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This lecture
1. Brief description of oxide crystal structures (simple and complex)
a. Ionic radii and Pauling’s rulesb. Electrostatic valencec. Bond valence, and bond valence sums
Why do certain combinations of atoms take on specific structures?
2. Counting electrons and simple electronic structures (largely avoiding transition metals)
3. Trends in the transition metals
My bookshelf
H. D. Megaw
O. Muller & R. Roy
I. D. Brown
B. G. Hyde &S. Andersson
Software: ICSD + VESTA
Momma , Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Cryst. 44 (2011) 1272–1276. [doi:10.1107/S0021889811038970]
Crystal structures of simple oxides [containing a single cation site]
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Oxides versus sulfides: TiS2
2H–TiS2
van der Waals gap (unlikely in oxides or fluorides, but occurs frequently in hydroxides)
This is the CdI2 structure.
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Shannon-Prewitt effective ionic radii
Radii assigned by systematically examining cation-anion pairs in oxides, fluorides etc.
May not work for other kinds of compounds
Be sensitive to coordination number and spin state
www.mrl.ucsb.edu/~seshadri/Periodic/index.html
Ionic radii and Pauling’s first rule (the radius ratio rule)
In brief: The cation-anion distance is the sum of cation and anion radii, and the number of anions around a cation (the coordination number) is a function of the radius ratio. Exemplified by AO2 compounds below. MRR is the mimimum radius ratio.
Pauling, The Nature of the Chemical Bond, 3rd Edn.Cornell University Press, Ithaca 1960
Compound rC (A) rC + rO (A) rC/rO Coordination MRR
CO2 �0.19(?) 1.16 (exp.) ? 2
SiO2 0.26 1.61 0.19 4 0.225
TiO2 0.605 1.955 0.45 6 0.414
CeO2 0.97 2.32 0.72 8 0.732
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Electrostatic valence and bond valence: Parameters for Mn
Mn 2 O -2 1.790 0.37 aMn 2 O -2 1.765 0.37 jMn 2 S -2 2.22 0.37 eMn 2 F -1 1.698 0.37 aMn 2 Cl -1 2.133 0.37 aMn 2 Br -1 2.34 0.37 eMn 2 I -2 2.52 0.37 eMn 2 N -3 1.849 0.37 jMn 2 N -3 1.65 0.35 eMn 3 O -2 1.760 0.37 aMn 3 O -2 1.732 0.37 jMn 3 F -1 1.66 0.37 bMn 3 Cl -1 2.14 0.37 bMn 3 N -3 1.837 0.37 jMn 4 O -2 1.753 0.37 aMn 4 O -2 1.750 0.37 jMn 4 F -1 1.71 0.37 bMn 4 F -1 1.63 0.37 eMn 4 Cl -1 2.13 0.37 bMn 4 N -3 1.822 0.37 jMn 6 O -2 1.79 0.37 eMn 7 O -2 1.827 0.37 eMn 7 O -2 1.79 0.37 bMn 7 F -1 1.72 0.37 bMn 7 Cl -1 2.17 0.37 b
bvsparm.cif
Brown, Shannon, Empirical bond-strength-bond-length curves for oxides, Acta Cryst. A 29 (1973) 266–281
Crystal structures of some complex oxides [containing two or more cation sites]
The major ternary structural families (Muller and Roy, page 3, redrawn and modified)
A3BX5
Ternary structural families
others
A2BX4
ABX4
ABX3
CaCO3
Perovskite
Hexagonal ABX3 (eg. BaNiO3 in the CsCrBr3 structure)
Pyroxenes and related structures (eg. diopside CaMgSi2O6)
Corundum and related structures (eg. ilmenite FeTiO3)
Zircon (ZrSiO4)
Scheelite (CaWO4)
Barite (BaSO4)
Ordered SiO2 derivatives
Ordered rutile derivatives
K2NiF4 (m = 1 Ruddlesden-Popper)
b–K2SO4
Olivine (Mg2SiO4 and for eg. LiFePO4)
Spinel (MgAl2O4)
CaFe2O4
Phenacite (Be2SiO4)
ABX2 (eg. LiCoO2 and CuFeO2)
A2B2X7 (eg. pyrochloreY2Ti2O7)
A2BX5
A2BX6
not listed by Muller and Roy
Will discuss compounds in highlighted boxes: Characterized by dense connectivity.
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Ordered double perovskites (elpasolites)
Ba2MgWO6 Ca2MgWO6
Rock-salt like ordering of dissimilar octahedra. Space group same as rock-salt: Fm–3m
Smaller A-ions associated with tilting as in simple perovskites.
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Hexagonal ABO3 structures
BaNiO3 LiNbO3 (ferroelectric R3c)
Ferroelectric YMnO3 (“YAlO3”)
Unusual 5-fold coordination (trigonalbibyramid) of MnO5
Ordered rutiles (the trirutile)
CoTa2O6: 3×TiO2 = Ti3O6; 3×Ti4+ = Co2+ + 2×Ta5+
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Sc Ti V CrMn
IIFe III
CoII Ni Cu Zn Ga Ge
Rh Ag Cd Sn
Mg
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Co, Rh III Ag Cd Sn
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Li
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In
ions on the A site
ions on the B site
A,B Jahn-Teller active
A,B DiamagneticCo II High single-ion anisotropy
Spinel AB2O4
Some ABO2 structures: Highly dense in-plane, and frequently metallic
LiCoO2 (ordered rock-salt) 3R–CuFeO2 (delafossite)
111-ordered with alternating octahedral LiO6 and CoO6 stacking
BO2 (CdI2) slabs separated by two-coordinate atoms, usually Cu+ and Ag+. Also unusually, Pd1+ and Pt1+.
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Counting electrons
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Some “real” electronic structures: MoS2 a d2 semiconductor
MoS6 prisms allow a crystal-field gap between the filled dz2 and the rest of the d
states. Structure matters !
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Transition metal compounds: Trends in energetics and insulator-to-metal transitions
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