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?

4. Different representations of NaCl

5. Different representations of NaCl
Asymmetric unit
Lattice points
Crystal 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 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) 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 oxide
Crystal structure related to NaCl but without corner and center atoms
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

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

14. Octahedral holes

15. Tetrahedral holes

16. Tetrahedral holes

17. Octahedral and tetrahedral holes

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 All alkali halides (except CsCl, CsBr, CsI – why?)
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 Carbides and nitrides (TiC, TiN, ZrC, NbC)
What would you predict the properties of these interstitial carbides to be?

23. NaCl-related structures
FeS2 (iron pyrite)
CaC2 (calcium carbide)

24. NaCl-related structures
CaCO3
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 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 (CaF2), where
the packing atom is Ca2+ with interstitial F–
(some images on fluorite/antifluorite, here and later pages, via Creative Commons license)

32. Fluorite structure type

33. Fluorite-like structures
PtN2
PbO
K2PtCl6
HgI2

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

36. Zincblende structure type

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

38. ZnS (zincblende) vs. Fluorite
How is ZnS (zincblende) related to fluorite?
CaF2 (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. Zincblende vs. wurtzite
ccp
hcp
Zincblende and wurtzite are examples of polymorphs
(Diamond and graphite are allotropes, which are elemental polymorphs)

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

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

46. GaAs

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

48. GaSe

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

50. Semiconductor structures

51. occur randomly, and often occurs in layers.
Layered structures
Fractional filling of tetrahedral and octahedral holes usually does not
occur 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. CdI2
Based 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)

56. TiS2 vs. FeS2

57. TiS2 vs. MoS2
Both are layered solids, but differ in how the sulfur atoms are oriented. Why?
TiS2
MoS2

58. TiS2 vs. MoS2

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)
MX2: CaF2, 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. Coordination number Geometry r+/r–
Radius ratio rules
Coordination number Geometry r+/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:
SiO2, BeF2  CN = 4
TiO2, MgF2  CN = 6
ZrO2, CaF2  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
Two views of the spinel crystal structure

68. Another view of the spinel crystal structure
Spinel structure
Another 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: AxByOz
What 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 structure
What would you predict to be common A-B combinations, and why?

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

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

75. What is the oxidation state
Fe3O4 (magnetite)
Is Fe3O4 a normal
or an inverse spinel?
To begin:
What is the oxidation state
of Fe in Fe3O4?
What 3dn electron
configuration(s)?

76. Octahedral vs. tetrahedral sites
Fe3O4
Octahedral vs. tetrahedral sites
Look for the d-orbital occupancy configurations that give the highest CFSE

77. Is NiFe2O4 a normal or an inverse spinel?

78. Is MIICr2O4 a normal or an inverse spinel?
Chromite spinels
Is MIICr2O4 a normal or an inverse spinel?

79. Experimental validation
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)?

80. Superexchange
Coupling between the 3d electrons of Fe3+ cations on tetrahedral and octahedral sites is through oxygen 2p electrons – “superexchange”

81. What type of magnetic coupling is present?

82. Other systems exhibiting superexchange
NiO
TiO