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IMPERFECTIONS IN SOLIDS’’ - Home - Materials Science ... in... · PDF filecrystalline structure ... materials are profoundly influenced by the presence of ... Why study Imperfections

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    IE-114 Materials Science and General Chemistry


  • 1) Imperfect crystal

    2) Types of Imperfections (Point, Linear, Area)

    3) Microscopic Examination of defects and

    the structure of materials


  • Perfectly ordered

    crystalline structure


    Such an idealized solid generally does not exist

    All solids contain large number of various

    defects or imperfections

    Defects may exist:

    1) In impure metals or alloys (Substitutional or interstitial foreign


    2) During solidification (e.g. Grain boundaries, dislocations, vacancies) 3) During deformation (e.g. Dislocations)

  • The properties (mechanical, optical, electrical, etc.) of the materials are profoundly influenced by the presence of imperfections (defects)

    The influence is not always adverse, often specific characteristics are enhanced.

    EXAMPLE 1: Mechanical property

    Materials are stronger when they have defects

    Pure iron & Fe-C alloy

    Pure iron : soft and ductile

    Fe-C alloy (steel) : strong and tough

    EXAMPLE 2: Electrical conductivity

    Electrical conductivity decreases when materials have defects

    Electrical conductivity of pure copper is higher than that of impure copper Impure Copper: Copper containing impurity (unwanted) elements

    Why study Imperfections in Solids?

  • O-Dimensional (point) defects

    (associated with one or two atomic positions)



    a) Interstitial atoms

    b) Substitutional atoms

    1-Dimensional (line) defects

    Dislocations (edge, screw and mixed dislocations)

    2-Dimensional (area) defects

    Stacking Faults

    External Surfaces

    Grain Boundaries (High angle and small angle grain boundaries)

    3-Dimensional (volume) defects

    Cracks, pores, foreign inclusions

    Types of Imperfections:

  • Vacancies

    Self interstitials

    Impurities (seen in solid-solution alloys)

    vacant atomic sites in a structure.

    Vacancydistortion of planes

    O-Dimensional (point) defects

    A lattice vacancy is equivalent to missing atom or ions (in case of ionic crystal).

    Formed during solidification or as a result of atomic vibration (atomic vibration increases by temperature)

    1) Vacancy

  • Equilibrium concentrations of


    * As T increases the number of vacancies increases exponentially.

    For most of the metals just below melting point, the fraction of vacancies (N/Nv) is

    on the order of 10-4. This means one lattice site out of 10.000 is empty.

  • Example:

    Find the equilibrium # of vacancies in 1m3 of Cu at 1000oC.



  • "extra" atoms positioned between atomic sites.


    of planes

    Atoms of same type accomodate into interstitial sites,

    which are not occupied under ordinary circumstances.

    Self interstitial defects produce large lattice distortion.

    Because self-interstitial atoms usually larger than the void

    space (interstitial sites).

    2) Self-Interstitials:

  • A pure metal consisting of only one type of atom just isnt

    possible; impurity or foreign atoms will always be present, and

    some will exist as crystalline point defects.

    The addition of impurity atoms to a metal will result in the formation of SOLID SOLUTION or a new second phase (, ,


    Solvent: Represents the element or compound that is

    present in the greatest amount (host atoms)

    Solute : An element or compound present in a minor

    concentration (e.g. Impurity atoms)

    3) Impurities in solids

  • A foreign atom (the solute), whether it be an impurity atom or deliberate

    alloying addition, can occupy one of two distinct positions in a crystal,

    (1) Substitutional alloy

    (e.g., Cu in Ni)

    (2)Interstitial alloy

    (e.g., C in Fe)

    Solid Solutions

    Solute atoms substitute for solvent atoms in a

    crystalline lattice Solute atoms( C, H, O, N) fit into spaces

    between solvent atoms in a crystalline lattice.

  • Some important features for

    substitutional solid solution

    1) Atomic size difference should be less than 15%. Otherwise the solute

    atoms will create substantial lattice distortions and a new phase will form.

    2) Crystal structure should be the same.

    3) Electronegativities should be similar to prevent the ionic bonding.

    4) Valances:Other factors being equal, a metal has a higher tendency to dissolve another metal of higher valency.

    EXAMPLE: Cu-Ni solid solution. The type is substitutional. WHY?

    Because: a) Radii for Cu and Ni are 0.128 and 0.125 nm respectively.

    b) They both have FCC structure.

    c) Their electronegativities are 1.9 and 1.8 for Cu and Ni respectively.

    d) The most common valence is +1 for Cu and +2 for Ni.

  • Impurity atoms fill the voids or interstices among the host atoms.

    Interstitial atoms introduce lattice strains since most of the interstitial atoms have atomic radii higher than interstitial sites radius

    For metals with a high APF, the interstitial positions are small in size and therefore the diameter of the impurity atoms should be smaller than that of the host atoms.

    The concentration of impurity atoms is low (

  • Summary of point defects

  • Specification of Composition

    Weight percent

    100x %BA




    mA = mass of component A

    Atomic percent

    nA = number of moles of component A= mA/ MWA

    Consider an alloy system containing components A and B;

    100x %BA




    MWA = molecular weight of A, gr/mol

  • Composition Conversions

    Assume that you have an A-B alloy;

    at. % A + at. % B =100 % wt. % A + wt. % B =100 % or

    at.% A = (wt.%A / MWA) / [(wt.%A / MWA) + (wt.%B / MWB)]

    at.% B = (wt.%B / MWB) / [(wt.%A / MWA) + (wt.%B / MWB)]

    Where MW is molecular weight of each component, gr/mol

    wt.% A = (at.%A x MWA) / [(wt.%A x MWA) + (wt.%B x MWB)]

    wt.% B = (at.%B x MWB) / [(wt.%A x MWA) + (wt.%B x MWB)]

    Convertion from wt% to at%

    Convertion from at% to wt%

  • cause slip between crystal plane when they move,

    produce permanent (plastic) deformation.

    Dislocation: It is a group of point defects forming a linear one

    dimensional defect in the structure of the material.

    Edge Dislocation

    Screw Dislocation

    Mixed Type of Dislocation

    Types of Dislocations

    Dislocations (edge, screw and mixed dislocations)

    Dislocations are introduced;

    during solidification of crystalline solids

    by the permanent deformation of crystalline solids

    1-Dimensional (line) defects

  • 1)Edge dislocation:

    Edge dislocation is shown by symbol

    Extra plane of atoms causes localized lattice distortion.

    The magnitude and direction of lattice distortion is expressed in terms

    of a Burgers vector, b, which is perpendicular to edge dislocation line.

    (Perpendicular to the plane of


    Atoms squeezed together

    Atoms pulled


    is created in a crystal by insertion of an extra half plane of atoms

  • Edge Dislocation Motion

  • Dislocation line is linear.

    Burgers vector is parallel to dislocation line.

    2) Screw Dislocation: can be formed in a perfect crystal by applying upward and

    downward shear stresses to regions of a perfect crystal

    Dislocation line

  • Edge dislocation

    Screw dislocation

    3) Mixed dislocations: very common

    Mixed dislocation has both edge and screw character

  • Nature of dislocation is defined by relative orientations of dislocation

    line and Burgers vector

    Dislocation line and Burgers vector (b)


    Edge Screw Mixed



    Perpendicular Parallel Neither parallel



    Direction and magnitude of Burgers vector;

    Direction : In the close packed crystallographic direction

    Magnitude: One interatomic distance

  • 2-Dimensional (area) defects

    Interfacial (area) defects are boundaries that have two dimensions and

    separate regions of different crystal structures or crystallographic


    External Area Defects Internal Area Defects

    Grain Boundaries

    Twin Boundaries

    Stacking Fault

    Phase boundaries

    External Surface

    1)External surface: is the boundary of material at which the

    structure terminates.

    e.g. Solid-gas, solid-liquid

    Surface atoms are not bonded (surface have higher energy state than the atoms at

    the inner parts of the structure). This energy is called surface energy (J/m2 or

    erg/cm2). To minimize this energy, materials minimizes the surface area.

  • 2) Grain boundary:

    Grain boundary may be defined as the interface between crystals that

    differ in crystallographic orientation, composition or dimension of the crystal

    lattice (in some cases in two or all of these).

    A) High Angle Grain Boundary

    B) Small Angle Grain boundary

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