This study systematically analyzed the effect of local ordering of B-cations (Zr and Ti) on the electronic, optical, and piezoelectric properties of PbZrxTi1-xO3 (PZT) using density functional theory calculations. The most stable structure found was a tetragonal phase with P4mm symmetry. Other stable phases included a polar orthorhombic phase and a non-polar triclinic phase. Analysis showed that different arrangements of B-cations led to variations in the electronic structure, polarization, and piezoelectric response of the materials. In particular, large piezoelectric coefficients e15 and e33 were associated with specific planar and axial arrangements of

1. The effect of mutual arrangement of B-
cations on electronic, optical and
piezoelectric properties of strained
PbZrxTi1-xO3 (PZT)
Alexander Bogdanov1,2, Anna Kimmel3,4
1. A.P. Vinogradov Institute of Geochemistry SB RAS, Irkutsk, RUSSIA
2. Irkutsk State Technical University, Irkutsk, RUSSIA
3. National Physical Laboratory, Teddington, TW11 0LW, UK
4. University College London, Gower St., WC1E 6BT, UK

2. INTRODUCTION
PZT is solid solution perovskite A(BB’)O3. The material demonstrates excellent
piezoelectric properties and is widely used in ferro- and piezo- applications.
Macroscopic phase and macroscopic
properties of PZT depend on the ratio of B-
cations (i.e. x) and their mutual arrangement.
In this work we study the correlation
of local arrangement of B-cations
with macroscopic phase, piezoelectric
and optical properties of PZT

3. METHODS
We conduct calculations of non-defect PbZrxTi1-xO3 phases at x=0.5 with
different mutual arrangements of Zr and Ti cations.
B-cation disorder: specific placing of Zr and Ti in B-cation sites of 40-atoms PZT cell.
Methods: DFT, GGA with PBE and Wu-Cohen functionals.
Optical, Ferro- and Piezoelectric properties: Linear Response theory and Density
Functional Perturbation Theory.
Simulation of Strain: relaxation of c-axis with constrained a and b axes.
21 43 5

4. STRUCTURAL PARAMETERS
21 43 5
Lattice tetra tetra triclin tetra rhomb
Group P4mm P4mm Cm Cm P1
a, Å 3.99 3.98 4.10 3.99 4.04
c, Å 4.20 4.26 4.00 4.22 4.04
|P|, C/m2 0.60 0.82 0.70 0.70 0.55
Energy, eV +0.07 +0.00 +0.04 +0.05 +0.02
Lattice tetra tetra tetra cubic tricl
Group P4/mmm P4/mmm C2/m C2/m P-1
a, Å 4.05 4.01 4.04 4.03 4.03
c, Å 4.01 4.05 4.01 4.03 3.99
Energy, eV +0.23 +0.20 +0.19 +0.21 +0.05
FERROELECTRIC
STATES
PARAELECTRIC
STATES

5. OPTICAL AND ELECTRONIC STRUCTURE
PROPERTIES
We have found a strong intermixing of Zr
and Ti d-states in our structures which
can give optical applications while PZT is
doped by non-isovalent cations
Optical band gap Eg~3.5 eV (from
optical spectra) does not show
significant dependence on Zr/Ti
arrangement, in agreement with
experimental results for thin films[*]
* M.P. Moret, M.A.C. Devillers, K. Wörhoff, P.K. Larsen, Journal of Applied Physics 92, 468 (2002).
Top of VB: oxygen 2p-states
Bottom of CB: Ti, Zr d-states
HOMO, #5 (FE) LUMO, #5 (FE)

6. 1 2 3 4 5
PIEZOELECTRIC PROPERTIES
e15 10.65 3.66 0.37 7.46 0.49
e31 0.27 0.37 -2.00 0.37 -0.35
e33 4.11 3.94 7.07 4.17 8.45
ε11 488.23 126.56 56.87 375.40 79.59
ε33 13.77 13.94 136.53 14.47 79.93
|P| 0.60 0.82 0.70 0.70 0.55
Pdirection [001] [001] [552] [001] [111]
tetra tetra triclin tetra rhomb
Piezoelectric coefficients, C/m2
Static dielectric permittivity
Spontaneous polarization, C/m2
Exp:
e33=11.9 Cm2
Low temperature,
pylycrystal Zr/Ti
50:50 *
Exp:
|P|=0.75 Cm2
single domain
crystal **
* Z. Q. Zhuang, M. J. Haun, S. J. Jang, and L. E. Cross, 6th IEEE International Symposium on
the Applications of Ferroelectrics, 1986, p. 394.
21 43 5

7. ORIGIN OF PIEZOELECTRIC RESPONSE e15
High polarization at xy plane occurs due to Ti plane is less
stressed than Zr one. This is due to Zr/Ti size ratio and Ti
“free volume” at applied σ5 shear strain.
1
Shear
strain σ5
P
e15=10.65 Cm2
Main factor – freedom to move Ti in xy plane
4
e15=7.46 Cm2

8. 5/27/2014
ORIGIN OF PIEZOELECTRIC RESPONSE e33
B
O
d
Force
Force
OO
No. dZr-O, Å dTi-O, Å e33, Cm2
1 1.97 1.77 4.11
2 1.98 1.75 3.94
3 2.04 1.91 7.07
4 1.95 1.79 4.17
5 2.02 1.89 8.45
Highest responses correspond to shortest distances
between B-cation and overlying oxygen atom.
Under mechanical stress B-cation shifts from the centre of
octahedra the more the less it was shifted initially.
Main factor – distance between B-cation and
overlying oxygen atom (along z-axis)s

9. Response to strain of Ps and eij of tetragonal
structures #2 and #4

10. Summary
• We studied systematically electronic, optical, piezoelectric response of PZT to
local ordering of B-cations. Tetragonal structure #2 (P4mm) was found to be
most stable among found phases, characterized by highest polarization. We also
found isoenergetic polar #4 (Cm) and non-polar #5 (P-1) phases.
• Analysis of electronic properties demonstrate dependence of electronic
structure on B-cations mutual arrangement, we found strong intermixing of Ti
and Zr d-states for #5.
• We found that structure #1, #4 give large e15 coefficients, which is due to plane-
to-plane arrangement of B-cations.
• The large e33 piezo-coefficient in #3, #5 is due to the small shift of B-cations from
centre of oxygen octahedra along c-axis (low P along c).
• The analysis of polarization and piezo-coefficients with respect to strain showed
that the gradients of piezo-coefficients strong depend on the B-cations mutual
arrangement.

11. 5/27/2014
Acknowledgements
We are thankful to Markus Gain (National Physical
Laboratory) and Andrew Mysovsky (Irkutsk State
Technical University) for important advices and quite
useful discussions.
The calculations were performed by HPC facilities of
Legion (UK), Fock (Irkutsk, RUSSIA).