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Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding.

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Presentation on theme: "Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding."— Presentation transcript:

1 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). Structures of Ionic and Covalent Solids (Ch. 8)

2 Structures of solids Amorphous (short-range order but no long- range periodicity) Crystalline (short-range order that propagates as long-range periodicity)

3 How would you describe the crystal structure of NaCl? Solid State Structures

4 Different representations of NaCl

5 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 Fractional coordinates are the positions of atoms in a normalized unit cell Regardless 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)

9 2D projections of 3D structures Projections (slices of the crystal) make it easier to visualize complex structures

10 What 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 Niobium oxide Crystal structure related to NaCl but without corner and center 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”).

13 Octahedral holes

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15 Tetrahedral holes

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17 Octahedral and tetrahedral holes Octahedral holes Tetrahedral holes

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19 Revisiting NaCl How 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 Many ionic solids crystallize in the NaCl (rocksalt) structure type All 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 What would you predict the properties of these interstitial carbides to be? Carbides and nitrides (TiC, TiN, ZrC, NbC)

23 NaCl-related structures FeS 2 (iron pyrite)CaC 2 (calcium carbide)

24 NaCl-related structures CaCO 3 NbO

25 “Hexagonal” NaCl structure What if we try to build the NaCl structure, except start with an hcp array of close packed atoms (instead of fcc)?

26 NiAs structure type

27 NiAs vs. NaCl structure We already looked at what types of solids crystallize in the NaCl structure type. What would you predict about the types of solids that 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?

29 Octahedral holes Tetrahedral holes Octahedral and 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 (CaF 2 ), where the packing atom is Ca 2+ with interstitial F – (some images on fluorite/antifluorite, here and later pages, via Creative Commons license)

32 Fluorite structure type

33 Fluorite-like structures PtN 2 K 2 PtCl 6 PbO HgI 2

34 Hexagonal fluorite? NiAs is the hexagonal analogue of NaCl. Is there a hexagonal analogue of fluorite?

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36 Zincblende structure type

37 Zincblende vs. diamond How does zincblende compare to diamond?

38 ZnS (zincblende) vs. Fluorite How is ZnS (zincblende) related to fluorite? CaF 2 (fluorite)

39 Zincblende structure type How would you derive zincblende from filling holes in a close packed lattice?

40 Zincblende vs. wurtzite Compare and contrast

41 Zincblende vs. wurtzite Compare and contrast (boat) (chair)

42 Zincblende vs. wurtzite What would you predict about the types of compounds that form zincblende vs. wurtzite?

43 ccp hcp Zincblende vs. wurtzite Zincblende and wurtzite are examples of polymorphs (Diamond and graphite are allotropes, which are elemental polymorphs)

44 GaAs What would you predict to be the structure of GaAs? Why?

45 Silicon (diamond structure) How many atoms per cell?

46 GaAs

47 GaSe What would you predict to be the structure of GaSe? Why?

48 GaSe

49 As What would you predict to be the structure of As? Why?

50 Semiconductor structures

51 Layered structures Fractional filling of tetrahedral and octahedral holes usually does not occur randomly, and often occurs in layers.

52 CdCl 2 (left) vs. CdI 2 (right) What types of properties would you expect from these solids?

53 CdCl 2 vs. CdI 2 Based on the structures, what would you predict about the types of compounds that would form the CdCl 2 and CdI 2 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 … TiS 2 vs. FeS 2 If TiS 2 is layered, why is FeS 2 a three dimensionally bonded structure (related to NaCl), despite the same 1:2 formula? TiS 2 (CdI 2 structure type) FeS 2 (pyrite structure type)

56 TiS 2 vs. FeS 2

57 TiS 2 vs. MoS 2 Both are layered solids, but differ in how the sulfur atoms are oriented. Why? TiS 2 MoS 2

58 TiS 2 vs. MoS 2

59 Structure prediction By 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) MX 2 : CaF 2, rutile

60 CsCl structure type

61 Rutile structure type

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 Radius ratio rules Coordination number Geometryr + /r –

64 Radius ratio rules While 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: SiO 2, BeF 2  CN = 4 TiO 2, MgF 2  CN = 6 ZrO 2, CaF 2  CN = 8 Despite 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 maps A more successful approach is based on periodic trends – electronegativity

66 Structure maps Mooser-Pearson plot correctly differentiates alkali halides, and suggests that radius ratio correlations may be coincidental…

67 Two views of the spinel crystal structure Spinel structure

68 Another view of the spinel crystal structure Spinel structure

69 ccp array of X n– anions (often O 2– ) 1/8 of the tetrahedral holes filled (“A” sites) 1/2 of the octahedral holes filled (“B” sites) Formula: A x B y O z What are x, y, and z? What is the empirical formula for a spinel? Spinel structure

70 What would you predict to be common A-B combinations, and why? Spinel structure

71 The mineral spinel is a “normal” spinel… The mineral spinel

72 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? Inverse spinels

73 Spinels have cations occupying both tetrahedral and octahedral sites. Consider a metal cation in a tetrahedral site… Spinels and CFSE

74 Consider a metal cation in an octahedral site… Spinels and CFSE

75 Is Fe 3 O 4 a normal or an inverse spinel? To begin: What is the oxidation state of Fe in Fe 3 O 4 ? What 3d n electron configuration(s)? Fe 3 O 4 (magnetite)

76 Octahedral vs. tetrahedral sites Fe 3 O 4 Look for the d-orbital occupancy configurations that give the highest CFSE

77 Is NiFe 2 O 4 a normal or an inverse spinel? NiFe 2 O 4

78 Is M II Cr 2 O 4 a normal or an inverse spinel? Chromite spinels

79 How do we probe experimentally whether these spinels are normal or inverse (e.g. that one cation prefers the tetrahedral site and another prefers the octahedral site)? Experimental validation

80 Coupling between the 3d electrons of Fe 3+ cations on tetrahedral and octahedral sites is through oxygen 2p electrons – “superexchange” Superexchange

81 What type of magnetic coupling is present? Magnetic coupling

82 NiO Other systems exhibiting superexchange TiO


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