Presentation on theme: "Structures of Ionic and Covalent Solids (Ch. 8)"— Presentation transcript:
1 Structures of Ionic and Covalent Solids (Ch. 8) Big-picture perspective:Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding that contribute to their unique properties and applications, but in many cases these concepts build on what we already know about molecules. We will begin by learning about how the structures of solids are described, and then move into fundamental aspects of chemical bonding in solids.Learning goals:Describe many crystal structures in terms of close-packed frameworks with systematic filling of octahedral and tetrahedral holes.Rationalize, using chemical principles, why certain crystal structures are stable for certain compounds but not for others, as well as why certain structural and bonding motifs are preferred for certain compounds relative to others.Predict which crystal structures are most favorable for a given composition using radius ratio rules and structure maps (and also appreciate the limitations of these approaches).Predict the preferred formation of normal or inverse spinels using arguments from transition metal chemistry (e.g. crystal field stabilization energies).
2 Structures of solids Crystalline (short-range order that propagates as long-range periodicity)Amorphous(short-range order but no long-range periodicity)
3 Solid State Structures How would you describe the crystal structure of NaCl?
5 Different representations of NaCl Asymmetric unitLattice pointsCrystal structure+=
6 Coordination numbers and geometries Coordination number of Na? Cl? Coordination geometries?
7 Coordination polyhedra Coordination polyhedra simplify the view of the structure and emphasize connectivity, but they de-emphasize bonding.
8 Fractional coordinates Regardless of lattice parameter (a), Fractional coordinates are the positions of atoms in a normalized unit cellRegardless of lattice parameter (a),there are atoms at:Cl (0,0,0)Na (½, 0, 0)Cl (½, 0, ½)Na (0, ½, ½)Cl (1, 0, 0) = (0, 0, 0)Na (½, 1, 0) = (½, 0, 0)1
9 2D projections of 3D structures Projections (slices of the crystal) make it easier to visualize complex structures
10 Crystal structure related to NaCl but without corner and center atoms Niobium oxideCrystal structure related to NaCl but without corner and center atomsWhat is the empirical formula of this niobium oxide compound?How many formula units are contained within the unit cell(molecular formula)?What are the oxidation states of Nb and O in this compound?What is the coordination number of Nb? O?Draw 2D unit cell projections and list fractional coordinates for all atoms
11 “White-Shaded” (W-S) compound Is this structure related to one of the structures we already studied (primitive cubic, bcc, hcp, fcc)? How?What is the empirical formula of this W-S compound?How many formula units are contained within the unit cell(molecular formula)?What are the oxidation states of W and S in this compound?What is the coordination number of W? S?Draw 2D unit cell projections and list fractional coordinates for all atoms
12 Systematic filling of holes Many inorganic crystal structures are based on close-packed arrays of spheres, with different structures derived by systematically filling the holes between packing atoms with other atoms (“interstitial atoms”).
19 Revisiting NaClHow would you “assemble” the NaCl structure by starting with a close-packed lattice of Cl– anions and filling in appropriate holes between the close-packed Cl– anions with Na+ cations?
20 Stacking sequence in NaCl We can write a description of the structure in terms of the stacking sequence of packing and interstitial atoms (look at vertical registry)
21 NaCl structure type All alkali halides (except CsCl, CsBr, CsI – why?) Many ionic solids crystallize in the NaCl (rocksalt) structure typeAll alkali halides(except CsCl, CsBr, CsI – why?)Transition metal monoxides(TiO, VO, … , NiO)Alkali earth oxides and sulfides(MgO, CaO, BaS, …)Carbides and nitrides(TiC, TiN, ZrC, NbC)
22 NaCl structure type Carbides and nitrides (TiC, TiN, ZrC, NbC) What would you predict the properties of these interstitial carbides to be?
27 NiAs vs. NaCl structureWe already looked at what types of solids crystallize in theNaCl structure type. What would you predict about the types of solidsthat would prefer the NiAs structure type? Same? Different? Why?
28 Tetrahedral structures So far we have filled only the octahedral holes, but there are also tetrahedral holes. What is the stoichiometry if we fill all of the tetrahedral holes?
30 Tetrahedral structures What does the vertical registry look like?
31 Fluorite (top left) and antifluorite (bottom left) We will focus on the fluorite structure (CaF2), wherethe packing atom is Ca2+ with interstitial F–(some images on fluorite/antifluorite, here and later pages, via Creative Commons license)
51 occur randomly, and often occurs in layers. Layered structuresFractional filling of tetrahedral and octahedral holes usually does notoccur randomly, and often occurs in layers.
52 What types of properties would you expect from these solids? CdCl2 (left) vs. CdI2 (right)What types of properties would you expect from these solids?
53 CdCl2 vs. CdI2Based on the structures, what would you predict about the types of compounds that would form the CdCl2 and CdI2 structure types?
54 Physical and chemical properties Layered structure tend to make plate-like crystals that are soft and slippery (solid-state lubricants). They cleave easily along van der Waals planes, and undergo interlayer chemical reactions (“intercalation”)
55 Going deeper … TiS2 vs. FeS2 If TiS2 is layered, why is FeS2 a three dimensionally bonded structure(related to NaCl), despite the same 1:2 formula?TiS2(CdI2 structure type)FeS2(pyrite structure type)
59 Structure predictionBy now we have seen several types of crystal structures, and there are many many more. How do we know when a certain compound will adopt a particular structure?Step back – what factors lead to the formation of a particular structure?Consider the simplest structures we’ve seen:MX: NaCl, CsCl, ZnS (zincblende / wurtzite)MX2: CaF2, rutile
62 Ionic structure stabilization Structures are stabilized by maximizing anion / cation contact.We can estimate the “best fit” from ionic radii(e.g. geometry, hard sphere close packing)
63 Coordination number Geometry r+/r– Radius ratio rulesCoordination number Geometry r+/r–
64 Radius ratio rulesWhile this model is simple and has its limitations and shortcomings,it can be used as one of several guidelines for structure prediction.It predicts the following correctly:SiO2, BeF2 CN = 4TiO2, MgF2 CN = 6ZrO2, CaF2 CN = 8Despite this success, though, it gets half of the simple MX halides wrong!!!It predicts that LiCl and LiBr should be ZnS-type and KF should be CsCl type!Analogous to our bonding models, we need a more sophisticated approach…
65 Structure mapsA more successful approach is based on periodic trends – electronegativity
66 Structure mapsMooser-Pearson plot correctly differentiates alkali halides, and suggests that radius ratio correlations may be coincidental…
67 Two views of the spinel crystal structure Spinel structureTwo views of the spinel crystal structure
68 Another view of the spinel crystal structure Spinel structureAnother view of the spinel crystal structure
69 Spinel structure ccp array of Xn– anions (often O2–) 1/8 of the tetrahedral holes filled (“A” sites)1/2 of the octahedral holes filled (“B” sites)Formula: AxByOzWhat are x, y, and z?What is the empirical formula for a spinel?
70 What would you predict to be common A-B combinations, and why? Spinel structureWhat would you predict to be common A-B combinations, and why?
72 Inverse spinels What is an inverse spinel? How would we know whether a spinel is “normal” or “inverse”?How would we predict whether a certain A-B combination would prefer to form as a “normal” or as an “inverse” spinel?Why would the difference between “normal” and “inverse” matter?
73 Spinels and CFSESpinels have cations occupying both tetrahedral and octahedral sites.Consider a metal cation in a tetrahedral site…
74 Consider a metal cation in an octahedral site… Spinels and CFSEConsider a metal cation in an octahedral site…
75 What is the oxidation state Fe3O4 (magnetite)Is Fe3O4 a normalor an inverse spinel?To begin:What is the oxidation stateof Fe in Fe3O4?What 3dn electronconfiguration(s)?
76 Octahedral vs. tetrahedral sites Fe3O4Octahedral vs. tetrahedral sitesLook for the d-orbital occupancy configurations that give the highest CFSE