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