Topic 7 Crystal Strucutre and Classification of Solids

baconossifiedMechanics

Oct 29, 2013 (3 years and 10 months ago)

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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