STRUCTURESTRUCTURE OFOF MATERIALSMATERIALS The Key to its Properties AA MultiscaleMultiscale PerspectivePerspective Anandh Subramaniam Materials and Metallurgical Engineering INDIAN INSTITUTE OF TECHNOLOGY KANPUR Kanpur- 208016 Email: [email protected] http://home.iitk.ac.in/~anandh Jan 2009 OUTLINEOUTLINE Properties of Materials The Scale of “Microstructures” Crystal Structures + Defects Microstructure With Examples from the Materials World PROPERTIES Structure sensitive Structure Insensitive E.g. Yield stress, Fracture toughness E.g. Density, Elastic Modulus Structure Microstructure What determines the properties? Cannot just be the composition! Few 10s of ppm of Oxygen in Cu can degrade its conductivity Cannot just be the amount of phases present! A small amount of cementite along grain boundaries can cause the material to have poor impact toughness Cannot just be the distribution of phases! Dislocations can severely weaken a crystal Cannot just be the defect structure in the phases present! [1] The presence of surface compressive stress toughens glass Phases & Their Distribution Composition Residual Stress Defect Structure [1] Metals Handbook, Vol.8, 8th Edition, ASM, 1973 Length Scales Involved Nucleus Atom Crystal Microstructure Component Defects Dislocation Stress fields Angstroms → Nanometers Microns Centimeters Unit Cell* Crystalline Defects Microstructure Component Grain Size *Simple Unit Cells • Casting Thermo-mechanical • Metal Forming Treatments • Welding Crystal • Powder Processing • Machining Atom Structure Microstructure Component • Avoid Stress Concentrators Electro- • Good Surface Finish magnetic Phases + Defects • Vacancies • Crystalline Structure • Dislocations • Quasicrystalline Residual based • Twins + • Amorphous • Stacking Faults Stress • Grain Boundaries • Ferromagnetic Property • Voids • Ferroelectric based • Cracks • Superconducting Processing determines shape and microstructure of a component • Casting Thermo-mechanical • Metal Forming Treatments • Welding Crystal • Powder Processing • Machining Atom Structure Microstructure Component • Avoid Stress Concentrators Electro- • Good Surface Finish magnetic Phases + Defects & their distribution • Vacancies • Crystalline Structure • Dislocations • Quasicrystalline Residual based • Twins + • Amorphous • Stacking Faults Stress • Grain Boundaries • Ferromagnetic Property • Voids • Ferroelectric based • Cracks • Superconducting Processing determines shape and microstructure of a component METAL SEMI-METAL BAND STRUCTURE ATOMIC SEMI-CONDUCTOR INSULATOR STATE / VISCOSITY LIQUID GAS SOLID LIQUID CRYSTALS STRUCTURE AMORPHOUS QUASICRYSTALS RATIONAL CRYSTALS APPROXIMANTS SIZE NANO-QUASICRYSTALS NANOCRYSTALS Crystal Atom Structure Microstructure Component Electro- magnetic Why is BCC Iron the stable form of Iron at room temperature and not the FCC form of Iron? 1 Atm G vs T showing regions of stability of FCC and BCC Iron (Computed using thermo-calc software and database developed at the Royal Institute of Technology, Stockholm) The Structure of Materials, S.M. Allen & E.L. Thomas, John Wiley & Sons, Inc. New York, 1999. Microstructure This functional definition of “microstructure” includes all lengthscales Phases + Defects • Vacancies • Dislocations Residual • Twins + • Stacking Faults Stress • Grain Boundaries • Voids • Cracks Microstructure Residual Phases + Defects + Stress • Vacancies • Dislocations • Twins • Stacking Faults • Grain Boundaries • Voids • Cracks Microstructure Residual Phases + Defects + Stress • Vacancies • Dislocations Defects (Crystalline) • Vacancies • Twins • Dislocations • Stacking Faults • Grain Boundaries Microstructural • Phase Transformation • Voids • Voids • Cracks • Cracks Component • Stress corrosion cracking • + Residual Surface Compressive Stress CRYSTALCRYSTAL STRUCTURESSTRUCTURES Crystal = Lattice (Where to repeat) + Motif (What to repeat) + = Unit cell of BCC lattice Crystal = Space group (how to repeat) + Asymmetric unit (Motif’: what to repeat) Progressive lowering of symmetry amongst the 7 crystal systems Cubic Hexagonal Tetragonal Trigonal Orthorhombic Monoclinic Increasing symmetry Triclinic Arrow marks lead from supergroups to subgroups 1. Cubic Crystals a = b= c = = = 90 º • Simple Cubic (P) [2] • Body Centred Cubic (I) – BCC • Face Centred Cubic (F) - FCC 4 2 Vapor grown NiO crystal Point groups 23, 3m,4 ,3m 432, 3 Tetrakaidecahedron m m (Truncated Octahedron) Pyrite Cube [1] [1] Fluorite Garnet [1] Dodecahedron [1] http://www.yourgemologist.com/crystalsystems.html Octahedron [2] L.E. Muir, Interfacial Phenomenon in Metals, Addison-Wesley Publ. co. Crystals and Properties (The symmetry of) Any physical property of a crystal has at least the symmetry of the crystal Crystals are anisotropic with respect to most properties The growth shape of a (well grown) crystal has the internal symmetry of the crystal Polycrystalline materials or aggregates of crystals may have isotropic properties (due to averaging of may randomly oriented grains) The properties of a crystal can be drastically altered in the presence of defects (starting with crystal defects) CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY 0D 1D 2D 3D (Point defects) (Line defects) (Surface / Interface) (Volume defects) Twins Vacancy Dislocation Surface Interphase Precipitate Impurity Disclination boundary Faulted Frenkel Dispiration Grain region defect boundary Voids / Schottky Twin Cracks defect boundary Stacking Thermal faults vibration Anti-phase boundaries 0D (Point defects) Vacancy Non-ionic Interstitial Impurity crystals Substitutional 0D (Point defects) Frenkel defect Ionic Other ~ crystals Schottky defect Imperfect point-like regions in the crystal about the size of 1-2 atomic diameters Vacancy Missing atom from an atomic site Atoms around the vacancy displaced Tensile stress field produced in the vicinity Tensile Stress Fields Relative size Interstitial Compressive Impurity Stress Fields Substitutional Compressive stress fields SUBSTITUTIONAL IMPURITY Tensile Stress Foreign atom replacing the parent atom in the crystal Fields E.g. Cu sitting in the lattice site of FCC-Ni INTERSTITIAL IMPURITY Foreign atom sitting in the void of a crystal E.g. C sitting in the octahedral void in HT FCC-Fe Interstitial C sitting in the octahedral void in HT FCC-Fe rOctahedral void / rFCC atom = 0.414 rFe-FCC = 1.29 Å rOctahedral void = 0.414 x 1.29 = 0.53 Å rC = 0.71 Å Compressive strains around the C atom Solubility limited to 2 wt% (9.3 at%) Interstitial C sitting in the octahedral void in LT BCC-Fe rTetrahedral void / rBCC atom = 0.29 rC = 0.71 Å rFe-BCC = 1.258 Å rTetrahedral void = 0.29 x 1.258 = 0.364 Å ► But C sits in smaller octahedral void- displaces fewer atoms Severe compressive strains around the C atom Solubility limited to 0.008 wt% (0.037 at%) Equilibrium Concentration of Vacancies Formation of a vacancy leads to missing bonds and distortion of the lattice The potential energy (Enthalpy) of the system increases Work required for the formaion of a point defect → Enthalpy of formation (H ) [kJ/mol or eV/defect] f Though it costs energy to form a vacancy its formation leads to increase in configurational entropy above zero Kelvin there is an equilibrium number of vacancies G = H T S SkConfig ln( ) Crystal Kr Cd Pb Zn Mg Al Ag Cu Ni kJ / mol 7.7 38 48 49 56 68 106 120 168 eV / vacancy 0.08 0.39 0.5 0.51 0.58 0.70 1.1 1.24 1.74 G (perfect crystal) T (ºC) n/N 500 1 x 1010 1000 1 x 105 4 Gmin 1500 5 x 10 2000 3 x 103 Equilibrium Hf = 1 eV/vacancy concentration 18 G (Gibbs energy) free G (Gibbs = 0.16 x 10 J/vacancy n (number of vacancies) Certain equilibrium number of vacancies are preferred at T > 0K Vacancies play a role in: Diffusion Climb Electrical conductivity Creep etc. 1D (Line defects) The shear modulus of metals is in the range 20 – 150 GPa G The theoretical shear stress will be m 2 in the range 3 – 30 GPa Actual shear stress is 0.5 – 10 MPa I.e. (Shear stress)theoretical > 100 * (Shear stress)experimental !!!! DISLOCATIONS Dislocations weaken the crystal DISLOCATIONS EDGE MIXED SCREW Usually dislocations have a mixed character and Edge and Screw dislocations are the ideal extremes Conservative Motion of dislocations (Glide) On the slip plane Motion of Edge dislocation Non-conservative Motion of dislocation (Climb) to the slip plane For edge dislocation: as b t → they define a plane → the slip plane Climb involves addition or subtrac tion of a row of atoms below the half plane ► +ve climb = climb up → removal of a plane of atoms ► ve climb = climb down → addition of a plane of atoms Mixed dislocations b t b Pure screw Pure Edge Role of Dislocations Creep Diffusion Fatigue (Pipe) Fracture Slip Structural Incoherent Twin Grain boundary (low angle) Semicoherent Interfaces Cross-slip Disc of vacancies Creep Dislocation climb ~ edge dislocation mechanisms in crystalline Vacancy diffusion materials Grain boundary sliding 2D (Surface / Interface) Grain Boundary The grain boundary region may be distorted with atoms belonging to neither crystal The thickness may be of the order of few atomic diameters The crystal orientation changes abruptly at the grain boundary In an low angle boundary the orientation difference is < 10º In the low angle boundary the distortion is not so drastic as the high-angle boundary → can be described as an array of dislocations Grain boundary energy is responsible for grain growth on heating ~ (>0.5T ) m Large grains grow at the expense of smaller ones