big-picture perspective: solids, and in particular inorganic solids, are everywhere around us....
TRANSCRIPT
![Page 1: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/1.jpg)
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)
![Page 2: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/2.jpg)
Structures of solids
Amorphous(short-range order but no long-
range periodicity)
Crystalline(short-range order that propagates
as long-range periodicity)
![Page 3: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/3.jpg)
How would you describe the crystal structure of NaCl?
Solid State Structures
![Page 4: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/4.jpg)
Different representations of NaCl
![Page 5: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/5.jpg)
Different representations of NaCl
Asymmetric unit Lattice points Crystal structure
+ =
![Page 6: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/6.jpg)
Coordination numbers and geometries
Coordination number of Na? Cl? Coordination geometries?
![Page 7: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/7.jpg)
Coordination polyhedra
Coordination polyhedra simplify the view of the structure and emphasize connectivity, but they de-emphasize bonding.
![Page 8: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/8.jpg)
Fractional coordinates
Fractional coordinates are the positions of atoms in a normalized unit cell
0
1
1
1
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)
![Page 9: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/9.jpg)
2D projections of 3D structures
Projections (slices of the crystal) make it easier to visualize complex structures
![Page 10: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/10.jpg)
• 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
![Page 11: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/11.jpg)
“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
![Page 12: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/12.jpg)
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”).
![Page 13: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/13.jpg)
Octahedral holes
![Page 14: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/14.jpg)
Octahedral holes
![Page 15: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/15.jpg)
Tetrahedral holes
![Page 16: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/16.jpg)
Tetrahedral holes
![Page 17: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/17.jpg)
Octahedral and tetrahedral holes
Octahedralholes
Tetrahedralholes
![Page 18: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/18.jpg)
![Page 19: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/19.jpg)
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?
![Page 20: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/20.jpg)
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)
![Page 21: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/21.jpg)
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)
![Page 22: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/22.jpg)
NaCl structure type
What would you predict the properties of these interstitial carbides to be?
Carbides and nitrides(TiC, TiN, ZrC, NbC)
![Page 23: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/23.jpg)
NaCl-related structures
FeS2 (iron pyrite) CaC2 (calcium carbide)
![Page 24: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/24.jpg)
NaCl-related structures
CaCO3 NbO
![Page 25: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/25.jpg)
“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)?
![Page 26: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/26.jpg)
NiAs structure type
![Page 27: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/27.jpg)
NiAs vs. NaCl structure
We already looked at what types of solids crystallize in theNaCl structure type. What would you predict about the types of solids
that would prefer the NiAs structure type? Same? Different? Why?
![Page 28: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/28.jpg)
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?
![Page 29: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/29.jpg)
Octahedralholes
Tetrahedralholes
Octahedral and tetrahedral holes
![Page 30: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/30.jpg)
Tetrahedral structures
What does the vertical registry look like?
![Page 31: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/31.jpg)
Fluorite (top left) and antifluorite (bottom left)
We will focus on the fluorite structure (CaF2), wherethe packing atom is Ca2+ with interstitial F–
http://wikis.lib.ncsu.edu/index.php/Fluorite/Antifluorite (some images on fluorite/antifluorite, here and later pages, via Creative Commons license)
![Page 32: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/32.jpg)
Fluorite structure type
![Page 33: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/33.jpg)
Fluorite-like structuresPtN2
K2PtCl6
PbO
HgI2
![Page 34: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/34.jpg)
Hexagonal fluorite?
NiAs is the hexagonal analogue of NaCl.Is there a hexagonal analogue of fluorite?
![Page 35: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/35.jpg)
![Page 36: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/36.jpg)
http://www.che.kyutech.ac.jp/chem24/hp/english/lecture/crystal%20structure/zincblende/zincblende.htm
Zincblende structure type
![Page 37: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/37.jpg)
Zincblende vs. diamond
How does zincblende compare to diamond?
![Page 38: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/38.jpg)
ZnS (zincblende) vs. Fluorite
How is ZnS (zincblende) related to fluorite?
CaF2 (fluorite)
![Page 39: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/39.jpg)
Zincblende structure type
How would you derive zincblende from filling holes in a close packed lattice?
![Page 40: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/40.jpg)
Zincblende vs. wurtzite
Compare and contrast
![Page 41: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/41.jpg)
Zincblende vs. wurtzite
Compare and contrast
(boat)
(chair)
![Page 42: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/42.jpg)
Zincblende vs. wurtzite
What would you predict about the types of compoundsthat form zincblende vs. wurtzite?
![Page 43: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/43.jpg)
ccp hcp
Zincblende vs. wurtzite
Zincblende and wurtzite are examples of polymorphs
(Diamond and graphite are allotropes, which are elemental polymorphs)
![Page 44: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/44.jpg)
GaAs
What would you predict to be the structure of GaAs? Why?
![Page 45: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/45.jpg)
Silicon(diamond structure)
How many atoms per cell?
![Page 46: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/46.jpg)
GaAs
![Page 47: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/47.jpg)
GaSe
What would you predict to be the structure of GaSe? Why?
![Page 48: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/48.jpg)
GaSe
![Page 49: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/49.jpg)
As
What would you predict to be the structure of As? Why?
![Page 50: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/50.jpg)
Semiconductor structures
![Page 51: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/51.jpg)
Layered structures
Fractional filling of tetrahedral and octahedral holes usually does notoccur randomly, and often occurs in layers.
![Page 52: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/52.jpg)
CdCl2 (left) vs. CdI2 (right)
What types of properties would you expect from these solids?
![Page 53: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/53.jpg)
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?
![Page 54: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/54.jpg)
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”)
![Page 55: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/55.jpg)
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)
![Page 56: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/56.jpg)
TiS2 vs. FeS2
![Page 57: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/57.jpg)
TiS2 vs. MoS2
Both are layered solids, but differ in how the sulfur atoms are oriented. Why?
TiS2MoS2
![Page 58: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/58.jpg)
TiS2 vs. MoS2
![Page 59: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/59.jpg)
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
![Page 60: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/60.jpg)
CsCl structure type
![Page 61: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/61.jpg)
Rutile structure type
![Page 62: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/62.jpg)
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)
![Page 63: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/63.jpg)
Radius ratio rules
Coordination number Geometryr+/r–
![Page 64: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/64.jpg)
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…
![Page 65: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/65.jpg)
Structure maps
A more successful approach is based on periodic trends – electronegativity
![Page 66: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/66.jpg)
Structure maps
Mooser-Pearson plot correctly differentiates alkali halides, and suggests that radius ratio correlations may be coincidental…
![Page 67: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/67.jpg)
Two views of the spinel crystal structure
Spinel structure
![Page 68: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/68.jpg)
Another view of the spinel crystal structure
Spinel structure
![Page 69: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/69.jpg)
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?
Spinel structure
![Page 70: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/70.jpg)
What would you predict to be common A-B combinations, and why?
Spinel structure
![Page 71: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/71.jpg)
The mineral spinel is a “normal” spinel…
The mineral spinel
![Page 72: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/72.jpg)
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
![Page 73: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/73.jpg)
Spinels have cations occupying both tetrahedral and octahedral sites.
Consider a metal cation in a tetrahedral site…
Spinels and CFSE
![Page 74: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/74.jpg)
Consider a metal cation in an octahedral site…
Spinels and CFSE
![Page 75: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/75.jpg)
Is Fe3O4 a normalor an inverse spinel?
To begin:
What is the oxidation stateof Fe in Fe3O4?
What 3dn electronconfiguration(s)?
Fe3O4 (magnetite)
![Page 76: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/76.jpg)
Octahedral vs. tetrahedral sites
Fe3O4
Look for the d-orbital occupancy configurations that give the highest CFSE
![Page 77: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/77.jpg)
Is NiFe2O4 a normal or an inverse spinel?
NiFe2O4
![Page 78: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/78.jpg)
Is MIICr2O4 a normal or an inverse spinel?
Chromite spinels
![Page 79: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/79.jpg)
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
![Page 80: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/80.jpg)
Coupling between the 3d electrons of Fe3+ cations on tetrahedral and octahedral sites is through oxygen 2p electrons – “superexchange”
Superexchange
![Page 81: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/81.jpg)
What type of magnetic coupling is present?
Magnetic coupling
![Page 82: Big-picture perspective: Solids, and in particular inorganic solids, are everywhere around us. Inorganic solids have unique aspects of structure and bonding](https://reader038.vdocuments.mx/reader038/viewer/2022110206/56649cd75503460f9499f387/html5/thumbnails/82.jpg)
NiO
Other systems exhibiting superexchange
TiO