Chapter 3 (part 3) The Structures of Simple Solids

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1 CHM 511 chapter 3 page 1 of 9 Chapter 3 (part 3) The Structures of Simple Solids Rationalizing Structures Ionic radii As noted earlier, a reference value is needed. Usually oxygen is assumed to be 140 pm. Trends are: 1. ionic radii increase going down a group (lanthanide contraction notwithstanding) 2. the radii of ions of the same charge decreases across a period 3. an ionic radius will decrease as the positive charge increases for a given cation 4. cations are smaller than anions of the same Z 5. for a given ion, a larger coordination number results in a larger radius Radius ratio method: taking a ratio of the ions' sizes, you can predict the coordination of the ions As the difference in size gets to be larger, the large ions will get closer together (small ions aren't there to keep them apart). Thus, like charges get close together and there is repulsion! EX. What would the CN be for NaCl and CsCl using the radius ratio method?

2 CHM 511 chapter 3 page 2 of 9 Structure maps Empirically derived plot of versus the average principle quantum number. This is for MX compounds (would need a different plot for MX2): EX. Given that the electronegativity of Ag is 1.9 and Br is 2.8, what would you predict for CN of AgBr? What does the radius ratio predict?

3 CHM 511 chapter 3 page 3 of 9 Energetics of ionic bonding Imagine the reaction between Na and Cl2, normalized to make one mole of product. If we break this into a series of steps and calculate the energy needed for each step we can determine how stable the ionic lattice is. The steps: 1. sublime the metal 2. ionization of Na(g) 3. dissociate the halogen 4. form Cl - (g) ions 5. bring the ions together The Born-Haber cycle is useful for predicting if a solid is largely ionic or not. If the measured value for Hf is close to the calculated value, the solid is largely ionic.

4 CHM 511 chapter 3 page 4 of 9 Calculating Lattice Enthalpy #2 Born-Meyer equation ΔH L N A z A z 4π d 0 B 0 e 2 1 d d 0 Α Where: d0 = distance between charges (in pm) za, zb = charges on ions NA = Avogadro s number o = permittivity constant d = constant of 34.5 pm e = electric charge A = Madelung constant, depends on the arrangement of ions (strictly, it is a value representing the coulomb energy of an ion pair in a crystal relative to the coulomb energy of an isolated ion pair). Takes into account alternating layers of counter ions and similar ions. ions with higher charges will form compounds with higher lattice enthalpies ions that are smaller will form compounds with higher lattice enthalpies The data: Ion Size(angstroms) Salt Lattice Enthalpy (kj/mol) Li (6) LiCl 853 Mg (6) MgCl Al (6) AlCl For size considerations Ion Size (angstroms) Salt Lattice Enthalpy (kj/mol) Li (6) LiCl 853 Na (6) NaCl 786 K (6) KCl 719 Cl (6) LiCl 853 Br (6) LiBr 815 I (6) LiI 757 Also may need to consider non-ionic interactions between atoms, i.e., London dispersion forces

5 CHM 511 chapter 3 page 5 of 9 The value in Born-Haber and Born-Meyer is comparison to experimental data. If calculations are close, the system is largely ionic; if the calculations deviate from experimental data, then some covalent character may be present. % error Thermal stabilities of ionic solids In general, large cations stabilize large anions (and vice versa) Consider the decomposition of carbonates. Salt Decomposition Temperature ( o C) MgCO CaCO SrCO BaCO

6 CHM 511 chapter 3 page 6 of 9 Stabilities of oxidation states Cations with high oxidation states are stabilized by small ions Recall: higher charges = higher lattice energy (more electrostatic attraction) Solubility A compound made of different-sized ions tends to be more water soluble that a compound made of similar-sized ions. Species Solubility (g/100 ml) Solubility (Molarity) Mg(OH) Ca(OH) Sr(OH) Ba(OH) To dissolve, MX(s) M + (aq) + X - (aq) Hydration enthalpy is inversely proportional to individual atom radii Lattice enthalpy is dependent on the distance between ions

7 CHM 511 chapter 3 page 7 of 9 Defects in Crystal Structures Throughout this chapter we have discussed structures of crystalline materials how did we define crystalline? Sometimes, however, imperfections can cause a crystal lattice to have defects. o Intrinsic defects: ones that occur in a pure material o Extrinsic defects: ones that occur due to an impurity (intentional or otherwise) o Point defects: occur at a specific location o Extended defects: occur in 1-, 2-, or 3-dimensional locations. Schottky Defect In essence, the equivalent of a formula unit (MX, MX2, or ABX3, etc.) is missing from the lattice. See below at the sodium chloride lattice. Frenkel Defect The migration of cations and/or anions to holes not normally containing those ions. See below for a AgBr lattice with a silver ion moved.

8 CHM 511 chapter 3 page 8 of 9 Color Centers Trapped electrons can give rise to colored crystal lattices, the location of the electron is known as an F-center (from the German word for color, Farbe) Non-stoichiometric compounds Most common for metal lattices in which the metal ion can adopt multiple different oxidation states (i.e., d- and f-metal compounds). FeO is rarely a 1:1 ratio when in contact with O2. The O2 causes oxidation of Fe 2+ to Fe 3+. The Electronic Structures of Solids Extended solids, whether metallic, covalent, or ionic can be modeled with molecular orbitals. Metallic conductor: a substance whose electrical conductivity decreases with rising temperature Semiconductor: a substance whose electrical conductivity increases with rising temperature Insulators are really just a special category of semiconductors Imagine a HUGE number of atoms forming molecular orbitals If each atom gives 1 electron, then the orbital array should be half-full. This level is called the Fermi level (though technically, the Fermi level should be measured at 0 K).

9 CHM 511 chapter 3 page 9 of 9 For metals, electrons are filled to the Fermi level and thermal energy can promote the electron to allow them to conduct around the metal. So why will an increase in temperature decrease the conductivity? For semimetals, s- and p-bands just meet (for insulators, there is a gap, called the band gap) Semiconductors Intrinsic semiconductors (no doping necessary): small band gap, therefore thermal energy used to promote electrons to the conduction band (upper band) Extrinsic semiconductors (doping necessary)-results in p- or n-type semiconductors Non-stoichiometric compounds can be n- or p-type depending on the metal: high oxidation state metals tend to form n-type (Fe2O3, MnO2, CuO, WO3); p-type form with metals have a low oxidation state (MnO, Cr2O3). Why does heat cause these to increase conductivity?