KJM5120 (& KJM9120) Defects and Reactions Welcome, information, and introduction Truls Norby Ch 1. Bonding, structure, and defects Department of Chemistry University of Oslo Centre for Materials Science and Nanotechnology (SMN) FERMIO Oslo Research Park (Forskningsparken) [email protected] http://folk.uio.no/trulsn KJM5120 (& KJM9120) Defects and Reactions Welcome! KJM5120 Defects and Reactions; Master level (KJM9120 Defects and Reactions; PhD level) Requirement to pass is different:
Curriculum Master: Normal letter marks are in use. F means failed. E or better means passed. PhD: Pass/fail. Pass requires the equivalent of B or better! Defects and Transport in Crystalline Solids, Per Kofstad and Truls Norby Compendium, ca. 300 pages Made available per Fronter and/or Semester page Per Kofstad (1929-1997) NOTE: Chapter 7 is taught for both KJM5120 and 9120, but is mandatory and examined only in KJM9120.
Exam: Oral examination. 30 minutes Truls Norby KJM5120 (& KJM9120) Defects and Reactions; Teaching Curriculum text: Defects and Transport in Crystalline Solids Teaching (normal): Alternative teaching, web based,: available on Fronter (http://blyant.uio.no) and KJM5120s semester pages Curriculum chapters as .pdf files Curriculum chapters contain Problems, partially with Solutions Lectures as PowerPoint presentations
Easy exercises as Word .doc files Answer the questions and optionally submit to teacher. Provides checkpoints of minimum learning, understanding, and skills. Teacher returns with comments Approx. 45 hours of Lectures & Problem-solving classes Catch-up seminar days with teacher present or as discussion group, after agreement with students. Communication Fronter: http://blyant.uio.no KJM5120s webpage: http://www.uio.no/studier/emner/matnat/kjemi/KJM5120/index-eng.xml email: [email protected] KJM5120 (& KJM9120) Defects and Reactions; Content and outcome
From the courses web-page 2010: The course gives an introduction to defects in crystalline compounds, with emphasis on point defects and electronic defects in ionic materials. The treatment then moves on to thermodynamics and interactions of defects, disorder, non-stoichiometry, and doping. Diffusivity and charge transport are deduced from mobility and concentration of defects, and are in turn used to describe conductivity, permeability, chemical diffusion, reactivity, etc. Finally, these properties are discussed in terms of their importance in fuel cells, gas separation membranes, corrosion, interdiffusion, sintering, creep, etc. The student will learn and know about different defect types and transport mechanisms in crystalline materials, and further, in simple cases be able to deduce how defect concentrations and transport parameters vary as a function of surrounding atmosphere, temperature, and doping. The student will understand the role of defect related transport in important applications and processes, and be able to deduce this mathematically in simple cases. Will be updated with KJM5120 vs KJM9120 info KJM5120 (& KJM9120) Defects and Reactions; Electrical current
conductance and fluxes of atoms and ions reaction, diffusion, creep, sintering, permeation, ionic conduction, etc. require transport. Transport in crystalline solids requires defects. Transport properties are defect-dependent properties. In this course we learn to quantitatively calculate and predict defect concentrations (defect chemistry; thermodynamics) and transport of defects (transport kinetics) and reversely
to interpret defect-dependent properties in terms of concentration and transport of defects. KJM5120 and KJM9120 Defects and Reactions; What do you need to know before we start? Webpage says: Recommended prior knowledge KJ102 / MEF1000 - Materials and energy, KJM1030 - Uorganisk kjemi, KJM3100 Chemistry of Materials, KJM3300 - Physical Chemistry, KJM5110 - Inorganic Structural Chemistry and MAT1100 - Calculus. We will however, try to make the course independent of prior knowledge, and introduce fundamentals needed. Nevertheless, the course is physical chemistry and especially physics students tend to express initial frustration over
equilibrium thermodynamics balancing chemical reactions periodic table and properties of the elements Others feel that some of the mathematical procedures are complicated. But they arent! Fear not: You can do it! And learn or repeat some fundamentals too, in addition to all the defects. Brief history of defects Early chemistry had no concept of stoichiometry or structure. The finding that compounds generally contained elements in ratios of small integer numbers was a great breakthrough! H2O CO2
NaCl CaCl2 NiO Understanding that external geometry often reflected atomic structure. Perfectness ruled. Variable composition (nonstoichiometry) was out. However, variable composition in some intermetallic compounds became indisputable and in the end forced reacceptance of non-stoichiometry. But real understanding of defect chemistry of compounds mainly came about from the 1930s and onwards, attributable to Frenkel, Schottky, Wagner, Krger, many of them physicists, and almost all German!
Frenkel Schottky Wagner First a brief glimpse at what defects are Defects in an elemental solid (e.g. Si or Ni metal) Point defects (0-dimensional) Line defects (1-dimensional) Dislocation (goes into the paper
plane) Row of point defects (here vacancies) Planar defects (2-dimensional) Vacancy Interstitial (not shown) Interstitial foreign atom Substitutional foreign atom Plane of point defects Row of dislocations Grain boundary Surface? Adapted from A. Almar-Nss: Metalliske materialer, Tapir, Oslo, 1991. 3-dimensional defects
Precipitations or inclusions of separate phase Be sure you know and understand at least the ones in red! Defects in an elemental solid (e.g. Si or Ni metal) Notice the distortions of the lattice around defects The size of the defect may be taken to be bigger than the point defect itself Adapted from A. Almar-Nss: Metalliske materialer, Tapir, Oslo, 1991. Defects in an ionic solid compound Cations drawn dark Anions drawn white Foreign species drawn coloured
Try to spot all the defects named What are the dimensionality of each defect? Notice how complex dislocations and grain boundaries generally are in ionic compounds Bonding Bonding Bonding: Decrease in energy when redistributing atoms valence electrons in new molecular orbitals. Three extreme and simplified models:
Covalent bonds: Share electrons equally with neighbours! Metallic bonds: Electron deficiency: Share with everyone! Strong, directional pairwise bonds. Forms molecules. Bonding orbitals filled. Soft solids if van der Waals forces bond molecules. Hard solids if bonds extend in 3 dimensions into macromolecules. Examples: C (diamond), SiO2 (quartz), SiC, Si3N4 Atoms packed as spheres in sea of electrons. Soft. Only partially filled valence orbital bands. Conductors. Ionic bonds: Anions take electrons from the cations! Small positive cations and large negative anions both happy with full outer shells. Solid formed with electrostatic forces by packing + and charges. Lattice energy.
Formal oxidation number Bonds in compounds are not ionic in the sense that all valence electrons are not entirely shifted to the anion. But if the bonding is broken as when something, like a defect, moves the electrons have to stay or go. Electrons cant split in half. And mostly they go with the anion - the most electronegative atom. That is why the ionic model is useful in defect chemistry and transport And it is why it is very useful to know and apply the
rules of formal oxidation number, the number of charges an ion gets when the valence electrons have to make the choice Bonding some important things to note Metallic bonding (share of electrons) and ionic bonding (packing of charged spheres) only have meaning in condensed phases. In most solids, any one model is only an approximation: Many covalent bonds are polar, and give some ionic character or hydrogen bonding. Both metallic and especially ionic compounds have covalent contributions In defect chemistry, we will still use the ionic model extensively, even for compounds with little degree of ionicity.
It works! and we shall understand why. Formal oxidation number rules Fluorine (F) has formal oxidation number -1 (fluoride) in all compounds. Oxygen (O) has formal oxidation number -2 (oxide) , -1 (peroxide) or 1/2 (superoxide), except in a bond with F. Hydrogen (H) has oxidation number +1 (proton) or -1 (hydride). All other oxidation numbers follow based on magnitude of electronegativity (see chart) and preference for filling or emptying outer shell (given mostly by group of the periodic table). The periodic table
The group number counts electrons in the two outermost shells. For groups 1-2 and 13-18 the last digit gives account of the sum of the number of outermost shell s and p electrons, where simple preferences for valence can be evaluated. For groups 3-12 the number gives account of the sum of outermost p and underlying d electrons, and where resulting valence preferences are more complex. Electronegativity Electronegativity is the relative ability to attract electrons in a bond with another element The chart depicts Pauling electronegativity as sphere size. F is the most electronegative element. The electronegativity increases roughly diagonally towards the upper righthand corner of the periodic table. From http://www.webelements.com Electron energy bands Electron energy bands In solids, electron orbital
energies form bands Conduction band: Lowest unoccupied band Valence band: Highest occupied band Band edge: EC Band edge: EV Band gap Eg = EC - EV Crystal structures Crystal structures
Many ionic and metallic structures can be seen as a packing of large ions or atoms with smaller ones placed in the voids in-between. Closest packing of spheres forms layers of hexagonal symmetry that can be packed ABAB or ABCABC Closest packed structures ABAB packing forms a hexagonal closest packing (hcp) ACABC packing turned 45 degrees forms a face-centered cubic (fcc) closest packing Voids (=holes, interstices)
Voids in hcp and fcc structures: Octahedral voids inbetween 6 large spheres Relatively large 1 per large sphere Tetrahedral voids inbetween 4 large spheres Relatively small 2 per large sphere; T and T Note: These may be filled by atoms or ions as part of the ideal structure. They are then not interstitials in defect-chemical terms. Interstitial defects can occupy only voids empty after the ideal structure has been formed.
Less close-packed packing Preferred at higher temperatures and when voids are filled by atoms too large to fit into the voids of the closest-packed structures Body-centered cubic (bcc) Simple cubic (sc) Some simple structures Learn these three structure types: rocksalt AX (e.g. NaCl)
fluorite AX2 (e.g. CaF2) fcc closepacked Ca2+, F- in all tetrahedral voids or, better, simple cubic F-, with Ca2+ in every other cube. perovskite ABX3 (e.g. CaTiO3) Here represented as fcc close-packed Na + (orange) Cl- (green) in octahedral voids or vice versa fcc close-packed A+3X (red and gray) B (blue) in octahedral voids between in AX 6 units
More structures in the compendium; less important Some simple classes of oxide structures with close-packed oxide ion sublattices Formula Cation:anion coordination Type and number of occupied voids fcc of anions hcp of anions MO 6:6 1/1 of octahedral voids
M2O3, ABO3 6:4 2/3 of octahedral voids Corundum: Al2O3, Fe2O3, Cr2O3 a.o. Ilmenite: FeTiO3 MO2 6:3 of octahedral voids Rutile: TiO2, SnO2 AB2O4 1/8 of tetrahedral and 1/2 of
octahedral voids Spinel: MgAl2O4 Inverse spinel: Fe3O4 Point defects Krger-Vink notation We will now start to consider defects as chemical entities We need a notation for defects. Many notations have been in use. In modern defect chemistry, we use Krger-Vink notation (after Krger and Vink). It describes any entity in a structure; defects and perfects. The notation tells us What the entity is, as the main symbol (A)
Where the entity is, as subscript (S) Chemical symbol of the normal occupant of the site or i for interstitial (normally empty) position Its charge, real or effective, as superscript (C) Chemical symbol or v (for vacancy) +, -, or 0 for real charges or ., /, or x for effective positive, negative, or no charge Note: The use of effective charge is preferred and one of the key points in defect chemistry. We will learn what it is in the following slides
A C S Effective charge The effective charge is defined as the charge an entity in a site has relative to (i.e. minus) the charge the same site would have had in the ideal structure. Example: An oxide ion O2- in an interstitial site (i) Real charge of defect: -2 O 2i O //
i Real charge of interstitial (empty) site in ideal structure: 0 Effective charge: -2 0 = -2 Effective charge more examples Example: An oxide ion vacancy Real charge of defect (vacancy = nothing): 0 Real charge of oxide ion O2- in ideal structure: -2 Effective charge: 0 (-2) = +2 v O v //// Zr Example: A zirconium ion vacancy, e.g. in ZrO2 Real charge of defect: 0
Real charge of zirconium ion Zr4+ in ideal structure: +4 Effective charge: 0 4 = -4 Krger-Vink notation more examples Dopants and impurities Y3+ substituting Zr4+ in ZrO2 Li+ substituting Ni2+ in NiO Li+ interstitials in e.g. NiO / Zr Y Li / Ni Li Electronic defects
Defect electrons in conduction band Electron holes in valence band e/ h i Krger-Vink notation also for elements of the ideal structure Cations, e.g. Mg2+ on normal Mg2+ sites in MgO Anions, e.g. O2- on normal site in any oxide Empty interstitial site
Mg x Mg O x O v x i Krger-Vink notation of dopants in elemental semiconductors, e.g. Si Si Silicon atom in silicon Boron atom (acceptor) in Si
Boron in Si ionised to B- Phosphorous atom (donor) in Si P Phosphorous in Si ionised to P+ P x Si x Si B / Si
B x Si Si Protonic defects Hydrogen ions, protons H+ , are naked nuclei, so small that they can not escape entrapment inside the electron cloud of other atoms or ions In oxidic environments, they will thus always be bonded to oxide ions O-H They can not substitute other cations In oxides, they will be defects that are
interstitial, but the interstitial position is not a normal one; it is inside an oxide ion. With this understanding, the notation of interstitial proton and substitutional hydroxide ion are equivalent. H i OH O Electroneutrality Electroneutrality One of the key points in defect chemistry is the ability to express electroneutrality in terms of the few defects and their effective
charges and to skip the real charges of all the normal structural elements positive charges = negative charges can be replaced by positive effective charges = negative effective charges positive effective charges - negative effective charges = 0 Electroneutrality The number of charges is counted over a volume element, and so we use the concentration of the defect species s multiplied with the number of charges z per defect z z[ s ] 0 s Example, oxide MO with oxygen vacancies, metal interstitials, and defect electrons: 2[v O ] 2[M i ] - [e / ] 0 or
2[v O ] 2[M i ] [e / ] If oxygen vacancies dominate over metal interstitals we can simplify: 2[v O ] [e / ] Note: These are not chemical reactions, they are mathematical relations and must be read as that. For instance, in the above: Are there two vacancies for each electron or vice versa? Stoichiometry and nonstoichiometry Stoichiometric compounds; intrinsic point defect disorders Schottky defects anti-Schottky defects
Cation vacancies and interstitials Anti- or anion-Frenkel defects Cation and anion interstitials (not common) Frenkel defects Cation and anion vacancies Anion vacancies and interstitials Anti-site defects Cation and anion swap (not common) Stoichiometric compounds: Intrinsic
electronic disorder Dominates in undoped semiconductors with moderate bandgaps Defect electrons and electron holes Nonstoichiometric compounds One point defect dominates, compensated by electronic defects. Examples for oxides: Metal deficient oxides, e.g. M1-xO
Metal excess oxides, e.g. M1+xO Metal interstitials are majority point defects, compensated by defect electrons Example: Cd1+xO Oxygen deficient oxides, e.g. MO2-y Metal vacancies are majority point defects, compensated by electron holes Examples: Co1-xO, Ni1-xO, and Fe1xO Oxygen vacancies are majority point defects, compensated by defect electrons Examples: ZrO2-y, CeO2-y Oxygen excess oxides, e.g. MO2+y
Oxygen interstitials are majority point defects, compensated by electron holes Example: UO2+y Extended defects Read about Defect associates Clusters Extended defects Shear structures
Infinitely adaptive structures (YZr v O ) in the text. They will not be much emphasised in this course. However, associates and clusters can be treated within the simple defect chemistry we will learn here, and thus be something you should know and understand Concluding remarks You should now have some insight into what defects are You know a nomenclature for them, with emphasis on effective charge
You know and can discuss some simple defect types and defect combinations of stoichiometric and non-stoichiometric compounds You can express electroneutrality conditions for given sets of defects The ionic model of bonding in compounds with formal oxidation numbers helps you to write and use defect chemistry You have gotten a brief insight or repetition of bonding, periodic properties of elements, electronic energy bands, and crystal structures to assist in the first steps of learning about defects and their nomenclature. Links (Google them ) Structures of Simple Inorganic Solids (Dr. S.J. Heyes, Oxford Univ. UK); Introduction, concepts, history, examples, illustrations, etc.
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