Materials Chemistry: Structure and Properties of Solids An overview of materials and solid-state chemistry?

Types of solids Amorphous –only short range order; no periodicity. –melting point over a large range. –Powder x-ray diffraction has broad peaks –glasses, polymers and supercooled liquids Crystalline. characterized by 3-dimensional periodicity (in perfect crystals) Powder x-ray diffraction has sharp peaks sharp melting points (in general) distinct morphology; well developed faces

Structure and Properties of Materials Solid-state and Crystalline structure Amorphous vs poly-crystalline vs single crystal What properties depend on solid-state structure (close packing, metals, voids… revision) (ionic structures: NaCl, CsCl; WO3… revision) MECHANICAL PROPERTIES ELECTRONIC PROPERTIES

Types of solids Liquid crystals. characterized by 1- or 2- dimensional order rod- or disc-like molecules

Types of solids Polymers only short range order; no periodicity. melting point over a large range.

Types of solids Quasicrystals e.g. rapidly cooled alloys both short- and long-range order but incompatible with translational periodicity (e.g. 5-dimensional symmetry s een in diffraction patterns)

Types of solids Nano-crystals (quantum dots) Nano-crystals (quantum dots) –solids of dimensions 1-100nm Nanocrystal of RuS 2 Semiconducting Nanocrystal

Nano-crystals (quantum dots) Nano-diamond Nano-diamond Fullerenes, or buckyballs, are soccer-ball-shaped molecules named for R. Buckminster Fuller, whose popular geodesic dome is structurally similar to a fullerene molecule. In first-principles simulations of nano-diamond, (a) the surface of a 1.4-nanometer nano-diamond with 275 atoms spontaneously rearranges itself into (b) a fullerene at about 300 kelvins. These carbon clusters have a diamond core (yellow) and a fullerene-like reconstructed surface (red). (c) A classic 60-atom carbon buckyball. Fullerenes, or buckyballs, are soccer-ball-shaped molecules named for R. Buckminster Fuller, whose popular geodesic dome is structurally similar to a fullerene molecule. In first-principles simulations of nano-diamond, (a) the surface of a 1.4-nanometer nano-diamond with 275 atoms spontaneously rearranges itself into (b) a fullerene at about 300 kelvins. These carbon clusters have a diamond core (yellow) and a fullerene-like reconstructed surface (red). (c) A classic 60-atom carbon buckyball.

Chemical Bonding in Solids Ionic Ionic Metallic Metallic

Chemical Bonding in Solids Covalent Covalent Molecular solids Molecular solids

Interatomic distances Ionic radii (Å) Ionic radii (Å) –Note: ionic radii are influenced by the crystal environment. e.g NaCl (crystal) Na-Cl distance is 2.83Å; gaseous NaCl distance is 2.36Å Na-Cl 2.83Å Mg-O1.98Å Si-O 1.74Å Covalent Covalent –The C-C (single) distance in diamond is 1.545Å, about the same for the average C-C distance in molecules (crystals and isolated) –C-C 1.545Å –Si-Si 2.352Å

Interatomic distances Metallic Metallic –metallic radius: half the distance between adjacent metal atoms (in a structure with coordination no. 12). e.g. R(Cu)=1.28Å; so Cu---Cu distance is 2.56Å –Surface studies: Cu---Cu is 1-10% lower at surface than in the bulk –Cu---Cu 2.56Å (fcc) –Au---Au 2.884Å (fcc) –W---W 2.741Å (bcc) Molecular (covalent) bond radius van der Waals (‘nonbonded’) radius

Example Crystal Structures Fe (bcc); Au (fcc) Fe (bcc); Au (fcc) CsCl (pc); NaCl, KCl (fcc) CsCl (pc); NaCl, KCl (fcc) ReO 3 (cubic); BaTiO 3 (cubic) ReO 3 (cubic); BaTiO 3 (cubic) diamond; graphite diamond; graphite fullerene fullerene molecular, protein, virus crystals molecular, protein, virus crystals

Properties of Solids: Mechanical properties Mechanical properties Mechanical properties Compressive or tensile stress Compressive or tensile stress Hardness Hardness Impact energy Impact energy Fracture toughness Fracture toughness Fatigue Fatigue Creep (used in the field of tribology) Creep (used in the field of tribology)

Mechanical properties Compressibility and Bulk modulus Compressibility and Bulk modulus response to stress is given by coefficients of proportionality (‘moduli’) Bulk modulus (K) is the inverse of compressibility (κ) and is a measure of hardness:

Mechanical properties Examples of bulk modulus for selected materials Examples of bulk modulus for selected materials Bulk modulus (K) is the inverse of compressibility (κ) and is a measure of hardness: C (diamond)442.3 GPa C (nanorods)491 GPa Au (fcc metal)220 GPa Cu (fcc metal)140 GPa W (bcc metal)310 GPa

Mechanical properties Bulk modulus of elements in the periodic table Bulk modulus of elements in the periodic table C (diamond) GPa C (nanorods) 491 GPa B 320 GPa Au (fcc metal) 220 GPa Cu (fcc metal) 140 GPa W (bcc metal) 310 GPa

Mechanical properties Tensile strain (ε) : Tensile strain (ε) : –distortion of the sample ε = (change in length)/(original length) ε = Δl/l Responses to stress (rheology) Responses to stress (rheology) –Consider: steel, rubber (elastic) – glass rod, ceramic (brittle) – copper metal, plastic (ductile) Tensile stress Tensile stress –tensile stress (σ) σ = Force/(cross section area) σ = F/A (what are the units?)

Experimental measurement of stress and strain Experimental measurement of stress and strain

Interpretation at the atomic level: stretching of atomic bonds and elastic deformation Interpretation at the atomic level: stretching of atomic bonds and elastic deformation

Hooke’s law is obeyed at small strain. The material is elastic in this region: Hooke’s law is obeyed at small strain. The material is elastic in this region: σ = Y ε σ = Y ε »where Y is Young’s modulus, or the modulus of elasticity, for the solid (gives a measure of ‘stiffness’) Elastic region

Stress-strain curves Dislocations begin to play a role at the elastic limit Dislocations begin to play a role at the elastic limit Slip planes in metals are important in this region.Slip planes in metals are important in this region. In general ccp metals (Cu, Au) are more ductile than hcp metals (Zn, Cd) In general ccp metals (Cu, Au) are more ductile than hcp metals (Zn, Cd) The modulus of elasticity often depends on the direction along which the stress is applied (i.e. anisotropic)The modulus of elasticity often depends on the direction along which the stress is applied (i.e. anisotropic)

Example: The interatomic distance along the direction in α- Fe (i.e. along the body diagonal) is 2.480Å (measured crystallographically). When a tensile stress of 1000MPa is applied along the direction, this interatomic distance increases to 2.489Å. Example: The interatomic distance along the direction in α- Fe (i.e. along the body diagonal) is 2.480Å (measured crystallographically). When a tensile stress of 1000MPa is applied along the direction, this interatomic distance increases to 2.489Å. α-Fe Calculate the modulus of elasticity (Young’s modulus) along the direction of α-Fe σ = Y ε σ = Y ε ε = ( )/2.480 = Therefore ε = ( )/2.480 = = 1000MPa/( ) = 275GPa Y = 1000MPa/( ) = 275GPa Note that 275GPa is the maximum Y for Fe. The minimum is 125GPa along the direction. Exercise: (i) Calculate the atom-atom distance along the direction (i.e. the a-axis) in unstressed α-Fe. (ii) Calculate the atom-atom distance along the direction Exercise: (i) Calculate the atom-atom distance along the direction (i.e. the a-axis) in unstressed α-Fe. (ii) Calculate the atom-atom distance along the direction under a tensile stress of 1000MPa. [Ans: 2.864Å; 2.887Å]

Stress-strain curves Stress-strain curves strength, ductility and toughness

Stress-strain curves Stress-strain curves high- and low- strength materials

Tensile test data for selected alloys Tensile test data for selected alloys Al 2 O ~1000 SiC470170

Other mechanical properties Other mechanical propertiesHardness Impact energy Fracture toughness FatigueCreep ( used in the field of tribology)

Hardness Hardness Abrasive hardness as a function of lattice enthalpy density OsB 2 and AlMgB 14

Hardness Hardness definitions of other scales Brinell hardness number is approximately proportional to tensile strength Brinell hardness number is approximately proportional to tensile strength Vickers Vickers Knoop Knoop Rockwell Rockwell Nano-indentation (AFM) Nano-indentation (AFM)

Structure and properties of materials Types of solids Types of solids Mechanical properties of materials Mechanical properties of materials Band theory, energy gaps, Fermi function Band theory, energy gaps, Fermi function Conductors and superconductors Conductors and superconductors Semiconductors, doping Semiconductors, doping Insulators, piezoelectrics, pyroelectrics Insulators, piezoelectrics, pyroelectrics