal structure was reported between 0.4 and 0.5 GPa.15 This high pressure phase was the same as the low-temperature ordered crystalline phase of adamantane at atmospheric pressure. Our previous work on [121] tetramantane demonstrated that it underwent a pressure-induced phase transition from the monoclinic P21/n structure to a triclinic P1 phase and that this phase transition could be attributed to the changes in the intermolecular packing.14 

Pressure has been demonstrated as a clean and powerful tool for tuning materials properties and opens a new dimension for novel materials synthesis.16,17 As a fundamental thermodynamic parameter, application of high pressure could lead to the formation of new carbon structures that are not achievable at ambient conditions. By compressing 0D bulky balls, 1D carbon nanotubes, 2D graphene, and 3D nanodiamonds, new forms of carbon allotropes with exotic properties have been discovered.18–20 In this study, we explored the structural stability and bonding configuration of diamantane under both nonhydrostatic and hydrostatic conditions. From XRD we found that the crystal structure of diamantane was very sensitive to deviatoric stress, while the Raman spectra of diamantane under nonhydrostatic conditions only showed continuous changes upon compression. These results suggest that the observed phase transitions are associated with unit cell distortions and molecular packing modifications under deviatoric stress.

High purity (>99%) diamantane samples were used in our experiments. Details regarding sample preparation can be found in previous work.5 To reach high pressure, a symmetric diamond anvil cell (DAC) with 500 μm diamond culets was used. A polycrystalline diamantane sample was loaded into the sample chamber created by drilling a 150 μm diameter hole in a preindented stainless steel gasket. A 5 μm diameter ruby ball was loaded for pressure calibration.21 Raman measurements were conducted with a 514 nm Ar+ laser using a Renishaw Invia system in the Extreme Environments Laboratory at Stanford University. No pressure transmitting medium was used for the Raman measurements. In situ high-pressure XRD experiments were conducted at beamline 16BMD of the Advanced Photon Source (APS), Argonne National Laboratory (ANL), beamline 12.2.2 of the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory (LBNL) and beamline 7-2 of the Stanford Synchrotron Radiation Light source (SSRL), SLAC National Accelerator Laboratory (SLAC). The incident monochromatic X-ray beam (λ = 0.4246 Å at APS, 0.4959 Å at ALS, and 0.775 Å at SSRL) was directed on the sample and the 2D Debye-Scherrer rings were collected on an image plate and integrated using FIT2D software.22 The JADE5 software package was applied to index diffraction patterns and refine unit cell parameters. We conducted three different kinds of XRD experiments, one with no pressure-transmitting medium, one with silicone oil (AP 150 Wacker), and one with helium as a pressure medium.

The Raman spectra of diamantane were measured as a function of pressure up to 19 GPa under non-hydrostatic conditions (i.e., without a pressure medium). We tentatively separated the Raman modes into three, distinct vibrational regions based on previous calculations:23,24 the CCC bending and CC stretching region between 200 and 900 cm−1, the CH wagging/CH2 twisting and CH2 scissoring region between 900 and 1600 cm−1, and the CH stretching region between 2800 and 3200 cm−1 as shown in Figure 1. Upon compression, only continuous changes were observed in the CC stretching/CCC bending region, while peak merging and splitting arose in the higher wavenumber regions which was quite similar with our previous work on [121] tetramantane.14 Upon decompression, the changes were reversible and all the Raman modes matched the starting spectrum.

FIG. 1.

Evolution of Raman spectra of diamantane with increasing pressure. (a) Pressure dependent Raman spectra of the CC stretching, CCC bending, CH wagging/CH2 twisting, and CH2 scissoring region from low pressure up to 19 GPa (bottom to top). We cut out the region between 1200 and 1400 cm−1 to avoid the intense first order diamond peak. (b) Pressure dependent Raman spectra of the CH stretching region from low pressure up to 19 GPa (bottom to top).

FIG. 1.

Evolution of Raman spectra of diamantane with increasing pressure. (a) Pressure dependent Raman spectra of the CC stretching, CCC bending, CH wagging/CH2 twisting, and CH2 scissoring region from low pressure up to 19 GPa (bottom to top). We cut out the region between 1200 and 1400 cm−1 to avoid the intense first order diamond peak. (b) Pressure dependent Raman spectra of the CH stretching region from low pressure up to 19 GPa (bottom to top).

Close modal

1. Non-hydrostatic conditions: No pressure medium

The XRD pattern at ambient conditions could be well indexed to a cubic Pa3 space group as previously reported for diamantane.1 The initial pressure was 0.8 GPa in the first pressure cycle. Interestingly, two new diffraction peaks were readily observed as shown in Figure 2(a). In a separate experiment conducted at SSRL, we used a Merrill-Bassett DAC and MgO as an internal pressure standard. This time the first data point was 0.15 GPa. However, again, the sample had already transformed.

FIG. 2.

(a) Evolution of integrated powder XRD patterns of diamantane with pressure under nonhydrostatic conditions. We have included diffraction pattern at ambient condition outside DAC here. Different phases are marked by different colors. The numbers on the right indicate pressure in GPa. (b) The small 2θ angle region shows the most notable changes between different phases.

FIG. 2.

(a) Evolution of integrated powder XRD patterns of diamantane with pressure under nonhydrostatic conditions. We have included diffraction pattern at ambient condition outside DAC here. Different phases are marked by different colors. The numbers on the right indicate pressure in GPa. (b) The small 2θ angle region shows the most notable changes between different phases.

Close modal

The new high-pressure phase could be indexed to the monoclinic Cc space group. Upon further compression to 3.5 GPa, another phase transition was observed as indicated by appearance of a new peak at the shoulder of the strongest diffraction peak (marked by the circle in Figure 2(b)). This phase could be indexed by the monoclinic Pc space group. This second high-pressure monoclinic phase persisted to the highest pressure in our experiments, as shown in Figure 2(a). Upon decompression, the high-pressure phase displayed some hysteresis before finally transforming back to the starting structure after the pressure had been fully released for a number of hours.

2. Quasi-hydrostatic conditions: Using silicone oil and helium pressure media

This category of molecular solids undergoes solid-solid phase transitions easily. Indeed, earlier work has demonstrated that deviatoric stress could play a vital role in triggering phase transitions or lowering transition pressure.25,26 In order to examine this possible effect, we conducted two quasi-hydrostatic compression experiments using silicone oil and helium as the pressure media. Figure 3 shows the experiment with silicone oil as a pressure-transmitting medium. At the initial pressure of 0.4 GPa, the diffraction pattern could be well indexed to the Pa3 space group, and the cubic phase persisted upon further compression up to 6.8 GPa. At 10.2 GPa, we observed the development of the first high-pressure monoclinic phase. The hydrostatic limit of silicone oil has been reported to be around 7 GPa,27,28 which coincides with the pressure region where we observed the transition. We did not observe the second high pressure monoclinic phase up to the highest pressure in our experiment (12 GPa). The sample again displayed significant hysteresis and sluggish transition kinetics, with the high pressure phase being initially recovered after pressure was released. Upon waiting for several days, the recovered sample eventually transformed back to the starting Pa3 space group. Figure 4 shows the compression cycle using helium as a pressure-transmitting medium up to 13 GPa obtained at APS. The starting cubic Pa3 phase remained stable to the highest pressure. We did not observe any high pressure phase transitions in this experiment. Analyses on how hydrostaticity affects pressure induced d-spacing changes in the cubic Pa3 phase are also carried out and the results are demonstrated in Figure 5.

FIG. 3.

(a) Evolution of integrated powder XRD patterns of diamantane with pressure under hydrostatic conditions using silicone oil as a pressure transmitting medium. Different phases are marked by different colors. The numbers on the right indicate pressure in GPa. Miller indices for the cubic Pa3 phase are given at the bottom. (b) An expansion of the figure shows the most notable changes between different phases.

FIG. 3.

(a) Evolution of integrated powder XRD patterns of diamantane with pressure under hydrostatic conditions using silicone oil as a pressure transmitting medium. Different phases are marked by different colors. The numbers on the right indicate pressure in GPa. Miller indices for the cubic Pa3 phase are given at the bottom. (b) An expansion of the figure shows the most notable changes between different phases.

Close modal
FIG. 5.

The evolution of different d-spacings in the cubic Pa3 phase with pressure. The open symbols represent d-spacing values obtained in helium while solid symbols represent d-spacing values obtained using silicone oil as a pressure transmitting medium.

FIG. 5.

The evolution of different d-spacings in the cubic Pa3 phase with pressure. The open symbols represent d-spacing values obtained in helium while solid symbols represent d-spacing values obtained using silicone oil as a pressure transmitting medium.

Close modal
FIG. 4.

Evolution of the integrated powder XRD patterns of diamantane with pressure under hydrostatic conditions using helium as the pressure medium. The numbers on the right indicate pressure in GPa. Miller indices for the cubic Pa3 phase are given at the bottom.

FIG. 4.

Evolution of the integrated powder XRD patterns of diamantane with pressure under hydrostatic conditions using helium as the pressure medium. The numbers on the right indicate pressure in GPa. Miller indices for the cubic Pa3 phase are given at the bottom.

Close modal

Our results demonstrate that the crystal structure of diamantane is extremely sensitive to nonhydrostatic conditions. The sample transformed immediately when external pressure was applied under nonhydrostatic conditions. The transition pressure in silicone oil was elevated to 7 GPa, which coincides with the hydrostatic limit of the pressure medium.28 Separate experiments with helium as a pressure medium confirmed the disparity in transition pressure was related to the quality of the pressure medium. This suggests that the role of deviatoric stress rather than the absolute pressure is a dominant factor for triggering this phase transition. Deviatoric stress has been demonstrated to play a vital role in triggering phase transformations and has also been reported to greatly reduce the transition pressure in some cases.25,26 In our study, the high symmetry starting cubic phase was only preserved under hydrostatic conditions. The distortion of the geometry of the unit cells and the molecules under deviatoric stress leads to the lowering of symmetry and results in the observed phase changes.

Lower diamondoids, e.g., adamantane, diamantane, and triamantane, are known to undergo solid-solid phase transitions.29 For example, adamantane undergoes a disordered to an ordered phase transition which could be triggered either by cooling down to 208 K or pressurizing up to 0.48 GPa.15,30 Diamantane is known to undergo three temperature driven solid-state phase transitions: at T = 35 K, 407 K, and 440 K, respectively.31 From in situ Raman spectroscopy under nonhydrostatic conditions, the ambient condition spectrum is identical to the spectra at both 0.5 GPa and 4 GPa in both the C-C and C-H regions except for minor changes in intensity and pressure driven peak shifts. This suggests that in the diamantane molecule its diamond-like carbon cages are retained. The anisotropic shrinkage of unit cell due to axial compression under nonhydrostatic conditions and the anisotropic compressibility of different axes could be the key for triggering this phase transition. Also, no evidence was found for the formation of higher diamondoids over the current pressure range.

The volume (V) as a function of pressure (P) for diamantane with silicone oil as the pressure transmitting medium was fit to a third-order Birch-Murnaghan (3rd B-M) equation of state (EOS):32,33

\begin{eqnarray}P\left( V \right) &=& \frac{{3K_0 }}{2}\left[ {\left( {\frac{{V_0 }}{V}} \right)^{\frac{7}{3}} - \left( {\frac{{V_0 }}{V}} \right)^{\frac{5}{3}} } \right]\nonumber\\&&\times\left\{ {1 + \frac{3}{4}( {K_0^{\prime} - 4} )\left[ {\left( {\frac{{V_0 }}{V}} \right)^{\frac{2}{3}} - 1} \right]} \right\}\end{eqnarray}
PV=3K02V0V73V0V53×1+34(K04)V0V231
(1)

(shown in Figure 6). By fixing V0 to be 1030.8 Å3 based on the ambient XRD data analysis (here we fixed V0 for all the fittings), we found the best fit yields K0 = 7.9(0.8) GPa and K0 = 17.7(2.5). For highly compressible materials such as molecular solids, the Vinet formula has been shown to provide a better representation of the EOS34–36 which has an exponential form:

\begin{equation}P\left( V \right) = 3K_0 \frac{{\big(1 - \big( {\frac{V}{{V_0 }}\big)^{\frac{1}{3}} } \big)}}{{\left(\frac{V}{{V_0 }}\right)^{\frac{2}{3}} }}{\rm exp}\bigg(\frac{3}{2}\left( {K_0^{\prime} - 1} \right)\bigg(1 - \bigg( {\frac{V}{{V_0 }}\bigg)^{\frac{1}{3}} } \bigg).\end{equation}
PV=3K0(1(VV0)13)VV023 exp (32K01(1VV013).
(2)

Using this formula, the best least square fits of the data give K0 = 9.4(0.7) GPa and K0 = 11.6(0.8). We also fit the P-V curve of diamantane in helium using 3rd B-M and Vinet EOS and found K0 = 5.0(0.6) GPa, K0 = 19.5(2.8) (3rd B-M), and K0 = 6.9(0.3) GPa, K0 = 10.8(0.3) (Vinet), respectively. The smaller bulk modulus measured in helium also supports the fact that it is a better pressure medium compared to silicone oil in terms of hydrostaticity.27,37

FIG. 6.

Evolution of unit cell volumes with pressure. Solid circles: Unit cell volume changes versus pressure with silicone oil as a pressure medium. Open circles: Unit cell volume changes versus pressure with helium as a pressure medium. The black solid curve is 3rd B-M EOS fitting for the Pa3 phase. The red dashed curve is Vinet EOS fitting for the Pa3 phase. Error bars associated with unit cell volume are smaller than the symbol size.

FIG. 6.

Evolution of unit cell volumes with pressure. Solid circles: Unit cell volume changes versus pressure with silicone oil as a pressure medium. Open circles: Unit cell volume changes versus pressure with helium as a pressure medium. The black solid curve is 3rd B-M EOS fitting for the Pa3 phase. The red dashed curve is Vinet EOS fitting for the Pa3 phase. Error bars associated with unit cell volume are smaller than the symbol size.

Close modal

We can see a dramatic discrepancy in EOS and bulk moduli for different pressure transmitting media as shown in Figure 6. In the low pressure region, both fits for the two pressure media data match each other reasonably well. However, differences in unit cell volume increase at higher pressure. This is a bit surprising since at low pressure (<1 GPa), silicone oil should be comparable to helium in terms of hydrostaticity.27 This systematic difference might arise from some possible structural factors such as topology of molecules, the intermolecular interactions,38 etc., and warrants future investigation.

The elastic properties of carbon based nanomaterials have been widely studied. For instance, bucky balls were found to have a high bulk modulus and be extremely incompressible due to their closed cage structure. The bulk modulus of bundled carbon nanotubes was found to be 37 GPa while the estimate for the bulk modulus of a single tube is significantly higher.39,40 In our case, the bulk modulus of diamantane was found to be relatively small with a large K0. This indicates that while diamantane is initially relatively easy to compress, the bulk modulus exhibits a large increase with pressure. It is in agreement with our previous experiments and the general trend of the enhanced incompressibility of this diamondoid family upon compression.14 Due to the dominance of the weak intermolecular van der Waals interactions, the low pressure bulk modulus is relatively small. With more void volume in the unit cell being squeezed out under pressure, the material becomes increasingly difficult to compress due to the stiffness of the diamond cage-like molecules themselves, thus leading to a dramatic increase in bulk modulus. This is consistent with observations of high K0 of other molecular solids under compression.41 

Diamondoids, this category of carbon-based nanomaterials, their properties under high pressure have not been well studied. We found that diamantane undergoes a series of deviatoric stress driven phase transitions at high pressure. Under nonhydrostatic conditions, the transformation to the first high-pressure monoclinic phase was completed below 0.15 GPa and a second phase transition took place at 3.5 GPa. Under hydrostatic conditions, with silicone oil as a pressure medium, the first phase transition did not occur until 7 GPa which coincided with the hydrostatic limit of silicone oil. In a helium experiment, no phase transition was observed up to the highest pressure (13 GPa) reached. The continuous changes in the C-C stretching region and the reversible Raman spectra are consistent with the absence of polymerization or decomposition. The phase transitions we observed are likely associated with the modification of the unit cell and the intermolecular packing rather than changes in carbon-carbon bonding within the molecules.

We thank Yongmoon Lee and Donghoon Seoung for valuable discussions regarding our work. This work was supported by the Department of Energy (DOE) Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-76SF00515. HPCAT operations are supported by DOE-NNSA under Award No. DE-NA0001974 and DOE-BES under Award No. DE-FG02-99ER45775, with partial instrumentation funding by NSF MRI-1126249. APS is supported by DOE-BES, under Contract No. DE-AC02-06CH11357. ALS is supported by DOE-BES, under Contract No. DE-AC02-05CH11231. SSRL is supported by DOE-BES, under Contract No. DE-AC02-76SF00515. We also acknowledge the financial support from the Deep Carbon Observatory.

1.
C.
Bostedt
,
L.
Landt
,
T.
Moller
,
J. E. P.
Dahl
, and
R. M. K.
Carlson
,
Nature's Nanostructures
(
Pan Stanford Publishing Co. Pte. Ltd.
,
2012
), pp.
169
194
.
2.
A. P.
Marchand
,
Science
299
,
52
(
2003
).
3.
J. E. P.
Dahl
,
J. M.
Moldowan
,
K. E.
Peters
,
G. E.
Claypool
,
M. A.
Rooney
,
G. E.
Michael
,
M. R.
Mello
, and
M. L.
Kohnen
,
Nature (London)
399
,
54
57
(
1999
).
4.
Z. B.
Wei
,
J. M.
Moldowan
,
S. C.
Zhang
,
R.
Hill
,
D. M.
Jarvie
,
H.
Wang
,
F. Q.
Song
, and
F.
Fago
,
Org. Geochem.
38
,
227
249
(
2007
).
5.
J. E. P.
Dahl
,
S. G.
Liu
, and
R. M. K.
Carlson
,
Science
299
(
5603
),
96
99
(
2003
).
6.
J. E. P.
Dahl
,
J. M.
Moldowan
,
Z.
Wei
,
P. A.
Lipton
, and
P. R.
Deniseivich
,
Angew. Chem., Int. Ed.
49
(
51
),
9881
9885
(
2010
).
7.
G. C.
McIntosh
,
M.
Yoon
,
S.
Berber
, and
D.
Tomanek
,
Phys. Rev. B
70
,
045401
(
2004
).
8.
T.
Sasagawa
and
Z. X.
Shen
,
J. Appl. Phys.
104
,
073704
(
2008
).
9.
W. L.
Yang
,
J. D.
Fabbri
,
T. M.
Willey
,
J. R. I.
Lee
,
J. E. P.
Dahl
,
R. M. K.
Carlson
,
P. R.
Schreiner
,
A. A.
Fokin
,
B. A.
Tkachenko
, and
N. A.
Fokina
,
Science
316
,
1460
(
2007
).
10.
W. A.
Clay
,
Z.
Liu
,
W.
Yang
,
J. D.
Fabbri
,
J. E. P.
Dahl
,
R. M. K.
Carlson
,
Y.
Sun
,
P. R.
Schreiner
,
A. A.
Fokin
, and
B. A.
Tkachenko
,
Nano Lett.
9
,
57
61
(
2009
).
11.
C.
Cupas
,
P. V. R.
Schleyer
, and
D.
Trecker
,
J. Am. Chem. Soc.
87
,
917
918
(
1965
).
12.
R.
Rao
,
T.
Sakuntala
,
S. K.
Deb
,
A. P.
Roy
,
V.
Vijaykumar
,
B. K.
Godwal
, and
S. K.
Sikka
,
J. Chem. Phys.
112
,
6739
(
2000
).
13.
V.
Vijayakumar
,
A. B.
Garg
,
B. K.
Godwal
, and
S. K.
Sikka
,
Chem. Phys. Lett.
330
,
275
280
(
2000
).
14.
F.
Yang
,
Y.
Lin
,
J. E. P.
Dahl
,
R. M. K.
Carlson
, and
W. L.
Mao
,
J. Phys. Chem. C
118
,
7683
7689
(
2014
).
15.
T.
Ito
,
Acta Crystallogr.
B29
,
364
365
(
1973
).
16.
R. J.
Hemley
,
Annu. Rev. Phys. Chem.
51
,
763
800
(
2000
).
17.
Y.
Lin
,
W. L.
Mao
, and
H. K.
Mao
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
8113
(
2009
).
18.
W. L.
Mao
,
H. K.
Mao
,
P. J.
Eng
,
T. P.
Trainor
,
M.
Newville
,
C. C.
Kao
,
D. L.
Heinz
,
J. F.
Shu
,
Y.
Meng
, and
R. J.
Hemley
,
Science
302
,
425
(
2003
).
19.
Y.
Lin
,
L.
Zhang
,
H. K.
Mao
,
P.
Chow
,
Y. M.
Xiao
,
M.
Baldini
,
J. F.
Shu
, and
W. L.
Mao
,
Phys. Rev. Lett.
107
,
175504
(
2011
).
20.
L.
Wang
,
B. B.
Liu
,
H.
Li
,
W. G.
Yang
,
Y.
Ding
,
S. V.
Sinogeikin
,
Y.
Meng
,
Z. X.
Liu
,
X. C.
Zeng
, and
W. L.
Mao
,
Science
337
,
825
(
2012
).
21.
H. K.
Mao
,
J.
Xu
, and
P. M.
Bell
,
J. Geophys. Res.
91
,
4673
4676
, doi: (
1986
).
22.
A. P.
Hammersley
, ESRF Internal Report, ESRF98HA01T, FIT2D V9.129 Reference Manual V3.1,
1998
.
23.
J.
Filik
,
J. N.
Harvey
,
N. L.
Allan
,
P. W.
May
,
J. E. P.
Dahl
,
S.
Liu
, and
R. M. K.
Carlson
,
Spectrochim. Acta, Part A
64
,
681
692
(
2006
).
24.
J.
Filik
,
J. N.
Harvey
,
N. L.
Allan
,
P. W.
May
,
J. E. P.
Dahl
,
S.
Liu
, and
R. M. K.
Carlson
,
Phys. Rev. B
74
,
035423
(
2006
).
25.
Y.
Lin
,
Y.
Yang
,
H.
Ma
,
Y.
Cui
, and
W. L.
Mao
,
J. Phys. Chem. C
115
,
9844
9849
(
2011
).
26.
A.
Kailer
,
Y. G.
Gogotsi
, and
K. G.
Nickel
,
J. Appl. Phys.
81
,
3057
(
1997
).
27.
S.
Klotz
,
J. C.
Chervin
,
P.
Munsch
, and
G. L.
Marchand
,
J. Phys. D: Appl. Phys.
42
,
075413
(
2009
).
28.
Y.
Lin
,
Q.
Zeng
,
W.
Yang
, and
W. L.
Mao
,
Appl. Phys. Lett.
103
,
261909
(
2013
).
29.
T. E.
Jenkins
and
J.
Lewis
,
Spectrochim. Acta
36A
,
259
264
(
1980
).
30.
C. G.
Windsor
,
D. H.
Saunderson
,
J. N.
Sherwood
,
D.
Taylor
, and
G. S.
Pawley
,
J. Phys. C: Solid State Phys.
11
,
1741
1759
(
1978
).
31.
T. E.
Jenkins
and
A. R.
Bates
,
J. Phys. C: Solid State Phys.
12
,
1003
1010
(
1979
).
32.
F.
Birch
,
Phys. Rev.
71
,
809
824
(
1947
).
33.
F. D.
Murnaghan
,
Am. J. Math.
59
,
235
260
(
1937
).
34.
P.
Vinet
,
J.
Ferrante
,
J. R.
Smith
, and
J. H.
Rose
,
J. Phys. C: Solid State Phys.
19
,
L467
L473
(
1986
).
35.
P.
Vinet
,
J.
Ferrante
,
J. R.
Smith
, and
J. H.
Rose
,
J. Geophys. Res.
92
,
9319
9325
, doi: (
1987
).
36.
P.
Vinet
,
J.
Ferrante
,
J. R.
Smith
, and
J. H.
Rose
,
Phys. Rev. B
35
,
1945
1953
(
1987
).
37.
M. B.
Kruger
,
J. H.
Nguyen
,
W.
Caldwell
, and
R.
Jeanloz
,
Phys. Rev. B
56
,
1
(
1997
).
38.
J.
Ruiz-Fuertes
,
D.
Errandonea
,
R.
Lacomba-Perales
,
A.
Segura
,
J.
González
,
F.
Rodríguez
,
F. J.
Manjón
,
S.
Ray
,
P.
Rodríguez-Hernández
,
A.
Muñoz
 et al,
Phys. Rev. B
81
,
224115
(
2010
).
39.
C. Q.
Ru
,
Phys. Rev. B
62
,
10405
(
2000
).
40.
U. D.
Venkateswaran
,
A. M.
Rao
,
E.
Richter
,
M.
Menon
,
A.
Rinzler
,
R. E.
Smalley
, and
P. C.
Eklund
,
Phys. Rev. B
59
,
10928
(
1999
).
41.
S. N.
Vaidya
and
G. C.
Kennedy
,
J. Chem. Phys.
55
,
987
(
1971
).