Mechanisms of ion migration in ceramic oxides [Elektronische Ressource] / von Mohammad Mazharul Islam
115 pages
English

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Mechanisms of ion migration in ceramic oxides [Elektronische Ressource] / von Mohammad Mazharul Islam

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115 pages
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Mechanisms of Ion Migrationin Ceramic OxidesVon der Naturwissenschaftliche Fakult atder Universit at Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonM.Sc. Mohammad Mazharul Islamgeboren am 27.07.1977in Dhaka, Bangladesch2005Referent Priv.-Doz. Dr. T. BredowKorreferent: Prof. Dr. K. JugTag der Promotion: 11.07.2005I would like to express my utmost gratitude to Priv.-Doz. Dr. T. Bredow for his whole-hearted guidance and invaluable help. His encouragement and advice have helped meto complete my thesis successfully.I am grateful to Prof. Dr. K. Jug for giving me an opportunity to work in his researchgroup. I thank him for his fruitful discussion.I am deeply indepted to Prof. C. Minot, Laboratoire de Chimie Theorique, UPMC,Paris, for allowing me to work in his research group, for his proper guidance and kindhospitality, during my stay in Paris.I would like to thank all my colleagues and friends for their help and encouragement.I thank the state of Lower Saxony for granting me the Georg-Christoph-Lichtenbergscholarship.AbstractBulk properties of Li O, B O and Li B O are investigated quantum-chemically. The2 2 3 2 4 7reliability of three density-functional theory (DFT) methods (PWGGA, PWGGA-US and PWGGA-PAW), two DFT-Hartree Fock (HF) hybrid methods (PW1PW andB3LYP) and the semiempirical method MSINDO is examined by comparison of calcu-lated results to available experimental data.

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Publié le 01 janvier 2005
Nombre de lectures 154
Langue English
Poids de l'ouvrage 2 Mo

Extrait

Mechanisms of Ion Migration
in Ceramic Oxides
Von der Naturwissenschaftliche Fakult at
der Universit at Hannover
zur Erlangung des Grades
Doktor der Naturwissenschaften
Dr. rer. nat.
genehmigte Dissertation
von
M.Sc. Mohammad Mazharul Islam
geboren am 27.07.1977
in Dhaka, Bangladesch
2005Referent Priv.-Doz. Dr. T. Bredow
Korreferent: Prof. Dr. K. Jug
Tag der Promotion: 11.07.2005I would like to express my utmost gratitude to Priv.-Doz. Dr. T. Bredow for his whole-
hearted guidance and invaluable help. His encouragement and advice have helped me
to complete my thesis successfully.
I am grateful to Prof. Dr. K. Jug for giving me an opportunity to work in his research
group. I thank him for his fruitful discussion.
I am deeply indepted to Prof. C. Minot, Laboratoire de Chimie Theorique, UPMC,
Paris, for allowing me to work in his research group, for his proper guidance and kind
hospitality, during my stay in Paris.
I would like to thank all my colleagues and friends for their help and encouragement.
I thank the state of Lower Saxony for granting me the Georg-Christoph-Lichtenberg
scholarship.Abstract
Bulk properties of Li O, B O and Li B O are investigated quantum-chemically. The2 2 3 2 4 7
reliability of three density-functional theory (DFT) methods (PWGGA, PWGGA-
US and PWGGA-PAW), two DFT-Hartree Fock (HF) hybrid methods (PW1PW and
B3LYP) and the semiempirical method MSINDO is examined by comparison of calcu-
lated results to available experimental data. The results at DFT level are also com-
pared for di eren t types of basis functions, either based on linear combinations of
atom-centered orbitals (LCAO), or on plane waves, as implemented in the crystalline
orbital program CRYSTAL and in VASP, respectively. The basis set dependence of the
calculated properties is investigated for the LCAO based methods. In the plane wave
based methods (PWGGA-US and PWGGA-PAW), ultrasoft pseudopotentials (US PP)
and projector-augmented wave (PAW) potentials are used to represent the core elec-
trons. The e ect of energy cuto (E ) on the calculated properties is investigated. Acut
comparative study is performed for the low and high space-group symmetry of trigonal
+B O . The cation vacancy and F center of Li O are investigated. Li ion di usion in2 3 2
+Li O is investigated by calculating the activation energy E for the migration of Li2 A
ion via cation vacancy. The calculated values are compared with the experiment. The
ionic conductivity in the (001) direction of Li B O is investigated. The calculated2 4 7
E values are compared with experimental results from the literature. The structureA
and stability of Li O (111) and (110) surfaces and the B O (001) surface are calcu-2 2 3
lated. The interface of Li O:B O nanocomposite is modeled by the combination of2 2 3
+supercells of Li O (111) and B O (001) surface. The migration of Li ion via cation2 2 3
vacancy is studied in the interface region. The calculated E is compared with thatA
in the nanocrystalline Li O, and it is shown that the conductivity is enhanced in the2
Li O:B O nanocomposite compared to that in Li O.2 2 3 2
Keywords: density-functional theory, pseudopotential, nanocomposites, interface re-
gionKurzzusammenfassung
Festk orpereigenschaften von Li O, B O und Li B O wurden mit Hilfe quantenchemis-2 2 3 2 4 7
cher Methoden untersucht. Die Rechnungen erfolgten auf der Basis von Dichtefunk-
tionaltheorie (PWGGA, PWGGA-US und PWGGA-PAW) und DFT-Hartree-Fock-
Hybridmethoden (PW1PW und B3LYP) sowie mit der semiempirischen Methode
MSINDO. Die erhaltenen Ergebnisse wurden mit experimentellen Daten verglichen.
Im Falle der DFT-Rechnungen wurden als Basiss atze sowohl Linearkombinationen
von atomzentrierten Basisfunktionen (LCAO), wie sie in der Kristallorbitalmethode
CRYSTAL implementiert sind, als auch ebene Wellen, die im Programm VASP be-
nutzt werden, verwendet. Im Falle der LCAO-basierten Methoden sind die berech-
neten Eigenschaften auf eine Basissatzabh angigkeit ub erpruft worden. Zur Darstel-
lung der inneren Elektronen wurden bei den Methoden mit ebenen Wellen (PWGGA-
US und PWGGA-PAW) ultraweiche Pseudopotentiale (ultrasoft pseudopotential) und
"projector-augmented wave" Potentiale verwendet. Weiterhin ist der E ekt des En-
ergiegrenzwertes ebener Wellen (E ) auf die berechneten Eigenschaften untersuchtcut
worden. In einer vergleichenden Studie wurden das niedrig- und hochsymmetrische
trigonale B O untersucht. Am Li O wurden Rechnungen fur die Kationenfehlstelle2 3 2
+und das F-Zentrum durchgefuhrt. Fur die Di usion von Li -Ionen im Li O ist die Ak-2
+tivierungsenergie E der Li -Wanderung ub er Kationenfehlstellen berechnet und mitA
experimentellen Daten verglichen worden. Die Ionenleitf ahigkeit in (001)-Richtung im
Li B O wurde untersucht und die erhaltene E mit dem Experiment verglichen. Die2 4 7 A
Struktur und Stabilit at der Li O (111)- und (110)- sowie die B O (001)- Ober achen2 2 3
wurden berechnet. Die Grenz ache von Li O:B O -Nanopartikeln ist durch eine Kom-2 2 3
bination von Superzellen der Li O (111)- und B O (001)- Ober achen modelliert wor-2 2 3
+den. Die Wanderung von Li -Ionen ub er Kationenfehlstellen in der Grenz achenregion
wurde untersucht. Ein Vergleich der berechneten Aktivierungsenergien zeigt, da die
Leitf ahigkeit im Li O:B O gegenub er dem reinen Li O erh oht ist.2 2 3 2
Schlagw orter: Dichtefunktionaltheorie, Pseudopotentiale, Nanopartikeln, Grenz achenregioni
Contents
1 Introduction 1
2 Quantum Chemical Background 3
2.1 Hartree-Fock Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Semiempirical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Models of Solids and Surfaces 17
3.1 Periodic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 Localized basis . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.2 Plane Wave basis . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Cyclic Cluster Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Experimental Background 29
5 Bulk Properties of Li O 312
5.1 Stoichiometric Li O: MSINDO-CCM results . . . . . . . . . . . . . . . 322
5.1.1 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.1.2 Convergence Test . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2 Stoichiometric Li O: DFT results . . . . . . . . . . . . . . . . . . . . . 362
5.3 Defect properties of Li O . . . . . . . . . . . . . . . . . . . . . . . . . . 412
5.3.1 Cation vacancy . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.3.2 F center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
+5.4 Di usion of Li ion in Li O . . . . . . . . . . . . . . . . . . . . . . . . 522
6 Bulk Properties of B O 582 3
6.1 B O with P3 21 space group . . . . . . . . . . . . . . . . . . . . . . . 602 3 1
6.2 Comparison between P3 21 and P3 space group . . . . . . . . . . . . . 631 1
7 Bulk Properties of Li B O 652 4 7
7.1 Structure Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.2 Binding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3 Band Structure and Density of States . . . . . . . . . . . . . . . . . . . 71ii
7.4 Electronic charge density . . . . . . . . . . . . . . . . . . . . . . . . . . 74
+8 Migration of Li ion in Li B O 772 4 7
8.1 Cation vacancy in lithium tetraborate . . . . . . . . . . . . . . . . . . . 77
+8.2 Migration of Li ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
9 Model System for the Li O:B O nanocomposite 842 2 3
9.1 Construction of the Li O:B O interface . . . . . . . . . . . . . . . . . 842 2 3
9.1.1 Surface energy of Li O . . . . . . . . . . . . . . . . . . . . . . . 852
9.1.2 Surface energy of B O . . . . . . . . . . . . . . . . . . . . . . . 872 3
9.1.3 Interface of Li O:B O nanocomposite . . . . . . . . . . . . . . 892 2 3
9.2 Defect properties in Li O:B O nanocomposite . . . . . . . . . . . . . . 922 2 3
9.2.1 Cation vacancy . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
+9.2.2 Migration of Li ion . . . . . . . . . . . . . . . . . . . . . . . . 93
10 Summary 96
References 981 Introduction 1
1 Introduction
In recent years, ceramic oxides have attracted considerable attention due to their broad
potential applications as advanced materials with controlled chemical, mechanical, elec-
trical, magnetic, and optical properties. Many of these properties are attributed to the
mobility of metal ions. A metal ion can migrate from a regular site to an intersti-
tial site or to an adjacent defect position. An important criterion for the probability
of these processes is the corresponding activation energy. Sometimes, it is di cult
to obtain this quantity with experimental techniques. Quantum chemical approaches
can be utilized to determine the activation energy for the elementary steps. Recent
experimental investigations for the Li O:B O nanocomposite show that the ionic con-2 2 3
ductivity increases with increasing B O content although B O is an insulator. A2 3 2 3
possible explanation discussed in the literature is the formation of lattice defects at the
phase boundary between nano-crystalline Li O and B O which leads to an enhanced2 2 3
+mobility of Li ions.

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