PX Structure and Dynamics of Solids

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					PX431 Structure and Dynamics of Solids

                  PART 2:
           Defects and Disorder

 Diane Holland   P160       d.holland@warwick.ac.uk
2. Defects and disorder (10L)

 Lectures 1-2: crystal defects – point, line and planar defects;
                dislocations and mechanical behaviour

 Lectures 3-5: point defects and non-stoichiometry; radiation induced
                defects; thermodynamics and stability of defects;
                elimination of defects

 Lectures 6-7: influence of defects on diffusion, ionic conductivity,
                optical and electronic properties

 Lectures 8-10:amorphous materials and glasses – formation and
                structure; structural theories; short and intermediate
                range order
                techniques for structural analysis – diffraction and the
                pair distribution function; total scattering; local probes
                (NMR, EXAFS, Mössbauer, IR and Raman)

M.T. Dove, Structure and Dynamics, OUP
Appendix A ( 6 pages only!)

S. R. Elliott, The physics and chemistry of solids, Wiley
Chapter 3

W. D. Callister, Materials Science and Engineering, Wiley
Chapters 4 & 7
   Disorder in crystalline materials
• No perfectly ordered materials
• Many materials are technologically of value because
  they are disordered/imperfect in some way:

  silicon devices – controlled levels of deliberate impurity
  additions (ppb) p-type : B       Si  B + h
                     n-type : P    Si  P + e

  steels – additions of 0.1 to 1 at% other metals to improve
           mechanical properties and corrosion resistance
stoichiometric compounds
  elements present in simple (small) integer ratios
  e.g. NaCl, BaTiO3

non-stoichiometric compounds
  e.g. Fe0.92O, Ca0.98Y0.02F2.02

Intrinsic defects   – do not change overall composition
                    – stoichiometric defects
Extrinsic defects   – created when foreign atom(s)
                    introduced or there is valence change
Types of defect:

Crystal imperfections
Orientational disorder
    Point defects
            Crystal imperfections
perfect crystal – all atoms on their correct lattice
(actual positions affected by extent of thermal vibrations
which can be anisotropic)

imperfect crystal
   extended defects
                         - dislocations
                         - grain boundaries
                         - stacking faults
                         - twinning
     Orientational disorder
groups of atoms which are non-spherically
       - ammonium salts
       - linear chains

                 Point defects
vacancies, interstitials, incorrect atoms
       - Schottky
       - Frenkel
       - substitution
               Extent of disorder
• Crystal imperfections - depends on preparation and
  mechanical history

• Orientational disorder - depends on temperature

• Point defects     - Schottky and Frenkel normally
                    v. low because formation energy high

      - Frenkel high in certain classes of materials e.g.

      - substitution to high degree in some materials
                                              - alloys
                                              - spinels

     - dislocations
     - grain boundaries
     - twinning
      Dislocations – linear defects
- growth
- stress

- metals more deformable than
  predicted (but can be
  strengthened by impurities)
- spiral growths on surface of
  some crystals
- reactions occur at active
  surface sites
                                   Transmission electron micrograph of
Types: edge, screw, intermediate   Ti alloy – dark lines are dislocations
                                   (Callister: Materials Science and Engineering)
Dislocations revealed by etching

                    ‘Etch pits’ produced by
                    preferential etching by acid of
                    the points where dislocations
                    intersect the surface

                  Edge dislocation

– partial plane of atoms

– lattice distorted where plane
Dislocations characterised by
the Burgers vector, b
-magnitude and direction
found by tracing loop around
the dislocation
- for metals, b points in a
close-packed direction and        (Callister: Materials Science and Engineering)

equals the interatomic spacing
                      Dislocation motion

(Callister: Materials Science and Engineering)

• – dislocation moves under application of a shear stress
    (easy for bonds to swap between atoms at dislocation since they are
    already strained)
(Callister: Materials Science and Engineering)

• Motion of dislocations called slip; the plane over which
  the dislocation moves is called the slip plane

• For an edge dislocation:
  b is perpendicular to the dislocation line
  b is parallel to the direction of motion of the dislocation
  line under an applied stress.
 Screw dislocation
               • partial slip of a crystal

      Shear    • on one side of dislocation line,
      stress     crystal has undergone slip; on
                 other side, crystal is normal

               • continued application of shear
                 stress causes dislocation to
                 move through crystal

               • b is parallel to dislocation line
                  (opposite to Edge)
               • b is perpendicular to motion of
                 this line
                  (opposite to Edge)

               • but b is parallel to direction of
                 shear and slip in both cases

(Callister: Materials Science and Engineering)
      dislocation loop

  • combined edge and screw dislocation
        - pure edge on one face;
        - pure screw on adjacent face;
        - mixed in-between

  • loops expand easily but asymmetrically
    because edge moves easier than screw

(Callister: Materials Science and Engineering)
              Pinning dislocations
• dislocations make metals
  easier to deform
• to improve strength of metals,
  need to stop dislocation motion

trap with:
- impurity atoms;
- other dislocations (work           trap
- grain boundaries.

                                    (Callister: Materials Science and Engineering)
    Effects of crystal structure
• Preferred set of slip planes on which dislocations can
  occur and also preferred slip directions for dislocation
  movement  slip system

• slip plane – plane having most dense atom packing
• slip direction – direction, in plane, having highest linear

• Energy required to move dislocation by one unit
  translation E |b| 2

    the most abundant dislocations in a material are those
   with the smallest value of b
In metals, direction of motion of dislocation is
usually parallel to one of the directions of close

Shear in close-packed direction by one unit b = d  E  d2,
where d is the diameter of the sphere (atom)


 Shear in non-close-packed direction by one unit b = d 2
  E  2d2
        Tensile F                                       Tensile F
        on crystal           Tensile force
b                            produces shear
                             force in slip plane

                     plane                             Resolved shear
                                                       in slip plane
                                            Stress on plane
                                   F        SA = F/Asp = F(cos )/A
                                            Critical resolved shear stress -
                                            Sb - parallel to direction of slip
                                            on slip plane
                     Sb                     Sb = SAcos  = (F/A)cos  cos 

                                            - angle between slip direction
                                            and stress axis
Slip plane                                  Maximum value of Sb occurs
area Asp                                    when  =  = 45o
                                           giving Sb = ½(F/A)

                 Cross-section of crystal   When slip plane is either
                 area A                     parallel or perpendicular to F,
                                            the resolved shear stress is 0
                                            and slip cannot occur.

                     Sb             

Slip plane
area Asp

                 Cross-section of crystal
                 area A
                     Slip Systems
Metal                 Slip plane          Slip direction   No. of slip
                         Face-centred     cubic
Cu, Al, Ni, Ag, Au    {111}               <1-10>           12
                         Body-centred     cubic
Fe, W, Mo             {110}               <-111>           12
Fe, W                 {211}               <-111>           12
Fe, K                 {321}               <-111>           24
                              Hexagonal   Close-packed
Cd, Zn, Mg, Ti, Be    {0001}              <11-20>          3
Ti, Mg, Zr            {10-10}             <11-20>          3
Ti, Mg                {10-11}             <11-20>          6

• FCC metals are generally more malleable and ductile than HCP or BCC
• BCC metals have many slip systems but planes are not close-packed
• HCP metals have few slip systems
                                            (Callister: Materials Science and Engineering)

AD, AF and DF are the 3 <110> slip directions
ADF and the equivalent upper faces of the
octahedron are the 4 {111} slip planes
3  4  12 slip systems
      Interfacial (planar) defects

• boundaries separating regions of different
  crystal structure or crystallographic
• e.g. external surfaces (see final section of
                            Grain boundaries
      Internal surfaces of a single crystal where ideal domains (mosaic)
      meet with some misalignment: high-angle and small(low)-angle.
      NB – in polycrystalline materials, grain boundaries are more extensive and may even
      separate different phases                         b

                                                                                  D = b/

                                                                           Small-angle grain
                                                                           equivalent to
                                                                           linear array of
                                                                           edge dislocations

                                                 bonding not fully satisfied  region of higher
                                                 energy, more reactive, impurities present.
(Callister: Materials Science and Engineering)

change in crystal orientation
during growth


(Callister: Materials Science and Engineering)

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