Materials Chemistry:Materials Chemistry:Structure and Properties of SolidsStructure and Properties of Solids

An overview of materials and solid-state chemistry?An overview of materials and solid-state chemistry?

Types of solidsTypes of solids

Amorphous Amorphous – only short range order; no periodicity.only short range order; no periodicity.– melting point over a large range.melting point over a large range.– Powder x-ray diffraction has broad peaksPowder x-ray diffraction has broad peaks– glasses, polymers and supercooled liquidsglasses, polymers and supercooled liquids

Crystalline. Crystalline. characterized by 3-dimensional periodicity characterized by 3-dimensional periodicity (in perfect crystals)(in perfect crystals)Powder x-ray diffraction has sharp peaksPowder x-ray diffraction has sharp peakssharp melting points (in general)sharp melting points (in general)distinct morphology; well developed facesdistinct morphology; well developed faces

Structure and Properties of MaterialsStructure and Properties of MaterialsSolid-state and Crystalline structure Solid-state and Crystalline structure

Amorphous vs poly-crystalline vs single crystalAmorphous vs poly-crystalline vs single crystalWhat properties depend on solid-state structureWhat properties depend on solid-state structure(close packing, metals, voids… revision)(close packing, metals, voids… revision)(ionic structures: NaCl, CsCl; WO3… revision)(ionic structures: NaCl, CsCl; WO3… revision)MECHANICAL PROPERTIESMECHANICAL PROPERTIESELECTRONIC PROPERTIESELECTRONIC PROPERTIES

Types of solidsTypes of solids

Liquid crystals. Liquid crystals. characterized by 1- or 2-characterized by 1- or 2-dimensional orderdimensional orderrod- or disc-like moleculesrod- or disc-like molecules

Types of solidsTypes of solids

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

Types of solidsTypes of solidsQuasicrystalsQuasicrystals

e.g. rapidly cooled alloyse.g. rapidly cooled alloysboth short- and long-range both short- and long-range order order but incompatible with but incompatible with translational periodicity translational periodicity (e.g. 5-dimensional symmetry (e.g. 5-dimensional symmetry sseen in diffraction patterns)een in diffraction patterns)

Types of solidsTypes of solids

Nano-crystals Nano-crystals (quantum dots)(quantum dots)– solids of dimensions solids of dimensions

1-100nm1-100nm

Nanocrystal of RuS2

Semiconducting Nanocrystal

Nano-crystals (quantum dots)Nano-crystals (quantum dots)

Nano-diamondNano-diamond Fullerenes, or buckyballs, are soccer-ball-shaped molecules named for R. Fullerenes, or buckyballs, are soccer-ball-shaped molecules named for R.

Buckminster Fuller, whose popular geodesic dome is structurally similar to a Buckminster Fuller, whose popular geodesic dome is structurally similar to a fullerene molecule. In first-principles simulations of nano-diamond, (a) the fullerene molecule. In first-principles simulations of nano-diamond, (a) the surface of a 1.4-nanometer nano-diamond with 275 atoms spontaneously 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 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). have a diamond core (yellow) and a fullerene-like reconstructed surface (red). (c) A classic 60-atom carbon buckyball.(c) A classic 60-atom carbon buckyball.

Chemical Bonding in SolidsChemical Bonding in Solids

Ionic Ionic

MetallicMetallic

Chemical Bonding in SolidsChemical Bonding in Solids

CovalentCovalent

Molecular solidsMolecular solids

Interatomic distancesInteratomic distances

Ionic radii (Å)Ionic radii (Å)– Note: ionic radii are influenced by the crystal environment. Note: ionic radii are influenced by the crystal environment. e.g NaCl (crystal) Na-Cl distance is 2.83Å; gaseous NaCl distance is 2.36Åe.g NaCl (crystal) Na-Cl distance is 2.83Å; gaseous NaCl distance is 2.36ÅNa-Cl Na-Cl 2.83Å2.83ÅMg-OMg-O 1.98Å1.98ÅSi-O Si-O 1.74Å1.74Å

CovalentCovalent– The C-C (single) distance in diamond is 1.545Å, about the same for the The C-C (single) distance in diamond is 1.545Å, about the same for the

average C-C distance in molecules (crystals and isolated)average C-C distance in molecules (crystals and isolated)– C-CC-C 1.545Å 1.545Å– Si-SiSi-Si 2.352Å 2.352Å

Interatomic distancesInteratomic distances

MetallicMetallic– metallic radius: half the distance between adjacent metal atoms (in a metallic radius: half the distance between adjacent metal atoms (in a

structure with coordination no. 12).structure with coordination no. 12).e.g. R(Cu)=1.28Å; so Cu---Cu distance is 2.56Åe.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 bulkSurface studies: Cu---Cu is 1-10% lower at surface than in the bulk

– Cu---Cu Cu---Cu 2.56Å (fcc)2.56Å (fcc)– Au---Au Au---Au 2.884Å (fcc)2.884Å (fcc)– W---W W---W 2.741Å (bcc)2.741Å (bcc)

MolecularMolecular(covalent) bond radius(covalent) bond radiusvan der Waals (‘nonbonded’) van der Waals (‘nonbonded’) radius radius

Example Crystal StructuresExample Crystal Structures

Fe (bcc); Au (fcc)Fe (bcc); Au (fcc) CsCl (pc); NaCl, KCl (fcc)CsCl (pc); NaCl, KCl (fcc) ReOReO33(cubic); BaTiO(cubic); BaTiO33(cubic)(cubic)

diamond; graphitediamond; graphite fullerenefullerene molecular, protein, virus crystalsmolecular, protein, virus crystals

Properties of Solids:Properties of Solids:Mechanical propertiesMechanical properties

Mechanical propertiesMechanical properties

Compressive or tensile stressCompressive or tensile stress HardnessHardness Impact energyImpact energy Fracture toughnessFracture toughness FatigueFatigue Creep (used in the field of tribology)Creep (used in the field of tribology)

Mechanical propertiesMechanical properties

Compressibility and Bulk modulusCompressibility 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:

TP

V)(

V1

κ1

κ

Mechanical propertiesMechanical properties

Examples of bulk modulus for Examples of bulk modulus for selected materialsselected 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

TP

V)(

V1

κ

1

κ

Mechanical propertiesMechanical properties

Bulk modulus of elements in the periodic tableBulk modulus of elements in the periodic table

•C (diamond) 442.3 GPa

•C (nanorods) 491 GPa

•B 320 GPa

•Au (fcc metal) 220 GPa

•Cu (fcc metal) 140 GPa

•W (bcc metal) 310 GPa

Mechanical propertiesMechanical properties

Tensile strain (ε) : Tensile strain (ε) : – distortion of the sampledistortion of the sample

ε = (change in length)/(original length)ε = (change in length)/(original length)ε = Δl/lε = Δl/l

Responses to stress Responses to stress (rheology)(rheology)

–Consider: steel, rubber (elastic)Consider: steel, rubber (elastic)

– glass rod, ceramic (brittle)glass rod, ceramic (brittle)

– copper metal, plastic (ductile) copper metal, plastic (ductile)

Tensile stressTensile stress

–tensile stress (σ) σ = Force/(cross section area)tensile stress (σ) σ = Force/(cross section area)

σ = F/A (what are the units?)σ = F/A (what are the units?)

Experimental measurement of stress and Experimental measurement of stress and strainstrain

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

Hooke’s law is obeyed at small strain. The Hooke’s law is obeyed at small strain. The material is elastic in this region:material is elastic in this region:

σ = Y ε σ = Y ε » where Y is Young’s modulus, or the modulus of elasticity, where Y is Young’s modulus, or the modulus of elasticity,

for the solid (gives a measure of for the solid (gives a measure of ‘stiffness’‘stiffness’))

Elastic regionElastic region

Stress-strain curvesStress-strain curves

Dislocations begin to play a Dislocations begin to play a role at the elastic limitrole at the elastic limit

•Slip planes in metals are important in Slip planes in metals are important in this region.this region.• In general ccp metals (Cu, Au) are In general ccp metals (Cu, Au) are more ductile than hcp metals (Zn, Cd)more ductile than hcp metals (Zn, Cd)•The modulus of elasticity often depends The modulus of elasticity often depends on the direction along which the stress on the direction along which the stress is applied (is applied (i.e.i.e. anisotropic) anisotropic)

Example: The interatomic distance along the <111> direction in Example: The interatomic distance along the <111> direction in αα--Fe (Fe (i.e.i.e. along the body diagonal) is 2.480Å (measured along the body diagonal) is 2.480Å (measured crystallographically). When a tensile stress of 1000MPa is applied crystallographically). When a tensile stress of 1000MPa is applied along the <111> direction, this interatomic distance increases to along the <111> direction, this interatomic distance increases to 2.489Å.2.489Å.

Calculate the modulus of elasticity (Young’s modulus) along the <111> direction of αα-Fe-Fe

σ = Y ε σ = Y ε

Therefore ε = (2.489-2.480)/2.480 = 0.00363ε = (2.489-2.480)/2.480 = 0.00363

Y = 1000MPa/(0.00363) = 275GPa = 1000MPa/(0.00363) = 275GPa

Note that 275GPa is the maximum Y for Fe. The minimum Note that 275GPa is the maximum Y for Fe. The minimum is 125GPa along the <100> direction.is 125GPa along the <100> direction.

Exercise: (i) Calculate the atom-atom distance along the <100> direction Exercise: (i) Calculate the atom-atom distance along the <100> direction ((i.e.i.e. the a-axis) in unstressed the a-axis) in unstressed αα-Fe-Fe. (ii) Calculate the atom-atom distance . (ii) Calculate the atom-atom distance along the <100> directionalong the <100> direction under a tensile stress of 1000MPa.

[Ans: 2.864Å; 2.887Å]

Stress-strain curvesStress-strain curves

strength, ductility and toughnessstrength, ductility and toughness

Stress-strain curves Stress-strain curves

high- and low- strength materialshigh- and low- strength materials

Tensile test data for selected alloysTensile test data for selected alloys

Al2O3 380 ~1000

SiC 470 170

Other mechanical propertiesOther mechanical properties

HardnessHardnessImpact energyImpact energyFracture toughnessFracture toughnessFatigueFatigueCreep Creep ( used in the field of tribology)( used in the field of tribology)

HardnessHardness

Abrasive hardness as a function of lattice Abrasive hardness as a function of lattice enthalpy densityenthalpy density

OsB2 and AlMgB14

HardnessHardness

definitions of other scalesdefinitions of other scales

Brinell hardness number is Brinell hardness number is approximately proportional approximately proportional to tensile strengthto tensile strength

VickersVickers KnoopKnoop RockwellRockwell Nano-indentation (AFM)Nano-indentation (AFM)

Structure and properties of Structure and properties of materialsmaterials

Types of solidsTypes of solids Mechanical properties of materialsMechanical properties of materials Band theory, energy gaps, Fermi Band theory, energy gaps, Fermi

functionfunction Conductors and superconductorsConductors and superconductors Semiconductors, dopingSemiconductors, doping Insulators, piezoelectrics, pyroelectricsInsulators, piezoelectrics, pyroelectrics