Download Lecture 25 – The Solid State: types of crystals, lattice energies and

2P32 – Principles of Inorganic Chemistry
Dr.M.Pilkington
Lecture 25 – The Solid State: types of crystals, lattice
energies and solubility’s of ionic compounds.
1. Types of crystals: metalic, covalent, molecular and ionic
2. Lattice energy
3. Solubility's of ionic compounds
4. Solubility's as a function of lattice and hydration energies
5. Perovskites and spinels
1. Types of Crystals

The realm of inorganic chemistry was considerably expanded in the early 20th
Century when X-ray diffraction revealed information on the structure of solids.

Solids are composed of atoms, molecules, or ions arranged in a rigid, repeating
geometric pattern
g
p
of particles
p
known as the crystal
y
lattice.

Crystals are usually categorized by the type of interactions operating among the
atoms, molecules or ions of the substance.

These interactions include ionic, metallic, and covalent bonds as well as
intermolecular forces such as hydrogen bonds, dipole-dipole forces and London
dispersion forces.

In the classification of crystals as well as categorizing them by their lattice
types, i.e. monoclinic, cubic, tetragonal etc… we can also classify them according
to their chemical and physical properties. In this respect, we have four types of
crystals, metallic, covalent, (covalent) molecular, and ionic.
1
1. Metallic Crystals

Metals – elements from the left side of the periodic table form crystals in
which each atom has been ionized to form a cation and a corresponding number
of electrons.

The cations are pictured to form a crystal lattice that is held together by a
“sea
sea of electrons
electrons” – sometimes called a Fermi sea.
sea

The electrons of the sea are no longer associated with any particular cation but
are free to wander about the lattice of cations.

We can therefore define a metallic crystal as a lattice of cations held
together by a sea of free electrons.
The sea analogy allows us to picture
electrons flowing from one place in
the lattice to another.

If we shape the metal (copper is a good example) into a wire. If we put electrons
in one end of the wire, electrons will be bumped along the lattice of cations until
some electrons will be pushed out of the other end.

The mobility of the delocalized electrons accounts for electrical conductivity.

Metals are characterized by their tensile strength and the ability to conduct
electricity.
l t i it

Both properties are the result of the special nature of the metallic bond.
Bonding electrons in metals are highly delocalized over the entire crystal.

The great cohesive force resulting from the delocalization is responsible for the
great strength noted in metals.

The bonding strength in metals varies with the number of electrons available as
well as with the size of the atoms.
atoms
i.e. Na – 1 valence electron m.p. 980C
Mg – 2 valence electrons m.p. 6490C
W – 6 valence electrons m.p. 60000C
2

Metal crystals all have a high density which means that they usually have the
hcp or fcc structure.

Magnesium, scandium, titanium, cobalt, zinc and cadmium have the hcp
structure.

Aluminium calcium,
Aluminium,
calcium nickel,
nickel copper,
copper palladium
palladium, silver,
silver platinum
platinum, gold and lead
have the fcc structure.

Alkali metals, iron, chromium, barium, and tungsten have the bcc structure.
2. Covalent Network Crystals

A covalent network crystal is composed of atoms or groups of atoms arranged
into a crystal lattice that is held together by an interlocking network of covalent
bonds.

Covalent bonds ((the result of the sharing
g of one or more pairs
p
of electrons in a
region of overlap between two or perhaps more atoms) are directional
interactions as opposed to ionic and metallic bonds, which are non directional.

For example diamond – each carbon is best thought of as being sp3-hybridized
and that to maximize the overlap of these hybrid orbitals, a C-C-C bond angle of
109.50 is necessary.

Hence the interactions are directional in nature.

Other examples of compounds that form covalent network crystals are silicon
dioxide (quartz), graphite, elemental silicon, boron nitride (BN) and black
phosphorous.
3

The structure of diamond is based on a fcc lattice. There are 8 C atoms at the
centre of the cube, 6 C atoms in the face centre, and 4 more within the unit
cell. Each C is tetrahedrally bonded to four others. This tightly bound lattice
contributes to diamond's unusual hardness. In graphite each C is bonded to
three others and the layers are held together only weakly.

Covalent crystals are hard solids that possess very high melting points.
They are poor conductors of electricity.
3. Molecular crystals

Very soft solids that possess low melting points.

They are poor conductors of electricity.

Molecular crystals consist of such substances as N2, CCI4, I2 and benzene.

Generally, the molecules are packed together as closely as their size and shape
will allow.

The attractive forces are mainly van der Waals (dipole-dipole) interactions.

Water molecules are held together by directional H-bonds.

Intermolecular forces in this case can either be nondirectional as is the case of
crystals of argon, or directional, as in the case of ice.

In the latter case, the H-O···H angle is 109.50, an angle determined by the
geometry of the individual water molecules.
4
Examples of molecular crystals:

Molecules of Argon
g gas
g
H-bonding of water molecules
to form the diamond structure
of ice.
ice
4. Ionic crystals

Hard and brittle solids.

They possess high melting points.



They are poor conductors of electricity, but their ability to conduct increases
drastically in melt.
The packing of spheres in ionic crystals is complicated by two factors :

charged species are present

anions and cations are generally quite different in size
Some general conclusions can be drawn from ionic radii :



within the same period the anions always have larger radii than the cations
the radius of the trivalent cation is smaller than that of the divalent cation,
which is smaller than that of the monovalent cation
It should be realized that the value of any ionic radius only serves as a useful
but approximate size of the ion.. The fact that the ionic radius of Na+ is 0.98Å
does not mean that the electron cloud of the ion never extends beyond this
value. It is significant because when it is added together with the radius of an
anion, e.g. Cl-, the sum is approximately equal to the observed interionic distance.
5
Formation of an Ionic Crystal – when two elements, one a metal with a low
ionization energy and the other a nonmetal with a highly exothermic electron
affinity are combined, electrons are transferred to produce cations and anions.

These forces are held together by non-directional, electrostatic forces known
as ionic bonds.
A hypothetical view of the formation of
s di m chloride,
sodium
hl id the
th constituent
stit
t elements
l m ts
are combined, electrons are transferred
and ionic bonds among the sodium and
chloride ions are formed.

Examples of compounds that form ionic crystals are CsCl , CaF2, KNO3, alumina,
Al2O3, zirconia, ZrO2 (very hard).

Cubic zirconia is an imitation diamond, when crystallized it can be used as a jewel
or it can be used as an industrial product for abrasion.
Melting Points of a Class of Ionic Compounds
LiF – 8450
BeO - 25300
NaF – 9930
MgO - 28520
KF – 8580
CaO - 26140
RbF – 7950
SrO - 24300
CsF- 6820
BaO – 19180
6
2. Lattice Energy
The energy change that accompanies the process in which the isolated gaseous
ions of a compound come together to form 1 mol of the ionic solid.

For a solid composed of monoatomic, single charged ions, such as NaCl, the
lattice energy is the energy corresponding to the reaction shown below:
Na+ (g) + Cl-

(g)
NaCl
(s)
Energy is released in such a process; the energy of the products is lower than
the energy of the reactants. (Remember exothermic thermodynamic quantities
carry a negative
i sign).
i )
Theoretical evaluation of Lattice Energy

First we consider the electrostatic interaction within an ion pair made up of one
sodium cation and one chloride anion.

Assuming the energy of the isolated gaseous ions is taken to be zero, the
potential energy of the ion pair is given by Coulomb’s law:
E = (Z+e)(Z-e)/r
where Z+ = integral charge on cation
Z- = integral charge on anion
e = fundamental charge on an electron
r = interionic distance as measured from center of cation to the center
of the anion
7

If we want the interionic distance to be in Angstrom units and the energy to be in
kJ the exact relationship for Coulomb’s law for one Na+Cl- ion pair is:
E = AZ+Z-/r
where A = 2.308 x
10-21
E = energy kJ
r = interionic distance
distance, Å
Å.




In a crystal we have to sum, all of the ionic interactions in the crystal.
i.e the total Coulombic energy for a Na+ cation must account for all the charged
species surrounding that cation.
For the NaCl lattice, there are 6 anions at a distance of r, 12 other cations at a
distance of √2, 8 anions at a distance of r√3, 6 cations at a distance of 2r and so
forth.
The sum of all of these Coulombic interactions will be the total Coulombic energy
gy
for one sodium chloride cation Ecoul and is given by the following equation:
Ecoul = 6AZ+Z-/r + 12AZ+Z+/r√2 + 8AZ+Z-/r√3 + 6A Z+Z+/2r …
Ecoul = AZ+Z-/r (6-12/√2 + 8/√3 – 6/2 ….)


This series is a constant and depends on the crystal structure
If sodium cations and chloride anions assumed the CsCl or zinc blende structure,
this equation would be different.

These unique series for each crystal structure are known as Madelung constants
(M)
Madelung Constants for Some Common Crystal Structures:
Crystal Structure
Coordination Number
Madelung Constant M
Sodium Chloride
6
1.748
Cesium Chloride
8
1.763
Zinc Blende
4
1.638
8

Using the symbol MNaCl for the Madelung constant unique to NaCl

Ecoul = AZ+Z-MNaCl/r

We can see that M varies with structure type and that it is higher for higher
coordination numbers

Ecoul is the total Coulombic energy for one sodium chloride cation, assuming that
all of the ions are point charges, charges that act as if they are at the very
centre of the hard spheres representing the ions.

If this is the case then Ecoul would be the lattice energy for NaCl

In reality however, this model must be used with caution as ions are not really
h d spheres,
hard
h
but
b electrons
l
surrounding
di a nucleus.
l

If hard spheres approach too closely to one another, a strong repulsive force will
result and we must also consider the energy of this interaction.
3. Solubilities of Ionic Compounds
For example NaCl
NaCl (s)
lattice energy
Na+(g) + Cl-(g)
H 2O
heat of soln
H 2O
Na+(aq) + Cl-(aq)

You need to put in energy to get the ions (salt) into ions in the gas phase.

This energy will be recovered when the ions become hydrated.

“high” lattice energy, “low” hydration energy – salt will be insoluble

“low”
low lattice energy.
energy “high”
high hydration energy – salt will be soluble.
soluble
9
4. Solubility's as a Function of Lattice Energy and Hydration Energies.
Example 1.
NaF
(s)
Na+(g) + F- (g)
H = +885 KJmol-1
Reverse of the lattice Energy
Na+ (g)
Na+ (aq)
H = -405 KJmol-1
F- (g)
F- (aq)
H = -497 KJmol-1
NaF(s)
Na+(aq) + F-(aq)
H = -17 KJmol-1
i
i.e.
exothermic
th
i
G = H-TS
Example 2
CaF2 or fluorite is insoluble in H2O
CaF2 (s)
Ca2+(g) + 2F-(g)
H = 2630 KJmol-1
Ca22+(g)
2F-(g)
Ca 22+ (aq)
2F-(aq )
H = -1592
1592 KJmol-11
H = -994 KJmol-1
CaF2 (s)
Ca
2+
(aq)
+ 2F-(aq)
H = +44 KJ mol-1
reaction is endothermic
10
5. Perovskites and spinels
Perovskites – formula
AIIBIVO3
i.e. Ca2+Ti4+O3
Structure – Ti 4+ ions
are at the corners of
the cube.
Ca2+ ion in the centre of
the cube
O2- at the edge of the
cube
b f
faces.
The +4 ion size must be between 0.414rO2- and 0.732rO2i.e. The +4 ion size 52-92 pm for Octahedral Coordination
and the +2 ion must be 100 pm or greater.
Both of these conditions must be met for ABO3 to be a perovskite.

Representation of a unit cell that is perovskite. The cell is cubic, with Ti4+
centres at the corners of the cube
cube, and O2- ions at the 12 edge sites
sites. The 12
12coordinate Ca2+ ion lies at the centre of the unit cell. Each Ti4+ centre is sixcoordinate, and this can be appreciated by considering the assembly of adjacent
unit cell in the lattice.
11

Perovskites are a large family of crystalline ceramics that derive their name
from a specific mineral known as perovskite (CaTiO3) due to their crystalline
structure.

The mineral perovskite, which was first described in the 1830’s by the geologist
Gustav Rose, who named it after the famous Russian mineralogist Count Lev
Aleksevich von Perovski, typically exhibits a crystal lattice that appears cubic,
though it is actually orthorhombic in symmetry due to a slight distortion of the
structure.

Members of the class of ceramics dubbed perovskites all exhibit a structure
that is similar to the mineral of the same name.

The characteristic chemical formula of a perovskite ceramic is ABO3, with the A
atom exhibiting a +2 charge and the B atom exhibiting a +4 charge. The atoms
of the unusual material are generally arranged so that 12 coordinated A atoms
mark the corners of a cube, octahedral O ions are featured on the faces of that
cube, and octahedral B ions are located in the center of the structure.

Superconductivity, a phenomenon characterized by the disappearance of
electrical resistance in various metals, alloys, and compounds when they are
cooled to very low temperatures, was first observed in 1911 by Heike Kamerlingh
Onnes.

In Onnes' early studies, he noted that the resistance of a frozen mercury rod
abruptly dropped to zero when cooled to the boiling point of helium, 4.2 Kelvin.
He also discovered that a material in a superconducting state can be returned to
its standard, nonsuperconducting condition through exposure to a strong
magnetic field of a certain critical value or by passing a large current through it.
12

Though such findings were considered important, and Onnes was even awarded
the Nobel Prize for Physics in 1913, the extremely cold temperatures required
to instigate superconductivity necessitated the use of liquid helium, which made
it cost p
prohibitive to utilize traditional superconductors
p
for many
y applications.
pp

The discovery of perovskite superconductors revolutionized this field, however,
and by 1987, superconductivity in these materials could be induced above 77K,
the boiling point of liquid nitrogen.

This significant advance made superconductors cheaper to cool to their critical
temperature, since liquid nitrogen is considerably less costly than liquid helium.

The first superconducting perovskite was discovered by IBM researchers
Bednorz and Mueller, who were examining the electrical properties of a family of
materials in the Ba-La-Cu-O system.

One of the materials they were studying was reported to have a critical
temperature of approximately 35 Kelvin, which was a benchmark in field of
superconductivity at the time.

For their discovery, which opened up an entirely new area of study since their
high-temperature superconductors did not conform to the BCS theory widely
believed to govern the activity of all superconductors known up to that time,
Bednorz and Mueller were awarded the Nobel Prize for Physics in 1987.

Meanwhile, between 1986 and 1988 the critical temperature for
superconductivity in perovskite ceramics was raised by more than 100 Kelvin, but
in recent y
years only
y several degrees
g
have been added to this remarkable
elevation.

Many of these minor increases in the critical temperatures of ceramic
superconductors have stemmed from the utilization of increasingly exotic
elements in the base perovskite.
13
Spinels – formula AB2O4



Octahedral and tetrahedral coordination occurs
A and B size must be compatible with octahedral
coordination by the oxygens.
i th
i.e.
the radii
dii must
st b
be b
between
t
52
52pm and
d 92
92pm.
The mineral Spinel
MgAl2O4 , Magnesium Aluminum Oxide
Uses: as a gemstone

Spinel is a very attractive and historically important
gemstone mineral. Its typical red color, although pinker,
rivals the color of ruby.

In fact, many rubies, of notable fame belonging to
crown jewel collections, were found to actually be
spinels.
spinels

Perhaps the greatest mistake is the Black Prince's Ruby
set in the British Imperial State Crown.

Whether these mistakes were accidents or clever
substitutions of precious rubies for the less valuable
spinels by risk taking jewelers, history is unclear.

The misidentification is meaningless
g
in terms of the
value of these gems for even spinel carries a
considerable amount of worth and these stones are
priceless based on their history, let alone their carat
weight and pedigree.
14

Today, expensive rubies are still substituted for by spinel in much the same way
a diamond is substituted by cubic zirconia. Not to commit a fraud or theft but to
prevent one. Spinel may take the place of a ruby that would have been displayed
in public by an owner who is insecure about the rubies safety.

The spinel probably is still valuable but better to lose a $100
$100,000
000 dollar spinel
than a $1 million dollar ruby!

Spinel and ruby are chemically similar.

Spinel is magnesium aluminum oxide and ruby is aluminum oxide. This is probably
why the two are similar in a few properties. Not surprisingly, the red coloring
agent in both gems is the same element, chromium.

Spinel and Ruby also have similar luster (refractive index), density and hardness.
Although ruby is considerably harder (9) than spinel, spinel's hardness (7.5 - 8)
still makes it one of the hardest minerals in nature.
The Mineral Franklinite





Chemical Formula: (Zn, Fe, Mn)(Fe, Mn)2O4, Zinc Iron Manganese Oxide
Class: Oxides and Hydroxides
Group: Spinel
Uses: Important ore of zinc and manganese
Franklinite is one of the minerals found at Franklin, New Jersey, a world famous
locality that has produced many formerly unknown and exotic mineral species. It
is f
found
u in large
g enough
ug quantity
qu
y to serve as a ore of
f zinc
z
and manganese,
m g
, two
w
important strategic and industrial metals. It forms octahedral crystals that are
typical of the spinel group of minerals. Specimens from Franklin often contain
the rounded black grains of franklinite surrounded by white calcite and/or
greenish willemite with a sprinkling of red zincite. Specimens of this exotic and
interesting mineral are truly valued by mineral collectors.
15
The Mineral Magnetite

Chemical Formula: Fe3O4, Iron Oxide

Class: Oxides and Hydroxides

Group: Spinel

Uses: Major ore of iron


Magnetite is a natural magnet, hence the name, giving it a very nice
distinguishing characteristic. Magnetite is a member of the spinel group which
has the standard formula A(B)2O4. The A and B represent usually different
metall ions
i
that
h occupy specific
ifi sites
i
iin the
h crystall structure. In
I the
h case of
f
magnetite, Fe3O4, the A metal is Fe +2 and the B metal is Fe +3; two different
metal ions in two specific sites. This arrangement causes a transfer of electrons
between the different irons in a structured path or vector. This electric vector
generates the magnetic field.
Magnetite, a magnetic compound is present in homing pigeons, migratory salmon,
dolphins, honeybees, and bats. Hence the term “animal magnetism”

Magnetite helps orientation and direction finding in animals. It is thought to help
certain migratory species migrate successfully by allowing them to draw upon the
earth’ss magnetic fields.
earth
fields

The topic of bird migration is complex and not fully elucidated, but magnetite as
a magnetic compass has been proposed to aid in navigation in certain families of
birds.
16

Magnetite was nicknamed lodestone and used by early navigators to locate the magnetic
North Pole. William Gilbert published De Magnete, a paper on magnetism in 1600, about the
use and properties of Magnetite.
Magnetic Compass

The magnetic compass is an old Chinese invention, probably first made in China during the
Qin dynasty (221-206 B.C.). Chinese fortune tellers used lodestones to construct their
fortune telling boards. Eventually someone noticed that the lodestones were better at
pointing out real directions, leading to the first compasses. They designed the compass on a
square slab which had markings for the cardinal points and the constellations.

Th pointing
The
i ti needle
dl was a lodestone
l d t
spoon-shaped
h
d device,
d i
with
ith a h
handle
dl th
thatt would
ld always
l
point south.

Magnetized needles used as direction pointers instead of the spoon-shaped lodestones
appeared in the 8th century AD, again in China, and between 850 and 1050 they seem to
have become common as navigational devices on ships.
17