Materials Engineering (Week 2) Flashcards

1
Q

The properties of materials are
directly related to what?

A

The properties of materials are
directly related to their crystal
structure.

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2
Q

What is the engineering relevance of The Structure of Crystalline Solids

A

-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)

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3
Q

Crystal structures are divided into … …
depending on their … … …

A

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)

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4
Q

Name all 7 crystal structures:

A

Cubic
Hexagonal
Tetragonal
Rhombohedral (Trigonal)
Orthorhombic
Monoclinic
Triclinic

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5
Q

Cubic crystal structure:

A

a=b=c
alpha=beta=gammar=90 (degrees)

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6
Q

Hexagonal crystal structure:

A

a=b =/ c
alpha = beta = 90
gammar = 120

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7
Q

Tetragonal crystal structure:

A

a=b=/ c
alpha = beta = gammar = 90

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8
Q

Rhombohedral (Trigonal)

A

a=b=c
alpha=beta=gammar =/ 90

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9
Q

Orthorhombic

A

a=/b=/c
alpha=beta=gammar = 90

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10
Q

Monoclinic

A

a=/b=/c
alpha=gammar = 90 =/ beta

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11
Q

Triclinic

A

a =/ b =/ c
alpha =/ beta =/ gammar

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12
Q

what are Reproducible way to describe, the positioning and structure of Crystalline solids

A

-Where atoms are in a material.

-What the crystalline planes and orientations are

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13
Q

Point coordinates for unit cell
corner are…

A

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.

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14
Q

Point coordinates Translation

A

Translation: integer multiple of
lattice constants → identical
position in another unit cell

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15
Q

Crystallographic Directions
what does an overbar represent

A

overbar represents a
negative index

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16
Q

Crystallographic Directions
Algorithm

A
  1. Vector repositioned (if necessary) to pass
    through origin.
  2. Read off projections in terms of
    unit cell dimensions a, b, and c
  3. multiply or divide all three numbers by a
    common factor to reduce them to the
    smallest integer values
  4. Enclose in square brackets, no commas
    [uvw]
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17
Q

Crystallographic Directions
Families of directions

A

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>.

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18
Q

Linear Density of Atoms equation

A

LD = no. of atoms / Unit length of direction vector

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19
Q

Crystallographic Directions in Hexagonal Crystals

A

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.

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20
Q

Crystallographic Directions in Hexagonal Crystals
Algorithm

A
  1. Vector repositioned (if necessary) to pass
    through origin.
  2. Read off projections in terms of unit cell dimensions a1, a2, a3, or c
  3. Adjust to smallest integer values
  4. Enclose in square brackets, no commas
    [uvtw]
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21
Q

Crystallographic Planes
MIller Indices:

A

Reciprocals of the (three) axial
intercepts for a plane, cleared of fractions &
common multiples. All parallel planes have
same Miller indices.

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22
Q

MIller Indices:
Algorithm

A
  1. Read off intercepts of plane with axes in
    terms of a, b, c
  2. Take reciprocals of intercepts
  3. Reduce to smallest integer values
  4. Enclose in parentheses, no
    commas i.e., (hkl)
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23
Q

If a plane doesn’t intercept an axis what do you set its intersection distance/ point at?

A

Infinity, so then when you divide the direction/ length by infinity you get 0

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24
Q

Family of Planes:

A

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.

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25
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
26
The atomic arrangement for a crystallographic plane can influence ...
catalytic and mechanical properties of a material.
27
We want to examine the atomic packing of crystallographic planes Planar density equation ≡
PD = Number of atoms centered on a plane / Area of plane
28
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.
29
Crystals as Building Blocks Some engineering applications require single crystals: (3)
diamond single crystals for abrasives turbine blades semiconductors for electronics applications
30
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.
31
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
32
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.
33
Isotropic
If grains are randomly oriented
34
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).
35
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.
36
Crystallographic points, directions and planes are specified in terms of...
indexing schemes.
37
Crystallographic directions and planes are related to...
atomic linear densities and planar densities.
38
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
39
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.)
40
Types of Imperfections (3)
Point defects Line defects Area defects
41
Point Defects (3)
Vacancy atoms Interstitial atoms Substitutional atoms
42
Vacancy atoms (Point defect)
vacant atomic sites (empty) in a structure. causing distortion in planes
43
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)
44
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
45
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
46
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.
47
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
48
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.
49
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.
50
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
51
Dislocations
-are line defects, -slip between crystal planes result when dislocations move, -produce permanent (plastic) deformation
52
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
53
Burger's vector, b expresses what?
magnitude and direction of lattice distortion
54
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
55
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
56
Surface defects can become what?
Surface defects can be adsorption sites for catalysis
57
Planar/interfacial defects
Interfacial defects are two-dimensional boundaries that separate regions with different crystal structures and /or crystallographic orientations
58
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.
59
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
60
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
61
A high angle grade boundary =
high angle of misalignment and vise versa
62
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
63
Bulk (Volume) defects (4)
- Pores - Cracks - Foreign inclusions - Other phases
64
When are bulk defects introduced
Bulk defects are usually introduced during processing and fabrication steps
65
Grain size can be specified in terms of ...
average grain volume, diameter or area.
66
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.)
67
The mechanical behavior of a material describes how ...
The mechanical behaviour of a material describes how a material deforms under an applied load
68
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
69
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).
70
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
71
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
72
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
73
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
74
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)
75
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
76
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
77
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
78
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).
79
Is the elastic modulus for every material the same in every direction?
No, we just normally assume so
80
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
81
Plastic Deformation
The plastic regime corresponds to the bonds being permanently deformed and do not springing back to their original equilibrium distance
82
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
83
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
84
* Materials that show little of no plastic deformation and break at small strains (<0.03) are...
Brittle Materials
85
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
86
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
87
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
88
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
89
Define Hardness
Resistance to permanently indenting the surface
90
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
91
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)
92
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
93
How is the engineering and true stress and strain related (equations):
True stress (sigma) = sigma (1+ε) True Strain (ε) = ln(1+ε)