KJM5120 and KJM9120 Defects and Reactions - folk.uio.no

KJM5120 and KJM9120 Defects and Reactions - folk.uio.no

Defect chemistry a general introduction Truls Norby 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 Brief history of structure, stoichiometry, and 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! Understanding that external geometry often reflected atomic structure. Perfectness ruled. Non-stoichiometry was out. Intermetallic compounds forced re-acceptance of non-stoichiometry. But real understanding of defect chemistry of compounds is less than 100 years old. Perfect structure Our course in defects

takes the perfect structure as starting point. This can be seen as the ideally defect-free interior of a single crystal or large crystallite grain at 0 K. Close-packing Metallic or ionic compounds can often be regarded as a closepacking of spheres In ionic compounds, this is most often a closepacking of anions (and sometimes large cations) with the smaller cations in

interstices Some simple classes of oxide structures with close-packed oxide ion sublattices Formula Cation:anion coordination Type and number of occupied interstices fcc of anions hcp of anions MO 6:6 1/1 of octahedral

sites NaCl, MgO, CaO, CoO, NiO, FeO a.o. FeS, NiS MO 4:4 1/2 of tetrahedral sites Zinc blende: ZnS Wurtzite: ZnS, BeO, ZnO M2O 8:4 1/1 of tetrahedral sites

occupied Anti-fluorite: Li2O, Na2O a.o. M2O3, ABO3 6:4 2/3 of octahedral sites Corundum: Al2O3, Fe2O3, Cr2O3 a.o. Ilmenite: FeTiO3 MO2 6:3 of octahedral sites

Rutile: TiO2, SnO2 AB2O4 1/8 of tetrahedral and 1/2 of octahedral sites Spinel: MgAl2O4 Inverse spinel: Fe3O4 The perovskite structure ABX3 Close-packing of large A and X Small B in octahedral interstices

Alternative (and misleading?) representation We shall use 2-dimensional structures for our schematic representations of defects Elemental solid Ionic compound Defects in an elemental solid From A. Almar-Nss: Metalliske materialer. Defects in an ionic compound Defect classes

Electrons (conduction band) and electron holes (valence band) 0-dimensional defects 1-dimensional defects Dislocations 2-dimensional defects

point defects defect clusters valence defects (localised electronic defects) Defect planes Grain boundaries (often row of dislocations) 3-dimensional defects Secondary phase Perfect vs defective structure Perfect structure (ideally exists only at 0 K) No mass transport or ionic conductivity No electronic conductivity in ionic materials and semiconductors;

Defects introduce mass transport and electronic transport; diffusion, conductivity New electrical, optical, magnetic, mechanical properties Defect-dependent properties Point defects intrinsic disorder Point defects (instrinsic disorder) form spontaneously at T > 0 K 1- and 2-dimensional defects do

not form spontaneously Caused by Gibbs energy gain as a result of increased entropy Equilibrium is a result of the balance between entropy gain and enthalpy cost Entropy not high enough. Single crystal is the ultimate equilibrium state of all crystalline materials Polycrystalline, deformed, impure/ doped materials is a result of extrinsic action Defect formation and equilibrium Free energy vs number n of defects

Hn = nH Sn = nSvib + Sconf G = nH - TnSvib - TSconf For n vacancies in an elemental solid: EE = E E + v E K = [vE] = n/(N+n) Sconf = k lnP = k ln[(N+n)!/(N!n!)] For large x: Stirling: lnx! xlnx - x Equilibrium at dG/dn = 0 = H - TSvib - kT ln[(N+n)/n] = 0 n/(N+n) = K = exp(Svib/k - H/kT) Krger-Vink notation for 0-dimensional defects Point defects

Electronic defects Vacancies Interstitials Substitutional defects Delocalised electrons electron holes Valence defects Trapped electrons Trapped holes Cluster/associated defects Krger-Vink-notation

A c s A = chemical species or v (vacancy) s = site; lattice position or i (interstitial) c = charge Effective charge = Real charge on site minus charge site would have in perfect lattice Notation for effective charge: positive / negative x neutral (optional) Perfect lattice of MX, e.g. ZnO

Zn Zn O 2 Zn x Zn 2O O x O vi v x i Vacancies and interstitials

v // Zn Zn v i O O // i Electronic defects e /

Zn h Zn O / Zn Zn O Foreign species Ag Ga N

/ Zn Zn / O F O Li i Protons and other hydrogen defects H+ H H-

H i OH O (OH)O OH i/ (2(OH)) H ix H O x MO2 How can we apply integer charges when the material is not fully ionic? v

O The extension of the effective charge may be larger than the defect itself (4M M v O ) much larger. (4M M 4O O v O ) but when it moves, an integer number of electrons also move, thus making the use of the simple defect and integer charges reasonable (4M M 4O O v O ) v

O Defects are donors and acceptors E H i Ec v Ox Ga Zn Ag / Zn v O v

x Zn v O v /Zn v //Zn Ev Defect chemical reactions Example: Formation of cation Frenkel defect pair: Zn xZn v ix v //Zn Zn i Defect chemical reactions must obey three rules: Mass balance: Conservation of mass Charge balance: Conservation of charge

Site ratio balance: Conservation of host structure Defect chemical reactions obey the mass action law Example: Formation of cation Frenkel defect pair: Zn xZn v ix v //Zn Zn i KF av // aZn Zn i aZn x av x Zn KF i av // aZn

Zn i aZn x av x Zn i [v //Zn ] [Zn i ] [v //Zn ][Zn i ] [Zn] [i] // [v ][Zn Zn i ] x x x

x [Zn Zn ] [v i ] [Zn Zn ][v i ] [Zn] [i] 0 SS vib SG 0 H 0 [v ][Zn ] exp exp exp RT R RT // Zn i Notes on mass action law

The standard state is that the site fraction of the defect is 1 Standard entropy and enthalpy changes refer to full site occupancies. This is an unrealisable situation. Ideally diluted solutions often assumed Note: The standard entropy change is a change in the vibrational entropy not the configurational. KF av // aZn Zn i

aZn x av x Zn i 0 0 0 SS SG H [v //Zn ][Zn i ] exp exp vib exp RT R RT Electroneutrality The numbers or concentrations of positive and

negative charges cancel, e.g. 2[v //Zn ] 2[Oi// ] [Ag /Zn ] [N O/ ] [e / ] 2[Zni ] 2[vO ] [Ga Zn ] [OHO ] [h ] Often employ simplified, limiting electroneutrality condition: 2[v //Zn ] 2[Zni ] or [v //Zn ] [Zni ] Note: The electroneutrality is a mathematical expression, not a chemical reaction. The coefficients thus dont say how many you get, but how much each weighs in terms of charge. Site balances Expresses that more than one species fight over the same site:

[OOx ] [vO ] [OH O ] [O] ( 1 in ZnO ) Also this is a mathematical expression, not a chemical reaction. Defect structure; Defect concentrations The defect concentrations can now be found by combining Electroneutrality Mass and site balances

Equilibrium mass action coefficients Two defects (limiting case) and subsequently for minority defects or three or more defects simultaneously Brouwer diagrams More exact solutions these are the themes for the subsequent lectures and exercises

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