Structures of Solids. Unit Cells - Not(?) Chapter 4 Ionic and Other Inorganic Solids. CHEM 462 Wednesday, September 22 T.

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Chapter 4 Ionic and Other Inorganic Solids CHEM 462 Wednesday, September 22 T. Hughbanks Structures of Solids Many dense solids are described in terms of packing of atoms or ions.

1 Chapter 4 Ionic and Other Inorganic Solids CHEM 462 Wednesday, September 22 T. Hughbanks Structures of Solids Many dense solids are described in terms of packing of atoms or ions. Although these geometric descriptions are often used and can appears as though solids are assembled from atomic marbles, the forces and physical laws that govern solid state structure and molecular structure are exactly the same. These are just useful ways to visualize and classify structures. See the class web site for longer animations. Also useful: Unit Cells - Not(?) Fig. 2.1 (p. 36) Text describes the shaded areas as unit cells. Are either of them really unit cells? Can you offer a better choice?

How many atoms are in the unit cell of an hcp element?

2 Graphite - Unit Cell Concepts See class web site for this animation Hexagonal ose Packing - Unit Cell All crystals are built up from units that are repeated throughout their structures, known as the unit cell. How many atoms are in the unit cell of an hcp element? Cubic ose Packing = Face-Centered Cubic The ABC stacking sequence generates packing of atoms with cubic symmetry. When viewed from the perspective of the cube, the cube is seen to have an atom in every face (facecentered cubic).

See class web site for this animation Body

3 See class web site for this animation Body Centered Cubic The third common dense metal structure is bodycentered cubic (bcc). This is not a close packing, but is nearly as dense. Each atom has 8 nearest neighbors and 6 only ~15% further away. Filling Holes in ose Packings ose-packed arrays possess an equal number of octahedral holes and twice as many tetrahedral holes.

Rocksalt () type: ccp stacked ; all octahedral holes filled Zinc-Blende (sphalerite, ZnS) Type ZnS (zinc-blende) is described as fcc arrays of S 2 ions with half the

4 Rocksalt () type: ccp stacked ; all octahedral holes filled Zinc-Blende (sphalerite, ZnS) Type ZnS (zinc-blende) is described as fcc arrays of S 2 ions with half the tetrahedral holes filled with Zn 2+ cations. antistructures have cation and anion positions (and compositions) swapped. ZnS is its own antistructure. Zinc-Blende = heteroatomic diamond

5 Flourite (CaF 2 ) Type CaF 2 (fluorite) is described as an fcc array of Ca 2+ ions with all tetrahedral holes filled with F anions. antistructures have cation and anion positions (and compositions) swapped. Li 2 O has an antifluorite structure. CdI 2 -type: hcp stacked I; half-filled octahedral coordination hole geometry: octahedral B A B A Cd 2 -type: ccp stacked ; half-filled CdI 2 BiI 3 -type: hcp stacked I; 1/3 rd -filled BiI 3 = BiI 6/2 Layers in BiI 3 (AB) and Cr 3 (ABC)

6 BiI 3 -type: ball & stick view Interpreting Polyhedral Pictures X = M = MX 6 = MoS 2 -type: Trigonal prismatic Mo C C trigonal prismatic B B A octahedral holes A

7 MoS 2 -type: A Lamellar Structure! Molybdenite ReO 3 and Perovskite Structures B O A Perovskite, ABO 3 = ABO 6/2 ; Examples: BaTiO 3, KNbO 3 ReO 3 = BO 3 Perovskite with a Shifted Origin Perovskite, ABO 3 = ABO 6/2 ; Examples: BaTiO 3, KNbO 3 ReO 3 = BO 3

8 BaTiO3 is a ferroelectric with spontaneous with a spontaneous polarization (cooperative allignment of dipoles throughout the crystal). Ionic Bonding; Lattice Energies Energy Lattice Energies - Details V = VCoulomb + Vrepulsion r = cation-anion distance ion - ion Coulomb interactions repulsions between ion cores eg., -type: (cgs units - a factor of 1/4!!0 must be included to convert to SI) V Coulomb = + 6 (e 2 / r )Z + Z + 12 (e 2 /!2r )(Z + ) (e 2 /!3r )Z + Z + 6 (e 2 / 2r )(Z + ) type: V Coulomb = N A (e 2 /r)[z + Z ]! A A = [ /!2 8 /!3 + 6 / 2 24 /!5 +...]!2!3 The Madelung constant: a geometrical parameter that is the same for all compounds of a given structure type Ion core Ion core repulsions Vrepulsion = + N A C exp{-(r/r*)} estimated from compressibilities, r* is always much smaller than a typical internuclear distance (~ Å). V = N A (e 2 /r)[z+ Z ]A + N A C exp{-(r/r*)} Minimize (set (dv/dr) = 0) to obtain: C exp{-(r min /r*)} = - e 2 [Z+ Z ] A r*/(r min ) 2 Alternative: Vrep = + NA (B/r n ) ion core n He 5 Ne 7 Ar 9 Kr 10 Xe 12 V min = N A (e 2 /r min )[Z+ Z ](1 r*/r min )A V min = N A (e 2 /r min ) [Z+ Z ](1 1 / n )A

9 Thermochemical (Born-Haber) Cycle M(g) + X(g) I(M) E X M + (g) + X (g) S M + ( 1 / 2 )D X2!H L M(s) + ( 1 / 2 )X 2 (g)!h f MX(s) Values for (kj/mol) S M : sublimation Enthalpy of Metal (298 K) 108 D X2 : dissociation Energy of X 2 bond (298 K) 242 I(M) : Ionization Enthalpy of Metal M 496 E X : electron attachment Enthalpy of X atom 349 H L : Enthalpy for separation of salt to ions theory Thermochemical (Born-Haber) Cycle M(g) + X(g) I(M) E X M + (g) + X (g) S M + ( 1 / 2 )D X2!H L M(s) + ( 1 / 2 )X 2 (g)!h f MX(s) H L = V min = N A (e 2 /r min )[Z+ Z ](1 - r*/r min )A for, r min = Å (5.162 a.u.) Experiment (Born-Haber cycle): H f = S M + ( 1 / 2 ) D X2 + I(M) E M H L for, measured value of H f is -411kJ/mol 776kJ/mol -411 = (242/2) H L H L = 787 (- 2 for C p correction) = 785 kj/mol Consequences of Lattice Enthalpies Electrostatic component stabilizing ionic solids gives us Lattice energy [Z A Z B ] d lattice spacing Thermal stabilities: Large Cations stabilize large Anions.

10 Effects of charge and size on lattice energies (m.p.s) melting points ( C) F 993 CaF MgO Sr CaO 2580 Br 747 Li 2 O >1700 SrO 2430 K O 1275 (subl) BaO 1923

Followed by metals and inert gases - close-packed structures Deviations: BCC metals 'Ionic' compounds strive to follow the principles.

Followed by metals and inert gases - close-packed structures Deviations: BCC metals 'Ionic' compounds strive to follow the principles. Reading: West 7 &8 Principles of Laves 1.Space Principle: Space is used most efficiently 2.Symmetry Principle: Highest possible symmetry is adopted 3.Connection Principle: There will be the most possible