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Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Covalent and Metallic Bonding Chemistry for Earth Scientists, DM Sherman University of Bristol Failures of Ionic Model: Ionic radius of S-2 NaCl structure CaS is highly ionic. Cell constant 5.70 Å Ca+2 radius = 1.14 Å* S-2 radius = 1.71 Å PbS (Galena) has cell constant of 5.94 Å Bond length = ½ x cell constant Pb+2 radius = 1.33 Å* S-2 radius = 1.64 Å * from bond lengths in oxides (Shannon, 1976) Page 1 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Failure of Ionic Model: Structure of CaF2 (Fluorite) Ionic Radius Ion IV Ca+2 F- 1.17 VI VIII XII 1.14 1.26 1.48 1.19 Using Pauling’s first rule: RCa (VI)/RF(IV) = 0.97 RCa (VIII)/RF(IV) =1.07 Predict Ca in 12-fold coordination RCa (VIII)/RF(IV) =1.24 Ionic radius of Fderived from one ionic compound does not transfer to another. Failure of Ionic Model: Sulfide Structures Triolite/Pyrrhotite (FeS) Molybdenite (MoS2) Cinnabar (HgS) Mackinawite (FeS) Page 2 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Chemical bonding: ionic vs. covalent When electrons are completely transferred between atoms to yield cations and anions, the atoms will be held together by ionic bonds. If atoms have similar electronegativities, they adopt closed-shell configurations by sharing electrons with each other; the atoms are held together by covalent bonds. Covalent Bonds • • • • Formed between atoms of similar electronegativity. Atoms are held together by “sharing electrons”. Sulfide minerals. Most organic compounds. In anhydrite (CaSO4), the S-O bond in SO4-2 ions is very covalent. The Ca-O bond is ionic. Page 3 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Metallic Bond • Extreme example of covalent bond: electrons are delocalized throughout the crystal. • Formed between metal atoms of similar electronegativity and with weakly held electrons. • Can form between metal atoms in sulfide minerals. Mackinawite (FeS) has metallic Fe-Fe bonds between shared FeS4 tetrahedra. Chalcophiles, Lithophiles, Siderophiles.." Page 4 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Chemical Bonding: Theoretical Pictures" Ionic Approximation Localized electrons (+ Crystal Field Theory) MgO FeO, SiO2 Molecular Orbital Theory (Covalent Bonds) Delocalized electrons Band Theory (Metallic Bonds) FeS Molecular Orbital Theory" Linear Combination of Atomic Orbitals (LCAO) The quantum states of a molecule are molecular orbitals (ψi). These are constructed by taking linear combinations of atomic orbitals (φi) to yield bonding molecular orbitals ψ = c1φ1 + c2φ2 − + + + = − − + − and antibonding molecular orbitals € ψ = c1φ1 − c2φ2 − + - + − = + − + − € Page 5 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Molecular Orbital Theory: π vs σ bonds" − + − σ-antibonding + π-antibonding + − − + − + + − − + + + − − − + py px π-bonding + − − + σ-bonding Molecular Orbital Theory: Simple Diatomic Molecules" Page 6 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Molecular Orbital Theory of Si-O bond" Si Atomic Levels In quartz, the Si-O bond is partially covalent: electrons are shared by the O(2p) and Si(3p) orbitals. 3p O Atomic Levels 2p π σ Energy The “core” atomic orbitals (e.g., Si 1s, 2s, 2p and O 1s) are highly localized and do not participate in bonding; they retain their atomic character. σ* π* σ* 3s σ 2s 1s 2p 2s 1s Molecular orbitals involving ligand p-orbitals and metal d-orbitals" − + σ-antibonding (eg symmetry) − + + − + − + − + − σ-bonding (eg symmetry) − − + + − − + + − − + + − + + − − + − − + − + + π-antibonding (t2g symmetry) + − + − + − − + − π-bonding (t2g symmetry) − + + Page 7 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Electronic Structures of Fe-Mn Oxides The d-orbitals can be viewed as antibonding molecular orbitals. The crystal-field splitting results from σ- vs. πantibonding. Energy Bands in Solids Page 8 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Insulators, Metals and Semiconductors Semiconduction in Sulfides Sulfide minerals tend to be opaque because of the small bandgap Pyrite (FeS2) Galena (PbS) Sphalerite (ZnS) Chalcopyrite (CuFeS2) Triolite (FeS) Molybdenite (MoS2) Page 9 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Semiconduction in Sulfides The semiconducting properties of sulfides can be exploited using geophysical measurements of outcrop electrical resistivity (conductivity). Mineral Formula Conductivity (S/m) Pyrite FeS2 20 to 2 x 104 Chalcopyrite CuFeS2 1 x 104 Pyrrhotite Fe1-xS 1 x 105 Arsenopyrite FeAsS 3 x 103 Galena PbS 3 x 104 Copper Wire: Cu 5.9 x 107 The “Octet Rule” and Valence Shell Electron Pair Repulsion Theory This is a useful model for predicting the structures of covalent molecules. It is especially useful for molecules constructed of first-row atoms (e.g., N, C, O and F). • In a molecule, each atom contributes the electrons in its outer shell (n-quantum number) as “valence electrons. • The total valence electrons are then grouped into electron pairs. • The electron pairs are distributed in the molecule so that each atom is surrounded by 8 valence electrons (except for H, which only wants 2). Page 10 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 The “Octet Rule” and Valence Shell Electron Pair Repulsion Theory Example: the water molecule (H2O) Each H (1s1) contributes 1 valence electron. The O atom (1s22s22p4) contributes 6 valence electrons. The only way to distribute the valence electrons in the molecule is as follows: Note: each line represents a pair of electrons. Repulsion between electron pairs causes the bent geometry.. Summary • Covalent bonds form when ions of high charge (e.g., Si+4, S+6) bond with anions (O-2). • Bonds with S-2 tend to be covalent. • Metallic bonds may form when transition metal cations are in close proximity. • Molecular Orbital Theory is the complete picture of bonding that embraces ionic, covalent and metallic bonds. • VSEPR can be used to predict the structures of covalent molecules. Page 11 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Crystal Field Theory The d-orbitals: Recall the shapes of the atomic orbitals. The d-orbitals are unique: the xy,yz and xz orbitals do not have electron density along the x, y and z-axes. The z2 and x2-y2 orbitals, however, point along the x y and z-axes.. Crystal Field Theory Splitting of the d-orbital energies when surrounded by ligands: Δtet = 4/9Δoct Energy xy (2/5)Δtet xz (3/5)Δoct yz xy (3/5)Δtet x2-y2 z2 x2-y2 z2 xz yz x2-y2 z2 (2/5)Δoct xy xz yz Page 12 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Crystal Field Stabilization Energy (CFSE) d3 configuration: (Mn+4 or Cr+3) z2 Energy x2-y2 xy xz yz xy xz yz x2-y2 z2 z2 x2-y2 xy CFSE =(2/5)Δtet xz yz CFSE = (6/5)Δoct Octahedral site preference energy = (6/5-4/9*2/5)Δoct = 1.02Δoct Δoct = 200-300 kJ/mole Crystal Field Stabilization Energy (CFSE) d5 configuration: (Mn+2 or Fe+3) z2 Energy x2-y2 xy xz yz xy x2-y2 CFSE = 0 z2 xz yz x2-y2 z2 xy xz yz CFSE = 0 Octahedral site preference energy = (6/5-4/9*2/5)Δoct = 0Δoct Page 13 Chemistry for Earth Scientists DM Sherman, University of Bristol 2011/2012 Crystal Field Stabilization Energy (CFSE) d8 configuration: (Ni+2) z2 Energy x2-y2 xy xz yz xy x2-y2 z2 CFSE =(2/5)Δtet xz yz x2-y2 z2 xy xz yz CFSE = (6/5)Δoct Octahedral site preference energy = (6/5-4/9*2/5)Δoct = 1.02Δoct Δoct = 200-300 kJ/mole Page 14