Chapter 3 (continued)
• Silicate Ceramics
• Primarily composed of
__________________.
• Two most abundant elements in
earth’s crust. The key components
of most soils, rocks, clays and sand.
• ________________
Chapter 3 (continued)
• basic unit ______
An _____ surrounded
by ________ in a
______________
• ______________
51% ionic
• This basic unit has a charge, but is made
neutral when they bond in _________
__________________ structures,
________________________________
(Figure 3.10)
1
Chapter 3 (continued)
Silica SiO2
• Each oxygen is ______________________
• overall this creates a 1:2 ratio of silicon to oxygen
• The charge is _______________
• Either a _________________________ structure
can result
Chapter 3 (continued)
Three crystalline forms:
• quartz
• cristobalite
• tridymite
• These are ____________
___________________
• not ________________
ρ = 2.65 g/cm3 for quartz
• very strongly bonded
Tmelt = 1710 ̊C
Figure 3.11
cristobalite
2
Chapter 3 (continued)
The Silicates
• ________ of the oxygens can be bonded
• 1 shared oxygen
(Si2O7) -6
• 2 shared oxygens
(Si3O9) -6
(Si6O18) -12
(SiO3)n-2n
a chain structure
Figure 3.12
• If an oxygen is _____________, another positive charge is
needed
Chapter 3 (continued)
• (Si2O5) -2
sheets
• the (-2) charge is associated
with the single bonded oxygen
• _________________ maintained
by ionic bonding with a layer
containing ______________
• Bonding _______ the sheet is
strong, weaker _________
the layers
• sheets slide past each other
• ex.
talc
Figure 3.13
3
Chapter 3 (continued)
Layered Silicates
• Kaolinite Clay
• only secondary atomic
bonding between sheets
Figure 3.14
Chapter 3 (continued)
Carbon
• Several polymorphic forms __________________
__________________
• Not a true ceramic, but:
ƒ graphite classified as such
ƒ diamond has a zinc blende structure
4
Chapter 3 (continued)
Diamond
• carbon in a _____________
arrangement
• same structure as
___________
• bonds are ________________
(Figure 3.16)
Chapter 3 (continued)
Diamond
(cont.)
• Interesting and attractive set of physical properties
ƒ hardest known material
ƒ ______ electrical conductivity
ƒ ___________ thermal conductivity
• gemstones, abrasives, thin films
5
Chapter 3 (continued)
Graphite
• layers of ____________
_________ carbon atoms
• strong ______________
_______ a layer, ______
secondary bonding
__________ layers
• an excellent lubricant
• high strength
• good chemical stability
(Figure 3.17)
Chapter 3 (continued)
SiO2 structures
__________
___________
___________
__________
Carbon structures
quartz - very strong
___________________
diamond - very strong
___________________
clay – moderate strength
sheets formed with ______
___________________
______________________
between sheets
graphite – very weak
sheets formed with strong
covalent bonds
_____________________
between sheets
glass – networks formed
polymers – weak material
with __________________ chains formed with _____
______________________ _________________
_____________________
between chains
6
Chapter 3 (continued)
Crystallographic Points, Directions, and Planes
• This is a notation system that lets us communicate about
crystal systems. The nomenclature is specific and will be
enforced.
• We’ll focus on the cubic unit cell
Chapter 3 (continued)
• Remember the standard coordinate system will place the
origin in the lower, left, back corner of the unit cell.
ƒ x-axis comes out of the page,
ƒ y-axis is to the right within the plane of the page
ƒ z-axis is up within the plane of the page.
7
Chapter 3 (continued)
Points
• Points are identified within the crystal lattice as their
location within the __________________________ ,
but scaled by the ___________________ .
• (1, 1, 1) instead of (a, a, a)
• Parentheses with commas
• A translation by an integer multiple in any or all directions,
leads to an identical position in another unit cell.
Chapter 3 (continued)
Directions
• The direction indices are the ___________ of the direction,
_________________________________________ and
__________________________________.
1
A vector is positioned so that it passes through the
origin. May be moved parallel to its current position.
2
The vector projections on the axes are determined.
3
These are reduced to the _____________________ .
8
Chapter 3 (continued)
Direction Nomenclature
• square brackets, no commas
• negative directions indicated by overbars
• (see Figure 3.22 and Example Problems 3.9 and 3.10)
• Directions are equivalent, when the atomic spacing along
each direction is the same.
(ex. [1 0 0], [0 1 0], [0 0 1], [1 0 0], [0 1 0], [0 0 1]
• Hexagonal crystals require 4 directional coordinates
Chapter 3 (continued)
Crystal Planes
• Planes are identified by the ________________.
• Defined as the reciprocals of the fractional intercepts, with
fractions cleared, which the plane makes with the axes.
• All _________________ have the same Miller indices
9
Chapter 3 (continued)
Procedure to Determine Miller Indices
1
Choose a plane that does not pass through the origin
2
Identify where the plane intercepts the coordinate axes.
A plane that is parallel to the axes has an intercept of 4
3
Take the ________________________________
4
Multiply or divide to find the __________________
Chapter 3 (continued)
Crystal Plane Nomenclature
• parentheses, no commas
• negatives are indicated by overbars
• Changing the sign of all indices, identifies a parallel plane
• The Miller indices of a plane are the same as the direction
coordinates of the vector perpendicular to the plane.
10
Chapter 3 (continued)
Alternate Method Determining Miller Indices
• Remember that the Miller indices of a plane are the same as
the vector perpendicular to the plane, and the changing the
sign of all Miller indices does not change the plane .
• This procedure works best for problems where you want to
identify the plane given a set of points
Chapter 3 (continued)
Alternate Method Procedure
1
Find _______________________ that lie in the plane.
2
Take the ______________ of these vectors. This finds the
vector perpendicular to both the original vectors. (The
right-hand rule.) This is a determinant.
3
Clear the fractions.
4
The direction indices of the resulting vector are the Miller
indices of the plane.
11
Chapter 3 (continued)
• example:
Determine the Miller indices of the plane that
passes through A = (1, 0, 0), B = (½, ½, 1)
and C = (0, 1, ½ )
• AB = [ ½ - 1
½ - 0 1 - 0 ] = [ -½ ½ 1 ]
• AC = [ 0 - 1
1-0
½ - 0 ] = [ -1 1 ½ ]
Chapter 3 (continued)
Example
(cont.)
• cross product = i ( ¼ - 1) - j ( -¼ + 1 ) + k ( - ½ + ½ )
• These are the Miller indices
• Any two vectors can work.
_____________
Try BC x CA
12
Chapter 3 (continued)
Linear and Planar Atomic Densities
• For both linear and planar densities,
ƒ you only include atoms if their ___________________
ƒ you treat the atoms as circles
ƒ you want a ____________ line segment or plane
Chapter 3 (continued)
Definitions
• linear atomic density = -----------------------------------------
• planar atomic density = ----------------------------------------
13
Chapter 3 (continued)
Close-Packed Crystal Structures
• Both FCC and HCP structures have packing factors of 0.74
• This is as high as possible.
• The difference between the two is demonstrated by Figures
3.29, 3.30, and 3.31.
Chapter 3 (continued)
A
A sites
B sites
A
B
B
C
B
C
B
B
C
B
B
A
B
C
C sites
14
Chapter 3 (continued)
Close-Packed Crystal Structures
(cont.)
• HCP has an __________ stacking sequence in the _______
_______________. Replication occurs every __________.
• FCC has an ________ stacking sequence in the closestpacked planes. Replication occurs every __________.
• The closely packed planes in the FCC structure are the
( 1 1 1 ) planes.
• The important difference in properties caused by this
stacking difference will be explained in Chapter 7.
Chapter 3 (continued)
HCP Stacking Arrangement
A sites
Top layer
B sites
Middle layer
A sites
Bottom layer
15
Chapter 3 (continued)
Crystalline, Polycrystalline and Noncrystalline Materials
• The regular packing demonstrated results in a single crystal
of a material.
• Most materials consist of many small crystals or _______.
These are termed _________________.
• There is atomic mismatch at the _____________. These
are important to the physical properties of a material.
• If a material does not demonstrate a regular packing
arrangement it is noncrystalline or amorphous.
Chapter 3 (continued)
Solidification
• (Not included in text)
• Related to the concepts of polycrystallinity and grain size.
• Can be split into 2 steps:
(1) _____________
(2) _____________
• 2 main mechanisms for nucleation
16
Chapter 3 (continued)
Homogeneous Nucleation
• When the "nucleus" starts with just the atoms themselves.
• Simplest form of nucleation
• When a pure metal is cooled below freezing point, slow
moving atoms bond together. This forms an ________.
Embryos are continuously being formed and redissolved.
• If an embryo gets large enough it is called a nucleus. A
nucleus must reach a _____________ before it is stable.
Chapter 3 (continued)
Homogeneous Nucleation
(cont.)
• 2 energy processes involved.
ƒ Energy _______ as atoms “join” the nucleus.
f (r3)
ƒ Energy _______ by nucleus to build new surfaces f(r2)
• With smaller nuclei, the area term dominates
redissolving more likely ( r2 > r3 )
• At larger nuclei, the volume term dominates
solidification more likely ( r3 > r2 )
17
Chapter 3 (continued)
Heterogeneous Nucleation
• Nucleation occurs on an ________, the container surface,
or another solid.
• _____________ than homogenous nucleation
For both types of nucleation:
• Each ____________________________ that has nearly
perfect packing.
• As these grains grow together there is a mismatch.
Chapter 3 (continued)
Polycrystallinity
18
Chapter 3 (continued)
Silica Glasses
• Silica can be made to exist as
glass
(a non-crystalline solid)
Si
Oxygen
crystalline solid
(see earlier in chapter)
Adapted from Fig.
3.18(b), Callister 6e.
Chapter 3 (continued)
• Common glasses are silica with
_________________ such as
CaO and Na2O
• They break the 3-dimensional
network by _______________
• The effect is to lower the
_________________ and
___________ of the glass
(Figure 3.41)
19