Raman spectrometry study of phase stability and phonon anharmonicity of
Al3BC3 at elevated temperatures and high pressures
Huimin Xiang, Fangzhi Li, Jingjing Li, Jiemin Wang, Xiaohui Wang et al.
Citation: J. Appl. Phys. 110, 113504 (2011); doi: 10.1063/1.3665197
View online: http://dx.doi.org/10.1063/1.3665197
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v110/i11
Published by the American Institute of Physics.
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JOURNAL OF APPLIED PHYSICS 110, 113504 (2011)
Raman spectrometry study of phase stability and phonon anharmonicity
of Al3BC3 at elevated temperatures and high pressures
Huimin Xiang,1,2 Fangzhi Li,1 Jingjing Li,1,2 Jiemin Wang,1 Xiaohui Wang,1
Jingyang Wang,1,a) and Yanchun Zhou1,3
1
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy
of Sciences, Shenyang 110016, China
2
Graduate School of Chinese Academy of Sciences, Beijing 100039, China
3
Aerospace Research Institute of Materials and Processing Technology, Beijing 100076, China
(Received 17 August 2011; accepted 27 October 2011; published online 2 December 2011)
In situ Raman spectra of Al3BC3 have been measured at elevated temperatures of up to 1000 C
and high pressures of up to 32 GPa. It is shown that there are no abnormal phonon shifts when the
measurement conditions were up to 1000 C or up to 27 GPa, which indicates a good structural
stability of Al3BC3 at high temperatures and pressures. The Raman active phonon modes were
assigned comprehensively to the corresponding vibration modes by first-principles calculations.
Interestingly, an abnormal softening of the E1g(559 cm–1) and E2g(578 cm–1) phonon modes were
observed when the pressure was higher than 27 GPa. Correlating the results with previous theoretical predictions of polymorphism in Al3BC3, the mode softening at higher pressures might originate
from the structural transformation (from hexagonal to tetragonal symmetry) involving changes of
Al and C coordination numbers. In addition, the phonon anharmonicity has been investigated by
studying the temperature and pressure dependence of the Raman peak shifts and broadenings.
Finally, the present work has highlighted that in situ Raman spectrometry study is a sensitive
method for investigating the structural stability and phonon anharmonicity of complex ceramics.
C 2011 American Institute of Physics. [doi:10.1063/1.3665197]
V
I. INTRODUCTION
Ternary metal borocarbides have been intensively investigated in recent years due to their attractive mechanical and
physical properties such as low density, high neutron absorption, high Young’s modulus, and fracture toughness.1–5
Among them, Al3BC3 has been considered as a promising
candidate for light-weight structural components and neutron
absorbers in the new generation nuclear reactors because of
its low density, high Young’s modulus, and high neutron
absorption.6,7 Kharlamov and Loichenko8 examined the electronic properties of sintered Al3BC3 and found it to be semiconductive. Hillebrecht and Meyer9 proved that this
compound was hydrolysis resistant, and both thermally and
chemically stable. Wang and Yamaguchi10 briefly investigated the thermal and mechanical properties of bulk Al3BC3.
Their results suggested that it was a brittle ceramic with high
hardness. They also showed that Al3BC3 has excellent oxidation resistance at moderate temperatures. Li et al.7 fabricated
a predominantly single phase, dense Al3BC3 ceramic, and
they found that its stiffness was sustained to 1600 C, which
renders it a promising high temperature structural material, it
is also a wear resistant ceramic because of its high hardness
and low modulus. Recently, Wang and collaborators predicted that Al3BC3 exhibits extremely low shear elastic moduli because of the presence of C-B-C units in the crystal
structure.6
a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected].
0021-8979/2011/110(11)/113504/7/$30.00
This ternary compound was firstly described as Al4BxC4
(x ¼ 13) by Matkovich et al.11 Later, Inoue et al.12 pointed out
that the reported Al4BxC4 (x ¼ 13) should in fact correspond
to the Al8B4C7 compound. In 1996, Hillebrecht and Meyer9 analyzed the crystal structure and reported the molecular formula as
Al3BC3. Furthermore, they presented the Raman and infrared
spectra of Al3BC3. The compound has two molecules in a unit
cell. As shown in Fig. 1, the crystal structure of Al3BC3 can be
described as corner-sharing Al5C trigonal bipyramids interleaved
by isolated linear C–B–C units along the c axis in the hexagonal
lattice. In the work of Hillebrecht and Meyer,9 the C-B-C group
was interpreted as an anion with 16 electrons which was isoelectronic to CO2. The authors interpreted the strong bands in the
Raman spectrum, for instance, a peak at 1041 cm–1 was assigned
to the s mode of the C-B-C group, the bands at 421 cm–1 and
560 cm–1 were assigned to the Al-C vibration modes. However,
there are five more experimental Raman peaks which need to be
interpreted. Up to now, the assignment of the Raman peaks of
Al3BC3 has not been fully accomplished.
In recent years, the phase stability of Al3BC3 has
attracted attention due to its similar crystal structure to that
of Mg3BN3. Al3BC3 was supposed to undergo a pressure
induced phase transformation similar to that was observed
for Mg3BN3.13 Solozhenko et al.14 measured the lattice parameters of Al3BC3 at room temperature up to 7.5 GPa and
at 1800 K from 2.5 to 5.3 GPa using x-ray powder diffraction
with synchrotron radiation but they did not observe structural
transformation under these experimental conditions. Later,
Wang et al. predicted a possible pressure-induced phase
110, 113504-1
C 2011 American Institute of Physics
V
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113504-2
Xiang et al.
J. Appl. Phys. 110, 113504 (2011)
II. EXPERIMENTAL AND CALCULATIONS
FIG. 1. (Color online) Crystal structure of Al3BC3.
transformation at 24 GPa (Ref. 15) by first-principles calculation. However, there has been no experimental proof
because of the high isotropic hydrostatic pressure required.
The influence of temperature on the phase stability of
Al3BC3 has also attracted attention. Hillebrecht and Meyer 9
reported that single crystals of Al3BC3 are not sensitive to
hydrolysis and are stable in air up to about 600 C. Recently,
Lee and Tanaka16 found that the decomposition of Al3BC3
occurred at 1400 C in flowing Ar using thermo-gravimetric
analysis (TGA) and x-ray diffraction (XRD). However,
because of the complex crystal structure and chemical bonds
in Al3BC3, TGA, and XRD measurements could not reveal
the heterogeneous changes of different chemical bonds at
elevated temperatures and high pressures clearly.
Raman shifts originate from the polarization of chemical
bonding and are sensitive to changes of the atomic force constants. This method is widely used to characterize specific
structural units or to study the structural changes when a crystal
is away from the equilibrium condition. Therefore, we expected
that an in situ Raman spectrometry study of Al3BC3 at elevated
temperatures and various pressures may be a suitable method to
investigate its phase stability. In addition, anharmonicity is also
important because intrinsic phonon scattering plays an important role on thermal properties, such as thermal expansion, heat
capacity and thermal conductivity for a solid.
In the present work, we have firstly calculated the theoretical Raman active phonon frequencies of Al3BC3 using firstprinciples calculations, and then identified, experimentally,
Raman peaks corresponding to the phonon modes. The structural stability was investigated by in situ measuring of the
Raman spectra of Al3BC3 at different temperatures and pressures. The phonon anharmonicity has been studied by examining the temperature and pressure dependence of the Raman
peak shifts and broadenings. The results have highlighted that
in situ Raman observations are a sensitive method for illustrating the structural stability of complex ceramics.
Bulk Al–B–C ceramic was fabricated through an in situ
reactive hot-pressing method at 1800 C for 2 h. The starting
materials were commercially available Al (99%, 300 mesh),
B4C (98%, 200 mesh), and graphite (98%, 200 mesh) powders. The molar ratio of Al:B:C was 3:1.1:3, and a dense pure
bulk Al3BC3 with a small amount of excess graphite was
obtained. Details of the synthesis have been described in our
previous work.7 Powders used for the Raman experiments
were made by crushing and grinding the as-sintered bulk
Al3BC3. The unpolarized Raman spectra of the sample were
collected on a LabRAM HR800 (HORIBA, France) equipped
with an air-cooled CCD array detector in the backscattering
configuration. A He-Ne laser (632.82 nm) with an incident
power of 20 mW was used as the excitation source, and the
spot size was focused to 2 lm. High-temperature Raman
analyses of Al3BC3 were carried out in flowing high pure
argon in a TS 1500 furnace (Linkam, England) in the range
from room temperature (RT) to 1000 C in 100 C increments
per step. For the high-temperature Raman analyses, the sample was heated to the desired temperature and held for 10 min
before collecting Raman spectra under ambient pressure.
High-pressure Raman analyses for Al3BC3 were carried out
using a diamond anvil cell (DAC) with beveled anvils at ambient temperature. A 70 lm thick pre-indented stainless-steel
gasket with a hole of 150 lm diameter served as the sample
chamber. Samples were loaded into the diamond anvil cells
using a 16:3:1 volume ratio mixture of methanol:ethanol:water solution as a pressure-transmitting medium.17 The pressure was calibrated by the ruby luminescence technique.18,19
The lattice dynamics calculations were implemented by
using the PHONON code compiled by Alfè,20 which employs
the force constant method. We calculated the first-principles
atomic Hellmann-Feynman forces induced by small displacements of selected atoms in a 2 2 1 Al3BC3 supercell
by the CASTEP code. Symmetrical non-equivalent atoms
were moved along the basal plane and the six-fold z axis,
respectively. The amplitudes were restricted to within 0.4%
of the lattice constants. Both positive and negative displacements were produced, and the atomic forces were averaged
to diminish systematic calculation errors. Subsequently, the
force constant matrix was computed by the PHONON code, and
simultaneously the translational invariance constraints were
used. Then, we obtained the phonon eigenfrequencies and
eigenvectors at special k-points. Using this method, we have
assigned the peaks in the experimental Raman spectra with
the theoretical Raman active phonon modes for Ti3SiC2,
Ti2AlC, and Cr2AlC.21
III. RESULTS AND DISCUSSION
Al3BC3 has the space group of D46h (P63=mmc). The zonecenter phonons can be classified by the irreducible representation of the point group D46h . Group theory analysis shows the
following symmetries of the phonon optical modes:
Coptic ¼2A1g þ 4A2u þ 4B1g þ 3B2u þ 2E1g þ 3E1u
þ 5E2g þ 3E2u ;
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(1)
113504-3
Xiang et al.
J. Appl. Phys. 110, 113504 (2011)
where the A1g, E1g, and E2g are Raman active, and A2u and
E1u are IR active. Using the polarization vectors, we identified the symmetry of all the optical phonon modes at the C
point. The theoretical Raman active phonon frequencies at
the C point with identified symmetries and dominant contributions from the structural units are summarized in Table I,
together with the presently measured and previously
reported9 experimental data for comparison.
Initially, we will present our theoretical analysis of the
Raman active modes and the corresponding atomic displacements (as shown in Fig. 2) assigned by the first-principles
calculations. The lowest band located at 35 cm–1 with the irreducible representation of E2g is associated with the shearing of an Al5C slab and a cooperative tilting of C-B-C
chains. This mode is undetectable in the present work,
because it is beyond the measurement limit of our experimental facility. The phonon mode at 173 cm–1 with E1g symmetry is dominated by the collective shear vibrations of Al2
and C2 atoms, together with the cooperative tilting of the
C-B-C chains. The phonon mode at 255 cm–1 with E2g symmetry is dominated by the collective shear vibration of Al1
and C1 atoms. The vibration magnitude is the same for Al1
and C1 atoms, as well as the unchanged Al1-C1 bond length.
The mode at 257 cm–1 with E2g symmetry also represents the
collective shear vibration of Al1 and C1 atoms. The atomic
movements of 255 and 257 cm–1, phonon modes are symmetric and antisymmetric, respectively, with respect to a C2
operation perpendicular to the six-fold principal axis. The
A1g mode centering at 426 cm–1 is ascribed to the vibration
of an Al2 atom along the c-axis. In addition, the phonon
modes with frequencies of 587 cm–1 and 588 cm–1, having
the E1g and E2g symmetry, respectively, are interpreted by
the vibration of Al2-C2 bonds and C-B-C chains, i.e., reverse
vibrations of Al2 and C2 atoms along the basal plane together with the cooperatively tilting of C-B-C chains. The
opposing movements of the Al1 and C1 atoms (stretching of
the Al1-C1 in an Al5C slab) along the basal plane corresponds to the phonon mode with E2g symmetry centered at
730 cm–1. The vibration of the C2 atoms along the c-axis has
the highest force constant and is located at 1039 cm–1. This
phonon mode corresponds to the vibration of C-B-C chains
TABLE I. Measured Lorentzian-fitted Raman shift xexp and corresponding
calculated shift (xcal), irreducible representations (Irrep.) and vibration
modes.
Raman shift (cm–1)
xcalc. xexpt. xref.
Symmetry
Vibration modes
Shear sliding of Al5C slab þ tilting of BC2
Shear sliding of Al2 and C2 atoms
Shear sliding of Al1 and C1 atoms
Shear sliding of Al1 and C1 atoms
Vibration of Al2 along the c-axis
Vibration of Al2-C2 bonds along
the basal plane þ tilting of BC2
35
171
255
257
426
587
588
730
—
171
246
276
420
559
578
680
—
171
248
680
E2g
E1g
E2g
E2g
A1g
E1g
E2g
E2g
1039
1040
1041
A1g
421
559
Vibration of Al1-C1 bonds
along the basal plane
Vibration of C2 atom along the c-axis
FIG. 2. (Color online) Schematics of the corresponding atomic displacements for the Raman-active phonons in the Al3BC3 unit cell. (a) E2g (35),
(b) E1g (171), (c) E2g (255), (d) E2g (257), (e) A1g (426), (f) E1g (587), (g)
E2g (588), (h) E2g (730), and (i) A1g (1039) (all units in cm–1).
in Al3BC3. The presently calculated Raman active modes are
consistent with the theoretical calculation of Wang et al.15
They calculated the bond-length contraction of Al3BC3 at
high pressures and revealed the most resistive and strongest
character of C-B-C units against the hydrostatic pressure.
The temperature dependence of the Raman spectra is
shown in Fig. 3. The Raman spectrum at room temperature
and ambient pressure appears to consist of 6 strong peaks
and several weaker peaks. Determined by the Lorentzian fitting routine, most of the peaks are resolved to center at certain frequencies. The results are presented in Table I to
compare with the theoretical results. The resolved positions
agree well with the theoretical calculations. The results are
also coincident with the work of Hillebrecht and Meyer.9
The vibrational frequencies at 171, 248, 421, 559, 680, and
1041 cm–1 that they reported are also listed in Table I. Hillebrecht et al. empirically assigned several phonon modes: the
bands at 421 cm–1 and 560 cm–1 to the Al-C stretching
modes, and a strong band at 1041 cm–1 to the s mode of the
C-B-C group. Besides the similar assignments, the experimental Raman peaks are comprehensively assigned to the
corresponding phonon modes in our work.
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113504-4
Xiang et al.
J. Appl. Phys. 110, 113504 (2011)
the Al-C modes, qualitatively consistent with the trend for
mode softening. Phonon frequency shifts and broadenings can
be analyzed by considering phonon-phonon interactions. The
analysis of Raman spectra is consistent with the Klemens process22 and Ridley process,23 which considers how one optical
phonon decays into two or three phonons. The three-phonon
process for decay of an optical phonon at the C point is relatively simple and yields a linear temperature dependence of
linewidth broadening of the Raman spectrum. If one considers
the four-phonon processes, the temperature dependence
becomes more complex and the temperature-dependent phonon
linewidth broadening Ci of mode i can be expressed as:
FIG. 3. (Color online) Temperature dependence of Raman shift of Al3BC3.
Fig. 3 shows that with increasing temperature, the
Raman peaks generally shift to lower frequencies. At higher
temperatures, several of the weaker modes either could not
be resolved from the background or their position could not
be determined reliably. Nevertheless, several strong peaks
remained distinct to the highest temperature measured and
used to monitor the effects of temperature on line position
and linewidth. The resolved Raman frequencies and linewidths of the strong peaks at different temperatures are listed
in Table II. It is shown that the Raman peaks with
E1g(171 cm–1), A1g(420 cm–1), and A1g(1040 cm–1) symmetry shift to lower frequencies linearly with respect to the
temperature increase. In addition, temperature-dependent
frequency shifts depend on the energy of the studied normal
mode. We divided the normal modes into two groups: Al-C
vibration dominated modes (E1g(171 cm–1), A1g(420 cm–1))
and C-B-C dominated modes (A1g (1040 cm–1)). It is apparent that the C-B-C mode undergoes more thermal softening
than the Al-C modes. The result suggests that the mode Grüneisen parameters decrease with mode frequencies and the
quasiharmonic softening of the normal mode is related to the
character of the structural units in the lattice.
The temperature dependence of the Raman peak widths
may provide further information about anharmonicity. Table II
shows that the absolute broadening of the normal modes demonstrates the similar tendency to that of the temperaturedependent frequencies. The C-B-C modes broaden faster than
TABLE II. Some measured Lorentzian-fitted Raman peaks frequencies
x (cm–1) and full-width half-maximum linewidths C (cm–1) under different
temperatures.
A1g
E1g
Temperature
RT
100 C
300 C
500 C
700 C
900 C
Dx= ð10–2) (cm–1 K–1)
DT
A1g
x
C
x
C
x
C
171
171
170
168
167
166
–0.65
3.1
2.3
3.0
3.0
3.5
4.8
420
419
416
413
410
407
–1.50
5.6
6.4
8.1
11.9
12.8
15.2
1040
1038
1031
1023
1017
1011
–3.40
7.4
8.1
11.3
16.5
19.5
25.6
2
Ci ðTÞ ¼ Ci ð0Þ þ Ai 1 þ hx ð0Þ=2k T
B 1
e i
"
#
3
3
þ
;
þ Bi 1 þ hx ð0Þ=3k T
2
B 1
e i
ðehxi ð0Þ=3kB T 1Þ
(2)
where Ci ð0Þ is a constant; A and B are parameters for threephonon and four-phonon processes, respectively. At ambient or
higher temperature, the contributions from the two terms vary as
T and T2, respectively. We fitted the linewidth broadenings listed
in Table II to the polynomial Ci ðTÞ ¼ Ci ð0Þ þ Ai T þ Bi T 2 . The
fitted A and B are 2.86 10–4 and 3.04 10–6, respectively, for
the E1g(171 cm–1) mode; 0.014 and –2.68 10–6, respectively,
for the A1g(420 cm–1) mode; and 0.015 and 6.42 10–6, respectively, for the A1g(1040 cm–1) mode. Taking the temperaturedependent phonon broadening of the A1g(1040 cm–1) mode as an
example, the three-phonon process is predominant at low temperatures; but the four-phonon contribution is about half of the
three-phonon process above 1000 C.
Some of the Raman peaks in Fig. 3 could not be identified when the temperature reaches 1000 C, because the thermal radiation background is enhanced at high temperature.
But there are 3 Raman peaks (as listed in Table II) that can
be clearly distinguished. These peaks correspond to the phonon modes dominated by the vibrations inside the Al5C
(171 cm–1), the C-B-C chains (1039 cm–1), and the Al2-C2
(420 cm–1) linking the two structural units in Al3BC3. The
results demonstrate that the crystal structure of Al3BC3 is
stable up to 1000 C.
Fig. 4 shows the pressure-induced Raman shifts when
the applied isotropic pressure is lower than 10 GPa. Compared with the temperature-dependent mode softening, the
peaks move in the opposite direction (mode hardening)
because of the bond length contractions and enhanced force
constants under applied pressure.24–26 The spectra drawn in
Fig. 4 change slightly when the pressure reaches 10 GPa.
The results indicate that Al3BC3 remains stable under the
10 GPa isotropic hydrostatic pressure. Here, we also focused
on the three phonon modes, E1g(171 cm–1), A1g(420 cm–1),
and A1g(1040 cm–1) to trace the pressure-dependent Raman
shifts. However, the absolute broadening of these normal
modes does not demonstrate the similar tendency to that of
the pressure-dependent frequency softening. The resolved
Raman frequencies and linewidths of the three peaks at different pressures are listed in Table III. It is shown that the
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113504-5
Xiang et al.
J. Appl. Phys. 110, 113504 (2011)
FIG. 4. (Color online) Low pressure dependence of Raman shift of Al3BC3.
Raman peaks shift to higher frequencies linearly with respect
to the pressure increase. In addition, pressure-dependent
frequency shifts depend slightly on the energy of the studied
normal modes. The linear fitting of the hardening rates
yield 0, 2.31, and 3.95 cm–1=GPa for the E1g(171 cm–1),
A1g(420 cm–1), and A1g(1040 cm–1) modes, respectively. On
the other hand, the linewidth broadening does not follow a
monotonic change with the increase of pressure.
In order to examine the structural stability of Al3BC3
under higher pressures, we ran high pressure measurements
(up to 32 GPa) in the diamond anvil cell, and the results are
shown in Fig. 5. Before the pressure reaches 27 GPa, the trend
of the peak shifts is similar to that in the low pressure range
(<10 GPa). But when the pressure reaches 30 GPa, abnormal
softening shifts of the E1g(559 cm–1) and E2g(578 cm–1) modes
are observed. From the symmetry analysis listed in Table I,
the E1g(559 cm–1) and E2g(578 cm–1) modes are dominated by
opposing vibrations of the Al2 and C2 atoms and are assigned
to the stretching or contraction of the Al2-C2 bonds along the
basal plane. Wang et al.15 predicted that Al3BC3 would
undergo a pressure induced phase transformation from a hexagonal to a tetragonal structure when the pressure is higher
than 24 GPa. During the phase transformation, the Al and C
atoms in the hexagonal structure change to the more symmetrical central positions in the tetragonal structure, leading to a
different bonding coordination between Al and C atoms along
the basal plane. In the hexagonal and tetragonal structures, the
TABLE III. Some measured Lorentzian-fitted Raman peaks frequencies
x (cm–1) and full-width half-maximum linewidths C (cm–1) under low
pressure.
A1g
E1g
Pressure (GPa)
0
2.1
3.9
5.5
8.2
9.9
Dx= (cm–1 GPa–1)
DP
A1g
x
C
x
C
x
C
171
174
172
172
174
174
0.00
9.5
8.6
6.9
7.9
10.6
9.6
420
425
429
432
439
443
2.31
7.3
7.1
6.9
7.1
6.7
6.6
1040
1050
1057
1062
1073
1080
3.95
9.4
9.3
9.8
9.8
10.5
10.0
C1=C2 atoms are coordinated by three and four Al1=Al2
atoms, respectively, along the basal plane. The transformation
in the crystal structure can be monitored by the abrupt changes
of the Raman shifts at high pressures. In the present experiment, the abrupt softening of the E1g(559 cm–1) and
E2g(578 cm–1) modes at high pressures might originate from
the changes of the coordination between Al and C atoms along
the basal plane. It is supposed that a structural transformation
of Al3BC3 starts occurring at high pressures. However, after
we removed the pressure and relaxed the measurement back
to the ambient condition, the newly obtained Raman spectrum
is similar to that of the virgin sample. The result suggests an
incomplete structural transformation of Al3BC3 at 32 GPa. If
one wants to confirm the phase transformation of Al3BC3 at
high isotropic pressures, a higher pressure is recommended
and the three modes, E1g(559 cm–1), E2g(578 cm–1), and
E2g(680 cm–1) modes, need to be traced. The reason is that the
values of these modes are determined by the force constants
of the Al1-C1 and Al2-C2 bonds along the basal plane, which
are related to the Al and C coordination numbers.
The shift of the Raman peaks at elevated temperature
arises from two aspects, the anharmonic frequency shift and
quasiharmonic lattice expansion. The experimental measurement of the temperature dependence of the phonon frequencies is the results of the two effects. One is associated with
the thermal expansion of the crystal; the other is related to
the higher-order anharmonicities, such as cubic and quartic
terms in the crystal potential.27,28 Based on the pressureinduced shifts of the Raman peaks demonstrated in Figs. 3
and 4, the quasiharmonic contribution can be identified.
The phonon frequency x ¼ xðV; T Þ is a function of volume V ¼ V ðP;
TlnÞxand temperature T. The volume expansion
and the anharmonic temperature effect
contribution @ @P
T
@ ln x
@T V can be separated by the following equations:
@ ln x
@ ln x
@ ln V
@ ln x
¼
þ
;
@T P
@ ln V T ! @T P
@T V
@ ln x
@ ln V
@ ln x
þ
;
¼
@ ln V
@T P
@T V
@P @P
T
a @ ln x
@ ln x
þ
;
(3)
¼
j
@P T
@T V
where a ¼ V1 @V
is the thermal expansion coefficient and
@T P
1 @V
j ¼ V @P T is the isothermal volume compressibility (i.e.,
@P
)). According
the reciprocal of bulk modulus (B ¼ V @V
T
to Eq. (3), the volume expansion effect and the anharmonic
temperature effect can be calculated if the values of the isobaric temperature and
isothermal
pressure
derivatives of freln x
@ ln x
and
quency shifts, i.e., @ @P
@T P , and a and B are
T
1
obtained. Here, we used a ¼ 6:67
106
@ K
(Ref. 29) and
@ ln x
ln x
B=153 GPa (Ref. 14), and @P T and @T P are obtained
from Figs. 3 and 4.
Table IV summarizes the calculated results. It is clear
that for each traced Raman frequency, the contribution of the
anharmonic temperature effect is one order of magnitude
larger than that from thermal expansion. For different phonon modes, the shifts caused by thermal expansion and
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113504-6
Xiang et al.
J. Appl. Phys. 110, 113504 (2011)
IV. CONCLUSIONS
FIG. 5. (Color online) High pressure dependence of Raman shift of Al3BC3.
anharmonicity are also different. The response of mode
E1g(171 cm–1) to temperature is the largest which means that
the softening of this mode is the fastest when the temperature
changes. While the pressure or the thermal expansion has the
greatest influence on E1g(567 cm–1) and has the lowest influence on E1g(171 cm–1). The mode Grüneisen parameters can
be calculated using the following equation:30
ci jT ¼ @ ln xi
@ ln xi
jT ¼ j1
jT :
@ ln V
@P
(4)
The results of ci are listed in Table IV. The RT mode
Grüneisen parameter ci is the measurement of the volume dependence of xI, i.e., the magnitude of the anharmonicity of a
material. From these values, we can easily find out that E1g
(567 cm–1) is the most anharmonic mode in the selected
modes. For a quasiharmonic system, the volume thermal
expansion can be expressed as:31
c Cv
;
a¼
BV
(5)
where B is the bulk modulus, V is the molar volume, and Cv
is the constant volume specific heat. Different Grüneisen parameters produce different thermal expansions, which mean
Al3BC3 is anisotropic in its thermal expansion. Compared to
a-Al2O3 (1.32),32 6H-SiC (0.96),32 and MgO (1.54),33 the
relatively small mode Grüneisen parameters of Al3BC3 mean
that using a theoretical method based on the Debye-model
approximation to estimate its thermal properties may lead to
satisfactory accuracy.
TABLE IV. Values of some optic phonons of Al3BC3 and their logarithmic
pressure and temperature derivatives and mode Grüneisen parameters (ci ).
@ ln x
ja
@T P
–1
(K )
–1
E1g(171 cm )
A1g(420 cm–1)
A1g(1040 cm–1)
@ ln x
@P
–1
@ ln x
T
–6
–39.7 10
–36.6 10–6
–32.5 10–6
@T
V
ci
(K–1)
(K )
–6
–1.24 10
–5.43 10–6
–3.86 10–6
–6
–38.7 10
–31.2 10–6
–28.6 10–6
0.19
0.81
0.58
The Raman spectra of Al3BC3 have been measured at
temperatures up to 1000 C and pressures up to 32 GPa. By
using first-principles calculation, all the Raman peaks are
assigned to the corresponding Raman-active phonons and
vibrational modes. The dominated atomic displacements of
each Raman active mode are also presented. The high temperature Raman analyses show that the structure of Al3BC3 can
be sustained to 1000 C. The phonon anharmonicity is discussed by examining the temperature dependence of the
Raman-active phonons, and the results show that the predominant process causing the broadening of the Raman peaks is
the three-phonons process at low temperature; the fourphonons process only needs to be considered at high temperature. The crystal structure of Al3BC3 remains stable up to
27 GPa isotropic hydrostatic pressure according to the high
pressure experiments. However, when the applied pressure
reaches 30 GPa, an abnormal softening of the E1g(559 cm–1)
and E2g(578 cm–1) phonon modes is observed. The abnormal
downward shift may originate from the structural transformation (from hexagonal to tetragonal symmetry) involving
changes of Al and C coordination numbers at high pressures.
The mode Grüneisen parameter ci has been calculated from
the high pressure Raman experiments. When compared to aAl2O3, MgO, the relatively small Grüneisen parameter of
Al3BC3 means the use of theoretical calculations based on
Debye-model approximation to estimate the thermal properties may be satisfactory. The present work also shows that in
situ Raman spectrometry analysis is sensitive and reliable for
investigating the temperature and pressure dependence of
crystal structure for complex compounds, because this method
can identify different responses of various chemical bonds
under various temperature and=or mechanical perturbations.
ACKNOWLEDGMENTS
This work was supported by the Natural Sciences Foundation of China under Grant Nos. 50672102, 50832008, and
51032006. The authors are grateful to Professor A. Oates from
University of Newcastle, Australia for improving the paper.
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