# Topic 7 Crystal Strucutre and Classification of Solids

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29 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Solids

Solids have “resistance” to changes in both
shape and volume

Solids can be
Crystalline or Amorphous

Crystals are solids that consist of a periodic
array of atoms, ions, or molecules

If this periodicity is preserved over “large”
(macroscopic) distances the solid has
“Long
-
range Order”

Amorphous solids

do not have Long
-
Range
Order

Short Range Order

Solids

Crystals Solids
:

Short
-
range Order

Long
-
range Order

Amorphous solids:

~Short
-
range Order

No

Long
-
range Order

Crystals

The periodic array of atoms, ions, or
molecules that form the solids is called
Crystal Structure

Crystal Structure = Space (Crystal) Lattice
+ Basis

Space (Crystal) Lattice
is a
regular periodic

arrangement of
points

in space, and is purely
mathematical abstraction

Crystal Structure
is formed by “putting” the
identical atoms (group of atoms) in the points
of the space lattice

This group of atoms is the
Basis

Crystal Structure and
Classification of Solids

Crystals

Crystal Structure = Space Lattice + Basis

Solids

Different solids can have the
same geometrical arrangements
of atoms

Properties are determined by
crystal structure, i.e. both crystal
lattice and basis are important

Example:

Si, Diamond (C), GaAs, ZnSe have
the same geometry

Si and C (Diamond) Form
“Diamond Structure”

GaAs or ZnSe form a structure
called “Zinc Blende”

http://www.neubert.net/Crystals/CRYStruc.html

Solids

Different arrangements of atoms (even the same
atoms) give different properties

Single layer is graphene

Solid Models: Close
-
Packed Spheres

Most atoms or ions forming solids have spherical
symmetry

Considering the atoms or ions as solid spheres we
can imagine crystals as closely packed spheres

Classification of Solids

Since we know the structure of atoms that
form solids, we can classify them via the
type of bonds that hold solids together

In this case we say that we classify solids
according to the nature of bonding

There are four classes of solids:

metallic, ionic, covalent, and molecular

All the forces holding solids together have
electrostatic origin

General Considerations

There must be an attractive force

An apparent candidate is the Coulomb Force

Here
r
is a distance between atoms (ions) forming a solid

What stops atoms (ions) from getting closer than they
do?

When ions are very close to each other, other forces arise.
These are the so
-
called
short
-
range repulsive forces
, due
to rearrangement of electrons as nuclei approach

Equilibrium distance,
r
0
, is point at which energy is at
a minimum, forces are balanced

General Considerations

Ionic Solids

Ionic crystals consist of the negative and positive
ions, attracted to each other

Electron from one of the atoms removed and transferred
to another: NaCl, AgBr, KCl

When the crystal is formed excess heat is generated

Crystalline Structure of NaCl

Ionic Solids

Let’s find the energy required to transfer an electron
from Na to Cl and then to form a NaCl molecule

To remove an electron from Na (ionize the atom) one
needs to “spend” 5.14eV
(compare with the ionization
energy of a hydrogen atom?)

Na + 5.14eV

+

+ e
-

When a Cl atom captures an electron, 3.62eV of energy is
released

Cl + e
-

-

+ 3.62eV

Ionic Solids

In solid, Na
+

and Cl
-

are brought together at the
distance
r
0

2.51Å [Å = 10
-
10
m = 0.1nm]

The total energy is lowered due to the Coulomb
attraction

The results is
-
5.73 eV

Thus when a
NaCl “molecular unit” of NaCl solid
is formed the following occurs

Na + 5.14eV

+

+ e
-

Cl + e
-

-

+ 3.62 eV

Cl
-

+
Na
+

Cl+5.73eV

Na + Cl

NaCl+
4.21eV

Ionic Solids

The energy gain for NaCl solid is
~ 4.21 eV per
NaCl pair

This is the energy required to break an NaCl
molecule and restore neutral Na and Cl atoms

This energy is huge (in 1 cm
3)
:

4.21
×
1.6
×
10
-
19

(Joules per pair)
×

3
×

10
22
(pairs) =
20200
J
oules

To more accurately calculate the total
electrostatic energy, need to calculate
interaction of each ion with all other ions in
the crystal

Ionic Solids

I
n ionic crystals all electrons are bound to
the ions:
There are no free electrons!!!

Thus
most

ionic crystals are insulators

There are ionic conductors, where ions, and
not electrons conduct: Example: AgI

Covalent Solids

The covalent bond is usually formed from two
electrons, one from each atom participating in the
bonding: These electrons are
shared

by the atoms

Quantum Mechanics is required to calculate binding
energies

The probability of finding electrons forming the bond
between the two atoms is high

Covalent bonds are very strong and directional

Covalent Solids

In general, since there are no free electrons, these
crystals are insulators or semiconductors

Crystalline Structure of Diamond

Compare

Covalent Solids

Ionic Solids

Mixed Bonding Solids

The electrons forming the covalent bond tend to be
localized in the region between the two atoms

If the atoms elements forming the covalent solid
are different

e.g., Zn & Se for ZnSe then the electrons a localized
closer to one of the atoms (with higher electron affinity)

We say that the bond is partially covalent and
partially ionic

Metallic Bond

Metals may be seen as collections of stationary
ions surrounded by a sea of electrons

Can be viewed as limit of covalent bonding, when
electrons are shared by
all the ions
in the crystal

The metallic bond is not directional

Molecular Solids

Very weak bonding: Dipole
-
Dipole Interaction

Liquid Crystals, Ice

low melting temperatures

Classification of Solids by
Conductivity

Another way of classifying solids, in
addition to (a) crystal structure and (b)
type of bonds between atoms is (c)
electrical conductivity

Conductors

Insulators

Semiconductors