Specify Composition of an Alloy

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Specify Composition of an Alloy

• Composition
• concentration or relative content of a specific
  element or constituent in an alloy
• Expressed in wt or atom

For a hypothetical alloy with two elements (1
2)

• - weight percent

m1 mass of component 1

• atom percent

nm1 number of moles of component 1 nm1 mi/A
g / (g/mol) mol (where A is atomic wt in
g/mol)
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Composition Conversions
Conversion from wt to atom
(atom of element 1)
(atom of element 2)
Conversion from atom to wt
(wt of element 1)
(wt of element 2)
A atomic wt (g/mol) C wt C atom
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Determine number of atoms/cm3 of 1 element in a
solid solution given the concentration of that
element in a specified wt.
NA 6.023 x 1023 atoms/mol C1 wt of that
element (element 1) ?1, ?2 density of
elements 1 and 2 (g/cm3) A1 atomic wt of
element 1 (g/mol)
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Linear Defects (Dislocations)

• one-dimensional defects around which atoms
  are misaligned
• slip between crystal planes result when
  dislocations move
• produce permanent (plastic) deformation.

Schematic of Zinc (HCP)
before deformation
after tensile elongation
slip steps
Adapted from Fig. 7.8, Callister 7e.
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Type of Linear Defects (Dislocations)

• Edge dislocation (?) -- occurs when an
  extra half-plane of atoms inserted in a crystal
  structure
• a linear defect that centers around the line
  that is defined by extra half-plane of atoms
• Dislocation line the line that extends along the
  end of the extra half-plane of atoms is
  perpendicular to plane of page (for an edge
  dislocation)
• Leads to lattice distortion
• Burgers vector, b measure of magnitude and
  direction of lattice distortion associated with a
  dislocation
• b is perpendicular to dislocation line (for an
  edge dislocation)

Above dislocation line, atoms squeeze together
Below dislocation line, atoms pulled apart
Less lattice distortion as distance from
dislocation line increases
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Edge dislocation (?)
Lattice planes
Edge dislocation line
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Type of Linear Defects (Dislocations)

• Screw dislocation C
• A crystal is cut along a plane only ½ the way
  through and ½ of crystal is twisted
• Formed by shear stress
• a twisting distortion where the dislocation line
  is the origin of the twist
• b is parallel to dislocation line

Lattice planes

• Burgers vector, b measure of magnitude and
  direction of lattice distortion associated with a
  dislocation

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Type of Linear Defects (Dislocations)

• Mixed Dislocation
• Most solids exhibit mixed dislocations exhibit
  components of edge and screw dislocations.

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Edge, Screw, and Mixed Dislocations
Adapted from Fig. 4.5, Callister 7e.
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• Dislocations are visible by electron microscopy
• Dislocations are introduced via
• solidification (slow cooling)
• during plastic deformation, and
• by thermal stresses (which occur during rapid
  cooling)
• Dislocation density increases with plastic
  deformation
• Due to dislocations, metals possess high
  plasticity characteristics ductility and
  malleability.

Titanium Alloy TEM image
Adapted from Fig. 4.6, Callister 7e.
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f12_20_pg434
Magnification limit
1 nm
10,000,000X
1,000,000X
50,000X
2000X
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Interfacial Defects

• Interfacial Defects
• Boundaries with 2 dimensions
• typically separate regions with different
  crystal structures and/or crystallographic
  orientations - two types

1. External Surface - crystal structure
terminates - surface atoms not bonded to
max nearest neighbors higher surface energy
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• 2. Grain Boundaries
• Separates two small grains or crystals having
  different crystallographic orientations in
  polycrystalline materials (p. 64, next slide)
• the interface separating two adjoining grains
  having two crystallographic orientations

High degree of crystallographic misalignment
Low degree of crystallographic misalignment
Adapted from Fig. 4.7, Callister 7e.

• Features
• Different degrees of atom misalignment
  (depicted)
• Atoms bonded less regularly along grain boundary
• Higher energy
• Higher chemical reactivity
• Impurity atoms tend to segregate along grain
  boundaries

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Polycrystalline refers to crystalline materials
that are composed of more than one crystal or
grains (collection of small crystals) see pp
64-65. Two grains meet along a grain boundary
(d).
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• Grain Boundaries
• disrupt the motion of dislocations through a
  material improve strength
• - a dislocation passing into grain B will have
  to change its direction of motion (p. 189)

Fig. 7.14
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• Grain Boundaries Formation via Solidification
• Solidification- result of casting (cooling) 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
• See also Fig. 3.17 (polycrystalline materials)

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Ceramic Defects (Sec. 12.5)
Point Defects in Ceramics a. Vacancy
Pair Schottky Defect - in an ionic solid, a
defect consisting of a cation-vacancy and anion
vacancy pair - maintains charge
neutrality b. Vacancy Interstitial Frenkel
Defect - in an ionic solid, a cation-vacancy
and cation-interstitial pair cation leaves
normal position and goes to interstitial
site -maintains charge neutrality
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Question 5.7 A sheet of steel 2.5 mm thick has
nitrogen atmospheres on both sides at 900 ?C and
is permitted to achieve a steady-state diffusion
condition. The diffusion coefficient for
nitrogen in steel at this temperature is 1.2 x
10-10 m2/s and the diffusion flux is found to be
1.0 x 10-7 kg/m2s. Also, it is known that the
concentration of the nitrogen in the steel at the
high-pressure face is 2 kg/m3. How far into the
sheet from this high pressure side will the
concentration be 0.5 kg/m3? Assume a linear
concentration profile.
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Example 5.2 (carburizing) Consider one such Fe-C
alloy (steel) that initially has a uniform carbon
concentration of 0.25 wt and is to be treated at
950 ?C (1750 ?F). If the concentration of the
carbon at the surface is suddenly brought to and
maintained at 1.2 wt, how long will it take to
achieve a carbon content of 0.8 w at a position
0.5 mm below the surface? The diffusion
coefficient for carbon in iron at this
temperature is 1.6 x 10-11 m2/s assume that the
steel piece is semi-infinite.
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