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

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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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Published 01 January 2005
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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. Due to this property, the Li O:B O nanocomposite has potential2 2 3
applications in battery systems, fuel cells or gas sensors. In the present work, the en-
+hanced mobility of Li ions in Li O:B O nanocomposite is investigated theoretically2 2 3
using both semiempirical and density functional theory (DFT) methods.
The structural, energetic and electronic properties of Li O, B O , and Li B O are2 2 3 2 4 7
studied with periodic quantum chemical calculations using the CRYSTAL03 package,
the VASP package and the cyclic cluster model (CCM) implemented in the semiem-
pirical method MSINDO. As a test for the methods, calculated bulk properties for all
these systems are compared with available experimental data.
Li O is a fast ionic conductor. Available experimental information on the ionic trans-2
+port in this system shows that the mobile species is the Li ion and the most likely
mechanism for its migration is via cation vacancies. Another prominant irradiation
defect is known as F center, an oxygen vacancy trapping two electrons. The forma-
tion energy of the cation vacancy and the F center in Li O is calculated. The e ect2
of relaxation and the in uence of defects on the electronic properties are investigated
+for the both types of defect in Li O. A possible mechanism of the Li migration is2
+investigated by calculating the energy barrier for the movement of Li from a regular
site to an adjacent cation vacancy defect position.1 Introduction 2
+Li B O (LTB) is a Li ion conductor along the (001) direction. In the present study,2 4 7
LTB is considered as the rst model system for the interface region of Li O:B O2 2 3
nanocomposite. The cation vacancy defect in LTB is investigated. The defect formation
energy is calculated and the e ect of relaxation is investigated for the defective system.
+The mechanism of Li ion migration is investigated by calculating the energy barrier for
+the movement of Li ions from regular sites to adjacent cation vacancy defect positions
along the tetragonal axis.
A more realistic model system of the Li O:B O interface region is created by combining2 2 3
surfaces of the two oxides. The surface energies of (110) and (111) surfaces of Li O2
and (001) surface of B O are calculated. Using the most favorable surface structures,2 3
such as, (111) for Li O and (001) for B O , the mixed model structure of Li O:B O2 2 3 2 2 3
is prepared. The mixed structure is optimized with the relaxation of all atoms in the
+interface region and the migration of a Li ion is studied.2 Quantum Chemical Background 3
2 Quantum Chemical Background
The Schr odinger equation [1{3] contains the essence of all chemistry. To quote Dirac:
"The underlying physical laws necessary for the mathematical theory of a large part
of physics and the whole of chemistry are thus completely known" [4]. The time-
independent Schr odinger equation is
^H =E (2.1)
^whereH is the Hamilton operator, is the wavefunction that contains all information
about the quantum system and E is the energy of the system. The nonrelativistic
^Hamilton operator H is expressed (in atomic units) for a system of N nuclei and n
electrons as,
N n N n n NX X X X X X1 1 Z 1 Z ZI I J2 2^H = r r + + (2.2)I i2M 2 r r RI Ii ij IJi i j>iI I J>I
The rst two terms describe the kinetic energy of the nuclei and the electrons, respec-
tively. HereM is the mass andZ is the atomic number of a nucleusI. The remainingI I
three terms de ne the potential part of the Hamiltonian and represent the attractive
electrostatic interaction between the nuclei and the electrons and the repulsive poten-
tial due to the electron-electron and nucleus-nucleus interactions, respectively. r isij
the distance between the electrons i and j, r is the distance between nucleus I andIi
electron i, and R is the distance between the nuclei I and J.IJ
Since nuclei are much heavier than electrons, they move more slowly. Hence, to a
good approximation, the electrons in a molecule can be considered to be moving in
the eld of xed nuclei. Within this approximation, the rst term of (2.2), the kinetic
energy of the nuclei, can be neglected and the last term of (2.2), the repulsion between
the nuclei, can be considered to be constant. The remaining terms in (2.2) are called
^the electronic Hamiltonian (H ). This separation of electronic and nuclear motionsel
is called the Born-Oppenheimer approximation [5]. The Schr odinger equation (2.1) is
reduced to the electronic Schr odinger equation,
^H =E (2.3)el el el el
^where H has the following simpli ed form,el
n N n nX XX X1 Z 1I2^H = r + (2.4)el i
2 r rIi iji i j>iI