lecture2-3 Imperfections in Solids.ppt
- 1. What makes steel considerably harder and stronger than pure iron? Why do we use very high purity copper as a conductor in electrical applications Why FCC metals (such as copper and aluminum) tend to be more ductile than BCC and HCP metals Objectives: Imperfections in solids
- 2. Imperfections in Solids • Introduction: Crystalline Defect- lattice irregularity having one or more of its dimensions on the order of an atomic diameter.
- 3. cont…
- 4. Point defects: Vacancies and self-interstitials, impurities in solids (solid solutions, interstitials and substitutional). Miscellaneous imperfections: dislocations, linear defects, interfacial defects, volume defects, atomic vibrations.
- 5. DEFECTS/IMPERFECTIONS POINT • VACANCY • INTERSTITIAL ATOM • SUBSTITUTIO NAL ATOM • FRENKEL • SCHOTTKY LINE • EDGE • SCREW • MIXED • SLIP • SCHMID LAW SURFACE • GRAIN BOUNDARY • TWIN /TILT BOUNDARY • STALKING FAULTS DEFECTS OFTEN HAVE PROFOUND EFFECT ON THE PROPERTIES OF THE MATERIAL
- 6. POINT DEFECTS When they occur: movement of atoms when they gain energy by heating during processing of materials (solidification) due to high temperature, as a consequence of radiation damage
- 7. POINT DEFECTS N-total number of atomic sites Qv- the energy required for the formation of vacancy T-absolute temperature (Kelvin) K-boltzmann const Vacancy and self interstitial The presence of vacancies increases degree of randomness in the crystal hence thermodynamic stability increases
- 9. Vacancy creation. In statistical mechanics, configuration entropy is the portion of a system's entropy that is related to the position of its constituent particles rather than to their velocity or momentum. It is physically related to the number of ways of arranging all the particles of the system while maintaining some overall set of specified system properties, such as energy. W k S ln W is the number of possible configurations
- 10. Derivation for number of vacancies N-total number of atomic sites n-number of vacant sites (N-n)-number of atoms f H Enthalpy increase due to one vacancy/ enathalpy of formation Total enthalpy of formation=n f H Configurational entropy W K S ln Where )! ( ! ! n N n N W n N n N n n N N K S ln ln ln S T H G
- 11. ) ln( ) ( ln ln n N n N n n N N TK H n G f Condition for stability 0 n G 0 ln n n N KT H f n n N KT H f ln n n N KT H f ln n N n KT H f ln
- 12. n N N n KT H f ln Fraction of vacancies N n KT H f exp KT H N n f exp
- 14. # Calculate the concentrate of vacancies in cu at room temperature(25oC).what temperature will be needed to heat treat copper such that the concentration of vacancies produced will be 1000 times more than the equilibrium concentration of vacancies at room temperature? Assume that 20,000cal are required to produce a mole of vacancies in copper. At room temp: cc vacancies nv / 10 815 . 1 8 The lattice parameter for FCC cu is 0.36151nm Number of atoms per cc= cc atoms Cu cc cell atoms n / 10 47 . 8 ) 10 16151 . 3 ( / 4 22 3 8 k molk cal mol cal cc atoms RT Qv n n k temp room at v 298 / 987 . 1 / 20000 exp . / 10 47 . 8 exp ) 298 ( 22 cc vacancies nv / 10 815 . 1 8
- 15. Solid solutions=solute+solvent (Host atoms) Impurities in the Solids Ex:sterling silver=7.5%cu+92.5% Ag In ambient environment pure silver is corrosion resistant but very soft . Alloying with Cu (impurity atom) adds mechanical strength also.
- 16. The formation of solid solution depends on: Atomic size factor: Difference in atomic radii between the two atom types is less than about +/-15%. Otherwise new phase with lattice distortions forms. Crystal structure: Both metal atom type must be same Electronegetivity: the more electropositive one, the more electronegative other, the greater is the likelihood that form an intermetallic compound instead a substitutional solid solution. Valence: higher valence metal dissolves more than lower valence. Ex for Substitutional : Cu(0.128nm), Ni(0.125nm),both FCC, Electro negetivity-1.9 and 1.8 Impurity atom: Intrstitial Impurity atom and Substitutional impurity atom Interstitial impurity atom: Ex: carbon(0.071nm) in pure iron (0.124nm)(up to max 2%)
- 17. The ratio of cations to anions is not alterd by the formation of either a Frenkel or Schotty defect. If no other defects are present , the material is said to be Stoichiometric Schotty Defect: Stoichiometric number of anions and cat ions Imperfections in Ceramics Frenkel defect Schotty defect In ionic crystals, defects can form on the condition of charge neutrality. Two possibilities are: Frenkel Defect: Vacancy interstitial pair, Covalently bonded materials
- 22. Dislocations-Linear Defects EDGE An extra portion of a plane of atoms, or half-plane, the edge of which terminates within the Crystal.
- 23. Slip: Deformation of a metallic material by the movement of dislocations through the crystal
- 25. SCREW Dislocation Burgers Vector: The magnitude and direction of the distortion associated with a dislocation is expressed in terms of Burgers Vector
- 26. SCREW
- 27. SCREW
- 28. SIGNIFICANCE OF DISLOCATIONS dislocations are most significant in metals and alloys they provide mechanism for plastic deformation(movement of dislocations) slip process is important for understanding mechanical behavior of materials if slip occurs, only a tiny fraction of all metallic bonds across the interface need to broken at any one time(and the force is smaller(103 to 104 smaller)than the expected strength from metallic bonds slip provides ductility in metals properties can be controlled by interfering with dislocations ex. Provide an obstacle which prevents dislocation from slipping unless we apply higher forces(so dislocations help in strengthening the metallic materials dislocation density(amount of dislocations present)total length of the dislocations per unit volume.106cm/cc for soft,1012cm/cc can be achieved by deforming the material
- 35. Slip: Deformation of a metallic material by the movement of dislocations through the crystal
- 36. Slip direction: the direction in the crystal in which dislocation moves Slip plane :the plane swept out by the dislocation line during slip. Normally the slip plane is close packed plane, if one exist in the crystal structure. Slip system : the combination of slip plane and slip direction SCHMID’S LAW Force required to initiate the slip process
- 38. Slip cannot occur if…..
- 39. Schematic representation of dislocation that has edge, screw, and mixed character
- 40. • Top View. Open circles denote atom positions above the slip plane. Solid circles , atoms position below. At point A, the dislocation is pure screw, while at point B, pure edge. For regions in between where there is curvature in the dislocation line the character is mixed edge and screw.
- 41. SURFACE DEFECTS • Grain boundary • Twin boundary • Tilt boundary
- 44. GRAIN BOUNDARIES Reduce grain size Increase the number of grains Increase the amount of grain boundary Any dislocation moves short distance before encountering with grain boundary Increased strength
- 45. Hall-Petch Strengthening is limited by the size of dislocations. Once the grain size reaches about 10 nm, grain boundaries start to slide. σo is a materials constant for the starting stress for dislocation movement ky is the strengthening coefficient (a constant unique to each material),
- 46. 1. Since the two grains are of different orientations, a dislocation passing into grain B will have to change its direction of motion; this becomes more difficult as the crystallographic misorientation increases. The grain boundary acts as a barrier to dislocation motion for two reasons: 2. The atomic disorder within a grain boundary region will result in a discontinuity of slip planes from one grain into the other.
- 48. TILT AND TWIN BOUNDARIES
- 52. MICROSCOPIC EXAMINATION • OPTICAL MICROSCOPY • ELECTRON MICROCSCOPY
- 53. (a) Polished and etched grains as they might appear when viewed with an optical microscope. (b) Section taken through these grains showing how the etching characteristics and resulting surface texture vary from grain to grain because of differences in crystallographic orientation. (c) Photomicrograph of a polycrystalline brass specimen. (Photomicrograph courtesy of J. E. Burke, General Electric Co.) 60.
- 54. (a) Section of a grain boundary and its surface groove produced by etching; the light reflection characteristics in the vicinity of the groove are also shown. (b) Photomicrograph of the surface of a polished and etched polycrystalline specimen of an iron chromium alloy in which the grain boundaries appear dark. SCANNING ELECTRON MICROSCOPY
- 56. GRAIN SIZE DETRMINATION Let n represent the grain size number, and N the average number of grains per square inch at a magnification of 100X.These two parameters are related to each other through the expression
Editor's Notes
- #18: Frenkel defect