Real crystals, crystal POINT DEFECTS Real crystals, crystal defects 4/34. VACANCY Real crystals,...

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Transcript of Real crystals, crystal POINT DEFECTS Real crystals, crystal defects 4/34. VACANCY Real crystals,...

  • Real crystals, crystal defects

    Real crystals, crystal defects 1/34

  • • The strength of real metals is less than 1% than

    that of calculated from ideal crystal models

    • Doping Si with 10-8 weight percent Boron increases its conductivity by two-times

    • CRYSTAL DEFECTS

    REAL CRYSTALS

    Real crystals, crystal defects 2/34

  • • Point defects (0 dim.)

    • Line defects (1 dim.) dislocations

    • Surface defects (2 dim.)

    • Volume defects (3 dim.)

    CRYSTAL DEFECTS

    Real crystals, crystal defects 3/34

  • • Vacancy (empty lattice space)

    • Self interstitial atoms

    • Foreign atoms (interstitial or substitutional

    places)

    POINT DEFECTS

    Real crystals, crystal defects 4/34

  • VACANCY

    Real crystals, crystal defects 5/34

    The vacancy is the

    absence of an atom from

    the lattice. The attractive

    and repulsive forces

    acting on the neighboring

    atoms are changed, so

    lattice distortion is

    produced in the

    environment of the

    vacancy.

  • SUBSTITUTIONAL ATOM

    Real crystals, crystal defects 6/34

    The substitutional atom is

    a foreign atom in the

    lattice. The attractive and

    repulsive forces acting on

    the neighboring atoms are

    changed, so lattice

    distortion is produced in

    the environment of the

    atom.

  • INTERSTITIAL ATOM

    Real crystals, crystal defects 7/34

    The interstitial atom is a

    foreign atom between the

    regular lattice positions.

    The attractive and

    repulsive forces acting on

    the neighboring atoms are

    changed, so lattice

    distortion is produced in the

    environment of the atom.

  • FRENKEL-MECHANISM

    Real crystals, crystal defects 8/34

    Due to high energy

    interaction (e.g. particle

    irradiation) an atom left the

    lattice site leaving a

    vacancy behind and mode

    into an interstitial position.

    It causes extreme lattice

    distortion.

  • WAGNER-SCHOTTKY MECHANISM

    Real crystals, crystal defects 9/34

    Atoms leaving the free surface, and atoms jump from the

    interior to their place. In this way a vacancy diffuses trough

    the lattice into the materials interior.

  • • Radiation – Atoms are moved out of the regular lattice position (e.g.

    Frenkel-pair)

    • Heat

    nü: number of empty lattice sites

    N: number of lattice sites

    Qü: activation energy

    k: Boltzmann constant

    T: temperature

    POINT DEFECTS

    Point defect density

    Exponential

    curve

    slope

    Real crystals, crystal defects 10/34

  • POINT DEFECTS IN ALLOYS

    Solid solution: base metal (A) + solved atom (B)

    Substitutional alloy

    e.g. Cu + Ni

    interstitial alloy

    e.g. Fe + C

    Second phase in solid solution

    or

    Second phase particle

    different chemical composition

    different structure

    Real crystals, crystal defects 11/34

  • EFFECT OF POINT DEFECTS

    Aluminium Copper

    Strain (%) Strain (%)

    S tr

    e s s (

    M P

    a )

    S tr

    e s s (

    M P

    a )

    soft Slow cooling

    quenchingNeutron irradiated

    Real crystals, crystal defects 12/34

  • • Large difference between theoretical and

    measured flow stress of metals.

    • Dislocation theory: plastic deformation does not

    happen in one step → dislocation motion

    DISLOCATIONS (1 D)

    Real crystals, crystal defects 13/34

  • 2 (1 )

    merőleges

    párhuzamos

    E

    G

    E G

     

     

     

     

     

     

    Poisson coefficient

    (ε - strain)

    Tensile stress

    Shear stress

    MECHANICAL PROPERTIES

    perpendicular

    parallel

    Real crystals, crystal defects 14/34

  • • Assumption: during the deformation the crystal planes slip in one step relative to each other by simultaneous motion of the atoms.

    • The stress what is necessary to start the plastic deformation calculated this way is 1-2 order of magnitude higher than the measured values.

    • Conclusion: during the plastic deformation the slip of crystal planes don’t occur in one step, but through a continuous motion; that is, there are regions where the slip already occurred, and others where didn’t.

    • The lines separating this regions are called dislocations.

    THEORETICAL YIELD STRESS

    Real crystals, crystal defects 15/34

  • DISLOCATIONS MOTION

    The analogy between

    the dislocations and

    the caterpillar

    Real crystals, crystal defects 16/34

  • BURGERS-CIRCLE

    Real crystals, crystal defects 17/34

    In a defect-free lattice starting from a lattice position and

    stepping the same distance to right, down, left and upward,

    we return to the starting point.

    If the crystal contains a dislocation, the starting and end

    point will be different. The vector connecting them is the

    Burgers-vector.

  • Dislocation line: l

    Slip plane.

    →fixed

    Burgers vector: b

    b  l,

    The line of the

    dislocation and the

    elemental deformation

    caused are

    perpendicular.

    EDGE DISLOCATION

    Extra half plane

    Real crystals, crystal defects 18/34

  • Dislocation line: l

    Burgers vector: b

    Slip plane is not fixed

    →glissile

    No extra half plane!

    b II l, The line of the dislocation and the

    elemental deformation

    caused are parallel.

    SCREW DISLOCATION

    The axis of the screw dislocation

    Real crystals, crystal defects 19/34

  • Partial slip

    A line in the space

    0-90°

    The angle between the line of the

    dislocation and the elemental

    deformation it causes is between 0

    and 90°.

    COMPOSITE DISLOCATION

    Real crystals, crystal defects 20/34

  • • Dislocation: border of slipped and non-slipped regions

    • Linear defect

    • Starts and ends on a crystal surface, ore forms a

    closed loop

    • Plastic deformation along the whole dislocation is

    constant

    • Burgers vector is in the closest packed plane and

    direction, and b = d

    Real crystals, crystal defects 21/34

    BASIC PROPERTIES OF DISLOCATIONS

  • • Macroscopic surface

    • Small angle grain boundary

    • High angle grain boundary

    • Phase boundary

    • Coherent phase boundary

    • Twin boundary

    • Stacking fault

    PLANAR DEFECTS

    Real crystals, crystal defects 22/34

  • • Atoms on the surface are at higher energetic state than in

    the crystal interior, because there are no atomic bondings

    at every directions.

    • Surface energy decreases if additional atoms join the

    surface.

    • Oxide layer formation.

    • Chemical reactions.

    MACROSCOPIC SURFACE

    surface

    Real crystals, crystal defects 23/34

  • Dislocations are arranged

    below each others

    SMALL ANGLE GRAIN BOUNDARY

    Real crystals, crystal defects 24/34

    The angle difference of the

    orientation of the regions separated

    by small angle grain boundaries:

     < 5°

  • During solidification the

    randomly oriented grains

    touch each other. Grains

    differ from each other

    only in orientation.

    HIGH ANGLE GRAIN BOUNDARIES

    Real crystals, crystal defects 25/34

  • SMALL AND HIGH ANGLE GRAIN BOUNDARIES

    Surface

    energy

    Small angle grain boundary High angle grain boundary

    Real crystals, crystal defects 26/34

  • PHASE BOUNDARY

    Coherent

    Low energy surface defect Semicoherent

    Incoherent

    High energy

    surface defect

    phase boundary

    Phase

    boundary

    Real crystals, crystal defects 27/34

  • • Atoms on the two sides of the boundary are similar

    • There can be found a plane in both phases where the

    atomic arrangement is similar

    • Orientation difference is fixed on the phase boundary

    COHERENT PHASE BOUNDARY

    Real crystals, crystal defects 28/34

  • • Coherent boundary, separates

    similar phases

    • The two sides of the boundary

    are mirror images

    • It can be formed during

    crystallization or plastic

    deformation in FCC or HCP

    materials

    TWIN BOUNDARY

    Real crystals, crystal defects 29/34

  • Parallel lines in a

    microscopic image

    TWIN BOUNDARY

    Real crystals, crystal defects 30/34

  • Du