Structural and vibrational behavior of $2H\text{−}{\mathrm{NbSe}}_2$ at high pressures

The high-pressure structural and vibrational properties of a layered transition metal dichalcogenide $2H\text{−}{\mathrm{NbSe}}_2$ were investigated using single-crystal x-ray diffraction and Raman spectroscopy, demonstrating its structural stability up to 35 GPa. The lattice compressibility changes character from being highly anisotropic at low pressures to largely isotropic at high pressures. Concomitantly, the interatomic bonds demonstrate highly anisotropic compression behavior with the Se-Se interlayer bonds compressing by >20%, while the intramolecular Se-Se distance shows a nonmonotonic pressure dependence with a maximum at ∼12 GPa. The nearest-neighbor central force lattice vibrational model yields pressure dependencies of the interatomic forces in qualitative agreement with bond length compression, providing insight into the vibrational properties of $2H\text{−}{\mathrm{NbSe}}_2$ at high pressures.

Figure 1

Crystal structure of $2H\text{−}{\mathrm{NbSe}}_2$. The bonds between the nearest-neighbor atoms are labeled.

Figure 2

Reconstructed reciprocal lattice plane of ${\mathrm{NbSe}}_2$ at (a) 10.3(5) GPa and (b) 34.6(5) GPa obtained from single-crystal x-ray diffraction data. The x-ray wavelengths are 0.3344 Å (GSECARS) and 0.3445 Å (HPCAT), respectively. The observed diffraction spots have been indexed (circled) and used to determine the structure of $2H\text{−}{\mathrm{NbSe}}_2$. Unindexed spots correspond to reflections from other crystallites; these could be observed because the grain size was close to the x-ray beam diameter.

Figure 3

The unit cell lattice parameters of $2H\text{−}{\mathrm{NbSe}}_2$ deduced from single-crystal and powder x-ray diffraction data. Please note the different vertical axes (color coded) for the $a$ and $c$ lattice parameters. The error bars (Table 1) for the lattice parameters are smaller than the symbol size. The solid lines are the best fits to the Vinet equations for the lattice parameters (see text) with the following parameters: $a_0=3.443\left(2\right)$; $B_0^a=244\left(23\right)\mathrm{GPa}$; $B_1^a=5.3\left(1.0\right)$; $c_0=12.547\left(8\right)$; $B_0^c=62\left(6\right)\mathrm{GPa}$; $B_1^c=6.8\left(5\right)$. Data from this paper are compared with those of Ref. [9].

Figure 4

(a) The linear compressibilities and (b) bond lengths vs pressure of $2H\text{−}{\mathrm{NbSe}}_2$ derived from single-crystal (SC) and powder x-ray diffraction (XRD) measurements. The inset to (a) shows the pressure dependence of the $c$/$a$ ratio (filled symbols: single crystal, open symbols: powder). Data from this paper are compared with those of Ref. [9].

Figure 5

Raman spectra of $2H\text{−}{\mathrm{NbSe}}_2$ at elevated pressures measured at HPSTAR. The modes are assigned and labeled following the literature [18, 19]. The atomic motions corresponding to the Raman active modes are shown in cartoons at the top. The excitation wavelength is 488 nm.

Figure 6

Raman frequencies of $2H\text{−}{\mathrm{NbSe}}_2$ at elevated pressures. Open symbols of different colors are data from this paper measured at EPL and HPSTAR (blue and green symbols, respectively). The error bars for the Raman frequencies are smaller than the symbol size. The pressure uncertainty is ±0.5 GPa. Solid lines are guides to the eye. Data at 0 GPa (x crosses) are from Ref. [18]. A dashed pink line shows the results of the nearest-neighbor central force model calculations of the $E_{2g}^2$ mode frequency (see text).

Figure 7

Interatomic central force constants of $2H\text{−}{\mathrm{NbSe}}_2$ at elevated pressures determined from the Raman frequencies.