Lone Pairs in the Solid State
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1 Lone Pairs in the Solid State Ram Seshadri Materials Department, Department of Chemistry & Biochemistry Materials Research Laboratory University of California, Santa Barbara CA Contributors: Guido Baldinozzi (ECP), Claudia Felser (Uni-Mainz), Brent Melot, Katharine Page, Nicola Spaldin (UCSB), Gavin Lawes (Wayne State), A. P. Ramirez (Lucent), P. M. Woodward (Ohio-State), P. S. Halasyamani (Houston), Umesh Waghmare (JNCASR), Karin Rabe (Rutgers), Craig Fennie (Argonne) Funding from the National Science Foundation [Career, CBC]
2 Molecular shape The shapes of molecules: van t Hoff (1874): CH 4 tetrahedron Werner (1893): Pt(NH 3 ) 2 Cl 2 planar Lewis (1915): Electron pairs and octets Sidgwick and Powell (1940): Foundations of Valence Shell Electron Pair Repulsion theory Bonding pairs and lone pairs are of equal importance and these distribute themselves to minimize interelectron repulsion Problems, for example, with the deviation from tetrahedral angles in H 2 O and NH 3 Proc. R. Soc. London A 176 (1940) 153
3 VSEPR Gillespie and Nyholm (1957): (1) that a lone pair repels electron pairs more than a bonding pair of electrons, (2) that a double bond repels other bonds more than a single bond; (3)... The tendency of the electrons pairs in a valency shell to keep apart is mainly due to the exclusion principle. Problems: Fails for XeO 3 Quart. Rev. Chem. Soc. 11 (1957) 339
4 Hyde and Andersson, Inorganic Crystal Structures, Wiley (1988): In many crystalline solids with cation-centered lone pairs, the lone pair occupies the same volume as an oxide or fluoride ion. However the cation-lone pair distance (in Å) is much shorter than the cation-anion distance: The solid state d 10 4s 2 Ga 0.95 Ge 1.05 As 1.26 Se 1.22 Br d 10 5s 2 In 0.86 Sn 0.95 Sb 1.06 Te 1.25 I 1.23 Xe d 10 6s 2 Tl 0.69 Pb 0.86 Bi 0.98 Po 1.06 Polyhedra of anions and lone pairs must have off-centric cations.
5 Andersson & Galy vs. Gillespie & Nyholm Traditional view Modified/corrected
6 Why is this important? Cation-centered lone pairs (often with Pb 2+ as the central cation, but also Sn 2+ and Bi 3+ ) are tremendously important for applications requiring off-centered polyhedra and their associated dipoles: Ferroelectric and piezoelectric materials, actuators Multiferroic materials Non-linear optical materials Ionic conductors High-refractive index materials (lead crystal) Semiconductor/semimetal to insulator transitions Phosphors (?)
7 This talk Density Functional calculations of the electronic structure of crystals, combined with special tools for visualization of lone pairs: What constitutes a lone pair? When are lone pairs stereochemically active? Lone pairs and inert pairs What is the cooperative behavior of lone pairs? Can lone pairs be used to design polar polyhedra? Can lone pairs be frustrated? DFT: Stuttgart TB-LMTO-ASA program [O. K. Andersen, O. Jepsen etc.] Electron localization functions (ELFs): An orbital independent measure of electron localization based on the pair probability of electrons. A. D. Becke and K. E. Edgecombe J. Chem. Phys. 92 (1990) 5397
8 The ELF with and -PbO BiOF B. Silvi and A. Savin, Nature 371 (1994) 683. J.-M. Raulot, G. Baldinozzi, R. Seshadri, and P. Cortona, Solid State Sciences 4 (2002) 467; R. Seshadri, Proc. Indian Acad. Sci. (Chem. Sci.) 113 (2001) 487.
9 NH 3 Electron density decorated by the ELF
10 XeO 3 Three-coordinate Xe, is described by Sten Andersson as being Xe outside a trigonal prism.
11 What is the composition of the lone pair? Orgel (1959): The lone pair cannot have purely s character when it is stereochemically active; it must admix with p. Bersuker (1984): Filled anion p states must play a role. anion p filled cation s & p empty typical oxide (BaO) cation s filled anion p filled cation p empty lone pair oxide (PbO) energy
12 What is the composition of the lone pair? A lone pair sorted structural field (IV-VI semiconductors): S Se Te massicot Ge GeS GeSe GeTe Sn SnS SnSe SnTe Pb PbS PbSe PbTe arsenic U. Waghmare, N. A. Spaldin, H. C. Kandpal, and R. Seshadri, Phys. Rev. B. 67 (2003) rock salt
13 What is the composition of the lone pair? Electronic structure of cubic AQ S Se Te Ge GeS GeSe GeTe Sn SnS SnSe SnTe Pb PbS PbSe PbTe When the lone pair is stereochemically active (as in GeS), cation s states are broader and are better mixed with anion p states. The mixing is intermediated by empty cation p. Cation s states are narrow and largely unmixed with anion p in cases when the lone pair is not stereochemically active (Cf. the inert pair effect).
14 Cooperative behavior The expression of cooperative stereochemical activity of the lone pair plays an important role in the development of polar behavior. PbTiO 3 above 766 K Pm-3m PbTiO 3 below 766 K P4mm Seshadri, Proc. Indian Acad. Sci. (Chem. Sci.) 113 (2001) 487. Even above the phase transition, the Pb 2+ ion (in Pb 2 NbYbO 6 ) is not really where it is supposed to be. Baldinozzi, Raulot, Seshadri, MRS Symp. Proc. 718 (2002) D
15 Lone pair cooperativity Octahedral rotations coupled with lone pair activity make PbZrO 3 antiferrodistortive (antipolar). PbZrO 3 below 503 K Pbam R. Seshadri, Proc. Indian Acad. Sci. (Chem. Sci.) 113 (2001) 487.
16 Lone pair cooperativity Pb 2 MnWO 6 Cubic paraelectric 445 K Orthorhombic antiferroelectric Pb 2 CoWO 6 Cubic paraelectric 300 K Incommensurate antiferroelectric 230 K Ferroelectric Pb 2 MgWO 6 Lone pair & d 0 SOJT distortions strongly coupled Pb 2 YbNbO 6
17 Multiferroics ABO 3 perovskites where A is lone pair active and is associated with ferroelectricity, while B is magnetic and associated with ferromagnetism BiMnO 3 : T. Atou, H. Chiba, K. Ohoyama, Y. Yamaguchi, and Y. Syono, J. Solid State Chem. 145 (1999) 639; R. Seshadri and N. A. Hill, Chem. Mater. 13 (2001) 2829.
18 Multiferroics Structural relaxation (DFT-LDA and DFT-LDA+U) indicates that the polar structure is actually not stable for BiMnO 3. P. Baettig, R. Seshadri and N. A. Spaldin, J. Am. Chem. Soc. 129 (2007) C2/c C2
19 Lone pairs and d 0 ions
20 Lone Pairs: Constitution; Sn 2+ vs. Pb 2+ vs. Bi 3+ in ternary systems Interactions that drive lone pair activity in more complex (than binary) systems: What are the periodic trends in lone pair activity? What is the cooperative/competitive nature of A O M networks? Experiments and calculations on ternary compounds: lone pair + d 0 + oxygen Scheelite (I4 1 /a) type -SnWO 4 (P213) Zircon (I4 1 /amd) type PbWO 4 (inactive) SnWO 4 (active) BiVO 4 (active) Why are these structures so different? -SnWO4 is quite unique.
21 Lone Pairs: Constitution; Sn 2+ vs. Pb 2+ vs. Bi 3+ in ternary systems E g = 2.9 ev cation s anion p antibonding cation s anion p bonding -10 With Sn 2+ there is hybridization and covalency between the Sn 6s, Sn 6p and O 2p orbitals. This leads to a highly stereoactive, localized lone pair. Pb 2+ in PbWO 4 does no show these features no lone pair activity ( inert ).
22 Lone Pairs: Constitution; Sn 2+ vs. Pb 2+ vs. Bi 3+ in ternary systems The differences arise because of energy levels are distinct (5s vs. 6s) and because of differences in charge: 2+ vs. 3+. In addition, how strongly oxygen bonds the second cation. Pb 2+ inert Sn 2+ covalent s and p Bi 3+ inert s and covalent p cation p anion p cation s M. W. Stoltzfus, P. M. Woodward, R. Seshadri, J.-H. Klepeis, and B. Bursten, Inorg. Chem. 46 (2007) 3839.
23 Lone pair frustration in pyrochlores: Charge ice The cubic (Fd-3m) structure of pyrochlore (CaNa)Nb 2 O 6 F [A 2 B 2 O 7 or A 2 B 2 O 6 O ] The A site often has lone-pair cations (Pb 2+ or Bi 3+ ). Polar materials in this structure type are rare however.
24 Lone pair frustration in pyrochlores: Charge ice (Bi 1.5 Zn 0.5 )(Zn 0.5 Nb 1.5 )O 7 (BZN) Cubic pyrochlore structure Non-ferroelectric Electric field tunable permittivity 1 MHz The large tunability and the low dielectric losses make BZN of potential interest for microwave tunable capacitor applications Levin et al., J. Solid State Chem. 168 (2002) 69. Q ~ 2000 (tan ~ ) ~ 180 Tunability: 55 % Why is there no phase transition? Lu, Stemmer, Appl. Phys. Lett. 83 (2003) 2411.
25 Lone pair frustration in pyrochlores: Charge ice Question : Is the absence of a phase transition related to the frustrated topology of the pyrochlore lattice? Is BZN a manifestation of charge ice? Pyrochlore Bi 2 Ti 2 O 6 O is cubic till 2 K: Hector, Wiggin, J. Solid State Chem. 177 (2004) 139. The Bi 2 O network in Bi 2 Ti 2 O 6 O, and the associated lone pair ELFs Seshadri, Solid State Sci. 8 (2006) 259.
26 Lone pair frustration in pyrochlores: Charge ice Other Bi compounds are not shy about transforming. Aurivillius phase SrBi 2 Ta 2 O 9 (SBT):
27 Lone pair frustration in pyrochlores: Charge ice The A atom network of connected A 4 tetrahedra in A 2 B 2 O 7 is frustrated with respect to certain kinds of magnetic ordering. Similarities with the crystal structure of ice I h : the notion of spin ice. Bramwell, Gingras, Science 294 (2001) ice spin ice
28 Lone pair frustration in pyrochlores: Charge ice The precise analogy with ice: Bernal-Fowler (1933) Ice rules Oxygens in ice-i h form a wurtzite (tetrahedral) lattice, with an O-O distance of 2.76 Å The 0.95 Å OH bond of H 2 O is retained in ice-i h Each oxygen must have two H at 0.95 Å and two at 1.81 Å, but which two?
29 Lone pair frustration in pyrochlores: Charge ice Pauling (1935): Ice-I h has residual entropy 16, 4-vertex models:
30 Lone pair frustration in pyrochlores: Charge ice Pauling (1935): Ice-I h has residual entropy 6 ways of arranging H around O so that ice rules are obeyed. Each bond has a 1/2 probability that the proton is is in an aceptable position. S = k B lnw and W = (6)(1/2)(1/2) = 3/2 calculated: 0.80 cal/k/mol measured: 0.82 cal/k/mol
![Lone pair frustration in pyrochlores: Charge ice Pb 2 Sn 2 O 6 : An ice analog [Pb 2 Sn 2 O 6 : Pb 2 is similar to H 2 O] lead-tin](/docs-images/73/69223246/images/31-2.jpg "yellow Morgenstern-Badarau, Michel, Ann. Chim. 6 (1971) 109. The Pb 2+ are like H in H 2 O. In which direction should they distort?")
31 Lone pair frustration in pyrochlores: Charge ice Pb 2 Sn 2 O 6 : An ice analog [Pb 2 Sn 2 O 6 : Pb 2 is similar to H 2 O] lead-tin yellow Morgenstern-Badarau, Michel, Ann. Chim. 6 (1971) 109. The Pb 2+ are like H in H 2 O. In which direction should they distort?
32 Lone pair frustration in pyrochlores: Charge ice Understanding structural details through neutron diffraction: Bi 1.5 Zn 0.5 B 1.5 Zn 0.5 O 7 [B = Nb (BZN); Ta (BZT); Sb (BZS)]
33 Lone pair frustration in pyrochlores: Charge ice O Bi 4 units show considerable disordering: incoherent displacements Melot, Rodriguez, Proffen, Hayward, Seshadri, Mater. Res. Bull. 41 (2006) 961; Levin et al. J. Solid State Chem. 168 (2002) 69.
34 Lone pair frustration in pyrochlores: Charge ice Ideal ordered supercell RMC structure Bi 1.5 ZnNb 1.5 O 7 : Incoherent displacements associated with the lone pair active Bi 3+ can be followed using real-space neutron techniques (NPDF, Los Alamos).
35 Lone pair frustration in pyrochlores: Charge ice Bi 2 Ti 2 O 7 : Compute instabilities calculations by Craig Fennie and Karin Rabe (Rutgers) suggest that it is potentially a ferroelectric with P ~ 40 μc/cm 2.
36 Lone pair frustration in pyrochlores: Charge ice What do the ferroelectric distortions in the Cm stucture look like? (a) Cubic (b) Cm Metrically still pseudocubic
37 Lone pair frustration in pyrochlores: Charge ice Dy 2 Ti 2 O 7 The residual entropy: Ramirez, Hayashi, Cava, Siddharthan, Shastry, Nature 294 (2001) 1495.
38 Lone pair frustration in pyrochlores: Charge ice Negative thermal expansion in ZrW 2 O 8 : An underconstrained system Mary, Evans, Vogt, Sleight, Science 272 (1996) 90.
39 Lone pair frustration in pyrochlores: Charge ice ZrW 2 O 8 Low frequency Einstein mode that characterizes the underconstrained degrees of freedom Ramirez, Kowach, Phys. Rev. Lett. 80 (1998) 4903.
40 Lone pair frustration in pyrochlores: Charge ice Bi 2 Ti 2 O 7 does indeed have signatures in the heat capacity that suggest local low energy modes that do not freeze out.
41 Lone pair frustration in pyrochlores: Charge ice Y 2 Ti 2 O 7 does not have these modes.
42 Lone pair frustration in pyrochlores: Charge ice Conclusions: Increasing evidence for the validity of idea that local coöperativity of off-centering can be frustrated by lattice geometry. Possibly a way of designing new high-k materials without phase transitions. Na 6 PbO 4
43 Lone pair frustration in pyrochlores: Charge ice One macroscopic consequence: High authority actuation using kagomé lattices. This paper shows that repetitive, infinite structures cannot be simultaneously statically, and kinematically, determinate.
The solid state. Ga Ge As Se Br d 10 4s 2. Sn Xe 1.49 I Sb Te In d 10 5s 2. Pb 0.
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