Phonon Spectra of Elpasolites Cs₂NaRF₆ (R=Y,Yb): Ab Initio Calculations

RESEARCH ARTICLE | DECEMBER 07 2015
Phonon spectra of elpasolites Cs2NaRF6 (R=Y,Yb): Ab initio
calculations 
Vladimir Chernyshev; Vladislav Petrov; Anatoliy Nikiforov; Dmitriy Zakiryanov
AIP Conf. Proc. 1694, 030004 (2015)
https://doi.org/10.1063/1.4937248
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17 June 2026 16:13:54
in the elpasolites Cs 2 NaYCl 6 and Cs 2 NaYBr 6
Phonon Spectra of Elpasolites Cs2NaRF6 (R=Y,Yb): ab initio
Calculations
Vladimir Chernyshev1,a), Vladislav Petrov1, Anatoliy Nikiforov1 and Dmitriy
Zakiryanov1
1
Ural Federal University, Ekaterinburg, Russia
a)
Corresponding author: Vladimir.Chernyshev@urfu.ru
Abstract. The influence of hydrostatic pressure on structure and dynamics of a crystal lattice of elpasolites Cs 2NaYbF6
and Cs2NaYF6 (S.G. 225) within ab initio approach is investigated. Frequencies and irreducible representations (irreps) of
phonon modes are determined. Elastic constants are calculated. The calculations are carried out within MO LCAO
approach using DFT method with hybrid functionalities of B3LYP and PBE0 in CRYSTAL09 periodic code. For the
description of rare earth ion the pseudopotential replacing internal orbitals including 4f orbitals was used. External 5s and
5p orbitals defining chemical bond were described by valence basis sets.
M2ALnX6 crystals (A, M – metal, Ln–rare earth ion, X – halogen), with structure of an elpasolite (S.G. 225)
attract attention of researchers as perspective optical matrixes [1,2,3,4,5].
Rare earth ions are in highsymmetric position, at doping they are replaced by impurity lanthanides. However,
there are still no researches on ab initio investigations of structure and dynamics of elpasolite Cs2NaRF6 (R=Y, Yb)
lattice. Recently calculations for Cs2NaYF6 have been made by means of GGA and LDA approximations with the
basis of plane waves [6]. It is important to carry out calculations for homologous crystals of Cs2NaRF6 using hybrid
DFT functionals which are well reproducing width of the band gap [7]. In this work the following stages were
consistently executed: the optimization of crystal structure, the calculation of a phonon spectrum and elastic
constants of Cs2NaRF6 (R=Y, Yb). The influence of hydrostatic pressure on crystal structure and frequencies of
phonons is investigated.
COMPUTATIONAL DETAILS
The calculations were carried out within MO LCAO approach implemented in CRYSTAL09 code [8]. The
hybrid-DFT B3LYP [9] and PBE0 [10] one-electron Hamiltonians was adopted both of them contain a mixture of
exact Hartree-Fock (20% and 25% respectively) and DFT exchange-correlation term. All electronic Gaussian basis
sets were used for sodium [11], yttrium [12] and fluorine [13]. Pseudopotential and valence basis set ECP46MDF
[14] were used for cesium, ECP59MWB-II [15,16,17] – for ytterbium, which are available on site [18].
The accuracy of evaluating the infinite Coulomb and exchange series was controlled by five parameters Ti,
which are set to 9, 9, 9, 20, 50. Reciprocal space was sampled by shrinking factor of 8, which suppose 29 points in
the irreducible Brillouin zone. The accurate predefined pruned grid was used for numerical integration (keyword
XLGRID). The convergence of self-consistent-field is controlled by threshold on energy 10-10 Hartree. Equilibrium
geometry optimization was performed by using analytical energy gradients with respect both atomic coordinates and
unit cell parameter. The quasi-Newtonian technique combined with the Broyden-Fletcher-Goldfarb-Shanno
algorithm was used for Hessian updating. Convergence was checked both on gradient components and nuclear
displacements with default tolerances 0.00003 a.u. and 0.00012 a.u. respectively. The calculation of the vibrational
frequencies were taken at the center of the first Brillouin zone i.e. Г point within the framework of the harmonic
TIM14 Physics Conference - Physics without frontiers
AIP Conf. Proc. 1694, 030004-1–030004-5; doi: 10.1063/1.4937248
© 2015 AIP Publishing LLC 978-0-7354-1341-2/$30.00
030004-1
17 June 2026 16:13:54
INTRODUCTION
approximation by diagonalizing the mass-weighted Hessian matrix constructed from numerical differentiations of
energy gradient with respect of atomic coordinates. For the elastic constants calculation was concerned two stressed
configurations with stress magnitude of 0.01.
RESULTS AND DISCUSSION
Elpasolite Cs2NaRF6, R = Y, Yb crystallizes in cubic
symmetry (space group 225) with atomic positions Cs
(0.25 0.25 0.25), Na (0.5 0.5 0.5), R (0,0,0), F (x, 0, 0)
(Figure 1). The results of calculation of the crystal
structure are in good agreement with the experimental
data [19, 20, 21]. The displacement x (0.23 ÷ 0.24) is in
good agreement with the experimental value (0.26) for
the isostructural compound Cs2NaErF6 [20]. The
calculated lattice parameters are compared with the
previous experimental results in Table 1.
FIGURE 1. Crystal structure of the elpasolite
TABLE 1. Lattice parameter and oxygen displacement x of elpasolites
Lattice
Constant, Ǻ
Cs2NaYbF6
B3LYP
9.168
PBE0
9.090
9.193
9.109
Exp.
9.075 [18]
9.028 [20]
B3LYP
PBE0
0.241
0.241
0.238
0.238
The quality of the calculation of the phonon spectrum cannot be achieved without adequate reproduction of the
band structure and the band gap [22]. The results of bandgap value calculations (Table 2) are in good agreement
with the experimental data [23].
TABLE 2. Bandgap value of elpasolites
Bandgap value, eV
Cs2NaYF6
9.9
10.6
10.3
B3LYP
PBE0
Exp.[22]
Cs2NaYbF6
9.8
10.5
-
The calculation of the elastic constants (Table 3) gave similar results for Cs2NaYF6 and Cs2NaYbF6.
Unfortunately, there are no experimental data for these compounds in the scientific press.
TABLE 3. Elastic constants and bulk modulus (GPa) of elpasolites
Cs2NaYbF6
Cs2NaYF6
PBE0, this work
PBE0, this work
LDA [6]
GGA [6]
C11
55
60
83
49
C12
25
24
24
18
C44
21
23
25
17
B
35
36
44
28
The calculation of the phonon spectrum was carried out taking into account LO-TO splitting (Tables 4-6).
B3LYP and PBE0 functionals give similar results, which are in a good agreement with the available experimental
data for Cs2NaYF6 [5]. There is no experimental data for Cs2NaYbF6, however, the calculated frequencies are in
good agreement with measurements for isostructural compound Cs 2NaTmF6 [5]. Analysis of the eigenvectors
showed that only fluoride ions participate in Raman-active Eg and Ag modes, in silent F1g and F2u modes and in
maximum frequency IR active F1u mode.
The results of calculation of the crystal structure and the phonon spectrum under hydrostatic pressure are given
in Tables 7-8. The calculation of the phonon spectrum at pressure of 5 GPa showed that E g mode and two F1u modes
030004-2
17 June 2026 16:13:54
x
Cs2NaYF6
with the highest frequencies changed maximally. The value of LO-TO splitting of F1u modes varied significantly
under hydrostatic pressure.
TABLE 4. Raman active modes, cm-1
Irrep
PBE0
B3LYP
Exp.[5]
Ions are involved in the mode
Cs2NaYbF6
F2g
F2g
Eg
Ag
69
205
363
463
67
206
349
452
65*
203*
373*
473*
Cs, F
Cs, Na, F
F
F
69
200
363
467
Cs, F
Cs, Na, F
F
F
Cs2NaYF6
F2g
70
F2g
211
Eg
376
Ag
465
Note ‘*’– Frequencies of Cs2NaTmF6
71
236
361
457
TABLE 5. IR active modes, cm-1
Irrep.
PBE0
LO
Ions are
involved in the
mode
B3LYP
TO
94
173
258
423
80
169
182
373
F1u
F1u
F1u
F1u
107
191
265
470
88
184
198
410
Cs2NaYF6
LO
TO
92
162
256
410
76
162
176
362
Cs,Na,R,F
Cs,Na,R,F
Cs,Na,R,F
F
101
182
259
459
81
181
186
401
Cs,Na,R,F
Cs,Na,R,F
Cs,Na,R,F
F
TABLE 6 Silent modes, cm-1
Irrep
PBE0
F1g
F2u
77
132
F1g
F2u
77
134
B3LYP
Cs2NaYbF6
69
131
Cs2NaYF6
73
137
030004-3
Ions are involved in the
mode
F
F
F
F
17 June 2026 16:13:54
F1u
F1u
F1u
F1u
Cs2NaYbF6
TABLE 7. The effect of pressure on the crystal structure (PBE0 method)
Pressure, GPa
x, frac.
0.240
0.246
0.249
0.251
0
5
10
15
Cs2NaYF6
Lattice Constant, Ǻ
9.090
8.782
8.585
8.437
x, frac.
0.238
0.244
0.247
0.249
Cs2NaYbF6
Lattice Constant, Ǻ
9.109
8.785
8.584
8.435
TABLE 8. The effect of pressure on frequencies (cm-1) of phonon modes (LO / TO), PBE0 method
Yb
Y
Ions are
involved
in the
mode
Pressure
0
5
0
5
F2g
69
86
70
86
F2g
205
216
211
218
Eg
363
412
376
429
Ag
463
505
465
481
F1u
94/80
105/101
107/88
121/112
F1u
173/169
272/173
191/184
243/179
F1u
258/182
226/239
265/198
282/262
F1u
423/373
471/423
470/410
518/461
F1g
77
94
77
89
F2u
132
148
134
145
Cs, F
Cs,
Na, F
F
F
Cs, Na,
R, F
Cs, Na,
R, F
Cs, Na,
R, F
F
F
F
CONCLUSION
ACKNOWLEDGMENTS
This work was supported by the Ministry of Education of the Russian Federation within the framework of the
project of the state task to perform scientific research № 3.57/.2014/K.
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Within MO–LCAO approach, using hybrid functionals DFT B3LYP and DFT PBE0 were calculated structure
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experimental data. The difference between calculated and experimentally measured bandgap is 5-8%. The effect of
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