PX431 Structure and Dynamics of Solids

1. PX431 Structure and Dynamics of Solids PART 2: Defects and Disorder Diane Holland P160 d.holland@warwick.ac.uk

2. 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)

3. 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

4. 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

5. stoichiometric compounds elements present in simple (small) integer ratios e.g. NaCl, BaTiO3 non-stoichiometric compounds non-integer 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

6. Types of defect: Crystal imperfections Orientational disorder Point defects

7. 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

8. Orientational disorder groups of atoms which are non-spherically symmetric -ammonium salts - linear chains Point defects vacancies, interstitials, incorrect atoms -Schottky - Frenkel - substitution

9. 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

10. CRYSTAL IMPERFECTIONS - dislocations - grain boundaries - twinning

11. Transmission electron micrograph of Ti alloy – dark lines are dislocations (Callister: Materials Science and Engineering) 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

12. Dislocations revealed by etching ‘Etch pits’ produced by preferential etching by acid of the points where dislocations intersect the surface http://en.wikipedia.org/wiki/Dislocation

13. 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)

14. 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)

15. 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)

16. Shear stress 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 (Callister: Materials Science and Engineering)

17. 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)

18. atom trap 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. (Callister: Materials Science and Engineering)

19. 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

20. b b 2d In metals, direction of motion of dislocation is usually parallel to one of the directions of close packing 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

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

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

23. F b  Sb  Slip plane area Asp  Cross-section of crystal area A

24. 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

25. (Callister: Materials Science and Engineering) FACE-CENTRED CUBIC 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

26. Interfacial (planar) defects • boundaries separating regions of different crystal structure or crystallographic orientation • e.g. external surfaces (see final section of module)

27. b D = b/ 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 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)

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