ОПТИКА И СПЕКТРОСКОПИЯ, 2014, том 116, № 6, с. 944-947
XV МЕЖДУНАРОДНЫЙ ФЕОФИЛОВСКИЙ СИМПОЗИУМ
y%K 548.0:535.34
AB INITIO INVESTIGATION OF PHONON SPECTRA IN GdLiF4 COMPOUND
UNDER HYDROSTATIC PRESSURE
© 2014 t. A. V. Petrova*, B. Minisini**, O. V. Nedopekin*, and D. A. Tayurskii*
* Institute of Physics, Kazan Federal University, 420008Kazan, Russia ** Institut Supérieur des Matériaux et Mécaniques Avancés du Mans, 72000 Le Mans, France
E-mail: Anastasia.Petrova@gmx.com Received November 18, 2013
Employing density functional theory (DFT) within the generalized gradient approximation, the GdLiF4 structure has been studied for a pressure range from 0 to 12 GPa. The influence of pressure on the lattice vibrational spectrum of the scheelite phase (I4i/a, Z = 4) has been evaluated by means of the "direct" approach, i.e., using force constants calculated from atomic displacements. As a result, the Raman and infrared modes have been identified and their dependencies on pressure have been investigated and compared with available experimental data. It has been found that instability of the crystal structure appears at pressures above 6 GPa.
DOI: 10.7868/S003040341406018X
INTRODUCTION
Nowadays the diode-pumped solid state laser materials have invoked major attention due to their potential to build small size laser system with high efficiency and long operating lifetime. The doped with rare earth ions GdLiF4 crystals are very promising for such systems development — the lasers using a Nd3+ doped crystal demonstrated the low threshold and high efficiency action [1]. Another interesting property of GdLiF4 that it is a positive uniaxial crystal, the natural birefringence compensates the birefringence induced by heating because of laser emission generation. Furthermore, in the GdLiF4 structure, the site symmetry for the lanthanide ion is ¿4. This site presents no inversion symmetry, so the mixture of the terms with even parity in the wave functions of the 4f multiplet makes the optical transitions permitted and of suitable intensity for laser emission.
Fluoride compounds like GdLiF4 have the CaWO4 type or scheelite type structure (/41/a, Z = 4), which is a superstructure of fluorite CaF2 (Fm3m, Z = 4) [2]. The fluorine atoms are located in a distorted simple cubic arrangement and the Li+ and Gd3+ cations are fourfold and eightfold coordinated by fluorines, respectively (Fig. 1).
The high-pressure behavior of GdLiF4 crystal was studied by measuring its angle-dispersive X-ray powder diffraction patterns as a function of pressure and temperature in a diamond anvil cell and a large-volume Paris—Edinburgh cell using a synchrotron radiation source [3]. Upon compression to about 11 GPa at room temperature, the stable structure is of the scheelite type. At higher pressures and T = 298 K, new reflections occur that cannot be explained with the fergusonite structural model previously observed
inYLiF4. The possible reason for such observations can be the growth of an amorphous component at the elevated pressures. All the transformations are largely irreversible upon decompression. Annealing of the sample at 13.1 GPa led to a nucleation of a solid solution series Gd1 _yLiyF3 _ 2y (P63/mmc, Z = 2) and traces of LiF. The new material Gd1 _ yLiyF3 _ 2y (P63/mmc, Z = 2) was recovered to ambient conditions but back transformed to a YF3 type phase (Pnma, Z = 4) after regrinding at room temperature for several hours.
The additional interest in the study of the phonon spectra of GdLiF4 compound was invoked by the fact that similar phonon calculations have been performed
A-axis
c-axis
Fig. 1. A tetragonal structure of GdLiF4 compound.
for YLiF4 isostructural crystal, which led to a deeper understanding of the mechanism of the phase transition occurring in this material under pressure [4].
The most of experimental studies were focused on magnetic properties of fluoride crystals [5—9]. Recently, it has been recognized that pressure dependencies of fluorides optical properties are not still well understood. An understanding of the lattice dynamics of GdLiF4 is important and indeed several relevant experimental studies have been published reporting Raman and infrared spectra [10, 11]. The purpose of the present work is to extend such a lattice dynamics study under pressure employing DFT
In the present paper, the Raman and infrared modes of GdLiF4 are studied for wide range of hydrostatic pressure and d®/dP derivatives are obtained. Also the analysis of the phonon spectra under pressure is carried out up to 12 GPa.
PHONON CALCULATION
Vibrational Spectra under Pressure
Employing DFT [12] using VASP 5.2 [13] (Vienna ab initio Simulation Package) program within the generalized gradient approximation, the GdLiF4 structure has been optimized for a pressure range from 0 to 12 GPa. The exchange—correlation functional was approximated by the gradient corrected form proposed by Perdew-Burke-Ernzerhof [14]. The electronic degrees of freedom were described using the projector augmented wave method. Full optimization of the structure was performed until the maximum force dropped below 0.002 eV/A-1 whereas the self-consistent field convergence criterion was set at 10-6 eV. The selected £-point spacing (0.5 eV/A) led to six symmetry independent ^-points and a high precision calculation with a plane-wave cut off of 500 eV was used to describe the electronic valence states. To smooth the Fermi step function, the Gaussian smearing with a-pa-rameter 0.1 eV was used. The non-magnetic approximation was used as well as the approximation where /-electrons of gadolinium ions are "kept frozen in the core". All of the above mentioned calculation parameters were chosen based on the study carried out in the paper [15], as the most suitable for the calculation of GdLiF4 structure.
The lattice vibrational properties were calculated within the harmonic approximation, using the PHONON code [16], part of MedeA® modeling interface [17]. In PHONON module the force constant matrix was calculated via atomic displacements from equilibrium positions by ±0.02 A. The interatomic interaction is taken into account within the distance range of 7 A, the size of supercell is large enough to ignore the distortions introduced by the boundary conditions in phonon spectra. The longitudinal optical (LO) and transversal optical (TO) mode splitting was
ra, THz 12
Z r X P r N
Fig. 2. The phonon dispersion curves at pressure 0 GPa.
not investigated in this work. Consequently, only TO modes at the r point were obtained.
To study the mechanism of pressure influence on the spectra, the phonon dispersion curves of GdLiF4 have been calculated within a range from 0 to 12 GPa. The Fig. 2 shows the phonon dispersion curves at pressure equal to 0 GPa.
Calculations of phonon dispersion curves were performed along the path which is defined in £-space in the direction of the quadratic Brillouin zone. The vertices which define the path have the following coordinates: Z(0.5, -0.5, -0.5), T(0, 0, 0), X(-0.5, 0, 0), P(-0.25, -0.25, -0.25), N(0, -0.5, 0).
It has been found that instability of the crystal structure appears at pressures above 6 GPa that can be seen from the appearance of the "negative frequencies" in the spectrum. It's important to note that in calculations made by MT (Mechanical-Thermal) module of VASP 5.2 the negative eigenvalue appears just above 10 GPa [15].
Raman and Infrared Modes under Pressure
The scheelite primitive cell (trigonal) containing two GdLiF4 units, has 36 degrees of freedom (including rigid translation) per wave vector. The 36 vibrational modes at the centre of the Brillouin zone are distributed among the irreducible representations of C4h as follows [6, 18]:
rvib = 3Ag + 5Bg + 5Eg + 5 Au + 3Bu + 5Eu.
One Au and one Eu mode correspond to rigid translations of the whole crystal. The other Au and Eu modes are infrared active with a dipole moment parallel with, and perpendicular to the crystalline axis c, respectively. The g modes are Raman active and correspond to
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PETROVA et al.
Frequency, cm 1 600 r
400
200
A
#
6
0 a
A A A A
T □ T □ T □ ▼ □
a a a a
■ ■ ■ ■
* Eg
" Ag
a a
m m Eg
t Ê t t tB • • • • »e
8 12 Pressure, GPa
Frequency, cm-1 600 r
400
200
• • • Eu
• •
• □ □ □ Au
□ □ + Au
□ « ♦ ♦ ♦ ♦
■ ■ ■ ■ - Eu
• • • • • • Eu
■ ■ ■ ■ ■ ■ Au
A A A A A ±Au
° O o O o Eu
8 12 Pressure, GPa
Fig. 3. Pressure dependence of phonon frequencies of the Raman active modes of GdLiF4.
Fig. 4. Pressure dependence of phonon frequencies of the infrared active modes of GdLiF4.
▼ Bg
B
B
A
g
B
g
0
4
0
4
the following components of the Raman polarizability tensor:
Ag • axx + ayy, azz-Bg • axx ayy, axy,
Eg • azx-, ayz-
The phonons of Bu symmetry are neither Raman nor infrared active. Raman modes of GdLiF4 at various pressures are shown in Fig. 3.
The 3®/dP slopes in the pressure intervals from 0 to 8 GPa (the step is 2 GPa) and from 9 to 12 GPa (the step is 1 GPa) have been calculated. The dividing of pressure range into two intervals is caused by some kinks in frequency curves of the Eg and Bg modes be-
Raman active modes in GdLiF
4
Symmetry Frequency, cm 1 Frequency, cm 1 [1]
A 145 -
250 261
411 410
Bg 148 145
204 208
305 309
355 356
398 410
Eg 124 <115
169 165
304 310
346 351
426 432
low 250 cm 1 which are seen near the pressure 8 GPa (Fig. 3). The slope of Eg Raman mode changes from —0.66 to —1.09 cm-1/GPa, the slope of Bg Raman mode changes from 0.44 to —0.21 cm- 1/GPa. The first Ag mode in the range from 0 to 8 GPa has the negative slope —0.35 cm-1/GPa but afterwards it becomes positive 0.15 cm-1/GPa. Similarly to the Ag mode, other Raman modes tend to increase with pressure. Three doublets were observed experimentally at ambient conditions above 250 cm-1, namely (Eg + Bg) modes at 309/310 and at 351/356 cm-1 and the (Ag +
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