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

INTRODUCTION

PZT is solid solution perovskite A(BB’)O3. The material demonstrates excellentpiezoelectric 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 correlationof local arrangement of B-cationswith macroscopic phase, piezoelectricand optical properties of PZT

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.

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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

FE

RR

OE

LEC

TR

IC

STA

TE

S

PA

RA

ELE

CT

RIC

STA

TE

S

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 (fromoptical spectra) does not showsignificant dependence on Zr/Tiarrangement, in agreement withexperimental 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)

1 2 3 4 5PIEZOELECTRIC 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 C\m2

Low temperature, pylycrystal Zr/Ti 50:50 *

Exp:

|P|=0.75 C\m2

single domain crystal **

* Z. Q. Zhuang, M. J. Haun, S. J. Jang, and L. E. Cross, 6th IEEE International Symposium onthe Applications of Ferroelectrics, 1986, p. 394.

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ORIGIN OF PIEZOELECTRIC RESPONSE e15

High polarization at xy plane occurs due to Ti plane is lessstressed 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 C\m2

Main factor – freedom to move Ti in xy plane

4

e15=7.46 C\m2

5/27/2014

ORIGIN OF PIEZOELECTRIC RESPONSE e33

B

O

d

Force

Force

OO

No. dZr-O, Å dTi-O, Å e33, C\m2

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 distancesbetween B-cation and overlying oxygen atom.

Under mechanical stress B-cation shifts from the centre ofoctahedra the more the less it was shifted initially.

Main factor – distance between B-cation and overlying oxygen atom (along z-axis)s

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

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.

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).