rocksalt_rutile_lect25

rocksalt_rutile_lect25 - Transition Metal Oxides Rock Salt...

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Unformatted text preview: Transition Metal Oxides Rock Salt and Rutile: Metal-Metal Bonding Chemistry 754 Solid State Chemistry Lecture #25 May 27, 2003 Chemistry 754 - Solid State Chemistry Rock Salt and Rutile: Structure & Properties Octahedral Molecular Orbital Diagram Rock Salt *(t2g) and *(eg) Bands *(e M-M Interactions Properties 3d Transition Metal Monoxides Magnetic Superexchange Rutile *(t2g) Bands, t and t Properties MO2 (M=Ti, V, Cr, Mo, W, Ru) Ru) Double Exchange in CrO2 Chemistry 754 - Solid State Chemistry 1 Rock Salt Crystal Structure M O y x Chemistry 754 - Solid State Chemistry Generic Octahedral MO Diagram t1u ( + ) a1g ( ) (n+1)p (n+1)s nd eg (dx2-y2, dz2) (n+1)d t2g (dxy, dxz, dyz) t1g & t2u Oxygen ) eg ( ) t2g ( O 2p (6) - t2g, t1u O 2p NB (6)-t1g, t2u t2g () O 2p (6) a1g, t1u, eg Transition Metal eg () t1u ( + ) a1g () Chemistry 754 - Solid State Chemistry 2 Simplified Band Structure (n+1)p [4] Bands of interest (n+1)s nd eg (dx2-y2, dz2) (n+1)d t2g (dxy, dxz, dyz) M-O [2] M-O [3] Oxygen O 2p (12) O 2p NB Transition Metal M-O M-O O 2p (6) a1g, t1u, eg Chemistry 754 - Solid State Chemistry 3d Transition Metal Monoxides Compound TiO (d2) VO (d ) MnO (d ) FeO (d ) CoO (d ) NiO (d ) 8 7 6 5 3 M-M Distance 2.94 2.89 3.14 3.03 3.01 2.95 Electrical Properties Metallic Intermediate Semiconductor Magnetic Properties Pauli Paramagnetic Intermediate AFM TN = 122 K Semiconductor AFM TN = 198 K Semiconductor AFM TN = 293 K Semiconductor AFM TN = 523 K AFM = Antiferromagnetic How can we understand this behavior? Metallic conductivity for a fairly ionic Ti2+-O2- bond? Semiconducting behavior for partially filled bands? Chemistry 754 - Solid State Chemistry 3 point (kx=ky=kz=0) Orbital Overlap in the t2g Band M M M M M M-O nonbonding point (kx=ky=/a, kz=0) M M M M M M-M bonding Band Runs Uphill from M-O antibonding M-M nonbonding Chemistry 754 - Solid State Chemistry point (kx=ky=kz=0) Orbital Overlap in the eg Band M M M M M M-O nonbonding point (kx=ky=/a, kz=0) M M M M M Band Runs Uphill from M-O antibonding Chemistry 754 - Solid State Chemistry 4 Band Structure Calculations 25 SrTiO3 25 TiO Energy (vs. O 2s) 20 20 15 15 10 X R M R 10 20 10 X R M R 10 20 k DOS (e/eV) k DOS (e/eV) The eg * band is more narrow in TiO because the Ti-O distance is considerably Tilonger and the overlap is smaller. The t2g * band is also slightly more narrow in TiO, except for near the -point, TiO, where Ti-Ti bonding lowers the energy and widens the band. Chemistry Chemistry 754 - Solid State Ti- Magnetic Structure MnO, FeO, CoO and NiO are all antiferromagnets MnO, FeO, with the structure shown below (for MnO). MnO). = eg t2g eg t2g = O Mn A F M The electrons align themselves in an antiparallel fashion due to AFM superexchange interactions arising primarily from the filled eg orbitals. The magnetic ordering temperature increases from Mn orbitals. Fe Co Ni due to increasing covalency (see Magnetism lecture). The magnetic ordering has implications for the electronic transport transport Chemistry 754 - Solid State Chemistry properties. 5 Mott-Hubbard Insulators The AFM coupling of ions is shown for FeO. The filled eg orbitals FeO. O stabilize AFM coupling. Notice that there is no mechanism for the eg eg minority spin electrons (shown in red) to move from one Fe ion to the t2g next without undergoing a spin flip t2g (the t2g orbitals of the same spin are occupied). eg eg Consequently the AFM coupling of ions forces a localization of the t2g t2g t2g electrons, even in the absence of a filled or completely filled band. This M-O-M Interaction is AFM () () is essentially the opposite of doubledoublewhen both TM have 1/2 filled exchange. Such compounds are configurations (d5-d5 or d3-d3) called Mott-Hubbard insulators. Mott- Fe Fe Chemistry 754 - Solid State Chemistry Rutile Crystal Structure z y x Chemistry 754 - Solid State Chemistry 6 MO2 with the Rutile Structure Compound TiO2 (d0) VO2 (d1) T>340K 1 M-M Distance 2.96 2.88 Electrical Properties Semiconductor Metallic Semiconductor Metallic Metallic Metallic Magnetic Properties Diamagnetic Paramagnetic Diamagnetic Ferromagnetic TC = 398 K Pauli Paramagnetic Pauli Paramagnetic VO2 (d ) T<340K 2.65;3.12 CrO2 (d2) MoO2 (d 2) RuO2 (d4) 3.14 2.52;3.10 3.14 Chemistry 754 - Solid State Chemistry c/a Ratio in Rutile-Type Oxides VO2 (T > 340K) Metallic V-V Even Spacing VO2 (T < 340K) Metallic V-V Alternating CrO2 Metallic Cr-Cr Even Spacing Cr- RuO2 Metallic Ru-Ru Even Spacing Ru- MoO2 Metallic Mo-Mo Alternating Mo- Chemistry 754 - Solid State Chemistry 7 M-M Overlap in the t2g Band point kx=0 ky=0 kz=0 0 M M M M-M bonding M M M M-M antibonding M M M M-M bonding M M M M-M bonding M M M M-M antibonding point kx=0 ky=0 kz=/a M M M M-M antibonding Chemistry 754 - Solid State Chemistry Combined M-O & M-M Effects The M-O * and M-M bonding interactions both make a MMcontribution to the t2g band. The M-O * interactions are dominant, but the M-M MMinteractions preturb the picture. The M-M & interactions Mare of minimal importance. As we fill up the t2g band we can roughly think of the following picture in terms of M-M bonding strength. MEF M-O M-M d6 TM Ion M-M d5 TM Ion M-M / M-M d2 TM Ion M-M d1 TM Ion DOS M-O * ~ M-M > M-M > M-M - Solid State Chemistry Chemistry 754 8 Tetragonal Structure (TiO2,CrO2,RuO2) Delocalized Electrons M-O [4] + M-M d eg M-O [2] + M-M d t2g Transition Metal EF RuO2 EF CrO2 EF VO2 EF TiO2 Oxygen 2p O 2p NB M-O M-O Z = 2 (M2O4) Chemistry 754 - Solid State Chemistry Band Structure Calculations 25 25 Energy (vs. O 2s) 20 20 15 15 10 X R M R 12 10 Z M Z R X 12 k DOS (e/eV) k DOS (e/eV) SrTiO3 TiO2 Chemistry 754 - Solid State Chemistry 9 Calculated Band Structure (Tetragonal, Z=2) 25 TiO2 25 VO2 25 CrO2 Energy (vs. O 2s) 20 20 20 15 15 15 10 Z M Z R X 10 Z M Z R X 10 Z M Z R X k Chemistry 754 - Solid State Chemistry Density of States (Tetragonal Structure) 25 TiO2 25 VO2 25 CrO2 Energy (vs. O 2s) 20 20 20 15 15 15 10 4 8 12 10 4 8 12 10 4 8 12 DOS (electrons/eV) Chemistry 754 - Solid State Chemistry 10 TiO2 Tetragonal Z=2 MoO2 Monoclinic Z=4 M M M M point a M M M M a M M a M M Bonding M-M Short=Bonding M-M Long=Bonding M M M-M Short=AB M-M Long=AB M M point a M M M M a M M a M M Antibonding M-M Short=Bonding M-M Short=AB M-M Long=AB M M Long=Bonding Chemistry 754-- Solid State Chemistry Pierls Distortion The dimerization which occurs in the rutile structure and it's effects on the band structure are similar to the Pierls distortion we discussed for a 1D chain of Hydrogen atoms, except that it occurs on top of the M-O * interactions. M- a E EF a E EF a a 0 a a 0 k /a k /a Chemistry 754 - Solid State Chemistry 11 Monoclinic Structure (VO2,MoO2) Delocalized Electrons M-O Antibonding d eg M-O [8] M-M [2] M-O [8] M-M [2] d t2g Localized Electrons M-M Bonding EF MoO2 EF VO2 O 2p NB M-O M-O Oxygen 2p Z = 4 (M4O8) Chemistry 754 - Solid State Chemistry Tetragonal (Z=2) 25 25 CrO2 Monoclinic (Z=4) MoO2 Energy (vs. O 2s) 20 20 Mo-O Mo-Mo 15 15 10 Z M Z R X 13 10 Z Y C 13 k DOS (e/eV) k DOS (e/eV) Chemistry 754 - Solid State Chemistry 12 CrO2 and RuO2 Why are alternating long-short M-M contacts, indicative of longMMetal-Metal bonding not observed in CrO2 and RuO2. The Metalelectron count suggests that the M-M levels should be full Mand the M-M * levels empty? MThere is a competition between localized M-M bonding (prefers Mdimers) and delocalized electronic transport in the M-O * band dimers) M(prefers equal spacing). Favors delocalized transport in the M-O * Mband Dominant in CrO2 (poor overlap) RuO2 (electron count) Favors M-M bonding Mand localized e- VO2 Intermediate Dominant in MoO2 Chemistry 754 - Solid State Chemistry CrO2 is ferromagnetic. A property which leads to it's use in magnetic magnetic cassette tapes. What stabilizes the ferromagnetic state? Double Exchange M M M M M M t* t|| Ferromagnetic: Delocalized transport of t* electrons allowed. allowed. t* Localized t|| electrons No M-M Bonding MDelocalized t2g electrons * t|| Antiferromagnetic: Delocalized Antiferromagnetic: transport violates Hund's Rule. Rule. Localized t|| electrons polarize itinerant (delocalized) t2g * (delocalized) electrons. Magnetism and conductivity754 - Solid State Chemistry Chemistry are correlated. 13 ...
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This note was uploaded on 06/11/2011 for the course CHEM 101 taught by Professor Stegemiller during the Spring '07 term at Ohio State.

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