Characterization of phase transitions by the analysis of crystal structures [Elektronische Ressource] / vorgelegt von Joachim Angelkort

Sujets

• Physik

Informations

• Publié par: universitat_bayreuth
• Publié le: 01 janvier 2009
• Nombre de lectures: 22
• Langue: Deutsch
• Poids de l'ouvrage: 9 Mo

Extrait

Lehrstuhl fur¨ Kristallographie
Characterization of phase
transitions by the analysis of
crystal structures
Abhandlung zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften
vorgelegt von
Joachim Angelkort
1. Gutachter: Prof. Dr. Sander van Smaalen
2. Gutachter: Prof. Dr. Hans F. Braun
Tag der Einreichung: 15. Juli 2009
Tag des Kolloquiums: 18. Dezember 2009Danksagung
Ich danke Prof. Dr. van Smaalen fur¨ die Moglic¨ hkeit, am Lehrstuhl fur¨ Kristallo-
graphie an spannenden Projekten mitgearbeiten haben zu durfen. Er stand jeder-¨
zeit fur¨ Diskussionen und Beratungen zur Seite. Sein Engagement sowie sein hoher
Anspruch an den Einsatz seiner Mitarbeiter trugen wesentlich zum Gelingen der
durchgefuhrten Experimente bei.¨
Ein großes Dankeschon¨ gilt Dr. Schonleb¨ er, der an der Betreuung der Doktoran-
den des Lehrstuhls Teil hatte. Viele Diskussionen mit ihm fuhrten zu einem besseren¨
Verstandnis¨ kristallographischer Sachverhalte.
Ich danke Alfred Suttner fur¨ die Synthese von Kristallen und Franz Fischer
fur die fortlaufende Reparatur und Instandhaltung der technischen Gerate, deren¨ ¨
Eigenleben ihn oft zur Entwicklung von unkonventionellen, gut funktionierenden
Methoden veranlasste.
Weiterhin danke ich allen derzeitigen und einstigen Mitarbeitern des Institutes,
die fur¨ ein angenehmes und fast familiare¨ s Arbeitsklima gesorgt haben.
iiiMeiner Mutter und meinem Bruder
iiiivContents
1 Introduction 1
2 Theoretical background 5
2.1 Theoryofstructuralphasetransitionsincrystals ........... 5
2.1.1 Continuousphasetransitions................... 6
2.1.2 Discontinuousphasetransitions...... 7
2.2 Thespin-Peierlstransition............. 9
3 Experimental techniques 11
3.1 GenerationofX-rayradiation......................1
3.1.1 ConventionalX-rayradiation .......1
3.1.2 Synchrotronradiation..12
3.1.3 Monochromatization.......................13
3.2 Single-crystalX-rayDiffractometers........14
3.2.1 ExperimentsonaMach3diffractometer..18
3.2.2 ExperimentsonaMAR345dtbdiffractometer.........20
3.3 Controlofthecrystaltemperature....................20
3.4 Crystalpreparation.................2
4 Crystal chemistry of selected transition-metal compounds 25
4.1 Thetransition-metaltrihalides......................25
4.1.1 Phase transitions of α-TiX (X=Cl,Br)............273
4.1.2 Phase transition of β-TiX (X=Cl,Br,I)...........283
4.2 Thetransition-metaloxyhalides.....................29
4.2.1 Crystalstructuresandmagneticbehavior............29
4.2.2 PhasetransitionsofTiOClandTiOBr..31
4.2.3 MagneticstructuresofFeOCl,CrOClandVOCl........32
vvi CONTENTS
5 Phase transition and crystal structure of the monomeric
Europium(II) thiolate Eu(SC H ) 3536 49 2
5.1 Introduction................................35
5.2 ResultsandDiscusion......36
5.3 Conclusions.4
5.4 ExperimentalSection...........................4
6 Low- and high-temperature crystal structures of TiI 473
6.1 Introduction.....................47
6.2 Experimentalsection..................51
6.3 Structurerefinements53
6.4 Discusion......................56
6.4.1 TiI and RuBr structuretypes........563 3
6.4.2 Thephasetransition..............60
6.5 Conclusions.....................61
7 Magnetoelastic coupling in CrOCl 63
7.1 Introduction.....................63
7.2 Experimental...........65
7.3 Results....6
7.3.1 Magnetic Susceptibility and magnetization . . .........6
7.3.2 X-raydiffraction ................69
7.4 Discussion.............73
7.5 Conclusions..........76
8 Inhomogeneous thermal expansion of layered CrOCl 77
8.1 Introduction................................7
8.2 Experimental79
8.3 Discusion..81
9 Summary 83
10 Zusammenfassung 87
A Supplementary material: Eu(SC H ) 9136 49 2
Btary material: TiI 1013CONTENTS vii
C Crystal twinning of TiI 1033
D Monoclinic angle in the unit cell of CrOCl 105
E Measured reflection profiles of CrOCl 107
E.1 Profiles of 2θ-dependent ω-scans.....................108
E.1.1 Profilesmeasuredonreflection(0-25)..108
E.1.2 Profilesmeasuredonreflection(204)..10
E.1.3 Profilesmeasuredonreflection(2-20)..112
E.2ScansonsuperstructurereflectionsofCrOCl..............14
E.3 Profile fitting for determination of the peak positions of CrOCl . . . . 117
F Additional structural parameters of CrOCl at different
temperatures 119
Bibliography 123
Parts of this thesis published in the scientific literature 133
List of Figures 137
List of Tables 140
Erkl¨arung 141viii CONTENTSChapter 1
Introduction
Symmetry is a property of one or several objects by which the geometrical shape
of the object or the geometrical interrelation between the objects is described. In
the case of a crystal structure the symmetry interrelates equal kinds of atoms to be
located at certain positions in space. One uses the term pseudo symmetry to refer
to a crystal structure which does not differ much from a structure with a higher
symmetry. The existence of a pseudo symmetry can be revealed by the finding that
the examined lattice parameters of the unit cell are in conflict with the demands of
the underlying symmetry or by the indication that some atoms of the structure are
displaced contradictory to the supposed symmetry.
Often the atoms of a particular chemical compound can be arranged to different
crystal structures giving rise to the formation of different stable phases. A phase is
a volume of matter which is physically and chemically homogeneous and which can
be assigned to one of the three states (gaseous, liquid, solid). Changes of system
parameters like pressure and temperature can cause a transformation of one state
of matter into another termed phase transition. In contrast to the gaseous state in
which any combination of gases forms a homogeneous mixture, i.e. a single phase,
different phases can coexist in liquids as well as in the solid state. The gaseous and
liquid phases are states of highest symmetry, while the crystalline state can have
different symmetries according to one of the 230 space groups. Additional possibil-
ities occur for the so-called aperiodic crystals. Phase transitions between different
solid states can be continuous or discontinuous (Chapter 2). At the transition point
of a discontinuous phase transitions different phases coexist.
In this thesis the term domain is used to indicate a small block in a large piece of
matter, which is in one of several states or which possesses one of several orientations
1