PX431 Structure and Dynamics of Solids PART 2: Defects and Disorder Diane

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)

References 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 : BSi  B + h n-type : PSi  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, BaTiO 3 non-stoichiometric compounds non-integer e.g. Fe 0.92 O, Ca 0.98 Y 0.02 F 2.02 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 positions (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 symmetric - 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. Superionics - substitution to high degree in some materials - alloys - spinels

CRYSTAL IMPERFECTIONS - dislocations - grain boundaries - twinning

Dislocations – linear defects Source: -growth -stress Evidence: -metals more deformable than predicted (but can be strengthened by impurities) -spiral growths on surface of some crystals -reactions occur at active surface sites Types: edge, screw, intermediate Transmission electron micrograph of 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 ends 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 equals the interatomic spacing (Callister: Materials Science and Engineering)

Dislocation motion – 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. (Callister: Materials Science and Engineering)

Screw dislocation partial slip of a crystal on one side of dislocation line, 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 Shear stress (Callister: Materials Science and Engineering)

Quarter 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 hardening; - grain boundaries. atom trap (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 density 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

b Shear in close-packed direction by one unit b = d  E  d 2, where d is the diameter of the sphere (atom) Shear in non-close-packed direction by one unit b = d  2  E  2d 2 In metals, direction of motion of dislocation is usually parallel to one of the directions of close packing b 2d

b Tensile F on crystal F Slip plane b Tensile F Resolved shear in slip plane Tensile force produces shear force in slip plane

Stress on plane S A = F/A sp = F(cos  )/A Critical resolved shear stress - S b - parallel to direction of slip on slip plane S b = S A cos  = (F/A)cos  cos   - angle between slip direction and stress axis Maximum value of S b occurs when  =  = 45 o giving S b = ½(F/A) When slip plane is either parallel or perpendicular to F, the resolved shear stress is 0 and slip cannot occur. b   Slip plane area A sp F SbSb Cross-section of crystal area A

b   Slip plane area A sp F SbSb Cross-section of crystal area A 

MetalSlip planeSlip directionNo. of slip systems Face-centredcubic Cu, Al, Ni, Ag, Au{111} 12 Body-centredcubic Fe, W, Mo{110} 12 Fe, W{211} 12 Fe, K{321} 24 HexagonalClose-packed Cd, Zn, Mg, Ti, Be{0001} 3 Ti, Mg, Zr{10-10} 3 Ti, Mg{10-11} 6 Slip Systems 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) FACE-CENTRED CUBIC AD, AF and DF are the 3 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 orientation e.g. external surfaces (see final section of module)

Grain boundaries D = b/  b 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 Small-angle grain boundary equivalent to linear array of edge dislocations bonding not fully satisfied  region of higher energy, more reactive, impurities present. (Callister: Materials Science and Engineering)

Twinning change in crystal orientation during growth mirror (Callister: Materials Science and Engineering)