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).
Structures of solids
Crystalline
(short-range order that propagates
as long-range periodicity)
Amorphous
(short-range order but no longrange periodicity)
Solid State Structures
How would you describe the crystal structure of NaCl?
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
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)
1
Cl (1, 0, 0) = (0, 0, 0)
Na (½, 1, 0) = (½, 0, 0)
1
0
1
2D projections of 3D structures
Projections (slices of the crystal) make it easier to visualize complex structures
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
“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
Tetrahedral
holes
Octahedral
holes
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
Carbides and nitrides
(TiC, TiN, ZrC, NbC)
What would you predict the properties of these interstitial carbides to be?
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 the
NaCl 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?
Octahedral and tetrahedral holes
Tetrahedral
holes
Octahedral
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), where
the 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 structures
PtN2
PbO
K2PtCl6
HgI2
Hexagonal fluorite?
NiAs is the hexagonal analogue of NaCl.
Is there a hexagonal analogue of fluorite?
Zincblende structure type
http://www.che.kyutech.ac.jp/chem24/hp/english/lecture/crystal%20structure/zincblende/zincblende.htm
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 compounds
that form zincblende vs. wurtzite?
Zincblende vs. wurtzite
Zincblende and wurtzite are examples of polymorphs
(Diamond and graphite are allotropes, which are elemental polymorphs)
ccp
hcp
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 not
occur 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?
MoS2
TiS2
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
Geometry
r+/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…
Spinel structure
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?
The mineral spinel
The mineral spinel is a “normal” spinel…
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?
Spinels and CFSE
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…
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)?
Fe3O4
Octahedral vs. tetrahedral sites
Look for the d-orbital occupancy configurations that give the highest CFSE
NiFe2O4
Is NiFe2O4 a normal or an inverse spinel?
Chromite spinels
Is MIICr2O4 a normal or an inverse spinel?
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)?
Superexchange
Coupling between the 3d electrons of Fe3+ cations on tetrahedral and
octahedral sites is through oxygen 2p electrons – “superexchange”
Magnetic coupling
What type of magnetic coupling is present?
Other systems exhibiting superexchange
NiO
TiO