Materials Engineering (Week 2) Flashcards
The properties of materials are
directly related to what?
The properties of materials are
directly related to their crystal
structure.
What is the engineering relevance of The Structure of Crystalline Solids
-Fracture and plasticity depend on crystal structure
-Also Corrosion, cracking, degradation (-ve aspects)
(– Stress-corrosion in musculoskeletal implants
– Chemical corrosion in oil rigs in harsh marine environments
– Hot corrosion in engines)
-Strengthening and stabilisation at atomic level
(Substituting atoms into existing crystal structure can toughen
materials)
Crystal structures are divided into … …
depending on their … … …
Crystal structures are divided into seven groups
depending on their unit cell geometry
We represent length as using abc, a being in x direction / axis, b in the y and c in the z.
Likewise for angles alpha, beta and gammar, where (alpha is the angle between y and z), (beta x and z), (gammar x and y)
Name all 7 crystal structures:
Cubic
Hexagonal
Tetragonal
Rhombohedral (Trigonal)
Orthorhombic
Monoclinic
Triclinic
Cubic crystal structure:
a=b=c
alpha=beta=gammar=90 (degrees)
Hexagonal crystal structure:
a=b =/ c
alpha = beta = 90
gammar = 120
Tetragonal crystal structure:
a=b=/ c
alpha = beta = gammar = 90
Rhombohedral (Trigonal)
a=b=c
alpha=beta=gammar =/ 90
Orthorhombic
a=/b=/c
alpha=beta=gammar = 90
Monoclinic
a=/b=/c
alpha=gammar = 90 =/ beta
Triclinic
a =/ b =/ c
alpha =/ beta =/ gammar
what are Reproducible way to describe, the positioning and structure of Crystalline solids
-Where atoms are in a material.
-What the crystalline planes and orientations are
Point coordinates for unit cell
corner are…
Point coordinates for unit cell
corner are 111 (not abc)
The position of a point within a unit cell is specified in
terms of its coordinates as fractional multiples of the unit
cell length, so 1a is the full unit cell length.
Point coordinates Translation
Translation: integer multiple of
lattice constants → identical
position in another unit cell
Crystallographic Directions
what does an overbar represent
overbar represents a
negative index
Crystallographic Directions
Algorithm
- Vector repositioned (if necessary) to pass
through origin. - Read off projections in terms of
unit cell dimensions a, b, and c - multiply or divide all three numbers by a
common factor to reduce them to the
smallest integer values - Enclose in square brackets, no commas
[uvw]
Crystallographic Directions
Families of directions
For some crystal structures nonparallel
directions with different indices are equivalent
→ families of directions <uvw></uvw>
Example: Directions in cubic crystals with the
same indices without regard to order or sign
are equivalent, e.g. [100], [100], [010], [010],
[001] and [001] all belong to the same family
<100>.
Linear Density of Atoms equation
LD = no. of atoms / Unit length of direction vector
Crystallographic Directions in Hexagonal Crystals
A four axis (Miller-Bravais) coordinate
system is used to achieve that all
equivalent directions have the same
indices.
*The axes a1
, a2 and a3 are contained
within a single plane (basal plane).
*The z axis is perpendicular to the
basal plane.
Four indices are used to describe
crystallographic directions [uvtw] in
hexagonal crystal structures.
corresponding to projections onto the
axes a1
, a2
, a3 and z.
Crystallographic Directions in Hexagonal Crystals
Algorithm
- Vector repositioned (if necessary) to pass
through origin. - Read off projections in terms of unit cell dimensions a1, a2, a3, or c
- Adjust to smallest integer values
- Enclose in square brackets, no commas
[uvtw]
Crystallographic Planes
MIller Indices:
Reciprocals of the (three) axial
intercepts for a plane, cleared of fractions &
common multiples. All parallel planes have
same Miller indices.
MIller Indices:
Algorithm
- Read off intercepts of plane with axes in
terms of a, b, c - Take reciprocals of intercepts
- Reduce to smallest integer values
- Enclose in parentheses, no
commas i.e., (hkl)
If a plane doesn’t intercept an axis what do you set its intersection distance/ point at?
Infinity, so then when you divide the direction/ length by infinity you get 0
Family of Planes:
A family of planes contains all planes that are
crystallographically equivalent {hkl}.
In cubic crystals all planes having the same indices
irrespective of their sign and order are equivalent.