Crystalline Arrangement of atoms

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Crystalline Arrangement of atoms
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Chapter 4IMPERFECTIONS IN SOLIDS

• The atomic arrangements in a crystalline lattice
  is almost always not perfect.
• There are defects in the way atoms are arranged
  in the crystalline solids.
• So we can say that in crystalline solids some
  Lattice Irregularities are always present.
• These crystalline defects are not bad. Some are
  intentionally introduced to improve the material.

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Types of Crystalline Defects

• POINT DEFECTS are classified on the basis of
  their geometry and dimensionallity.
• POINT DEFECTS
• (Vacancies, self interstitials, impurity atoms)
• LINE DEFECTS (one dimensional) (Dislocations)
• INTERFACIAL DEFECTS (two dimensional) (Grain
  Boundaries)

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VACANCYi.e. an atom missing from lattice position
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IMPURITY ATOMS
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POINT DEFECTS
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Interstitials
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Crystalline Defects
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Vacancies

• Vacancies are always present in the crystalline
  solids.
• Vacancies are created during process of
  solidification or due to thermal agitations of
  lattice atoms.
• At a given temperature there is always present an
  EQUILIBRIUM CONCENTRATION of VACANCIES.

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EQUILIBRIUM CONCENTRATION OFVACANCIES

• Equilibrium concentration of vacancies increase
  with temperature!

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MEASURING ACTIVATION ENERGY
We can get Q from an experiment.
Measure this...
Replot it...
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ESTIMATING VACANCY CONC.
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Find the equil. of vacancies in 1 m of Cu
at 1000 oC.
Given
Answer
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Impurities in Solids

• Pure metal containing only one type of atoms
  Not Possible
• Impurity atoms are always present.
• These atoms exists as point defects.
• In alloys, impurity atoms (alloying element
  atoms) are intentionally added.
• An alloy is usually a solid solution of two or
  more types of atoms.
• e.g. Fe C ? Steel

SOLVENT
SOLID SOLUTION
SOLUTE
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TYPES OF SOLID SOLUTIONS

• SOLID SOLUTION

SUBSTITUTIONAL SOLID SOLUTION Solute atoms
replace (substitute) the solvent atoms in the
solvent lattice
INTERSTITIAL SOLID SOLUTION Solute atoms occupy
the interstitial sites of the solvent lattice
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Solid Solutions
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Conditions For Substitutionl Solid Solubility

• Four Conditions must be satisfied for obtaining
  appreciable (large) solubility of the
  substitutional solute in a given solvent lattice.
• Atomic Size Factor The atomic size difference
  between the solute and solvent atoms must be less
  than ? 15.
• Crystal Structure Crystal structure of both
  solute and solvent must be same.
• Electronegative The electro negativity
  difference must be small. If this difference is
  large ionic compound will form instead of solid
  solution.
• Valence Higher valance metals will dissolve
  easily than low valance metals.

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Ni Cu Will they have large Solid
Solubility? Check! 4 conditions
Ni Cu Atomic Size 0.125
nm 0.128 nm Crystal structure FCC
FCC Electronegativity 1.8
1.9 Valence 2
1 Answer Yes they will
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HOW about CU Zn
Zn Cu Atomic Size
0.133 nm 0.128 nm Crystal structure
HCP FCC Electronegativity 1.6
1.9 Valence 2
1 Answer No they wont
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SPECIFICATION OF COMPOSITION

• Two most common ways to specify the composition
  or concentration are
• Weight or mass percent weight of a particular
  element relative to the total alloy weight.
• Atom percent number of moles of an element in
  relation to the total moles of the elements in
  the alloy.
• Weight
• where m1 and m2 represent the weight or mass of
  elements.
• Atom
• where No. of moles (nm) (mass in grams) /
  Atomic weight

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SPECIFICATION OF COMPOSITION (Contd.)

• COMPOSITION CONVERSIONS
• Weight to Atom
• Atom to Weight

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SPECIFICATION OF COMPOSITION (Contd.)

• Weight to Kg/m3 ( mass of one component per
  unit volume of material)

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Example 4.2

• Derive Equation 4.6a
• Solution
• Total alloy mass,

Atom of element 1,
Simplifies to
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DISLOCATIONS

• Dislocations are LINEAR DEFECT and represent a
  line around which atoms in the crystalline
  lattice are misaligned.
• Two Types of Dislocations
• EDGE DISLOCATION
• SCREW DISLOCATION
• Also MIXED DISLOCATION

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EDGE DISLOCATIONRepresented by a half atomic
plane the edge of which ends within the crystal
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EDGE DISLOCATION
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EDGE DISLOCATION
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SCREW DISLOCATION
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SCREW DISLOCATION
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MIXED DISLOCATION
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MIXED DISLOCATION
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BURGERS VECTOR

• Burgers Vector b represents the magnitude and
  direction of lattice distortion created by the
  dislocation.
• FOR EDGE DISLOCATION b is perpendicular to
  dislocation line.
• FOR SCREW DISLOCATION b is parallel to
  dislocation line.

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BURGERS VECTOR

• FOR METALLIC MATERIALS
• The BURGERS VECTOR for a dislocation lies along a
  closed packed direction.
• The Magnitude of the BURGERS VECTOR is equal to
  the interatomic or interpalnar spacing.

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BURGERS VECTOR
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DISLOCATIONS
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4.5 Interfacial Defects

• Interfacial defects are boundaries that have two
  dimensions and normally separate regions of the
  materials that have different crystal structures
  and/or crystallographic orientations.
• These imperfections include external surfaces,
  grain boundaries, twin boundaries, stacking
  faults, and phase boundaries.
• EXTERNAL SURFACES
• One of the most obvious imperfection boundaries
  is the external surface
• The crystal structure terminates
• Surface atoms are not bonded to the maximum
  number of nearest neighbors ? higher energy state
  than interior atoms.
• To reduce this energy, if possible materials tend
  to minimize surface area ? not possible for
  solids.

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INTERFACIAL DEFECTS(GRAIN BOUNDARIES)

• Boundary separating two small grains or crystals
  having different crystallographic orientations in
  polycrystalline materials.
• Within the boundary region, which is probably
  just several atom distances wide, there is some
  atomic mismatch in a transition from the
  crystalline orientation of one grain to that of
  an adjacent one.
• Various degrees of crystallographic misalignment
  between adjacent grains are possible ( Figure
  4.7).

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4.5 Interfacial Defects (Contd.)

• Tilt boundary
• One simple small-angle grain boundary
• Figure demonstrates how a tilt boundary having an
  angle of misorientation q results from an
  alignment of edge dislocations.
• Twist boundary
• When the angle of misorientation is parallel to
  the boundary
• Due to an array of screw dislocations

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• The atoms are bonded less regularly along a grain
  boundary ? interfacial or grain boundary energy
  similar to surface energy.
• Grain boundaries are more chemically reactive
  than the grains themselves as a consequence of
  this boundary energy.
• Impurity atoms often preferentially segregate
  along these boundaries because of their higher
  energy state.
• Because of less total boundary area, the total
  interfacial energy is lower in large or
  coarse-grained materials than in fine-grained
  ones.
• Grains grow at elevated energy to reduce the
  total boundary energy