A Riefer

A Widhalm

And A Zrenner

G Berth

M Rüsing

S Neufeld

S Sanna

W G Schmidt

CiteSeerX

Ferroelectrics, 447:63–68, 2013
Copyright © Taylor & Francis Group, LLC
ISSN: 0015-0193 print / 1563-5112 online
DOI: 10.1080/00150193.2013.821893
Vibrational Fingerprints of LiNbO3-LiTaO3
Mixed Crystals
S. SANNA,1 A. RIEFER,1 S. NEUFELD,1 W. G. SCHMIDT,1
G. BERTH,2 M. RÜSING,2 A. WIDHALM,2 AND A. ZRENNER1
1Lehrstuhl für Theoretische Physik, Universität Paderborn, Warburgestraße 100,
33098 Paderborn, Germany
2Center for Optoelectronics and Photonics (CeOPP) and Department Physik,
Universität Paderborn, Warburgestraße 100, 33098 Paderborn, Germany
Atomistic simulations in the framework of the density functional theory have been used
to model morphologic and vibrational properties of lithium niobate–lithium tantalate
mixed crystals as a function of the [Nb]/[Ta] ratio. Structural parameters such as the
crystal volume and the lattice parameters a and c vary roughly linearly from LiTaO3 to
LiNbO3, showing only minor deviations from the Vegard behavior. Our ab initio calcu-
lations demonstrate that the TO1, TO2 and TO4 vibrational modes become harder with
increasing Nb concentration. TO3 becomes softer with increasing Nb content, instead.
Furthermore, the investigated zone center A1-TO phonon modes are characterized by
a pronounced stoichiometry dependence. Frequency shifts as large as 30 cm−1 are ex-
pected as the [Nb]/[Ta] ratio grows from 0 to 1. Therefore, spectroscopic techniques
sensitive to the A1 modes (such as Raman spectroscopy), can be employed for a direct
and non-destructive determination of the crystal composition.
Keywords Ferroelectrics; vibrational properties; LiNbO3; LiTaO3; mixed crystals
I. Introduction
Both lithium niobate (LiNbO3, LN) and lithium tantalate (LiTaO3, LT) are optical ma-
terials widely used for a variety of applications ranging from optical modulators over
photo-refractive and acoustic devices to frequency doubling. Thereby mainly the piezo-
and ferroelectric properties of the materials are exploited. In particular, LN is probably the
most important electro-optic material, while LT is mainly employed as a LN replacement
for shorter wavelength applications [1]. Both materials crystallize within the R3c space
group and share several common physical and chemical properties. Commercially available
crystals are usually Czochralsky grown and lithium deficient ([Li] /[Nb], [Ta] < 1), which
results in a highly defective structure of congruent composition. Above the Curie tempera-
ture (607◦C for LT and 1142◦C for LN) a phase transition to a high-symmetry paraelectric
phase (space group R3̄c) occurs.
Mixed crystals have recently attracted the attention of the scientific community, as they
offer the possibility to tune the physical properties by varying the composition. Lithium
niobate-tantalate (LNT, LiNb1-xTaxO3) is one of the simplest ferroelectric mixed crystals,
Received September 19, 2012; in final form March 13, 2013.
∗Corresponding author. E-mail: simone.sanna@uni-paderborn.de
[191]/63
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64/[192] S. Sanna et al.
which shows quite unusual physical properties. In particular, the existence of a composition
with zero birefringence at room temperature is unique in ferroelectric nonlinear-optical
materials. Indeed, within this composition the crystal is optical isotropic and yet electrically
polar [2, 3].
Despite the huge potential in electro-optic and acousto-optic devices and the extensive
use of the end-compounds LN and LT, relatively little is known about the mixed crystals
[4]. This is mainly due to the difficulty to grow compositionally homogeneous crystals with
traditional methods such as the Czochralski growth from a lithium rich melt. In fact, despite
the isomorphism of the end compounds and the similar radii and valence of Ta and Nb,
the large separation of the solid-liquid lines in the LN-LT phase diagram makes the crystal
growth across the composition range a technically demanding task. However, the growth
of homogeneous crystals by several techniques has been demonstrated recently [2].
In this contribution, we investigate the structural and vibrational properties of ferro-
electric LiNb1-xTaxO3 over the whole composition range by first-principles simulations.
The relevance of the paraelectric phase in technological applications is extremely limited
by the high Curie temperature. Therefore it will not be investigated in this work. To our
knowledge, our work represents the first theoretical modeling of LNT mixed crystals.
II. Methodology
Total energy density functional calculations have been performed within the PW91 formu-
lation of the generalized gradient approximation (GGA) [5] as implemented in the VASP
simulation package [6]. PAW potentials [7] with projectors up to l = 3 for Nb, Ta and
l = 2 for Li, O have been used for the calculations. The electronic wave functions are
expanded into plane waves up to a kinetic energy of 400 eV. Our work is therefore on
the same footing of previous calculations on LN bulk crystals [8]. This approach yields
lattice parameters a and c as well as internal parameter z, u, and w for the end compounds
LiNbO3 and LiTaO3 within 1–2% of the experimental values. Rhombohedral supercells
containing 20 atoms (i.e. a 2 × 1 × 1 repetition of the LN primitive cell) were used in
order to model Ta concentrations of 0%, 25%, 50%, 75% and 100%. The influence of the
cation distribution in the mixed crystals on energetics, geometries and phonon modes is
accounted for by averaging over the different configurations realizable with our supercells.
Thus, our calculations refer to stoichiometric, compositionally homogeneous crystals: the
investigation of the commonly used congruent materials is beyond the goals of this work.
Also, the influence of local stoichiometry fluctuations or intrinsic defects is not investigated
here. A -centered 8 × 8 × 8 k-point mesh was used to carry out the integration in the
Brillouin zone. The atomic positions were allowed to relax until the Hellman-Feynman
forces acting on each atom were lower than 10 meV/Å. The phonon modes and frequencies
are calculated using the frozen-phonon approach [9]. This approach does not include the
long-range electric fields that accompany longitudinal phonons. For this reason, we limit
ourselves to the investigation of transverse modes.
III. Results
In the first step the equilibrium lattice parameters are calculated for all the investigated
concentrations. Thereby, atomic positions and primitive vectors are optimized at fixed
volume for a set of 15 different volumes in the range of ±5% of the measured LN volume.
The total energy as a function of the cell volume is then fitted to the Murnaghan state
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LiNbO3-LiTaO3 Mixed Crystals [193]/65
190 200 210 220 230 240 250 260
Volume (Å
3
)
-158.5
-158
-157.5
-157
-156.5
E
ne
rg
y 
(e
V
)
x=1.00
x=0.75
x=0.50
x=0.25
x=0.00
0 20 40 60 80 100
Niobate in %
217
218
219
220
221
222
223
C
el
l v
ol
um
e 
(Å
3 )
LiTaO
3
LiNbO
3
Figure 1. Lattice parameters of the LiNbxTa1-xO3 mixed crystals: Murnaghan fit of the calculated
data (left hand side) and calcuated unit cell volume as a function of the Nb concentration (right hand
side). The volume grows roughly linearly from LiTaO3 to LiNbO3.
equation [10]
E (V ) = V0 B
B
′
[
1
B
′ − 1
(
V0
V
)B ′ −1
+ V
V0
]
+ const (1)
where B is the bulk modulus, B′ its first derivative and V0 the equilibrium volume. The
calculated point are perfectly fitted by the state equation as shown in Fig. 1 (left hand side).
A further calculation is then performed at the Murnaghan minimum in order to find the
equilibrium total energy and structural parameters for each composition. The Murnaghan
state equation also yields information about the crystal response to external pressure (the
bulk moduli B and B′), which however, is not discussed in this work. As shown in Fig. 1
(right hand side), the supercell volume grows almost linearly from LT to LN (Vegard
behavior), while minor deviations from the linearity of the lattice parameters a and c are
observed. This is in agreement with recent X-ray diffraction measurements [2] and older
experimental data [11]. The volume difference of about 2% between LiTaO3 and LiNbO3
reflects the differences in atomic size between Ta and Nb [12].
In the second step the phonon modes are modeled within the frozen-phonon approach
at the calculated equilibrium geometries. The -TO modes of crystals belonging to the R3c
space group (such as the end compounds LN and LT) can be classified on the basis of their
symmetry into A (four A1, five A2) and E (nine) modes. The A2 modes are not Raman active
and will not be discussed in this work. An analysis of the phonon eigenvectors allows to
classify the calculated modes as A1 (if the mode preserves the full crystal symmetry), as
A2 (symmetry preserved, the ions of the same type vibrate in antiphase) and E modes (the
crystal symmetry is not preserved, the mode is doubly degenerate). The eigenvectors of
the four A1 modes investigated in this work are represented in Fig. 2 (labeled by TO1 to
TO4). The plotted displacement patterns lead to a change of the crystal polarization, which
explains why the A1 modes are both Raman and Infrared visible.
Within the DFT calculations, the LN A1 modes are found at 235, 254, 323, and
609 cm−1, and the corresponding LN modes at 200, 242, 348, and 577 cm−1. Within
deviations of at most 30, but typically about 10 cm−1 (which is mainly due to anharmonicity
effects), the calculated frequencies match the experimental findings, both for LN and LT
[14–16]. The accuracy of our calculations is thus comparable to earlier frozen-phonon
calculations [9, 13].
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66/[194] S. Sanna et al.
Figure 2. Eingenvectors of the four vibrational transversal branches (TO1 to TO4) of LiNbO3 and
LiTaO3. Arrows represent schematically the displacement patterns (see text for further details).
As shown in Fig. 2, TO1 is essentially a z-vibration, with the Nb,Ta ions vibrating in
antiphase with the oxygen octahedra. TO2 is a z-vibration as well, in which only the Li ions
are displaced from the equilibrium positions. TO3 and TO4 essentially involve the oxygen
octahedra and the ionic displacements take place in the xy-plane. While TO3 consists of
an almost rigid rotation of the whole octahedra, in TO4 the displacement pattern is more
complex. The ions in one oxygen plane rotate about the trigonal axis as in TO3, while
the ions of the other plane show a typical breathing movement. The oxygen octahedra
are thus distorted and the mode is occupied at considerably higher energies than TO3. A
more detailed description of the TO-mode eigenvectors can be found, among others in [13].
The description of the displacement patterns of the non symmetry-conserving E modes is
beyond the goals of this study.
The frequencies of the A1 modes for the mixed crystals are compiled in Table 1 and
plotted as a function of the Ta concentration in Fig. 3. As the Ta ions (atomic mass 180.95
amu) are much more massive than the Nb ions (atomic mass 92.906 amu), one would expect
much harder phonon modes for LN than for LT. Furthermore, depending on the participation
of Nb,Ta to the different modes (represented in Fig. 2), the frequency dependence of the four
phonons is expected to be different. Indeed, while TO1 (displacement of the Nb,Ta ions with
respect to the oxygen octahedra) shows a strong composition dependence, TO2 (involving
solely Li ions) is only slightly blue-shifted from LT to LN. While TO1, TO2 and TO4
become harder with increasing Nb concentration, TO3 softens continuously from LiTaO3
Table 1
Zone center phonon frequencies (in cm−1) calculated for several LiNb1-xTaxO3
stoichiometries. The TO3 mode becomes blue-shifts with increasing Ta concentration, while
the other become softer
Composition
Mode LN LN.75T.25 LN.50T.50 LN.25T.75 LT
TO1 235 229 214 208 200
TO2 254 244 241 242 242
TO3 323 327 335 342 348
TO4 609 598 588 582 577
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LiNbO3-LiTaO3 Mixed Crystals [195]/67
Figure 3. Composition dependence of the four A1 TO-modes in LiNb1-xTaxO3 mixed crystals. The
dashed line is the linear fit of the calculated points. (Color figure available online).
to LiNbO3. This behavior cannot be simply explained by the different atomic mass, but is
related to the different binding of the Ti and Nb ions with the oxygen sublattice. Indeed, it has
been previously attributed by Caciuc and Postnikov [15] to a comparatively harder oxygen
rotation in LiTaO3. The TO3 mode shows, however, a less pronounced dependence on the
composition with respect to other TO phonons. Because of their pronounced composition
dependency, the TO modes are true fingerprints of the crystal stoichiometry. In particular
TO1 and TO4 can be used to identify the crystal composition by direct and non-destructive
Raman measurements.
IV. Conclusions
The morphologic and vibrational properties of LiNb1-xTaxO3 mixed crystals have been
modeled within the density functional theory. The crystal volume grows roughly linearly
from LiTaO3 to LiNbO3. The lattice parameters a and c of the rhombohedral structure
exhibit only small deviations from a linear dependence on the composition. The zone center
phonon modes (TO -modes) have been calculated with the frozen phonon approach. Our
models predict a pronounced stoichiometry dependence of several phonons, in particular
the TO1 and TO4 transversal optic modes show a frequency shift as large as 30 cm−1 as the
Nb concentration grows from 0 to 1. The stoichiometry dependence has been explained,
depending on the involved atomic species either by the Nb-Ta atomic mass difference or by
the different Nb-O and Ta-O atomic bond. According to our calculation, these phonons are
true fingerprints of the crystal stoichiometry. Therefore Raman spectroscopy measurements
can be used to identify the crystal composition in a direct and non-destructive manner.
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Acknowledgments
The Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged for financial
support. Calculations are performed within supercomputer time grants provided by the
HLRS Stuttgart and the Paderborn PC2.
References
1. R. S. Weis and T. K. Gaylord, Lithium-niobate - summary of physical-properties and crystal-
structure. Appl. Phys. A, vol. 37, pp. 191–203 (March 1985).
2. A. Bartasyte, A. M. Glazer, F. Wondre, D. Prabhakaran, P. A. Thomas, S. Huband, D. S. Keebl,
and S. Margueron, Growth of LiNb1-xTaxO3 solid solution crystals. Mat. Chem. and Phys., vol.
134, pp. 728–735 (June 2012).
3. I. G. Wood, P. Daniels, R. H. Brown, and A. M, Glaze, Optical bire-fringence study of the
ferroelectric phase transition in lithium niobate tantalate mixed crystals: LiNb1−xTaxO3. J. Phys.:
Condens. Matter, vol. 20, pp. 235237–235242 (May 2008).
4. D. Xue, K. Betzler, and H. Hesse, Dielectric properties of lithium niobate–tantalate crystals, Sol.
Stat. Comm., vol. 115, pp. 581–585 (Aug. 2000).
5. J. P. Perdew and Y. Wang, Accurate and simple density functional for the electronic exchange
energy: Generalized gradient approximation, Phys. Rev. B, vol. 33, pp. 8800–8802 (June 1986).
6. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations
using a plane-wave basis set. Phys. Rev. B, vol. 54, pp. 11169–11186 (Oct. 1996).
7. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B, vol. 50, pp. 17953–17979 (Dec.
1994).
8. W.G. Schmidt, M. Albrecht, S. Wippermann, S. Blankenburg, E. Rauls, F. Fuchs, C. Rödl, J.
Furthmüller, and A. Hermann, LiNbO3 ground- and excited-state properties from first-principles
calculations. Phys. Rev. B, vol. 77, pp. 035106–035112 (Jan. 2008).
9. W. G. Schmidt, F. Bechstedt, and G. P. Srivastava, III-V(110) surface dynamics from an ab initio
frozen-phonon approach, Phys. Rev. B, vol. 52, pp. 2001–2007 (July 1995).
10. F. D. Murnaghan, The compressibility of media under extreme pressures, Proc. Nat. Acad. Sci.
USA vol. 30, pp. 244–247 (Sept. 1944).
11. F. Shimura, Y. Fujino, Crystal growth and fundamental properties of LiNb1−yTayO3, J. Cryst.
Growth, vol. 38, pp. 293–301 (June 1977), and references therein.
12. E. Clementi, D. L. Raimondi, and W. P. Reinhardt, Atomic Screening Constants from SCF
Functions, J. Chem. Phys., vol. 38, pp. 2686–2689 (June 1963).
13. S. Sanna, G. Berth, W. Hahn, A. Widhalm, A. Zrenner and W. G. Schmidt, Vibrational properties
of the LiNbO3 z-surfaces, IEEE Transactions on ultrasonics, ferroelectrics and frequency control,
vol. 58, pp. 1751–1756 (September 2011).
14. C. Rapitis, Assigment and temperature dependence of the Raman modes of LiTaO3 studied over
the ferroelectric and paraelectric phases, Phys. Rev. B, vol. 38, pp. 10007–10019 (Nov. 1988).
15. V. Caciuc and A.V. Postnikov, Ab initio zone center phonons in LiTaO3: Comparison to LiNbO3,
Phys. Rev. B, vol. 64, pp. 224403–224409 (Nov. 2001).
16. A. Ridah, M. D. Fontana, and P. Bourson, Temperature dependence of the Raman modes in
LiNbO3 and mechanism of the phase transition, Phys. Rev. B, vol. 56, pp. 5967–5973 (Sep.
1997).
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Vibrational Fingerprints of LiNbO 3 -LiTaO 3 Mixed Crystals

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Vibrational Fingerprints of LiNbO 3 -LiTaO 3 Mixed Crystals

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