Macroscopic and microscopic deformation of the piezoelectric Li_1tn2SO_1tn4_1tn.H_1tn2O, Li_1tn2SeO_1tn4_1tn.H_1tn2O and BiB_1tn3O_1tn6 crystals under an external electric field [Elektronische Ressource] / vorgelegt von Oleg Schmidt

Oleg Schmidt

Sujets

• Physik

Informations

• Publié par: universitat_siegen
• Publié le: 01 janvier 2010
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 13 Mo

Extrait

Macroscopic and microscopic
deformation of the piezoelectric
Li SO H O, Li SeO H O and BiB O2 4 2 2 4 2 3 6
crystals under an external electric eld
DISSERTATION
zur Erlangung des Grades eines Doktors
der Naturwissenschaften
vorgelegt von
Dipl.-Phys. Oleg Schmidt
geb. am 12.07.1981 in Toparski/Karaganda (SU)
eingereicht beim Fachbereich Physik
der Universitat Siegen
Siegen 2010Gutachter: Prof. Dr. Ullrich Pietsch
Prof. Dr. Ladislav Bohaty
Tag der mundlic hen Prufung: 24.09.2010
iiContents
Introduction 1
1 Elastic, piezoelectric and dielectric properties of crystals 3
1.1 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Electric polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Pyroelectric and ferroelectric crystals . . . . . . . . . . . . . . . . . 6
1.3 Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 X-ray di raction by crystals under an static external electric eld 9
2.1 X-ray di raction by unperturbed crystals . . . . . . . . . . . . . . . . . . . 9
2.2 Electron density distribution in . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Multipole re nement of the electron density . . . . . . . . . . . . . 11
2.2.2 DFT calculations of the electron density . . . . . . . . . . . . . . . 12
2.2.3 Topological analysis of the electron density . . . . . . . . . . . . . . 13
2.3 External and internal strain of a crystal induced by an applied electric eld 14
2.3.1 Determination of the piezoelectric constants of a crystal by means
of X-ray di raction . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Re nement of the electric- eld-induced atomic displacements in a
crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Description of the eld-switching X-ray di raction experiments 25
3.1 Setup of the static eld-switching experiment . . . . . . . . . . . . . . . . 25
3.2 Setup of the time-resolved experiment . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Physical origin of the Bragg peak oscillations . . . . . . . . . . . . . 31
4 Electric- eld-induced response of Li SOH O, Li SeOH O and BiB O sin-2 4 2 2 4 2 3 6
gle crystals 33
4.1 Lithium sulfate monohydrate, Li SOH O . . . . . . . . . . . . . . . . . . 332 4 2
4.1.1 Multipole-model re nement of the electron density and properties
of the chemical bonds . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.2 X-ray di raction study of Li SOH O under the in uence of an2 4 2
applied external electric eld . . . . . . . . . . . . . . . . . . . . . . 40
4.1.3 Model used for the description of the electric- eld-induced atomic
displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.4 Re nement of the piezoelectric constants d and atomic displace-2jk
ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Lithium selenate monohydrate, Li SeOH O . . . . . . . . . . . . . . . . . 482 4 2
4.2.1 Properties of the chemical bonds . . . . . . . . . . . . . . . . . . . 49
4.2.2 Electric- eld-induced atomic rearrangement . . . . . . . . . . . . . 54
iiiContents
4.2.3 Comparison of the bond-selective response strength of di erent piezo-
electric crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Bismuth triborate, BiB O . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 6
4.3.1 X-ray determination of the piezoelectric constants . . . . . . . . . . 60
4.3.2 Internal strain induced in BiB O by external electric elds applied3 6
in di erent crystallographic directions . . . . . . . . . . . . . . . . . 62
4.3.3 Neutron di raction study of the internal strain . . . . . . . . . . . . 68
5 Time-resolved X-ray di raction study of the dynamic piezoelectric response
of crystals 73
5.1 Measurements with the rst rectangular Li SOH O (010) crystal plate . . 742 4 2
5.1.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2ts with the second rectangular Li SOH O (010) crystal plate 832 4 2
5.3 X-ray di raction investigations of the piezoelectrically induced crystal vi-
brations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.1 Supplementary measurements performed with other Li SOH O2 4 2
and BiB O crystal plates . . . . . . . . . . . . . . . . . . . . . . . 873 6
6 Summary 89
Appendix 91
A.1 Publications arising from the thesis . . . . . . . . . . . . . . . . . . . . . . 91
A.2 Talks given at conferences, colloquiums and workshops . . . . . . . . . . . 91
A.3 Financing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A.4 All ( I=I) data observed and calculated for Li SOH O, Li SeOH Oa 2 4 2 2 4 2
and BiB O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 6
A.5 VHDL source code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Bibliography 105
Acknowledgments 113
ivIntroduction
X-ray di raction is the major experimental tool for the investigation of the microscopic
structure of crystals. A highly redundant set of Bragg intensities can be collected almost
automatically with high precision and can be used to obtain accurate atomic positions,
atomic displacement parameters and electron-density distributions in crystals. In gen-
eral, these quantities describe a crystal at the static equilibrium, i.e. in the absence of
any external in uences. However, probing the microscopic response of the crystal to an
external perturbation is still a challenge for modern X-ray structure analysis. The main
aim of such experiments is to understand how the speci c features of the structural net-
work are responsible for the physical properties of a crystal and how the crystal structural
parameters can be tuned to control the property of interest.
The types of perturbations which are usually applied to a crystal in an X-ray di raction
experiment are high pressure, high or low temperature, laser irradiation and external high
voltage [1, 2, 3, 4]. The speci c response of the crystal to such perturbations de nes
its intrinsic physical properties, e.g. the development of the macroscopic polarization
under the in uence of an applied electric eld is known as dielectricity, whereas the
formation of the mechanical strains is referred to as the converse piezoelectric e ect [5, 6].
Although many technical applications are essentially based on both of these phenomena,
their microscopic nature is not yet well understood. Starting with the pioneering work
by Fujimoto (1978) [7] on LiNbO , the atomistic origin of the piezoelectric e ect has so3
far been investigated for only a very narrow class of compounds, such as AgGaS [8],2
KD PO [9, 10], KH PO [11], GaAs [4], ZnSe [4], -SiO [12, 13] and -GaPO [14]. In2 4 2 4 2 4
this context, X-ray di raction under an external electric perturbation has turned out to
be a promising experimental tool for obtaining an understanding of the piezoelectric e ect
at the microscopic level. Nevertheless, till now the fundamental relationship between the
atomic arrangement, the electron density distribution and the piezoelectric properties of
a crystal could not be explained in full detail for any single structure [15]. The great
advantage of the X-ray di raction technique is that the atomic redistribution within the
unit cell of a crystal caused by an applied electric eld and the corresponding macroscopic
deformation (pure lattice strain keeping the atomic fractional coordinates constant) of the
crystal can be simultaneously and separately studied using one and the same sample. The
4 small displacements of the atomic positions ( R 10 A, [14]) may be evaluated from
Bragg intensity changes. At the same time, the lattice strain manifests itself as small
3angular shifts of di raction curves ( ! 10 , [16]).
The aim of this work consists of three parts: First of all, the investigations of the
bond-selective response of piezoelectric crystals ought to be extended on the Li SOH O,2 4 2
Li SeOH O (is isostructural with Li SOH O) and BiB O compounds. In particular,2 4 2 2 4 2 3 6
the behavior of the LiO , SO , SeO , BO , BO and BiO structural units under an ex-4 4 4 4 3 6
ternal electric eld should be analyzed and compared with the results obtained for crystal
structures built up from similar atomic groups. Thus, the rst part of this work represents
a continuation of the measurements that have proved to be successful in previous studies
on the microscopic response of a crystal to an external electric perturbation. Normally,
1Contents
the measurement of the time dependence of the processes initiated in a crystal by a fast
change of an applied electric eld enables deeper insights into the nature of the physical
properties of the crystal. But from the beginning the experimental technique used for
switching the external electric elds was not designed to generated dynamic processes
in crystals, as the static (i.e. time-averaged) properties of the crystals were of interest
only. This disadvantage of the old eld-switching technique is the origin of the second
subject of this thesis that deals with further developments of the experiment to the time-
resolved measurements of the dynamic processes in crystals. Finally, within the scope
of this work th