Chap11-Part5

Chap11-Part5 - 1
 Structures
of
Solids


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Unformatted text preview: 1
 Structures
of
Solids
 Solids
can
be
either
crystalline
or

amorphous.
 In
crystalline
solids,
the
components
are
arranged
in
a
highly
 ordered,
repe99ve
structure.

These
materials
typically
have
 flat
surfaces
called
faces
that
make
well‐defined
angles
with
 each
other.

Examples
are
quartz
&
diamond.
 In
amorphous
solids,
the
components
do
not
have
long‐range
 highly
ordered
structures.

These
materials
lack
faces
and
 well‐defined
shapes.

Examples
are
rubber
and
glass.
 2 Crystalline
Solids
 pyrite
(FeS2)
 iron
sulfide
 fluorite
(CaF2)
 calcium
fluoride
 amethyst
(SiO2)
 silicon
dioxide
 3 Comparison
of
Crystalline
and
Amorphous
Silicon
Dioxide
 The
structures
are
three‐ dimensional.

The
two‐ dimensional
building
block
has
 a
fourth
oxygen
atom
coming
 out
of
the
plane
and
 interac9ng
with
other
silicon
 atoms.
 crystalline,
in
which
par9cles
 are
in
highly
ordered
 arrangement.
 4 Comparison
of
Crystalline
and
Amorphous
Silicon
Dioxide
 –  amorphous,
in
which
 there
is
no
par9cular
 order
in
the
 arrangement
of
 par9cles.
 5
 Lead
crystal,
(also
called
crystal),
is
lead
glass.

Lead
oxide
 added
to
the
molten
glass
gives
lead
“crystal”
a
much
higher
 index
of
refrac9on
than
normal
glass,
and
consequently
much

 greater
"sparkle".
 glass
bowl
 Waterford
“crystal”
bowl
 6 Unit
Cells
 Crystalline
solids
are
build
from
numerous
repea9ng
structures
 called
unit
cells.

In
the
example
of
a
wallpaper
paTern
shown
 above,
each
blue
square
is
a
unit
cell.

The
unit
cell
could
also
 be
defined
with
the
purple
icons
at
the
corners.
 7 Crystal
La:ces
 A
crystal
can
be
described
by
a
3D
array
 of
points
called
a
crystal
laXce.
 Each
point
in
the
laXce
is
called
a
laXce
 point.
 The
laXce
points
describe
the
ver9ces
of
 the
unit
cell,
and
correspond
to
iden9cal
 environments
in
the
crystal.
 A
simple
example
is
when
the
crystal

 consists
of
iden9cal
atoms
and
each
laXce

 point
defines
the
posi9on
of
an
atom.
 Units
cells
are
parallelepipeds
–
3D
structures
in
which
each
of
the
six
surfaces
is
 a
parallelogram.

The
unit
cell
is
defined
by
the
shapes
of
the
parallelograms
and

 the
angles
that
the
surfaces
make
with
each
other.

 a
parallelogram
 8 Types
of
La:ce
Systems
 These
laXce
systems
are
a
grouping
of
crystal
structures
according
 to
the
axial
system
used
to
describe
their
laXce.
 Each
laXce
system
consists
of
a
set
of
three
axes
in
a
par9cular
 geometrical
arrangement.

 There
are
seven
laXce
systems.

 9 1.
Triclinic
 The
triclinic
laXce
is
the
least
symmetric
of
 the
14
three‐dimensional
Bravais
laXces.

 It
is
the
only
laXce
type
that
itself
has
no
 mirror
planes.
 Eg:
Wollastonite
(CaSiO3)
 10 2.
Monoclinic
 ‐ Forms
a
rectangular
Prism
 ‐ 
Hence
two
vectors
are
perpendicular
 ‐ Eg:
Gypsum
(CaSO4.2H2O)
 Primi9ve
 monoclinic
 Centered
 monoclinic
 11 3.
Orthorhombic
 Simple
 Orthorhombic
 Base‐centered
 Body‐centered
 Orthorhombic
 Orthorhombic
 Face‐centered
 Orthorhombic
 ‐All
three
vectors
are
perpendicular
to
each
other
 12 4.
Rhombohedral
 Vectors
of
equal
length
and
not
perpendicular
 Eg:
Hema9te
(Fe2O3)
 13 5.
Tetragonal
 Tetragonal
crystal
laXces
result
from
 stretching
a
cubic
laXce
along
one
of
 its
laXce
vectors,
so
that
the
cube
 becomes
a
rectangular
prism
with
a
 square
base
(a
X
a)
and
height
(c,
 which
is
different
from
a).
 Simple
 Tetragonal
 Body‐centered
 Tetragonal
 Eg:
Ru9le
(TiO2)
 14 6.
Hexagonal
 A
diamond
shaped
or
hexagonal
base
with
 sides
of
equal
length
(a
=
b).
The
base
is
 perpendicular
to
the
longest
side
(length
c)
of
 the
unit
cell
 An
atom
is
centered
on
each
corner
of
the
 unit
cell.
An
atom
is
also
centered
inside
the
 unit
cell.
 15 Highly
Symmetric
 7.
Cubic
 Eg:
Pyrite
(FeS2)

 Simple
 Cubic
 Body‐centered
 Cubic
 Face‐centered
 Cubic
 The
simplest
case
is
the
cubic
unit
cell
in
which
all
sides
are
 squares
and
the
angles
are
all
90o.
 16 14
Bravais
LaXce
 structures

 Wikipedia
17 Cubic
Unit
Cells
 Each
sphere
corresponds
to
a
laXce
point.
 LaXce
points
are
 only
at
the
corners.
 LaXce
points
are
 at
the
corners
&
 one
is
at
the
center
 LaXce
points
are
 at
the
corners
&
 at
the
centers
of

 each
face.
 18
 Cubic
Unit
Cells
 19
 Crystal
Structure
of
Table
Salt
(NaCl)
 Na+
 Cl‐
 20
 Crystal
Structure
of
NaCl:

Face‐Centered
Cubic
 Cl‐
 Na+
 The
unit
cell
can
be
defined
with
the
ver9ces
corresponding
either

 to
the
chlorine
atoms
(lej)
or
the
sodium
atoms
(right).


In
this
 schema9c
representa9on,
the
volumes
of
the
atoms
have
been
 reduced.

Note
that
one
atom
is
in
the
center
of
the
unit
cell.
 21
 RelaPve
Atomic
Sizes
in
the
NaCl
Unit
Cell

 edge
 There
are
12
edges
 per
cubic
cell.
 22
 How
many
atoms
per
unit
cell
in
NaCl
crystals?
 Chlorine:
 6
faces
(1/2
atom
per
face)
=
3
atoms
 8
corners
(1/8
atom
per
corner)
=
1
atom
 total
=
4
atoms
 Sodium:
 1
center
(1
atom
per
center)
=
1
atom
 12
edges
(1/4
atom
per
edge)
=
3
atoms
 total
=
4
atoms
 23
 The
geometric
arrangement
of
ions
in
crystals
of
LiF
is
the
same
as
that

 in
NaCl.
The
Unit
cell
of
LiF
is
4.02Ao
on
an
edge.
Calculate
the
density
 
of
LiF.
 24
 The
geometric
arrangement
of
ions
in
crystals
of
LiF
is
the
same
as
that

 in
NaCl.
The
Unit
cell
of
LiF
is
4.02Ao
on
an
edge.
Calculate
the
density
 
of
LiF.
 FCC
structure:

4
Li+
and
4
F‐
atoms
in
the
unit
cell.
 Atomic
mass
of
Li+
=
6.94
amu
 Atomic
mass
of
F‐
=
19
amu

 25
 The
geometric
arrangement
of
ions
in
crystals
of
LiF
is
the
same
as
that

 in
NaCl.
The
Unit
cell
of
LiF
is
4.02Ao
on
an
edge.
Calculate
the
density
 
of
LiF.
 FCC
structure:

4
Li+
and
4
F‐
atoms
in
the
unit
cell.
 Atomic
mass
of
Li+
=
6.94
amu
 Atomic
mass
of
F‐
=
19
amu

 Mass
of
LiF
in
unit
cell
=
4(6.94)
+4(19)
=
103.8
amu
 Density
=
mass/volume

 26
 1
amu
=
1.66
X
10‐27
kG
=
1.66
X
10‐24
g
 1g=
1/1.66X10‐24
=
6.024X1023
amu
 27
 The
geometric
arrangement
of
ions
in
crystals
of
LiF
is
the
same
as
that

 in
NaCl.
The
Unit
cell
of
LiF
is
4.02Ao
on
an
edge.
Calculate
the
density
 
of
LiF.
 FCC
structure:

4
Li+
and
4
F‐
atoms
in
the
unit
cell.
 Atomic
mass
of
Li+
=
6.94
amu
 Atomic
mass
of
F‐
=
19
amu

 Mass
of
LiF
in
unit
cell
=
4(6.94)
+4(19)
=
103.8
amu
 Density
=
mass/volume

 


















(103.8amu)









(1g)









(1Ao)3
 Density
=

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐


‐‐‐‐‐‐‐‐‐‐‐‐


‐‐‐‐‐‐‐‐‐‐‐‐


 



















(4.02
Ao)3









6.02X1023







(10‐8
cm)3
 Density
=
2.65
g/cm3
 28
 Close
Packing
of
Spheres
 How
atoms
pack
in
crystals
?
Observe
the
fruit
arrangements
in
fruit

 Markets?
 Two
repea9ng
structures
are
shown.


 In
(b),
called
hexagonal
close
packing,
the
sequence
is
ABABAB…
 In
(c),
called
cubic
close
packing,
the
sequence
is
ABCABCABC…
 29
 Close
Packing
of
Spheres
 hexagonal
 cubic
 In
both
structures,
each
atom
has
12
nearest
neighbors
(6
in‐plane,
3
above
and
3

 below).

The
coordina9on
number
is
thus
12.

Also
in
both
structures,
74%
of
the

 total
volume
is
occupied
by
atoms
and
26%
is
occupied
by
free
space.
 In
a
primi9ve
cubic
arrangement,
the
coordina9on
number
is
6
and
the
occupied
 volume
is
52%.
In
a
body‐centered
cubic
arrangement,
the
coordina9on
number
 is
8
and
the
occupied
volume
is
68%.

The
structure
in
(c)
is
face‐centered
cubic.

 30
 Bonding
in
Solids
 31
 Molecular
Solids
 These
materials
are
held
together
by
non‐covalent
bonds
(dipole‐dipole,

 London
dispersion,
and
hydrogen
bonding
interac9ons).
 Because
the
forces
are
rela9vely
weak,
these
materials
are
rela9vely
 soj
and
have
rela9vely
low
mel9ng
points
(e.g.,
below
200oC).
 Most
compounds
that
are
gases
or
liquids
at
room
temperature
form

 molecular
solids
at
low
temperatures
(e.g.,
Ar,
H2O
and
CO2).
 32
 Molecular
Solids
 The
proper9es
depend
not
only
on
the
strength
of
the
interac9ons
but
on

 the
ability
of
the
molecules
to
close‐pack.

(a)
Benzene
has
a
higher
mel9ng
 point
than
toluene
because
benzene
can
pack
more
closely.
(b)
Benzene
has
 a
lower
boiling
point
than
toluene
because
toluene
has
stronger
intermolecular
 interac9ons
in
the
liquid
state.
(c)
Phenol
has
both
higher
mel9ng
points

 and
boiling
points
because
its
OH
group
allows
for
hydrogen
bonding.
 33
 Covalent‐Network
Solids
 These
materials
are
held
together
by
networks

 of
covalent
bonds
(e.g.,
quartz
or
SiO2).
 They
are
very
hard
and
have
very
high
mel9ng

 points
(1000’s
oC).
 Diamond
is
an
array
of
carbon
atoms
bonded
 to
other
carbon
atoms
by
single
C‐C
bonds.
 Graphite
is
also
a
carbon‐based
solid
but
 has
a
different
structure.

The
atoms
are

 arranged
in
hexagonal
layers
where
each
 atom
bonds
to
three
others
in
the
layer.


 The
planes
of
bonded
hexagons
are
held

 together
by
noncovalent
dispersion
forces.

 34
 Ionic
Solids
 These
materials
are
held
together
by
ionic
(i.e.,
electrosta9c)
 interac9ons.
 The
material
strengths
vary
greatly
with
the
charges
on
the

 interac9ng
ions:
 
Na(+)Cl(‐)
melts
at
801oC
&
 
Mg(2+)O(2)
melts
at
2852oC.
 There
are
several
basic
types
of
crystal
structures
found
in
 ionic
solids.
 35
 Ionic
Solids:

(1)
NaCl
Crystal
Structure
 type:
face‐centered
cubic
 coordina9on
#
for
Na+:

6
Cl‐
 coordina9on
#
for
Cl‐:

6
Na+
 Other
compounds
with
this

 crystal
structure:
 Cl‐
 Na+
 LiF,
KCl,
AgCl,
CaO
 36
 Ionic
Solids:

(2)
CsCl
Crystal
Structure
 Cs+
 Cl‐
 Cl‐
 or
 Cs+
 type:
body‐centered
cubic
 coordina9on
#
for
Cs+:

8
Cl‐
 coordina9on
#
for
Cl‐:

8
Cs+
 other
compounds
with
this
structure:
CsBr,
AlCo,
BeCu,
MgCe
 37
 Ionic
Solids:

(3)
ZnS
Crystal
Structure
 S2‐
 Zn2+
 type:
face‐centered
cubic
coordina9on
#
for
Zn2+:

4
S2‐ 
 
 
coordina9on
#
for
S2‐:

4
Zn2+
 
 
 
 other
compounds
with
this
structure:

AgI,
BeS,
CuCl,
HgS
 38
 Ionic
Solids:

(3)
ZnS
Crystal
Structure
 39
 Ionic
Solids:

(3)
ZnS
Crystal
Structure
 40
 Ru9le
is
a
mineral
composed
of
Ti
and
O.

Its
unit
cell
is
shown
below.


 red
=
O
 grey
=
Ti
 What
is
the
chemical
formula
of
this
mineral?
 (a)
Find
the
number
of
Ti
atoms
per
unit
cell.
 (b)
Find
the
number
of
O
atoms
per
unit
cell.
 (c)
Determine
the
formula.



 41
 Ru9le
is
a
mineral
composed
of
Ti
and
O.

Its
unit
cell
is
shown
below.


 red
=
O
 grey
=
Ti
 What
is
the
chemical
formula
of
this
mineral?
 (a)
Find
the
number
of
Ti
atoms
per
unit
cell.
 #
Ti
per
unit
cell
=
1
center
(1
atom/center)
+
8
corners
(1/8
atom/corner)
=
2
atoms.
 (b)
Find
the
number
of
O
atoms
per
unit
cell.
 42
 Ru9le
is
a
mineral
composed
of
Ti
and
O.

Its
unit
cell
is
shown
below.


 red
=
O
 grey
=
Ti
 What
is
the
chemical
formula
of
this
mineral?
 (a)
Find
the
number
of
Ti
atoms
per
unit
cell.
 #
Ti
per
unit
cell
=
1
center
(1
atom/center)
+
8
corners
(1/8
atom/corner)
=
2
atoms.
 (b)
Find
the
number
of
O
atoms
per
unit
cell.
 #
O
per
unit
cell
=
4
face
(1/2
atom/face)
+
2
center
(1
atom/center)
=
4
atoms.
 (c)
Determine
the
formula.



 43
 Ru9le
is
a
mineral
composed
of
Ti
and
O.

Its
unit
cell
is
shown
below.


 red
=
O
 grey
=
Ti
 What
is
the
chemical
formula
of
this
mineral?
 (a)
Find
the
number
of
Ti
atoms
per
unit
cell.
 #
Ti
per
unit
cell
=
1
center
(1
atom/center)
+
8
corners
(1/8
atom/corner)
=
2
atoms.
 (b)
Find
the
number
of
O
atoms
per
unit
cell.
 #
O
per
unit
cell
=
4
face
(1/2
atom/face)
+
2
center
(1
atom/center)
=
4
atoms.
 (c)
Determine
the
formula.


TiO2
 44
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