Local structure and symmetry of paramagnetic ions in ferroelectric ceramics [Elektronische Ressource] / vorgelegt von Hrvoje Meštrić

Sujets

• Physik

Informations

• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2006
• Nombre de lectures: 25
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Local structure and symmetry of
paramagnetic ions in ferroelectric ceramics
Vom Fachbereich Chemie
der Technischen Universit¨at Darmstadt
zur Erlangung des akademischen Grades eines
Doctor rerum naturalium (Dr. rer. nat.)
genehmigte
Dissertation
vorgelegt von
Dipl.-Phys. Hrvoje Meˇstri´c
aus Varaˇzdin in Kroatien
Berichterstatter: Prof. Dr. Klaus-Peter Dinse
Mitberichterstatter: Prof. Dr. Rolf Sch¨afer
Tag der Einreichung: 24.01.2006
Tag der mu¨ndlichen Pru¨fung: 22.05.2006
Darmstadt 2006
D 17This study is a result of the work carried out from October 2002 to January
2006 at the Eduard-Zintl-Institute for Inorganic and Physical Chemistry, Darmstadt
University of Technology, under the supervision of Prof. Dr. Klaus-Peter Dinse.
It was conducted and financed as a part of the Joint Research Project 595 Electric
Fatigue in Functional Materials of the German Science Foundation.Acknowledgements
I wish to thank to all the people who supported me throughout this work and
contributed to this study. Especially I would like to thank to ...
... my supervisor Prof. Dr. Klaus-Peter Dinse;
... my project leader Dr. Ru¨diger-Albert Eichel;
... Prof. Dr. Michael B¨ohm for proofreading;
... Prof. Dr. Rolf Sch¨afer for agreeing to be coreferent of the thesis;
... and the other members of our research group: Dipl. Ing. Bj¨orn Corzilius, Dr.
Ing. Armin Gembus, Dipl. Geol. Ulla Henkes, Dr. Ing. Peter Jakes, Dr. Ing. Elvir
Rami´c,Dr. NorbertWeidenundViktorTissenfortheirgeneroushelpandpermanent
support;
... Dipl. Ing. Thomas Kloss, Dipl. Ing. Christopher Neumann and Dipl. Ing.
Christian Quick for their contributions as undergraduate students.
The present study would not be possible without help and interdisciplinary co-
operation with many research groups. I would like to express my acknowledgements
to...
...Dr. Hans Kungl and Prof. Dr. Michael J. Hoffman at the Institute of Ceramics
in Mechanical Engineering, University of Karlsruhe for providing the samples;
...Dipl. Ing. Kristin Sch¨onau, Dr. Martin Knapp, Dr. Helmut Ehrenberg and
Prof. Dr. HartmutFuessattheMaterialsScienceDepartment,DarmstadtUniversity
of Technology for high resolution diffraction measurements;
...Dipl. Ing. Sonja Laubach, Dipl. Ing. Stefan Laubach and Prof. Dr. Peter C.
Schmidt at the Eduard-Zintl-Institute on the Darmstadt University of Technology
for performing ab initio calculations;
...Dr. Andrew Ozarowski, Dr. Johan van Tol and Dr. Louis Claude Brunel at
the Center for Interdisciplinary Magnetic Resonance, National High Magnetic Field
Laboratory on the Florida State University for high-field EPR measurements;
...Dipl. Phys. Emre Erdem, Dipl. Phys. Joachim Hoentsch and Prof. Dr. Rolf
B¨ottcher from the Institute of Experimental Physics, University of Leipzig for high-
temperature and Q-band EPR measurements;
...Dipl. Ing. Nina Balke, Dr. Doru Lupascu, Dr. Rhuzong Zuo and all other
members of SFB 595 Joint Research Project.
I would particularly like to thank to my wife Klara and to my whole family.CONTENTS
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Part I Theory 15
2. Ferroelectric materials . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Electric properties of crystals . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Ferroelectric behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Ferroelectric crystals . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Microscopic description of ferroelectrics . . . . . . . . . . . . . 19
2.2.3 Ferroelectric domains and poling . . . . . . . . . . . . . . . . 20
2.2.4 Polarisation hysteresis loop . . . . . . . . . . . . . . . . . . . 22
2.2.5 Antiferroelectricity . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.6 Fatigue and ageing . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Role of defects in ferroelectrics . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Point defects . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Defect chemistry in perovskite compositions . . . . . . . . . . 25
2.3.3 Impact of defects on ferroelectric properties . . . . . . . . . . 27
3. Paramagnetic ions in crystal field . . . . . . . . . . . . . . . . . . 29
3.1 Free ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 One-electron atom . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2 Many-electron atoms . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.3 Paramagnetic ions . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.4 Effective spin Hamiltonian . . . . . . . . . . . . . . . . . . . . 33
3.2 Ions in a crystal field . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Crystal field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Crystal field potential . . . . . . . . . . . . . . . . . . . . . . 38
3.3 S-state ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Energy levels for S-state ions. . . . . . . . . . . . . . . . . . . 39
3.3.2 Spin Hamiltonian for S-state ions in a crystal field . . . . . . . 40
3.4 Overview of the Newman superposition model . . . . . . . . . . . . . 43
3.4.1 Role of the Newman superposition model . . . . . . . . . . . . 43
3.4.2 Assumptions of the Newman superposition model . . . . . . . 44
3.4.3 The Newman superposition model for the spin Hamiltonian . 458 Contents
4. Electron paramagnetic resonance. . . . . . . . . . . . . . . . . . . 49
4.1 Physical backgrounds of electron paramagnetic resonance . . . . . . . 49
4.1.1 The resonance phenomenon . . . . . . . . . . . . . . . . . . . 49
4.1.2 Thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.3 Transition probabilities . . . . . . . . . . . . . . . . . . . . . . 51
4.1.4 Line widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Perturbative solutions for the spin Hamiltonian . . . . . . . . . . . . 53
4.2.1 High-field approximation . . . . . . . . . . . . . . . . . . . . . 53
4.2.2 Low-field approximation . . . . . . . . . . . . . . . . . . . . . 56
4.3 EPR spectra of polycrystalline samples . . . . . . . . . . . . . . . . . 60
4.4 Numerical simulations of EPR spectra . . . . . . . . . . . . . . . . . 62
Part II Experiments and results 65
5. Overview of experiments . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1 X-band EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1.1 Microwave source . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1.2 Resonant cavities . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.3 Signal detection . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1.4 Magnet unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 W-band EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.1 Microwave source . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.2 Resonant cavities . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.3 Magnet unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 High-frequency EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3.1 Microwave sources . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3.2 Sample holder . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3.3 Signal detection . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3.4 Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6. Structural calculations . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 Newman superposition model – previous studies . . . . . . . . . . . . 75
56.1.1 NSM parameters for 3d ions . . . . . . . . . . . . . . . . . . 75
6.1.2 Application of the NSM for perovskite structures . . . . . . . 76
6.2 Newman superposition model – calculation procedure . . . . . . . . . 78
6.2.1 Computational algorithm. . . . . . . . . . . . . . . . . . . . . 78
6.2.2 Limitations of the NSM . . . . . . . . . . . . . . . . . . . . . 81
7. Lead titanate: experiments . . . . . . . . . . . . . . . . . . . . . . . 83
7.1 Introduction to PbTiO . . . . . . . . . . . . . . . . . . . . . . . . . 833
7.1.1 Preparation of PbTiO . . . . . . . . . . . . . . . . . . . . . . 843
7.1.2 Determination of the crystal structure of PbTiO . . . . . . . 843Contents 9
7.2 Previous EPR measurements . . . . . . . . . . . . . . . . . . . . . . . 87
3+7.3 EPR measurements of Fe centre in PbTiO . . . . . . . . . . . . . 883
3+7.3.1 Low frequency measurements of Fe :PbTiO . . . . . . . . . 883
3+7.3.2 W-band measurements of Fe :PbTiO . . . . . . . . . . . . . 903
3+7.3.3 High frequency measurements of Fe :PbTiO . . . . . . . . . 933
3+7.4 Determination of the spin Hamiltonian parameters of Fe :PbTiO . 953
3+7.4.1 Perturbational analysis of the Fe :PbTiO spectra . . . . . . 953
3+7.4.2 Numerical simulations of the Fe :PbTiO spectra . . . . . . . 973
8. Lead titanate: structural calculations . . . . . . . . . . . . . . . 99
3+8.1 The NSM analysis of Fe in PbTiO . . . . . . . . . . . . . . . . . . 993
3+8.2 DFT analysis of Fe :PbTiO . . . . . . . . . . . . . . . . . . . . . . 1033
8.2.1 DFT analysis of undoped PbTiO . . . . . . . . . . . . . . . . 1033
3+8.2.2 DFT analysis of Fe -doped PbTiO . . . . . . . . . . . . . . 1053
3+8.3 Discussion of the structure of Fe :PbTiO . . . . . . . .