Computer modelling of
structural and defect properties
of stoichiometric lithium niobate
Robert A Jackson
School of Physical & Geographical Sciences
Keele University
Keele, Staffordshire ST5 5BG, UK
r.a.jackson@keele.ac.uk
http://www.robajackson.com
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Acknowledgements
Mário Valerio, Romel Araujo (Aracaju, Brazil)
László Kovács, Krisztián Lengyel (Budapest, Hungary)
Günter Borchardt, Peter Fielitz (Clausthal, Germany)
Bud Bridges (Santa Cruz, USA)
… and the workshop organisers for the invitation!
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Relevant publications
(some hard copies available)
• [1] R A Jackson, M E G Valerio
‘A new interatomic potential for the ferroelectric and paraelectric
phases of LiNbO3’
Journal of Physics: Condensed Matter, 17, 837-843 (2005)
• [2] R M Araujo, K Lengyel, R A Jackson, L Kovács, M E G Valerio
‘A computational study of intrinsic and extrinsic defects in LiNbO3’
Journal of Physics: Condensed Matter, 19, 046211 (2007)
• [3] R M Araujo, M E G Valerio, R A Jackson
‘Computer modelling of trivalent metal dopants in lithium niobate’
Journal of Physics: Condensed Matter, 20, 035201 (2008)
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Plan of talk
•
•
•
•
•
Motivation & background
Brief introduction to methodology
Potential derivation & structural properties
Defect properties
Ongoing & future work
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Motivation & background
• The interatomic potential published by Donnerberg and coworkers in 1989-90 was widely used. However:
(i) advances in computational software
and
(ii) the continued interest in the material and the availability of new
experimental data
prompted us to revisit and re-derive the potential
(published in 2005).
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Potential derivation
• The potential was fitted to simultaneously
reproduce the structures of LiNbO3a, Li2O and Nb2O5
to allow consistency in later defect calculations.
• The GULP codeb was used, employing the free
energy option (allowing temperature dependence
of the structure to be treated).
a
S C Abrahams, P Marsh, Acta Cryst., B 42, 61 (1986)
b J Gale, see: http://projects.ivec.org/gulp/
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Brief details of the potential*
• Full ionic charges on Li, Nb and O.
• Buckingham potentials describe the interactions
between Li-O, Nb-O & O-O.
• A shell model is employed for O.
• A 3-body bond bending potential describes the ONb-O interactions.
*R A Jackson, M E G Valerio, J Phys.: Condensed Matter, 17, 837 (2005)
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Structural agreement
Ferroelectric phase
Exp. [1]
This work
Donnerberg potential
0K
295 K
0K
295 K
a=b
5.1474
5.1559
5.1868
5.2271
5.2631
c
13.8561
13.6834
13.7103
14.2730
14.2167
Paraelectric phase
Exp. [2]
This work
Donnerberg potential
0K
293 K
0K
293 K
a=b
5.2924
5.1530
5.0919
2.3030
2.3042
c
13.8462
13.8418
13.2111
5.6412
5.6402
[1] S C Abrahams, P Marsh, Acta Cryst. B, 42, 61 (1986)
[2] H Boysen, F Altorfer, Acta Cryst. B, 50, 405 (1994)
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Lattice parameter as a function of temperature
T/K
aexp (Å)
acalc (Å)
a ()
cexp (Å)
ccalc (Å)
c ()
0
-
5.1559
-
-
13.6834
-
10
-
5.1745
-
-
13.7035
-
295
5.1474
5.1868
0.77
13.8561
13.7103
-1.06
297
5.1483
5.1864
0.74
13.8631
13.7101
-1.10
523
5.1700
5.2133
0.84
13.8700
13.7200
-1.08
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Modelling defect properties
• Using the Mott-Littleton method, energies of
formation of the intrinsic defects in LiNbO3 were
calculated.
• These allow predictions to be made about the
defect chemistry of the material.
(See Araujo et al: Journal of Physics: Condensed Matter, 19, 046211 (2007))
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Mott-Littleton approximation
© Mark Read
Region I
Ions are strongly perturbed by the
defect and are relaxed explicitly with
respect to their Cartesian coordinates.
Region II
Ions are weakly perturbed and
therefore their displacements, with the
associated energy of relaxation, can be
approximated.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Formation energies for basic defects
(in stoichiometric LiNbO3)
Defect
0K
293 K *
[1] model II
VLi’
9.81
9.71
9.8
VNb’’’’’
127.56
127.45
117.3
VO
18.98
18.91
19.5
Lii
-7.08
-7.12
-8.87**
Nbi
-104.12
-104.25
-110.68**
Oi’’
-9.47
-9.64
-16.08**
NbLi
-98.37
-98.49
-99.5
LiNb’’’’
-113.99
[1] Donnerberg et al, Phys. Rev. B.,
40, 11909 (1989)
* Temperature taken into account
via lattice expansion.
** Deduced values since paper
does not report these values.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Frenkel, Schottky and pseudo-Schottky energies*
(per defect)
Defect
0K
293 K *
[1]
Li Frenkel
1.37
1.30
0.93
Nb Frenkel
11.72
11.60
6.26
O Frenkel
4.76
4.64
3.42
Schottky
LiNbO3
3.95
3.85
3.91
PseudoSchottky Li2O
1.81
1.80
1.94
PseudoSchottky Nb2O5
5.09
5.07
2.85
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
*Calculated for
information only
since defects are
more complex.
Expected trends in
values are
observed.
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Models to explain the observed
experimental data
• The simple Frenkel and Schottky models do not
explain the observed behaviour in LiNbO3.
• For example, the NbLi + 4VLi’ defect cluster
has a formation energy of –63.61 eV.
• We needed to consider possible reactions that
give rise to such defects.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Explaining the observed nonstoichiometry
• Following the work of Kovács and Polgár*, we
considered models based on antisite or interstitial
Nb compensated by Li or Nb vacancies.
• 3 possible reactions were considered (see next
slide):
* L Kovács and K Polgár, Crystal Research and Technology, 21, K101 (1986)
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Possible defect reactions that give
rise to Li deficiency
Antisite Nb compensated by Li vacancies
5LiLi + ½Nb2O5  4V’Li + NbLi + 5/2Li2O
 E(reaction) = -0.98 (-2.52*) eV per Li2O formula unit
Antisite Nb compensated by Nb vacancies
5LiLi + 4NbNb + ½Nb2O5  5NbLi + 4VNb’’’’’ + 5/2Li2O
 E(reaction) = 29.8 eV per Li2O formula unit
Interstitial Nb compensated by Li vacancies
5LiLi + ½Nb2O5  5VLi’ + Nbi + 5/2Li2O
 E(reaction) = 0.49 eV per Li2O formula unit
* ‘Bound’ defect configuration
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Conclusions from the reactions
• If the reaction energies are calculated, using the
basic defect energies already obtained, we
concluded that:
– only the antisite Nb/Li vacancy model is
energetically favourable.
– of the other two mechanisms, the interstitial
Nb/Li vacancy model is more favourable than the
antisite Nb/Nb vacancy model.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Divalent and trivalent dopants
• The incorporation of a range of dopant ions in
LiNbO3 was modelled.
• Divalent and trivalent ion substitution was
considered.
• Charge compensation is needed for substitution
at either the Li+ or Nb5+ site.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Dopant ions considered
• Reference [2]: M2+ dopants Mg, Mn, Fe, Co, Ni, Zn, Sr,
Cd, Ba & Pb, and M3+ lanthanide dopants Ce-Lu.
• Reference [3] focused on M3+ dopants: Sc, Cr, Fe and In.
[2] Journal of Physics: Condensed Matter, 19, 046211 (2007)
[3] Journal of Physics: Condensed Matter, 20, 035201 (2008)
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Summary of modelling procedure
• The GULP code is used to calculate the
substitution energies, e.g. M2+ at the Li+ site,
denoted by MLi in Kroger-Vink notation.
• The substitution energies are then converted
into solution energies, which give the total
energy involved in the process:
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Solution energies
• Assuming M2+ substitution at the Li+ site, a
possible scheme could be:
MO + 2 LiLi → MLi + VLi’ + Li2O
• This assumes charge compensation by Li
vacancies, but other possibilities are considered.
• The same idea is applied to M3+ dopants.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Predicted doping schemes: M2+ ions
• From the calculations, the following predictions
are made based on lowest energies:
• Co-doping at both Li+ and Nb5+ sites, except for
Fe2+ and Cd2+ for which substitution at the Nb5+
site with charge compensation by Nb - Li antisite substitution is preferred.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Predicted doping schemes: M3+ ions
• The predicted scheme for all the lanthanide ions
and Sc, Cr and Fe is self-compensation:
M2O3 + LiLi + NbNb → MLi + MNb’’ + LiNbO3
• For In, the preferred scheme involves doping at
the Nb5+ site with charge compensation by Nb-Li
anti-sites.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Further calculations – M4+ & co-doping
• Calculations have also been performed on Hf4+
doping, and a range of pairs of co-doped ions.
• These results will be submitted for publication,
possibly in the ‘Lithium Niobate: Properties and
Applications’ special journal issue being
planned.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Some relevant experimental data
• Studies of M2+ & M3+ dopants in LiNbO3 have included:
Mn2+ - LiNbO3: Darwish et al, NIMB, 141, 679-683 (1998)
 Supports the idea of Mn2+ self compensation; does not give dopant
concentration.
Mg2+ - LiNbO3: González-Martínez et al, Opt. Comm., 282, 1212-1219 (2009)
 Dopant concentration 0.0714-0.2422 mol%; suggests that self
compensation occurs ‘after a certain dopant concentration level’.
Er3+, Cr3+ - LiNbO3: Dierolf & Sandmann, J. Lum., 125, 67-79 (2007)
 Mainly assumes Li site occupancy, but dopant concentration is unclear as
several samples have been used.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Comparison with recent experimental data
• Bud Bridges recently published a paper:
‘EXAFS evidence for a primary ZnLi dopant in LiNbO3’
(F Bridges et al, Phys. Rev. B 85 064107 (2012))
• This doesn’t find any Zn at the Nb site, but may not be
directly
comparable
with
the
calculations
(concentration effects, stoichiometry of sample?)
• EXAFS measurements on In have also been performed.
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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General comments on comparison
with experimental data
• The calculation results reported are at infinite dilution,
so no concentration effects are considered.
• In recent work we are looking at finite dopant
concentrations in other materials, and this could be
done for dopants in LiNbO3 (needs persons and €€€).
• There may be issues with the stoichiometry of the older
crystal samples (i.e. are we comparing ‘like with like’?)
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Ongoing and future work
• Results on tetravalent dopants and co-doping is
still to be published.
• Bud Bridges has detailed EXAFS data on Zn & In
doped LiNbO3, which we are hoping to reproduce.
• We are in discussions with Peter Fielitz and Günter
Borchardt about modelling defects using some
different reaction schemes (talk at 12:00
tomorrow).
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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Thank you!
International Workshop on Stoichiometric Lithium Niobate, Goslar, Germany, September 2013
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International Workshop on Stoichiometric
Lithium Niobate, Goslar, Germany,
September 2013
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