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.
Crystallographic Planes (hexagonal crystals)
In hexagonal unit cells the same idea is used. Four
indices (hkil) are used to achieve that all equivalent
planes have the same indices
The atomic arrangement for a crystallographic plane can
influence …
catalytic and mechanical properties of a material.
We want to examine the atomic packing of
crystallographic planes
Planar density equation ≡
PD = Number of atoms centered on a plane / Area of plane
Packing density and slip
What are slips?
Slip occurs on the most densely packed
crystallographic planes and in the directions that
have the greatest atomic packing.
Crystals as Building Blocks
Some engineering applications require single crystals: (3)
diamond single
crystals for abrasives
turbine blades
semiconductors for
electronics applications
Crystals as Building Blocks
Properties of crystalline materials
often related to crystal structure (1)
-Example: Quartz fractures more
easily along some crystal planes
than others.
Polycrystals
Most engineering materials are polycrystals
Each “grain” is a single crystal.
* If grains are randomly oriented, overall component properties are not directional.
- Grain sizes typ. range from 1 nm to 2 cm
Anisotropy
Physical properties of single crystals of some
substances depend on the crystallographic direction
in which measurements are taken.
E.g. elastic modulus, electrical conductivity, etch
rates (e.g. silicon)
* Directionality of properties = anisotropy is associated
with atomic/ionic spacing in the crystallographic
direction investigated.
* Degree of anisotropy increases with decreasing
structural symmetry → triclinic structure are highly
anisotropic.
Isotropic
If grains are randomly
oriented
Single vs Polycrystals:
Single:
-Properties vary with
direction: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron
Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are oriented:
material is textured /
anisotropic (e.g. magnetic
texture for iron).
X-Ray Diffraction (calc spacing between planes of certain crystals): (3)
-Diffraction gratings must have spacings comparable to
the wavelength of diffracted radiation.
-Can’t resolve spacings less than the wavelength
-Spacing is the distance between parallel planes of
atoms.
Crystallographic points, directions and planes are
specified in terms of…
indexing schemes.
Crystallographic directions and planes are related
to…
atomic linear densities and planar densities.
Materials can be single crystals or polycrystalline.
Material properties generally vary with … crystal
orientation (i.e., they are anisotropic), but are generally
non-directional (i.e., they are isotropic) in …
with randomly oriented grains.
single
polycrystals
Imperfections in solids can effect what?
give an example
Imperfections in solids can have a profound effect on the
properties of materials,
e.g. mechanical properties of metals
change significantly when alloyed.
(e.g., grain boundaries control crystal slip).
Defects may be desirable or undesirable
(e.g., dislocations may be good or bad, depending
on whether plastic deformation is desirable or not.)
Types of Imperfections (3)
Point defects
Line defects
Area defects
Point Defects (3)
Vacancy atoms
Interstitial atoms
Substitutional atoms
Vacancy atoms
(Point defect)
vacant atomic sites (empty) in a structure.
causing distortion in planes
Equilibrium Concentration:
Vacancies
Equation
- Equilibrium concentration varies with temperature!
No. of defects / No. of potential
defect sites (Each lattice site is a potential vacancy site) =exp (-Activation energy / Boltzmann’s constant x Temp)
Nv / N = exp ( -Qv / kT)
Measuring Activation Energy
Using the following equation Nv / N = exp ( -Qv / kT)
ln both sides, and plot a graph ln (Nv / N) against 1/T
gradient = -Qv / k
Observing Equilibrium Vacancy Conc.
Low energy electron
microscope to view
* Increasing T causes
surface island of
atoms to grow, because the equilibrium Vacancy conc.
increases via atom motion from the crystal to the
surface, where they join the island
Island grows/shrinks to maintain
equil. vancancy conc. in the bulk
Point defects
Self-Interstitials:
-“extra” atoms positioned between atomic sites.
causing distortion of planes.
In metals a self interstitial causes large distortions in
the lattice and exist in significantly lower
concentrations than vacancies.
Impurities in solids (2)
give one example
Pure metals consisting of one type atom
are impossible.
* Most commonly used metals are alloys,
i.e. impurities added intentionally
e.g. alloying silver with copper increases its
mechanical strength
Point Defects in Alloys
(2 outcomes in impurity ‘B’ is added to host ‘A’)
Solid solution of B in A (i.e., random dist. of point defects)
Substitutional solid solution or Interstitial solid solution
Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
–different composition
–often different structure.
Imperfections in Solids
Conditions for substitutional solid solution (S.S.) (4)
– 1. delta r (atomic radius) < 15%
– 2. Proximity in periodic table
* i.e., similar electronegativities
– 3. Same crystal structure for pure metals
– 4. Valency
* All else being equal, a metal will have a greater tendency
to dissolve a metal of higher valency than one of lower
valency
If the electronegativity difference is too great, the metals will
tend to form intermetallic compounds instead of solid solutions.
Imperfections in Solids
Specification of composition (2 equations)
weight percent
C1 = (m1 / m1 + m2) x 100
m1 = mass of component 1
atom percent
C’1 = (n subm1 / n subm1 + n subm2) x 100
n subm1 = number of moles of component 1
Dislocations
-are line defects,
-slip between crystal planes result when dislocations move,
-produce permanent (plastic) deformation
Imperfections in Solids
Line defects (3)
Linear Defects (Dislocations)
– Are one-dimensional defects around which atoms are
misaligned
* Edge dislocation:
– extra half-plane of atoms inserted in a crystal structure the
edge of which terminates within the crystal
– b ⊥ to dislocation line
* Screw dislocation:
– spiral planar ramp resulting from shear deformation
– b parallel to dislocation line
Burger’s vector, b expresses what?
magnitude and direction of
lattice distortion
Imperfections in Solids:
Edge Dislocation (2)
- Atoms above
dislocation are
squeezed together,
the ones below are
pulled apart - The magnitude of
distortion
decreases with
distance from the
dislocation line
Motion of Edge Dislocation (processs)
Dislocations move in response to an external stress σ.
* Dislocation motion requires the successive bumping of a half plane of atoms
* Bonds across the slipping planes are broken and remade in succession.
* As soon as a critical shear stress is reached, the dislocation starts
moving and deformation is no longer elastic but plastic, because the
dislocation will not move back when the stress is removed
Surface defects can become what?
Surface defects can be adsorption sites for
catalysis
Planar/interfacial defects
Interfacial defects are two-dimensional
boundaries that separate regions with
different crystal structures and /or
crystallographic orientations
Planar/interfacial defects (2 types)
- External surfaces
reconstruction of surfaces to reduce surface
energy due to dangling bonds - Grain boundaries
Boundary separating two grains with different
crystallographic orientations.
Solidification
Solidification- result of casting of molten material
– 2 steps
* Nuclei form
* Nuclei grow to form crystals – grain structure
Start with a molten material – all liquid
Crystals grow until they meet each other
Grain Boundaries
- regions between crystals
- transition from lattice of
one region to that of the
other - slightly disordered
- Interfacial energy
analogous to surface
energy - low density in grain
boundaries
– high mobility
– high diffusivity
– high chemical reactivity
A high angle grade boundary =
high angle of misalignment
and vise versa
Planar Defects in Solids (2)
One case is a twin boundary (plane)
– Essentially a reflection of atom positions across the twin
plane.
Stacking faults
– For FCC metals an error in ABCABC packing sequence
– Ex: ABCABABC
Bulk (Volume) defects (4)
- Pores
- Cracks
- Foreign inclusions
- Other phases
When are bulk defects introduced
Bulk defects are usually introduced
during processing and fabrication steps
Grain size can be specified in terms of …
average grain volume, diameter or area.
Can the number and types of defects be varied and controlled?
The number and type of defects can be varied
and controlled (e.g., T controls vacancy conc.)
The mechanical behavior of a material
describes how …
The mechanical behaviour of a material
describes how a material deforms under an
applied load
The mechanical behavior of a material is derived from what?
The mechanical behaviour of a material is derived from the
chemical bonding present
An approximation of chemical bond acting as springs is useful
for determining the mechanical properties of materials
Separating atoms:
what does the shape of the potential energy curve for a PE- Distance graph describe?
- The shape of the potential energy curve
describes the difficulty in separating different
atoms - A ‘sharper’ potential well indicates more
difficulty in separating the two atoms (whereas a gradually curve means atoms can be more easily seperated).
Measuring mechanical properties
Mechanical properties of materials could be
found by separating atoms from one another
but this is difficult (although note that not
impossible!) as the size of atoms are small
* Materials are large, so mechanical testing is
carried out on these!
* Mechanical testing involves separating the
atoms in the material by applying a force
Mechanical testing
* We need to know two quantities in order to
decide if the atoms are easy to separate:
– The force that is applied to separate the atoms in
the material
– The distance the atoms separate by, shown as the
amount the material deforms under the applied
force
Mechanical testing equipment is used to apply what?
Mechanical testing equipment is used to apply
a displacement (exert a force, tensile or compressive), and record the force
What is an elastic response of a material?
If we apply force continually then there
will be a corresponding continual
displacement
All materials will show a linear response
to this applied force
* If the force is removed then material
returns to its original size
* This linear response indicates an elastic
response of a material
Common States of Stress (5)
Simple tension: cable
Torsion (a form of shear): drive shaft
Simple compression
Bi-axial tension: Pressurized tank (pushing out)
Hydrostatic compression: Fish underwater
For each state of stress, use the Ao (inital cross- sectional area)
Measurement of strain
*Strain gauges are small conductive grids
that are bonded to the surface of a test
coupon.
*The change resistance is directly related to
the strain on the specimen
Features on this stress-strain curve allow us to
understand what?
Features on this stress-strain curve allow us to
understand the mechanical properties of a
material
Hooke’s Law
A linear relationship between
stress and strain is known as
Hooke’s Law.
The gradient is known as the Elastic Modulus E
such that sigma = E x strain
The elastic modulus E tells us what?
The elastic modulus E tells us how easy it is to pull apart the bonds in
the material, (the lower the easier it is to pull apart).
Is the elastic modulus for every material the same in every direction?
No, we just normally assume so
Poisson’s ratio, v:
When we tensile test the material, there will be caused an axial strain εA and a transverse strain εT.
The Poisson’s ratio (ν)
describes this through:
v = - (εT / εA)
v has dimensionless units
Plastic Deformation
The plastic regime corresponds to
the bonds being permanently
deformed and do not springing
back to their original equilibrium
distance
What does Plastic Deformation cause in materials?
Plastic deformation causes necking and an associated large
reduction in the cross-sectional area of the material with strain
Materials that show plastic deformation up to
large strains are known as…
Ductile Materials
Ductile materials can often fail in a
process known as ‘necking’. This is
when significant plastic
deformation occurs locally
- Materials that show little of no plastic
deformation and break at small strains (<0.03)
are…
Brittle Materials
Give Examples of Ductile and Brittle Materials
EXAMPLE 1 – Bone is typically a ductile material. Plastic deformation
can often be repaired. At old age, bone can become brittle
EXAMPLE 2 – Tooth has a high elastic modulus but is brittle. Large
deformation is not desirable as gum damage may occur
EXAMPLE 3 – Skis need to be fairly ductile due to bending and impact
which often occurs
Toughness
- Toughness is an important material parameter that decribes
the amount of energy absorbed before fracture
The area defined by the curve is
equal to ½ force x extension.
If we consider the units, this
gives Nm or J
Therefore, a tough material
requires a large energy (J) in
order to fracture
Ultimate Strength (σf)
Ultimate Strength (σf) is generally the maximum
amount of force per unit area that the material can
sustain.
- Note: strength is sometimes defined in terms of the
testing configuration i.e. tensile strength, compressive
strength
Yield strength (σy)
Yield strength (σy) is the maximum force per unit area
that a material can sustain before plastic deformation
occurs
- Sometimes the stress just before the material fails is
lower than the ultimate strength and is typically called
the rupture point
Define Hardness
Resistance to permanently indenting the surface
Large hardness means:
– resistance to plastic deformation or cracking in
compression
– better wear properties
- Hardness is directly related to tensile strength i.e. a
material with a large tensile strength is also hard
A larger hardness value indicates a resistance
of the material to permanent indentation
True stress and strain
The true stress in the material (σT) must therefore be related
to the cross-sectional area at a particular instance in time (Ai)
by:
Sigma sub(T) = F / Ai
- The true strain εT has to be corrected based on the initial
length l0 and the sample length at a particular instance in time
li using:
εT = ln( li / lo)
Do we use engineering stress and strain or true stress and strain?
While true stress and strain are most
accurate for characterising material
properties, engineering stress and strain
are the easiest to measure and are almost
always used in mechanical testing
How is the engineering and true stress and strain related (equations):
True stress (sigma) = sigma (1+ε)
True Strain (ε) = ln(1+ε)
