Inorganic Chemistry
Article
focused on the equation of state (EOS) or bulk modulus/
compressibility by static compression experiments combined
with synchrotron X-ray diffraction observations, only providing
the structural stability and compressibility under high pressure,
without information about the shear-related proper-
ties.15,17,19,22,23
Recently, our newly developed technique of in-house
ultrasonic measurements in a large volume press (LVP)
enabled precise measurements of compressional and shear
wave velocities, elasticity at high pressure when synchrotron X-
ray/neutron beams are not available.5,20,21,32,33 In this work,
for the first time, we report sound velocities, elasticity, and
elasticity-related properties of stoichiometric δ-MoN poly-
crystals under high pressure using LVP-based ultrasonic
measurement techniques complemented with first-principles
calculations. The compressional (VP) and shear (VS) wave
velocities of δ-MoN are measured at pressures up to ∼13 GPa,
from which the bulk and shear moduli, their pressure
derivatives, and elasticity-correlated mechanical/thermal prop-
erties are derived, as compared with the results from our
theoretically predicted results and previous studies.
EXPERIMENTAL AND THEORETICAL DETAILS
■
High P−T Synthesis and Characterization. The stoichiometric
hexagonal δ-MoN powders are fabricated at 5−5.5 GPa and 1300 °C
with a duration of 5−10 min in a hinge-type large volume press19
through a high-pressure solid-state metathesis reaction of a mixture of
Na2MoO4 (∼99.5%) and hexagonal boron nitride (hBN) (>99.9%)
powders with a molar ratio of 1:2, which is described in eq 1
Na2MoO + 2BN = MoN + 2NaBO2 + 1/2N2
(1)
4
Figure 1. (a) Experimental cell assembly for the current in-house
sound velocity measurements at high pressure in a multi-anvil
apparatus. (b) Waveform data of the compressional (50 MHz) and
shear (30 MHz) wave echoes for submicron polycrystalline δ-MoN at
a peak pressure of ∼13 GPa, exhibiting the echoes from the interfaces
of the WC cubic anvil, the Al2O3 buffer rod and the δ-MoN specimen,
respectively.
The prepared run products were purified using pure water to remove
excess Na2MoO4 and NaBO2 by-products, and then placed in a high-
temperature oven for drying at ∼350 K. To obtain high-quality
specimens for high-pressure ultrasonic measurements, the stoichio-
metric polycrystalline bulk δ-MoN were synthesized at ∼10 GPa and
1100 °C for 30 min in a Walker-type high-pressure press using the as-
prepared δ-MoN powders as the starting material. The well-sintered
polycrystalline δ-MoN bulk specimens were characterized by energy-
dispersive X-ray diffraction (XRD) at the X17B2 beamline at NSLS,
scanning electron microscopy-energy-dispersive X-ray (SEM-EDX:
NovaNano at SUStech), and Archimedes density measurements.
High-Pressure Ultrasonic Measurements. Sound velocities of
compressional and shear waves for polycrystalline δ-MoN at high
pressure have been simultaneously measured in a multi-anvil large
volume press. A schematic high-pressure cell assembly used for the
current ultrasonic measurements is shown in Figure 1a. Briefly, a piece
of LiNbO3 foil with 10° Y cut was used as a transducer, which was
mounted on a well-polished truncated face of a tungsten carbide
(WC) cubic anvil for receiving and generating compressional and
shear wave echoes at various pressures.
To reduce the acoustic energy loss, all surfaces of the transducer-
mounted WC anvil, Al2O3 buffer rod, and δ-MoN specimen were
well-polished using diamond paste with a grain size of 1 μm. Travel
times for the compressional (P) and shear (S) waves were
simultaneously measured with standard errors of 0.2 and 0.4 ns,
respectively.20,21,32,33 In this study, polycrystalline alumina acted as
both a pressure marker and a buffer rod, which was embedded
between the δ-MoN specimen and the WC cubic anvil. Based on the
travel times of shear waves vs pressures for the Al2O3 buffer rod, the
current cell pressures were calibrated.33 To obtain a (quasi)-
hydrostatic environment for the δ-MoN sample, a very soft cell
assembly (soft Sn rod as the backing material) was designed and used
in this in-house ultrasonic measurement experiment, instead of
heating/annealing the conventional “high-temperature cell assembly”
to relax/reduce internal stress/strain when synchrotron X-ray/
neutron beams are available.5,33
Based on the pre-measured initial sample length and the zero-
pressure density, the corresponding sample lengths under various
pressures can be estimated by Cook’s equation, which is described as
a function of the travel times for both the compressional and shear
waves.5,33 After measuring the sample length of the recovered sample,
we find that the change in the sample length is within 1 μm as
compared to the initial value, indicating that almost no plastic
deformation occurred during the current experiments. Elasticity of
bulk modulus and shear rigidity and their pressure dependences are
fitted by applying the third-order finite-strain equations. Uncertainties
in the bulk and shear moduli are within ∼1.5%.5,20,21,32,33
Representative acoustic signals of the compressional and shear
waves for polycrystalline δ-MoN at the maximum pressure of ∼13
GPa are shown in Figure 1b. Echoes from the different interfaces (i.e.,
the WC anvil-buffer rod interface, the buffer rod-sample interface, and
the sample-backing material interface) can be clearly observed and
identified, which ensures precise measurement of the travel times even
at the highest pressure.
First-Principles Calculations. In the current theoretical calcu-
lations, interactions between ionic cores and electrons are determined
by applying ultrasoft pseudo-potentials. Exchange-correlation poten-
tials are performed by the generalized gradient approximation (GGA)
of density functional theory (DFT).34,35 For the pseudo-potential
calculation, the valence electron densities are defined as Mo (4d55s1)
and N (2s22p3). The electronic wave functions are treated as a plane
wave basis with a cut-off energy of 500 eV. The corresponding
Monkhorst−Pack k-points are set to be 10 × 10 × 9. At a certain
external pressure/stress, full optimization of the cell should be
B
Inorg. Chem. XXXX, XXX, XXX−XXX