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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 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)
Structures of solids
Amorphous(short-range order but no long-
range periodicity)
Crystalline(short-range order that propagates
as long-range periodicity)
How would you describe the crystal structure of NaCl?
Solid State Structures
Different representations of NaCl
Different representations of NaCl
Asymmetric unit Lattice points Crystal structure
+ =
Coordination numbers and geometries
Coordination number of Na? Cl? Coordination geometries?
Coordination polyhedra
Coordination polyhedra simplify the view of the structure and emphasize connectivity, but they de-emphasize bonding.
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)
2D projections of 3D structures
Projections (slices of the crystal) make it easier to visualize complex structures
• 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
“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
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”).
Octahedral holes
Octahedral holes
Tetrahedral holes
Tetrahedral holes
Octahedral and tetrahedral holes
Octahedralholes
Tetrahedralholes
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?
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)
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)
NaCl structure type
What would you predict the properties of these interstitial carbides to be?
Carbides and nitrides(TiC, TiN, ZrC, NbC)
NaCl-related structures
FeS2 (iron pyrite) CaC2 (calcium carbide)
NaCl-related structures
CaCO3 NbO
“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)?
NiAs structure type
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?
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?
Octahedralholes
Tetrahedralholes
Octahedral and tetrahedral holes
Tetrahedral structures
What does the vertical registry look like?
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)
Fluorite structure type
Fluorite-like structuresPtN2
K2PtCl6
PbO
HgI2
Hexagonal fluorite?
NiAs is the hexagonal analogue of NaCl.Is there a hexagonal analogue of fluorite?
http://www.che.kyutech.ac.jp/chem24/hp/english/lecture/crystal%20structure/zincblende/zincblende.htm
Zincblende structure type
Zincblende vs. diamond
How does zincblende compare to diamond?
ZnS (zincblende) vs. Fluorite
How is ZnS (zincblende) related to fluorite?
CaF2 (fluorite)
Zincblende structure type
How would you derive zincblende from filling holes in a close packed lattice?
Zincblende vs. wurtzite
Compare and contrast
Zincblende vs. wurtzite
Compare and contrast
(boat)
(chair)
Zincblende vs. wurtzite
What would you predict about the types of compoundsthat form zincblende vs. wurtzite?
ccp hcp
Zincblende vs. wurtzite
Zincblende and wurtzite are examples of polymorphs
(Diamond and graphite are allotropes, which are elemental polymorphs)
GaAs
What would you predict to be the structure of GaAs? Why?
Silicon(diamond structure)
How many atoms per cell?
GaAs
GaSe
What would you predict to be the structure of GaSe? Why?
GaSe
As
What would you predict to be the structure of As? Why?
Semiconductor structures
Layered structures
Fractional filling of tetrahedral and octahedral holes usually does notoccur randomly, and often occurs in layers.
CdCl2 (left) vs. CdI2 (right)
What types of properties would you expect from these solids?
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?
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”)
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)
TiS2 vs. FeS2
TiS2 vs. MoS2
Both are layered solids, but differ in how the sulfur atoms are oriented. Why?
TiS2MoS2
TiS2 vs. MoS2
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
CsCl structure type
Rutile structure type
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)
Radius ratio rules
Coordination number Geometryr+/r–
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…
Structure maps
A more successful approach is based on periodic trends – electronegativity
Structure maps
Mooser-Pearson plot correctly differentiates alkali halides, and suggests that radius ratio correlations may be coincidental…
Two views of the spinel crystal structure
Spinel structure
Another view of the spinel crystal structure
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?
Spinel structure
What would you predict to be common A-B combinations, and why?
Spinel structure
The mineral spinel is a “normal” spinel…
The mineral spinel
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
Spinels have cations occupying both tetrahedral and octahedral sites.
Consider a metal cation in a tetrahedral site…
Spinels and CFSE
Consider a metal cation in an octahedral site…
Spinels and CFSE
Is Fe3O4 a normalor an inverse spinel?
To begin:
What is the oxidation stateof Fe in Fe3O4?
What 3dn electronconfiguration(s)?
Fe3O4 (magnetite)
Octahedral vs. tetrahedral sites
Fe3O4
Look for the d-orbital occupancy configurations that give the highest CFSE
Is NiFe2O4 a normal or an inverse spinel?
NiFe2O4
Is MIICr2O4 a normal or an inverse spinel?
Chromite spinels
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
Coupling between the 3d electrons of Fe3+ cations on tetrahedral and octahedral sites is through oxygen 2p electrons – “superexchange”
Superexchange
What type of magnetic coupling is present?
Magnetic coupling
NiO
Other systems exhibiting superexchange
TiO