Prin&Appl MSE 2001
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Chapter 6 Noncrystalline and Semicrystalline Materials Introduction Glass Transition Temperature Viscous Deformation Structure and Properties of Oxide Glasses Structure and Properties of Amorphous and Semicrystalline Polymers Structure and Properties of Rubbers and Elastomers Introduction The emphasis thus far has been on crystalline materials There are numerous engineering materials that lack the long range translational periodicity of a crystalline material These noncrystalline materials are referred to as either amorphous glassy or supercooled liquids Theoretically any material can form an amorphous structure if the cooling rate from the melt is sufficiently rapid to suppress crystal formation This chapter will emphasize the structural considerations that facilitate the development of an amorphous structure Nth Order Phase Transition The usual definition of the order of a transition is in terms of the behavior of derivatives of the Gibbs free energy An nth order transition is one in which discontinuities appear only in the nth and higher derivatives of G with respect to T and p The ordinary firstorder transition have discontinuities in The ordinary secondorder transition have discontinuities in a 1an 1V J 1an 16323 2 KT 2 VanVaTapr VapT VapzT 2 924 4 i j CHg 4 63 6T V 5T N p 6T p 8T V I7 Some Glass Forming Systems Elements Oxides Halides Sulfides Selenides Tell urides N itrides Sulfates Carbonates Polymers Metallic Alloys S Se P SiO2 B203 P205 GeO2 AsO2 BF2 AIF3 ZnCl2 AgClBrlPbCl2Br2l2 AS283 Sb2S3 Various compounds of TI Sn Pb As Sb Bi Si and P Various compounds of TI Sn Pb As Sb Bi and Ge KNO3CaNO32 and many mixtures containing alkali and alkaline earth nitrates KHSO4 and many other binary and ternary mixtures K2CO3MgCO3 Polystyrene PMMA polycarbonate PVC Au4Si Pd4Si FeSiB alloys Altransition metal rare earths Glass Transition Temperature Glassy State A state of material in the absence of longrange order below the glass transition temperature 9 large scale mobility is frozen9 atomic movement requires long time Rubbery State A state of material in the absence of longrange order above the glass transition temperature atomic movement takes shorter time Window glass vs Rubber band What if you give them a good blow using a hammer Glass transition temperature the temperature below which the physical properties of amorphous materials vary in a manner similar to those of a solid phase glassy state and above which amorphous materials behave like liquids rubbery state J1 Glass Transition Specific Volume for a Variety of Materials The slope normalized by the volume V is the volumetric thermal expansion coefficient ocv a Z 1 dV Specific volume Speci c volume ocyCrystal I I I I I I I I I I I I I I I I I T m Temperature T g Tm Temperature Liquid to glass solid transformation in a pure substance The glass transition temperature T9 is not an equilibrium transformation temperature Liquid to crystalline solid transformation for a pure substance Tm is an equilibrium transformation temperature Glass Transition Specific volume aVCrystal I I I I I T m Temperature Below Tm material tends to crystallize The crystal formation crystallization occurs over a period of time because the establishment of longrange order LRO requires atomic rearrangement by diffusion Speci c volume I I I I I I I I I I I T g Tm Temperature It is possible to avoid crystallization by cooling at a sufficiently high rate so as to suppress the diffusion necessary to establish LRO in the crystal The volume of the collection of atoms continues to decrease with the slope characteristic of the liquid below the melting temperature forming a supercooled liquid Glass Transition The Effect of Cooling Rate on the Glass Transition Temperature Tg Liquid T T1gtT2 TTltgt TgTT Supercooled liquid Specific Volume Temperature gt Liquid to Semicrystalline Solid Transformation TmltT Liquid state molecular motion is very large TgltTltTmz Rubbery state supercooled liquid molecular motion is relatively large Tltng Glassy state molecular motion is very small 9 Frozen state Why is Tm used as a boundary between rubbery state and liquid state Viscous Deformation Comparison of the Response of a Solid and a Liquid to a Shear Stress oc Unit of viscosity poise P A dx Pgcm s 239 0C 7 d r 2 Gy r 777 777 G shear modulus n shear viscosity Time independent Time dependent Viscous Deformation Temperature Dependence of Viscosity Fluidity Viscosity 06Xp 777706Xp Question Calculate the viscosity of molasses at 100 C assuming an activation energy of 30 kJmol 77250C SOP Solution zwza gii 77T1 noeXpQRT1 R T2 T1 r 1 1 W 441P 8314Jm01K373K 298K J The Effect of Temperature on the Viscosity of a SodaLimeSilicate Glass 1016 Strainfree 1014 Ange t 9 in about 0m 15 minutes 1012 3 1010 E Deforms at g 10 Swenmg a controlled g Ponnt rate gt 106 Working Readily 104 Point formable 102 1 200 400 600 800 1000 1200 1400 1600 Temperature C Repeat Units for SiO2 Structure 1094 Telnhedron I CZquot I I I Igt Si I aquot SiOA4 tetrahedron 2Dimensional Silicate Structures O Silica glass Crystalline silica Zachariasen s Rules for Oxide Glass Formation Oxide glass networks are composed of oxygen polyhedra Coordination of each oxygen atom in the glass network should be 2 Coordination number of each metal atom in the glass network should be 3 or 4 8203 system Zachariasen s Rules for Oxide Glass Formation Oxide polyhedra share corners not edges or faces Each polyhedron should share at least 3 corners Shared corners 0 Shared edge 8203 system Network Formers and Modifiers Network Formers Network Modifiers Sio2 U20 Geo2 K20 128 A3205 M920 BaO CaO ZnO PbO Network Modifiers Repeat Units 04 Tetrahedron SiO4394 tetrahedron C2H4 Met C2H4 mer in polyethylene Structure and Properties of Amorphous and Semicrystalline Polymers Formation polymerization of Poly ethylene from a Basic Chemical Unit of C2H4 39 39 39 39 W 39 i39 Hr 99 CgtCgt 9999 39 H H H H H H H H H H Ethylene Repeating unit for Poly ethylene Basic building poly ethylene chain block ITI ljl ITI ljl H ITI ITI ljl used in making translucent lightweight and quot39lt3lt33lt3lt33 lt3lt3 tough plastics films containers insulation H H H H H H H H etc H H H H H H H H 393393393393393393393393 3Ilalss transition tempega ure14g8gc eting temperature H H H H H H H H Amorphous density at 25 C 0855 gcm3 Poly ethylene chains pack well because the side groups are only hydrogen Crystalline density at 25 C 100 gcm3 Molecular weight of repeat unit 2805 gmol 21 Degree of Polymerization DP Wtth W 0 0 099999 gtHn HHHHHH HH n the number of monomeric unit gt10000 The degree of polymerization Another Example Poly vinyl Chloride Poly ethylene terephthalate PET or PETE one of the polyesters Film fibers clothing drink bottle 3 O O C C CH Densnty 1370 kgm 2 Young modulus E 2800 3100 MPa 0 0 CH2 n Tensile strength 00 55 75 MPa Glass temperature 75 C melting point 260 C Poly styrene PS CHCH2 CHcH2CHCH2CHCH2CHCH2CHcH2Tcllz Containers toys amp foams styrene polystyrene Density 1050 kgm3 Specific Gravity 105 Young39s modulus E 30003600 MPa Tensile strength St 46 60 MPa Glass temperature 95 C Melting point 240 C Nylon 66 one of the polyamides Carpet fiber apparel airbags tires 0 H H2 H2 quotE I H2 H2 ropes conveyor belts and hoses H H2 H2 Poly pphenyleneterephthalamide PPTA or Kevlar Fibers and bulletproof vests One of the most strong polymers H gt H 0 ion 0 a H c I A quot4 H I I 0 o N Q N 393 gt lt H39 I q POly tetra uomethylene PTFE bearings bushings gears slide plates II II One of the most hydrophobic polymers With the lowest frictional coefficient 9 3 ln F F 24 Thermoplastic Polymer and Thermoset Polymer Thermoplastic polymer capable of softening or fusing melting when heated and of hardening again when cooled eg various linear polymers no chemical crosslinking poly ethylene poly propylene and Poly ethylene terephthalate Thermoset polymer not capable of melting when heated and of hardening again when cooled Eg crosslinked polymer 9 The curing crosslinking process makes threedimensional network structure in polymeric material eg various polymers with chemical crosslinking Vulcanized rubber Bakelite a Phenol Formaldehyde Resin used in electrical insulators and plastic wear Ureaformaldehyde foam used in plywood particleboard and mediumdensity fibreboard Melamine resin used on worktop surfaces Polyester Resin used in glassreinforced plasticsfibreglass GRP Epoxy Resin eg Thermoplastic and Thermoset Polyesters PET Polyester with saturated Polyester with unsaturated bonds along the chain bonds along the chain Thermoplastic PETbased thermoset polymer Crosslinking with a polystyrene monomer Thermoset polymer 26 Thermoset Polymer Structure of Crosslinked Rubber Unsaturated bonds are used to form crosslinks with crosslinker 39 39B39 39 W BW W39 B39 39 39 BW CICC CICICCCI CCICICICICCCI HDoubI H H H Crossmnked H Is e H H T H WWW w 1 w w W H 1 w quot399ICIC99ICCF9 39 quot39939IC99939C99quot39 HHRHHHRH HHHHHHRH Vulcanized rubber Bakelite Thermoset Polymer Thermoset Polymer Some thermoset polymers are crosslinked eg earlier Some thermoset polymers are linearchain polymers eg 28 Poly pphenyleneterephthalamide PPTA or Kevlar Fibers and bulletproof vests One of the most strong polymers Cotton wood 29 Molecular Weight of Polymers Molecular weight Number average molecular weight Weight average molecular weight Polydispersity 30 Molecular Weight of Polymers Weight average molecular weight ZWMf zenM Number average molecular weight ZWM A7 2 1quot Mw n ZNi ZNiMZ Zwi wiszMl M the molecular weight of polymer chain 1 M the number of polymer chains that have M Polydispersity P D w the product of N andM 3 Molecular Weight of Polymers Weight average molecular weight 2Nz39Mi2 2wiMi Number average molecular weight ZWM A7 2 i ZlIWZ Z 2 1 quot 2M ZNzMz 2W wiZNMi Polydispersity MW M the molecular weight of polymer chain 1 PD 2 V N the number of polymer chains that have M 71 w the product of N andM n1000 n1000 Each weighs 0 n1 weighSzO weighs MO M 2M00Oz M M M MHz 0 30 0M0 n 3 3 2 2 2 szMO 2W 0 PD 1 W M000 1 PD 3 Molecular Weight of Polymers Number average molecular weight Weight average molecular weight ZWMfl 2W ZNM N Z i niZ i szl Zl w i M ZN ZO Mquot ZN ZNM 2W g M i W N w 39 Mi Ni ni wi wi 1quot 39 139 39 100 5 025 500 0125 200 10 050 2000 0500 ni number fraction wi weight fraction 300 5 025 1500 0375 n M 5x10010gtlt2005gtlt300 4000 5105 200 20 2 2 2 A7 5gtlt100 10gtlt200 5gtlt300 900000225 4000 W 5x10010gtlt2005gtlt300 M E1125 Number of polymer chain Fraction of polymer chain 33 Molecular Weight Distribution for Typical Polymers Number average Weight average Amount of polymer Molecular weight gt lfthe distribution is broadened to have more contribution from larger molecular weight the difference between Mn and MW becomes increased 9 The polydispersity increases PD10 9 monodisperse distribution The importance of the molecular weight MW and its distribution MWD 9 MW and MWD influence most of the properties of any polymers such as mechanical thermal electrical optical transport solution interfacial and thermodynamic properties 33 34 Chain conformation vs Chain configuration Conformation conformational isomer is produced mainly by rotation of atoms and groups around a bond C C f 0 A c c O l n D Jgt Energy kcalmol l cis CiS l gauch gauche trans gf O t l O 60 120 180 240 300 360 Torsion angle degree L 6 6139s trans and gauche FIGURE 26 Conformations in polyethylene Rotational Isomeric State RIS Approximation Each molecules is treated as existing only in discrete torsional angle states corresponding to the potential energy minima e to different combination of t g and g 9 The continuous distribution of torsion angle space I is replaced by a distribution over many discrete states w A3 60 120 180 240 300 Torsion angle degree 5 l 00 L 1 Energy kcalmol L l O O 360 36 Diversity of polymer chain conformation Let s consider an alkane chain with n carbons Question How many different conformations can it take Assumption RIS Each bond can take one out of only three states which are 9 9 and t C C C n2 C n1 in C in n2C Onumber of conformations 0 3Hn3 For a case of n1000 ie its molecular weight14000 forjust single chain even using extremely simplified three states RIS approximation 03997 0476 How about multiple chain system We should have some statistical way to investigate polymer conformation 37 Chain configuration configurational isomer determined by tacticity of polymer Tacticity is simply the way pendant groups are arranged along the backbone Chain of a polymer CH3 egPolymethylmethacryatePMMA CH2 In 330 o c OCH3 00 13 CCH3 30 Him CH3 cO Hm 30 CH3 lllal 30 I l CH3 Hm CH3 OCH3 meso dyadm racemic dyadr heterotactic triad mr atactic syndiotactic triad rr isotactic PMMA syndiotactic PMMA and atactic PMMA Once polymer chain has a specific tacticity it cannot have other tacticities through the rotation of bond in backbone If you really want You need to break the bonds Tacticity in Polystyrene CH2CH isotactic syndiotactic atactic P8 P8 P8 40 Factors Affecting Crystallinity in Polymers Factors influencing the efficiency of packing polymer chains The size of the side groups The extent of chain branching Tacticity The complexity of the repeat unit The degree of secondary bonding 4 The size of the side groups Bulky side group The extent of chain branching branching and thus stron er intermolecularforces and tensile stren th HDPE can be produced by chromiumsilica catal sts Zie lerNatta catal sts or metallocene catal sts The lack of branching is ensured by an appropriate choice of catalyst eg chromium catalysts or HDPE ZieglerNatta catalysts and reaction conditions 9 high crystallinity HDPE is defined by a density of greater or equal to 0941 gcm3 HDPE has a low degree of LDPE is defined by a density range of 0910 0940 gcm3 LDPE has a high degree of short and A long chain branching which means that the chains do not pack into the crystal structure as well It has therefore less strong intermolecular forces as the instantaneousdipole induceddipole attraction is less This results in a lower tensile strength and increased duct y LDPE is created LDPE by free radical polymerization The high degree of branches with long chains gives molten LDPE unique and desirable flow properties 9 low crystallinity 42 Tacticity crystallizable The complexity of the repeat unit lt3 lt3 3914 3914 O CAQC O CHZ CHZ L v8 l 9 In H H The degree of secondary bonding H H CH2 CIH VS O H n 43 Semicrystalline Polymers orientati normal to 1 Spherulites aggregates of crystalline and noncrystalline regions The Maltese cross is a pattern that develops because of the imagining technique Semicrystalline Polymers Polymers are never fully crystallized 44 Because the macromolecules are highly entangled in the melt and diffusion rates are low the chains do not have sufficient time to completely disentangle during solidification text book 9 It sounds that 100 crystallization is impossible due to kinetic reason Really Really 9 Answer is NO What if we control it to proceed during infinite time What is the reason we discussed for the impossibility of perfect crystal with a big size More important reason is from thermodynamics ENTROPY 45 Rubbers Natural Rubber HC 3 H CC g L 2 2 Cis14poly isoprene Synthetic Rubber CHTTH CH CHTCHTCHZCH CHr S I Sulfur bridge 3 SulfurcrossIink C CH2 CHCH CH2 n gt T CH2 CHCH CH2 n T C CH2 H H CHz CHz CHZCH CHZ Poly butadiene Rubbers Thermoset Elastomer Conventional thermoset polymer 1 crosslinking 1 OOO mers 9 Light crosslinking 9 Flexible rubber Thermoset Elastomer 1 crosslinking 10 mers 9 Heavy crosslinking 9 Hard amp brittle material 7 It can be deformed several hundred percent and recover substantially completely 46 Thermoplastic Elastomer 0HCH CHCHCH CHATECHCH Poly styrene block Morphology Poly butadiene block Poly styrene block 888 triblock copolymer No chemical crosslinking 9 It can be melted and solidified Islands of hard styrene blocks take the role as crosslinking points Sea of soft butadiene part has elastomeric property Chapter 7 Phase Equilibria and Phase Diagrams Introduction The onecomponent phase diagram Phase equilibria in a twocomponent system The eutectic phase diagram The peritectic phase diagram The monotectic phase diagram Complex diagrams Phase A chemically and structurally homogeneous region of a material A part of a system physically distinct macroscopically homogeneous and of xed or variable com os39 ion It is mechanically separable from the rest of the system That is a phase is a region within which all the intensive variables vary continuously whereas at least some of them have discontinuities at the borders between phases ice water ice water 9 2 phases solid phase liquid phase I want to drink 2phase system consisting of solid water and liquid water Phase diagram Graphical representation ofthe combination of temperature pressure composition or other variables for which speci c phases exist at equilibrium State point a position on the phase diagram 10000 3 2 supercrillcal uid pnssure bar gas Pressure arm 390 0C 10 C tomparatule Temperature Phase diagram of Carbon dioxide CO2 Phase diagram of Water H2O OneComponent Phase Diagrams water Gibbs Phase Rule for systems in equilibrium F 2 32quot 1 a g F 2 F 1 91 F 2 01 F o Component a chemical species whose concentration in a phase can be varied independently of the other species concentration Number of degrees of freedom in equilibrium is the number of variables p T or composition that can be independently adjusted without disturbing equilibrium Tempemture cc 2000 1600 1200 Example of OneComponent Phase Diagrams a Liquid mm Pressure kbar iron Sio2 TwoComponent Phase Diagrams Temperature Pressure Composition for materials A and B Composition of onecomponent F 1 system For one state point in closed system we need three variables p T amp X p T XComposition 9 3D space NEE2 component system t 1 tquot 3quot E F 2 F 1 m 91 g F 2 XB increasing fractiox 01 gt F o TwoComponent Phase Diagrams Specification of composition Atomic percentage atomic fraction Weight percentage weight fraction wt of A atomic wt of A gtlt 100 wt of A atomic wt of A wt of B atomic wt of B atomic of A 2 atomic of A gtlt atomic wt of A gtlt 100 atomic of A gtlt atomic wt of A atomic of B gtlt atomic wt of B wtofA Question1 Calculate the atomic fraction of copper in aluminum for a two component alloy containing 5 wt copper Atomic mass is 6355 for Cu and 2698 for AI TwoComponent Phase Diagrams TIMJIH 1 II The copper nickel phase diagram Adapted from Phase Diagrams a f Binary Nickel Alloys P Nash Editor 1991 Reprinted by permission of ASM International Materials Park OH b A portion of the copper nickel phase diagram for which compositions and phase amounts are determined at point B C Temperature quot O 40 80 100 1500 l I I 2800 1500 Liquid 1453 C 2600 1400 r Solidus line Liquidus line 2400 1300 1200 7 2200 1100 39 i 2000 1085 C 1000 l 0 40 80 100 Cu Composition Wt Ni Ni perature F Te m CuNi phase diagram Both Cu and Ni have the same crystal structure FCC similar radii electronegativity and valence gtFc P1 a E m a E cu H TwoComponent Phase Diagrams Phase boundaries liquidus boundary and solidus boundary In a singlephase field the composition of the phase is the composition of the alloy In a two phase field the amount of each phase and the composition of each phase can be determined using a tie line and the lever rule In a singlephase field the composition of the phase is the composition of the alloy TwoComponent Phase Diagrams CuNi phase diagram l llllll 03 Schematic l i i representation of the 0 System is development of inary microstructure during q b the e uilibrium 39 solidi cation of a 35 1300 7 a 46 NJ 1e 2 components Wm NMWU Cu Cu and NI alloy isomorphous ie complete solubility of one component in another on phase 5 field extends from 1200 O to 100wt Ni Consider Co 35wtNi Equilibrium cooling 0020 30 40 Composition WPo Nl TwoComponent Phase Diagrams If we know T and Co initial composition then we know the composition of each phase CuNi system Examples C0 35 wt Ni At 1300 C 1300 Liquid Only liquid L g Wine CL C0 35 wt Ni W At 1150 C E i Only solid a Liquid Ca C0 35 wt Ni 1200 p At TB E I I l l Both0iandL quot 39 l 39 I 20 30 l l 40 l 50 CL Cliquidus 32 Wt NI CL CO C Com osition wt Ni Cot Csolidus M p b TwoComponent Phase Diagrams If we know T and Co then we know the amount of each phase given in wt CuNi C0 35 wt Ni System At 1300 C I t Only liquid L WL 100 Wt W0c 0 Wt 1300 Liquid At 1150 C Tieline MLiqUid Only solid on g WLOwtWa1OOwt g At TB 1200 aLiquid i Both 0c and L f I WLSRS IE t 43354332 73 wt 20 act t 40 t 50 Wu RRS c posni mm Cquot 35324332 27 wt a The lever rule Hamsters They hibernate Assumption Type B hibernates earlier than Type A Type A starts hibernation in colder day than Type B does 14 When Types A and B got together they had a party As the weather gets colder and colder In summer they m39x and They start hibernating happily play together em 8 47 39 l Ix 39 i l 1 lt39 rt J 39 Closed system 39 losed System One phase Two phases 39 39 0 u 5 Total composmon 50 o Still Active phase No More ACtlve phase Composition of B 286 ComPOSition 01 BS 80 Total composition is not changed 50 Temperature Cl 0 1600 Composition al N I 1500 1400 1300 1200 1100 2800 Liquid 145st 7 2600 Liquidus Ime Solldus line 7 2400 2200 39 2000 Composition Mau Nil Nil rm Ni AGAH TAS Temperature quotFl If temperature gets down and reach the liquidus line all Ni atoms in the system sense it and prepare to solidify themselves Q What would be the most distinct atomic property showing dramatic change with decreasing temperature during this process Due to the different interatomic interaction they have different phase behavior as well as different transition temperature Effect of Cooling Rate Fast cooling rate 9 More local heterogeneity Slow cooling rate 9 More homogeneous structure T C CuNi 1300 system L 35wt 1146M L 2 MNI 1200 u 4wtN MNI wtNl 11nn l I 39 3o 35 4o 50 Adapted from Flues Co Wt Nl Canister 69 Slow rate of cooling Equilibrium structure Fast rate of cooling Cored structure Uniform C or First or to solidfy 35quot N n l 46wtNi Last 0 to solidfy lt 35wtNi Temperature TwoComponent Phase Diagrams 1 X0 Xlfl Xsfs 02 Composition XB L 1 X02X11 fsXsfs X0Xl leSXSfS X0Xl fsXsXl XoXz fs XS X1 18 The Lever Rule in a TwoComponent System 4 XsXL Xo XL Ilt Xs Xo gt ML XSXOf MS XOXL M L total XS XL Mtotal XS XL fS Temperature TwoComponent Phase Diagrams 02 Composition XB Composition XO for each alloy Alloy 1 02 Alloy 2 03 Alloy 3 05 Alloy 4 06 Alloy 5 08 Composition of the liquid for each alloy Alloy 1 02 Alloy 2 02 Alloy 3 02 Alloy 4 02 Alloy 5 02 ForAlloy 2 03 03 083 08 02 fL Composition of the solid for each alloy Alloy 1 08 Alloy 2 08 Alloy 3 08 Alloy 4 08 Alloy 5 08 03 02 f3 017 08 02 Analysis of an Isomorphous Phase Diagram Temperature fl xl fS XS T1 1 06 0 085 T2 063 05 037 077 XOOI6O T3 044 045 056 072 T4 029 04 071 068 T5 0 03 1 06 At temperature T2 077 060 060 050 f 077 050 ft 077 050 f1 063 f3 037 At temperature T3 072 060 060 045 fl 072 045 S 072 045 fl 044 f 056 10 20 30 4o 50 60 45 Analysis of an Isomorphous Phase Diagram Temperature fl XI fS XS T1 1 06 0 085 T2 063 05 037 077 XO050 T3 044 045 056 072 T4 029 04 071 068 T5 0 03 1 06 At temperature T4 L 39d 068 060 W fl 068 040 fl 029 060 040 fs 068 040 fs071 Temperature C 0 TwoComponent Phase Diagrams 22 Pure metal Alloy 200 CompOSItIon XB Time gt 0 TIme gt 23 TwoComponent Phase Diagrams isomorphous system has complete solubility of one component in another CuNi phase diagram l39im m quot2 uTllc coppcrrmckcl phase diagram Adapicd from Phase Dltlgl r S af muly Niukd Alloy P Nash Editor 1991 copperrnickel phase diagram or which compositions and plum amounts are determined at point Bi Tenipevalwe no 1500 i 1400 i 1300 f 1200 100 NEST 1000 0 CU Culllpuslllul a 7 m Liquid Liauims line DA l l l 20 110 60 Campus ton wt tn Nlr m7 2800 An isomorphous system is only possible for substitutional solid solution The substitution occurs randomly on their E FCC lattice sites because the Cu and Ni 39 W atoms are so similar i CuNi alloy Excellent corrosion resistance Used for watercooled heat exchangers 8 ENS 9 HumeRothery Rules The size difference between the solute and solvent must be no greater than 15 The eleictronegativities of the two atomic species must be comparable o The valence of the two species must be similar The crystal structures of the two species must be the same TwoComponent Phase Diagrams Four isomorphous systems Formation of substitutional solid solution Temperature C Temperature C CuNi 10 20 30 40 50 60 70 80 90 100 Cu I I Ni Atonnc percent nickel Ag Au 0 10 20 30 40 50 60 70 80 90 100 Ag Au Atomic percent gold Temperature C Temperature C 1500 GeSi 1400 1412 1300 1200 l 100 1000 940 900 0 10 20 30 40 50 60 70 80 90 100 G S39 e Atomic percent silicon l NiOMgO 2800 2600 2400 2200 2000 0 10 20 30 40 50 60 7O 80 90 100 N10 MgO Mole percent MgO All the HumeRothery rules are satisfied 24 TwoComponent Phase Diagrams 25 Deviation from ideal behavior Congruent melting minimum Interaction between Aand B is relatively good in liquid state and thereby solidification becomes hard from the free energy point of view 9 requiring lowertemperature Congruent mellting L 3 quot 39 39 l e39 tion between A and B is relatively good in I o d state T elting becomes hard from the free energy point of TA A S l A view 9 requiring h g 1ertemperature s 5 Ideal solid i A B XVI XBH molar gibbs free energy 9 Free Energy and Phase Diagram At High T solid liquid composition X 3 molar gibbs free energy 9 At intermediate T composition X B molar gibbs free energy 9 26 At LOW T liquid solid composition X B Free Energy and Phase Diagram iiqmd How to minimize the Gibbs free energy TO 39 Constraint 1 X078 lww md me mini temperature T 1 soiid conStramt 2 Gm 26mm zqm Gmd solid A x3 x0 x E Liquidus and solidus line is determined at the point where the chemical potentials of the phases are the same mniar gibbs free energy 9 a A xsxo x s cumposmon X3 28 Eutectic Phase Diagrams eutektos meaning 39easily melted TA TB Temperature Composition XB Feeling Eutectic Phase Diagrams Eutectic System TA 9 3 E 8 E a Xglincrwsing rmuo Composition XB Ideal Bad solid Even worse solid L V Clustering tendency in solid Increases Eutectic Phase Diagrams T Ideal solution TA L L 0 TB Tu a I Tr R T A B A x X2 3 YB X B gt Ten pmquot u m 30 Eutectic Phase Diagrams 1 TA Onephase liquid 1 T v I T 605 X i 9 9 S i 0 1 two 55 2 1 phase to 3 l One 4 5 phase 39 hase 5 solid Eutectlc Isotherm X EOIid Q I 3 g a g l T h I39d 9 U p g wo p ase SCI 33 O m I T I X 39 3 0c 1 Composition XB Temperature Eutectic Phase Diagrams Eutectic point I l l l l l l Eutectic Isotherm l l l l l I I TB snMOS X2 Composition XB F 2 specify temperature and composition F 1 specify temperature or the composition of one of the phases F 0 temperature and compositions of the phase are fixed 33 Eutectic Phase Diagrams Hypoeutectic Hypereutectic A Temperature Composition XB Hypoeutectic containing less ofthe secondary component than the eutectic composition Hypereutectic containing more ofthe secondary component the eutectic composition 34 Eutectic Phase Diagrams Eutectic Reaction Symbolic expression Liquid lt gt Solid 1 Solid 2 Llt gtOLB 35 Eutectic Phase Diagrams Question from the following eutectic phase diagram Temperature fL 1 The fraction of primary solid that L forms under equilibrium cooling at the eutectic temperature X02027 3 faszL XO a XL Xa 27 B XB 2 The fraction of liquid with the eutectic composition that will transform to two solid phases below the eutectic isotherm eut X0Xa 27 20 0412 XL Xa 37 20 36 Eutectic Phase Diagrams Question from the following eutectic phase diagram 3 The amount of or and B that will form from the liquid just below the eutectic isotherm f X Xf 73 37 0 X Xa 73 20 X5 Xa 37 20 X Xa 73 20 0679 Temperature fl 0321 B The fraction of alloy composed of eutectic or and 3 ff ffwfa 0412gtlt 0679 0280 ff f f O412gtlt 1 0679 0132 37 Eutectic Phase Diagrams Question from the following eutectic phase diagram 4 The total amount of or phase in the alloy at a temperature just below the eutectic temperature Temperature flotal 0868 X Xa 73 20 Another way ff ff ff 0588 0280 0868 f P Portion from solid in L0 faew Portion that becomes solid in ocB via euteCtiC liClUid in Ha Temperature Eutectic Phase Diagram What does this mean Composition XB 38 Phase Diagrams Containing Two Eutectics 39 4o Peritectic Phase Diagrams Symbolic expression Liquid Solid 1 lt gt Solid 2 L0Llt gtB 41 Peritectic Phase Diagrams T Tempe urc TA L L a V 0 TB I u 0539 m a L 39I empc ruturc Temperature quot C Peritectic Phase Diagram Question Determine the composition and relative amounts of each phase present just above and below the peritectic isotherm for each of the three alloy compositions indicated X1 O125 wt X2O17O wt X3O35O wt X1 X2 X3 Xi 4 9125 wo IC Xz 017 W10 C riff 5035 wa C 15580 Fe 005 010 015 020 0125 030 035 040 045 050 055 060 065 070 075 Weight ercemageearbon Above peritectic 42 Below peritectic Alloy I 0125 7 009 fL 053 7 009 mm 0 053 7 0125 017 7 0125 fa 053 7 009 7 039920 017 009 0563 0125 009 0 f7 017 009 0437 Alloy 2 fL 017 009 z 053 7 009 0182 O f a 053 017 053 009 0318 O f y 0 10 single phase Alloy 3 fL 035 7 009 035 017 053 009 03959 053 7 017 0500 0 53 035 f 5 053 009 0 409 0 f 0 053 035 7 053 017 0500 43 Monotectic Phase Diagrams Over some portion of the phase diagram two insoluble liquids form Through monotectic isotherm twophase Liquid state becomes twophase LiquidSolid state Why is it eutectic isotherm TE Analysis of a Monotectic Phase Diagram Liqoc 39 Liq bzLiq T2 9 V L qcnw gt 5 4 v I 5 m aLiq lag V V II I Liq E T5 39 pump T6 3 a I i T J I I l 39 l r l I 39 A 39e 10 20 2530 4039 so so 70 Vsaas90 9aB s 15 27 32 76182 87 9a Composition Temperature 45 Analysis of a Monotectic Phase Diagram 4 Liquid Immiscibility gt Liquidus 1 Li uidus Solidus q Solidus Solvus B Composition Temperature m A Q 4 OJ f 46 Analysis of a Monotectic Phase Diagram Alloy 2 Alloy 2 at T3 f 080 032 11 080 027 fll 091 Composition Temperature Labeling Complex Phase Diagrams TB Composition XB 47 Temperature Labeling Complex Phase Diagrams L Chapter 1 Materials Science and Engineering Types of materials StructurePropenyProoess relationships Warner The Science and Design of Engineering Materia 5 Second Edition imn Chicago iL 1999 Role of Materials Technology determines prosperity and power Breakthroughs in technology are linked to the development of new materials and processes examples39 weapons from swords to modern energetic materials to shock absorbing materials electronics Sibased transistors in computers phones play stations aircraft and space shuttles ef cientengines lightweight frames temperature insulation telecommunications optical bers solar cells etc Major classes of materials Metals Ceramics Polymers Composites Semiconductors Structure of Materials Elecllnn All matter is composed of atoms Inside an Atom All atoms are composed of nucleus and electrons All nucleus consist of protons and neutrons Properties ofan atom are determined by 1 number of electrons or protons in a neutral atom 2 mass 3 distribution ofelectrons in orbits 4 energy of electrons 5 ease of adding or removing electrons to create a charged ion Properties of materials depend on what atoms they are made ofand how these atoms are arranged Structure of Materials How atoms are held together By primary ionic covalent metallic or secondary van der Waals bonds What is the difference between primary and secondary bonds Primary bonds involve either the transfer of electrons from one atom to another or sharing electrons between atoms Secondary bonds occur only due to interaction between electrical dipoles center of positive charge is different from the center of negative charge the dipole can be either permanent induced or temporary lCTSSQEZZL Primary bonds are much stronger 39 V O 1 331 A second molecule Can we predict the bonding type Charged separauon Yes wnll discuss next time t mm 39 g 1 39 0 ls bonding Important for understanding materials V ggfgg yg s Yes itwill determine materials properties Metals Copper used for over 7000 years initially as tools and now as cables and heat conductors Gold used for over 7000 years as jewelry coins and n es and heat conductors Silver used for over 6000 years as coins jewelry cables me icine Iron used for over 3000 years as tools and weapons Aluminu m used for over 200 years cables ets airplanes cans Titanium used for over 60 years rockets airplanes marines armor consumer etc uv I 500000 c 00 1200 BC 20th century time Stone age Bronze age Iron age Si age tools 39om stones Coppertin alloy produced harder and stronger electronics wood bones By melting Cu over re it than bronze is harder amp stronger than pure Cu Metals Mechanical 0 Thermal 39 Electrical Structural Common properties Strong and tough but have high density Metals resist brittle fracture by loading ductile 39 Could be good thermal conductors eg Cu Au 0 Moderate temperature resistance meltingT Al 660 Ag 900 Au 1060 Cu 1080 Fe1540Ti 1670 andW 34220 0 Structure has free electronsquot making metals good electrical conductors oAtoms are located in regularly de ned repeating positions a crystal Metals Delocalized cloud of valence electrons Ion cores of 2 charge Part of the electrons are delocalized and shared by all the atoms forming a cloud or sea of free electrons Free electrons are responsible for high conductivity of metals Electron cloud shields positively charged atomic cores from each other and repulsive forces do not develop during high impact stress preventing fractures and making metals ductile will discuss later Ceramics Sand 39 cements used for over 8000 years now believed that tops of Egyptian pyramids were cast from cement 39 Clays used for over 25000 years for sculpture pottery bricks tiles 39 Glass used for over 5000 years Thermal amp electrical insulation Graphite Ceramics Common properties Mechanical Strong have moderate density Thermal Electrical Structural Ceramics bend little before they break brittle Could have high AIN Aluminum nitride or low ZrO2 Zirconium dioxide thermal conductivity High temperature stability chemically resistant Structure has no free electrons thus poor electrical conductivity used as insulators Combination of metallic and nonmetallic atoms Many but not all ceramics are crystalline Crystalline Solid SiO2 disordered glass or ordered crystal structure Ceramics Ionic covalent or mixed bonding atoms atoms 07 7 7 o e o V MRING 0F ANSFER 0F ELECTRONS ELECTRON A 0 W molecule positive negative ion ion covalent bond ionic bond Figure 2 5 Essential Csll Elolagy 2a a 20m Garland Samuel The absence of free electrons make these materials good electrical insulators Since all electrons are tightly bound it is difficult to make new bonds thus good chemical resistance of ceramics Due to tight bonds atoms are not free to move making ceramics brittle Polymers 39 Amber mineralized resin used for over 6000 years as jewelry 39 Latex used for over 3000 years by Mayan who discovered methods for treating natural rubberthat were not reproduced until 19 h century modern use over 200 years 39 Cellulose wood fiber used in paper and textiles 39 Polystyrene used since 1931 for a variety of objects as fairly rigid economical plastic as a foam it is used in virtually all meat and poultry trays 39 Nylon used since 1939 forfishing line toothbrush bristles stockings track pants shorts swimwear active wear windbreakers bedspread and draperies 39 Teflon used since 1946 for coating on cookware soil and stain repellant forfabrics and textiles chemical industries 39 Kevlar used since 1965 for body armor bicycles five times strongerthan the same weight of steel Polymers Common properties Mechanical Low density Can be ductile or brittle Commonly relatively low strength Thermal Commonly low thermal conductivity Temperature sensitive Electrical Most polymers electrical insulators Structural Long chain molecules with repeating groups Easy to form into complex shapes Disordered or semicrystalline H H H H H EWHHHHu 39 1x0xC CxlC1Cl HlHlHlHlHlH H H H H H Composites 239 or more materials are combined to achieve unique combination of properties eg rigidity strength and low density Adobe brick straw is mixed with mud or clay an adhesive with strong compressive strength to achieve smaller and uniform more cracks in the clay greatly improving the strength Plywood used for over 5500 years thin slabs of wood held together by a strong adhesive making the structure strongerthan just the wood itself CarbonCarbon used for over 30 years highlyordered graphite fibers embedded in a carbon matrix to achieve lightweight material with low thermal expansion coefficient thus highly resistant to thermal shock or fracture due to rapid and extreme changes in temperature CarbonEpoxy used for over 30 years highlyordered graphite fibers embedded in epoxy dramatically improve its mechanical properties including strength and toughness Cermet composite of ceramics and metal high temperature electronic components resistors capacitors Semiconductors Silicon the 2nd most abundant element in the earth s crust used in semiconductor devices incl integrated circuits Germanium in 1871 Dmitri Mendeleev predicted it to exist as a missing analogue to Si the element was discovered in 1886 originally used in transistor industry instead of Si now employed in infrared spectroscopes and other optical equipment which require extremely sensitive infrared detector GaAs Gallium arsenide used in diodes incl lightemitting diodes LEDs transistors integrated circuits le and analog devides such as oscillators and amplifiers CdTe Cadmium telluride used in solar cells as an infrared optical material for optical windows and lenses SlC Silicon carbide used in high temperature high power electronics as substrates for nitrides growth in cutting tools as abrasives injewelry Bonding similar to ceramics Mechanical properties similar to ceramics Representative strengths of the various material types Strength psi 300000 200000 100000 Polymers PEEK Nylon Polyethylene Typical carbon glass Kevlar fiber strength 39 500000 psi Ceramics SiC Si3N4 39 ZI39OZ A1203 r Carbon epoxy Kevlar epoxy Boron polyimide 39 Carbon polyimide Glass polyester 39 quotMetals I quot High strength CompositesVi 39 steel quot Alloy steel i CuBe alloy L Nickel alloy Titanium alloy CuZn brass Aluminum alloy Zinc alloy Jobb ir alloy Lead From D R Askeland The Science and Engineering of Materials Strength Correlation Between Strength and Ductility Ge 796 f re Measure of Ductility Strength Correlation Between Strength and Ductility True improvement in performance Measure of Ductility Increase in StrengthtoDensity Ratio over time We Slur D A A h A nances M m t A re Hechmcai Systems Natmnai p i 1 u H 199D i Washingtnn DC Natmnai Academy a 2EIEIEfrDm Increasing sophistication of human manipulation of materials StructurePropertyProcess relationship Structure 39 Atomic Nano Micro Macro Property 39 Mechanical 39 Physical electrical magnetic optical thermal elastic chemical Process 39 Material history Chapter 4 Point Defects and Diffusion Introduction Point Defects Impurities Solid State Diffusion Introduction Defects and Impurities Number of Fe atoms in 1 cm3 For BCC Fe one unit cell with a0287 nm has two Fe atoms of Fe atoms in 1cm3 2 846gtlt1022 Considering such huge number of atoms it should not be surprising that some mistakes happen in the atomic arrangement Types mistakes M 1 IE egg W21 Point defects Linear defects Planar defects Introduction Defects and Impurities Questions Example semiconductor Are these defects undesirable What effect do the defects have on properties of materials Can we control the defects for our purpose Point Defect defined as an imperfection that involves a few atoms at most 71 Point Defects Perfect crystal Why does the nature choose imperfect one AG AH TAS Gibbs Free Energy G Enthalpy H Perfect crystal is favorable Entropy 8 Perfect crystal is unfavorable If each site is unique and distinguished from others Point Defects Temperaturedependency of the vacancy concentration No of defects Activation energy N 7 exp Qp VN jk l Boltzmann39s constant 138 10 3923 JatomK 862 x 105 eVat om K No of potential Tcmpcmnnc d Each lattice site is a potential vacancy site Point Defects Temperaturedependency of the vacancy concentration N How to determine the activation energy 7D exp E N kT Measure this Replotit ND exponential dependence defect concentration Example Effect of Temperature on the Vacancy InC Concentration of Nickel 0001 0002 0003 1 Melting Temperature Room Temperaturei 25 QC 0 NV NI exp RT CV exp Qrvi 1nCv R T 1T 1K Question 1 Calculate the concentration of vacancies in Cu at m temperature 298 K and iust below the melting point 1356 K given that the activation energy is approximately 83600 Jmol and the gas constant R is 831 JmolK Use this formula C zexp Qfv V RT What would be the CV if we heat up the system higher than 1356 K Point Defects H 4mjgtf jug it 1 1 Vacancies and Interstitials in Ionic Crystals xii f HE 1 5 Hj Lquot m u L Schottky defect 1VCI and 1VNa Schottky defect 2VC39 and 1VMg2 Point Defects Vacancies and Interstitials in Ionic Crystals The defect involves a cation The defeCt inVO39VeS 3 anion The cation defect is more common because of the size of the cation compared to the size of the anion Impurities Solvent Solute Solvent atoms atoms of the primary atomic species Solute atoms impurities Solute Interstitial Solid Solution Substitutional Solid Solution When impurities lie in the space When impurities substitute for the between the solvent atoms solvent atoms Interstitial solid solutions normally form 1 only when the interstitial atoms are significantly smaller than the solvent atoms and 2 are comparable in size to the interstitial sites they occupy Not possible to formulate precise rules describing the requirement for the formation of interstitial solid solution Possible to define the requirement for the formation of substitutional solid solution HumeRothery Rules Guidelines for Solubility The size difference between the solute and solvent must be no greater than 15 The electronegativities of the two atomic species must be comparable The valence of the two species must be similar The crystal structures of the two species must be the same This is required if the alloy are to form a continuous series of solid solutions Examples would be CuNi and SiGe Impurities in Ionic Crystals Na C1 1 One Mg2 ion substitutes for the Na ion 2 But this substitution results in one extra positive charge How to compensate for this additional positive charge Since no additional anions are available the most frequent result is the effective removal of a single positive charge through the formation of Na vacancy Question 2 Consider a sample of MgO 100 g containing 02 weight percent Li2O as an impurity Compute the additional vacancv concentration that arises because of the presence of the impurity Use the molar masses Li 6941 gmol 0 15999 gmol Mg 24305 gmol Diffusion l 39 139quotwi lquot l l fiil l l Ci l l li l llquot li for lfl l l liil all I39I vl l l 1 lie Ll ll teal litizlr39l dlufurrtl rmliltcslfii A phenomenon of random motion causing a system to decay towards uniform conditions 0 O Extracellular space 39 o o o 39 o o o O C O o O o o O O O O Lipid bilayer l cell membrane l l o 390 0 a I n g I 0 3 02 i l Intracellular space I TIME Not ReverSible Not Reversible I I Non equilibrium Non equilibrium Application of Diffusion Example Carburization of Steel surface Iron carbide Fe3C Extra carbon combines with iron to form strong iron carbide particles having excellent wear resistance 9 The carburized surface is ideal for applications such as gears and crankshafts in automotive engines Initial stage Cu Diffusion SelfDiffusion diffusion without concentration gradient Label some atoms After some time InterDiffusion diffusion with concentration gradient After some time Diffusmn NI Cu Cur DiHL hlmi O 0 DD bl Concentratron of Ni Cu Concentralion of Ni Cu O PDSitIOI I Posilion it Ci Fick s First Law Factors affecting atomic transport Concentration gradient Jump distance Ax Structure A atoms Temperature The net diffusion flux J J DC1 C2Ax D the diffusion coefficient cm2s B atoms Question3 A thin plastic membrane is used to separate hydrogen from a gas stream At steady state the concentration of hydrogen on one side of the membrane is 0025 molm3 on the other side it is 00025 molm3 and the membrane is 100 um thick Given that the flux of hydrogen J through the membrane is 225X10396 molm2s calculate the diffusion coefficient D for hydrogen 20 2 Temperature Dependence of Diffusivity Q D D0 6Xp E Increasing T Decreasing LT Arrhenius form 1111 111190 ybmx o 1T K1 Q Why does such Arrhenius form work very well Temperature Dependence of Diffusivity D 2 D0 exp Increasing T Decreasing T lnD Physical meaning of DO textbook D0 is a constant with unit cm2s lnD A virtual diffusion coefficient at T based on the assumption that the current mechanism is valid up to T 9 Usually it is not realistic because if we have phase transition diffusion T mechanism will also be changed ll 8 H ll 0 Temperature Dependence of Diffusivity Phase transition 10399 1010 BCC U c E 1011 FCC 0 1012 103 I I 00007 00008 00009 0001 1T K1 Depending on the phase they have different slope activation energy 23 24 Question4 For low concentration of Zn in Cu the diffusion coefficient of Zn has been measured to be 367x103911 cm2s at 1000 K and 832x103918 cm2s at 600 K Determine a the activation energy for this process and then b the value of the diffusion coefficient at 450 K Mechanisms of Atomic Transport Vacancy Diffusion 1 Atom interchange from a normal lattice position to an adjacent Mulluu ol a has n substllunonal alum I I a I I V i Q d y x vacant lattice site 9 I I WM 2 The extent of vacancy diffusion Jr C is controlled by the concentration 9 f I o of these defects 7 K 7 3 The direction of vacancy motion 3 I39 7 7 k V is opposite to direction of V V diffusing atoms Interstitial Diffusion mm M mm ml We 01 mm alom before difluswon atom aim mnmnn 1 Typical interstitial atoms hydrogen carbon nitrogen and oxygen i I I 2 In most metals Interstitial I I I diffusion occurs muc 39 rapidly than vacancy diffusion 26 Mechanisms of Atomic Transport Interstitial solid solution Substitutional solid solution Counter flow of Vacancies and solute gt C L D C UJ l Position Steady State VS Non Steady State Concentration Gradient Constant with time Changed with time Steady state Non Steady state Fick s First Law Fick s Second Law JD dx 27 Steady State VS Non Steady State gt steadystate diffusion not commonly encountered in engineering materials gt in mi poin stair Oanceutratmn oi HUSHin speucs Distance 29 Fick s Second Law Describes the diffusion of atoms molecules particles etc when the concentration gradient is changed with time The rate of change of the number of atoms in 6C the slice is equal to the rate that atoms are EdVJin Jomd14 entering the slice minus the rate that atoms are d dAdx leaMinthislice V dX E Jim Jout at 6x 6C 6 lt C I at 6x CHigbii JOUt CLow 6C 6D 6x at 6x 2 dv 6C 2 D6 C 5 6x2 Steady State VS Non Steady State Concentration Gradient Constantwith time Changed with time Steady state Non Steady state Fick s First Law Fick s Second Law 43 dx J 2 066 at 6x2 30 Diffusion of Carbon into a SemiInfinite Slab Fick s Second Law General Solution for Fick s Second Law 2 2135 gt M1ef L at 6x Cs CO 2Dt erfx Ix eXp t2 dt 72 0 Error function e39fx expitzdt x2 The Gaussian Gx A e m function where 6 IS referred to as the spread or standard deviation and A is a constant 2 1 7 The normalized Gaussran Gltgt oe Z 2 function The relation between the normalized TGxdx Erf gaussian distribution and the error function ix The Complementary Error function Gx me Erfcx 2 m erfcxlierfxi Ie uzdu W X Thin Film Solution cxtt1 33 ThinFilm 5 4 2 O 2 4 6 Distance from interface With increasing time the solute spreads throughout the diffusion couple 34 35 Thin Film Solution 2 Concentration 8C D a C decreases at 5x2 with time I Concentration 39 increases gt with time Concentration lt increases Concentration c with time x2 X O X C xal 2 CX Mm p 4Dr Chapter 3 Crystal Structures Introduction Bravais Lattice Crystals with One Atom per Lattice Point Miller Indices Densities and Packing Factors of Crystalline Structures Interstitial Positions and Sizes Crystals with Multiple Atoms per Lattice Site Liquid Crystals Single Crystals and Polycrystalline Materials Polymorphism XRay Diffraction Chapter 3 Crystal Structures A crystal is a solid in which the constituent atoms molecules or ions are packed to have a long range order as well as a short range order ln crystal its unit structure is repeated in all three or two spatial dimensions Many materials metals ceramics and polymers crystallize in a regular array with basic building blocks being at repeated regular intervals The structure is determined by the bond character and energy minimization Properties are dependent upon the type of bond and the structure Bravais Lattice and Unit Cells Lattice 1 an infinitely extended 3dimensional point array 2 each point is surrounded by an identical group of neighboring points Basis group of things located on the lattice 39 Lattice Basis crystal structure I Unit Cells l quotliml l ia u llll fill vil w39lxlszl39jl li lbw fil lel t a miifl e l Lil r 2Mi llii f i Wm Unit cell Cell parameters a b and I Bravais Lattice and Unit Cells 7 crystal systems Axial Crystal Svsrem Relationships Interaxiaf Angles Unit Ce Geometry Cubic a b C L 8 y 90 a a A it I Hexagonal a b r a 8 90 1 120 1 bx Tetragonal a b r a 3 y 90 Bravais Lattice and Unit Cells 7 crystal systems continued Rhombolledral a b cquot w 8 y 90 77 5 Ol lllOl39hOlIlbiC a a b as c u 8 y 90 Mmmdinic a as b 72 c r y 90 5 3 Triclmic a 9395 b 35 r r 7139 B a5 y 7 39 90 14 Bravais Lattices P primitive I body centered F face centered C base centered l39ilombohedral C llblC hexagonal tetragonal Ol thm homblc monorluuc trlclmlc trlgonal c 7 El 3 a b a C a a a b C a quot C a Zeb Structure of Tungsten a Body Centered Cubic BCC Phase Lattice Fractions of atoms in the unit cell Hard sphere packing unit cells Geometry of the hard Sphere BCC Structure lt a gt ao A r l r l aoxl lt 32 use x Distance between the centers of adjacent atoms Geometry of the hard Sphere BCC Structure 2i7rr3 3 Hard Sphere Packing pf 3 a Fractions of 3 Z 4 quot atoms in the 4r unit cell a f 4 3 Number of atomsunit cell 237T7 8 corners x 18 1 in center 2 pf Packing factor pf 4r 3 Number of spheres x vol of spherevol of unit cell Face Centered Cubic FCC Phase Fractions of atoms in the unit cell Hard sphere packing Copper is an FCC material Distance between the centers of adjacent atoms Packing Factor Hard Sphere FCC Structure Hard Sphere Packing Fractions of atoms in the unit cell Number of atomsunit cell 6 faces x 12 8 corners x 18 4 Packing factor pf Number of spheres x vol of spherevol of unit cell 4g7rr3j pf 3 Density of Selected Elements Hard Sphere Approximation M Density 2 V MC MW 2 atoms j mass D we atom V a3 MC 800 Hard sphere packing 4 2 atomsunit cell a T FCC Hard sphere packing 4 atomsunit cell a 13 Hexagonal Structure F r 5 395 39 y Hexagonal aquot closed packed HCP k o H Hard sphere HCP I t Nearest neighbors in the HCP structure TABLE 32 I cum structure chamcmistics a some metals Atoms per Coordination Structure an versus r Cell Number Packing Factor Examples Simple cubic SC 30 2r 1 6 052 Polonium Po azMn Bodycentered a0 4w 2 8 068 Fe Ti w Mo Nb cubic Ta K Na V Zr Cr Facecentered a0 4r 4 12 0 74 Fe Cu Au Pt Ag cubic Pb Ni Hexagonal dose ao 2r 12 074 Ti Mg Zn Be packed 0 z 1633510 Co Zr Cd Q Why does an element metal prefer a type of packing rather than others Miller Indices The most common convention to describe specific points directions and planes in the crystal lattice system 1 Coordinates of points 2 Indices of directions 3 Indices of planes Coordinates of a Point Directions in a Crystal Miller Indices hkl Square bracket Get 2 points that lie in the direction Subtract coordinates of the tail from tip Clear fractions Write integers in square brackets Negative integers are indicated by putting a bar over the integer Directions in 3 Crystal Miller lndices hkl Examples 20 Family of Directions in a Cubic Crystal 001 Too 010 000 010 100 21 Planes in a Crystal Miller lndices hkl Z Cube Face 00 001 l 0 0 01 oo y 1 Identify coordinate intercepts of the plane 2 Take the reciprocal of the intercepts 3 Write integers in parentheses no commas Planes in a Crystal Miller Indices th Cube Faces 1 Identify coordinate intercepts of the plane 2 Take the reciprocal of the intercepts 3 Write integers in parentheses no commas 22 23 Planes in a Crystal Miller lndices bk 2 Through the Cube 00 00 12 0 o 2 1 Identify coordinate intercepts of the plane 2 Take the reciprocal of the intercepts 3 Clear fractions by multiplying but do not reduce to lowest integers 4 Write integers in parentheses no commas 24 Planes in a Crystal Miller lndices th Z 001oo 000 y X 1 Identify coordinate intercepts of the plane 2 Take the reciprocal of the intercepts 3 Clear fractions by multiplying but do not reduce to lowest integers 4 Write integers in parentheses no commas 5 Negative integers are indicated by a bar over the integer Planes in a Crystal Miller Indices hkl 1T0 000 Planes in a Crystal Miller lndices hkl Plane F Plane A Plane B Plane V E X Plane C iquot Plane D 1 Identify coordinate intercepts of the plane 2 Take the reciprocal of the intercepts 3 Clear fractions by multiplying but do not reduce to lowest integers 4 Write integers in parentheses no commas 5 Negative integers are indicated by a bar over the integer Planes in a Crystal Miller Indices th PIaneA E 39 Pane B z l r i Plane C i 1 A I 4 Plane D Plane F I Plane Intercepts zPIane Indices mmbnwgt co 001 111 l 100 l 10012 12 12 001 111 110 001 102 221 28 Family of Planes in a Cubic Crystal 100 T00 010 0T0 100 brace Amorphous ice Ice Ih Ice lc Ice II Ice III Ice IV Ice V Ice VI Ice VII Ice VIII Ice IX Ice X Ice XI Ice XII Ice XIII Ice XIV Ice XV Characteristics ice is an ice lacking crystal structure Amorphous ice exists in three forms lowdensity LDA formed at atmospheric pressure or below high density HDA and very high density amorphous ice VHDA forming at higher pressures LDA forms by extremely quick cooling of liquid water quothyperquenched glassy waterquot HGW by depositing water vapour on very cold substrates quotamorphous solid waterquot ASW or by heating high density forms of ice at ambient pressure quotLDAquot Normal hexagonal crystalline ice Virtually all ice in the biosphere is ice Ih with the exception only of a small amount of ice Ic Metastable crystalline variant of ice The oxygen atoms are arranged in a diamond structure It is produced at temperatures between 130150 and is stable for up to 200 K when it transforms into ice Ih It is occasionally present in the upper atmosphere A crystalline form with highly ordered structure Formed from ice Ih by compressing it at temperature of 190210 K When heated it undergoes transformation to ice III A crystalline ice formed by cooling water down to 250 K at 300 MPa Least dense ofthe highpressure phases Denser than water Metastable rhombohedral phase Does not easily form without a nucleating agent A crystalline phase Formed by cooling water to 253 K at 500 MPa Most complicated structure of all the phases A tetragonal crystalline phase Formed by cooling water to 270 K at 11 GPa Exhibits A cubic phase The hydrogen atoms39 position is disordered the material shows The hydrogen bonds form two interpenetrating lattices A more ordered version of ice VII where the hydrogen atoms assume fixed positions Formed from ice VII by cooling it beyond 5 C A tetragonal metastable phase Formed gradually from ice III by cooling it from 208 K to 165 K stable below 140 K and pressures between 200 and 400 MPa It has density of 1 16 gcm slightly higher than ordinary ice Protonordered symmetric ice Forms at about 70 GPa An lowtemperature equilibrium form of hexagonal ice It is A tetragonal metastable dense crystalline phase It is observed in the phase space of ice V and ice VI It can be prepared by heating highdensity amorphous ice from 77 K to about 183 K at 810 MPa A monoclinic crystalline phase Formed by cooling water to below 130 K at 500 MPa The protonordered form of ice V An orthorhombic crystalline phase Formed below 118 K at 12 GPa The protonordered form of ice XII The predicted but not yet proven protonordered Densities of Crystalline Structures Linear Density Number of atoms centered along direction within one unit cell L Length of the line contained within one unit cell FCC lattice 110 x Atoms touching along the 110 direction dZ y 6 BCC lattice 110 111 1 FCC 110 pp 1 BCC 111 Pr d2 39 r105 4rao y Atoms touching along the 111 direction Closepacked Direction 1 The directions with the highest linear density 2 The atoms are in direct contact 30 31 Densities of Crystalline Structures Planar Density Number of atoms centered an a plane within one unit cell p P Area of the plane contained within one unit cell FCC lattice 1 FCC 111 p 2J 7 1 FCC110 pL W Portion of sphere on the plane Closepacked Plane 1 The plane with the highest planar density If 2 The atoms are in direct contact DensItrikigl AWEWstalline Structures Volur rCPetric Density pV the Number of ator eeemol ayaer E a2r J5 c4 r J Number of atoms 6 In a unit cell 2 1 pV 4J5r3 39 12 Interstitial Positions The APF is less than 10 for all crystals 9 There is still plenty of room inside crystals The size and position ofthe holes in crystals 9 interstices Interstitial Positions in FCC ll I O Octahedral sites 4 Tetrahedral sites 8 Interstitial Positions 34 Octahedral positions Tetrahedral positions a J a 2 4 s 37 a 575 X o 4 Iquot 8 Kr 0414 Kr 0225 2 0 dog 39 51 4 2 ao o A o BCC T v 6 12 Kr 0155 Kr 0291 HCP o 3 6 12 Kr0414 Kr0225 Example Crystals with Multiple Atoms Per Lattice Site 1 T 35 Example 36 Crystals with Multiple Atoms Per Lattice Site FCC unit cell with Na located at FCC positions FCC unit cell with Cl39 located at FCC positions Example Crystals with Multiple Atoms Per Lattice Site Diamond Cubic Structure 37 Geometry 2 atomslattice point FCC lattice 8 atomsunit cell Group IVB C 6 Si 14 Ge 32 Example Crystals with Multiple Atoms Per Lattice Point Perovskite Structure CaTiO3 Example Crystals with Multiple Atoms Per Lattice Site Simple tetragonal Offset between top plane of Ba ions and top of center 02 ion BaTiO3 W Offset between central Ti4 ions and midplane of 0239 ions Piezoelectric material Example 4393 Crystals with Multiple Atoms Per Lattice Site Crystalline polyethylene Models for polymer crystal e I cafolded model Crystals with Multiple Atoms Per Lattice Site Models for polymer crystal 5mm hawtan 45 Liquid Crystals mil 1 llm39mv IvyWu MN llllllllm Smectic A phase if IllVMlIIl imIIII m4 willIllI l Nematic phase Smectic C phase Chiral phase CO39Umnar Phase i i ll Nematic the molecules have no positional order but they have longrange orientational order Smectic the smectics are positionally ordered along one direction In the Smectic A phase the molecules are oriented along the layer normal while in the Smectic C phase they are tilted away from the layer normal Chiral the chiral nematic phase exhibits chirality handedness This phase is often called the cholesteric phase because it was first observed for cholesterol derivatives Columnar molecules assemble into cylindrical structures to act as mesogens Originally these kinds of liquid crystals were called discotic liquid crystals Mesogen unit of liquid crystal Single Crystal A single crystal monocrystal is a crystalline solid in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample with no grain boundaries Iquotquotquotquotquot39 1 rm c run Gold Diamond Polyethylene L Quartz Diamond USing CVD MFI zeolite wll l l39llii ll ily ii Grain boundary it Polycrystalline material composed of many grains separated by thin regions called grain boundaries Unit cell orientations in grain A Unit cell orientations in grain B 48 Polycrystalline Aluminum Increasing Grain Size gt Decreasing Grain Boundary Surface AreaUnit Volume Decreasing Grain Boundary EnergyUnit Volume Allotropy and Polymorphism Allotropy is a behavior exhibited by certain chemical elements these elements can exist in two or more different forms known as allotropes of that element In each different aotrope the element39s atoms are bonded together in a different manner Polymorphism is the ability of a solid material to exist in more than one form or crvstal structure Polymorphism can potentially be found in any crystalline material including polymers and metals and is related to aotropy which refers to elemental solids Allotropy and Polymorphism Graphite gt CE gt 39gt gt lt ltlt 51 Isotropy and Anisotropy When the properties of a material are independent of the direction in which they are measured the material is termed isotropic When properties depend on direction the material is anisotropic Graphite Thermal expansion W C axis direction is more prominent than a and b axis direction C a b Ci39l IJ Crystal Structure Determination Atomic scale structures on the order of 0550 A requires X rays The periodic arrangement of atoms leads to the constructive and destructive of the X ravs The interpretation of the scattering phenomena leads to a determination of the location of atoms in the crystal structure The scattering is affected by the electron density of the atoms in the crystal structure when Xrays are used XRay Xrays are electromagnetic waves with wavelength of005025 nm Wave Interference Composite wave Constructive interference Destructive interference Waves have the same phase Waves have different phases inphase outofphase WWWWWWW numwmmmm um m El Young s experiment Diffraction of Light XRay Diffraction 56 Path length 2a Path length 1a 0 Path length 2b Path length 1a AB BC I Path length 3c Path length 1a 2AB BC AB BC d39sin 9 AB BC 2dsin 9 CD m El XRD pattern example A msazmn cmm3me Al powder result Xray 2a m w Diffractometer Xray Diffraction Patterns DNA Diamond XRay Diffraction For a cubic crystal Face Centered Cubic FCC Selection Rules h k I must be all odd or all even 100 absent 200 present 110 absent 111 present VV VV Body Centered Cubic BCC Selection Rules The sum of h k I must be even 100 absent 200 present 110 present 111 absent VV VV 60 Question We observed the signal at 2638quot for 111 plane Determine a the dspacing for the 111 plane b the lattice parameter aO c the atomic radius for Al FCC Use 101542 nm and Bragg s law with n1 Question For BCC iron calculate a the interplanar spacing dhkl and b the diffraction angle for the 220 set of planes The lattice parameter a0 for Fe is 02866 nm The wavelength 9 is 01790 nm and the order of reflection n is equal to 1 5 Xray Diffraction Scaltcied s llErlCLll wavtlcls quot whatever atom Plane pOIEmZEd X ray W W 39 1 We shoot xrays with the same wavelength a crystal consisting of atoms 2 The xrays hit the atoms in the crystal 3 The xrays are diffracted or scattered by the atoms The scattered xrays have the same wavelength with the incident x rays elastic scattering The direction of scattering It would be various but xrays scattered by the atoms with the same spatial condition direction have the same direction Anyway only the xrays with the constructive interference can be observed Wave Interference Composite wave Constructive interference When the waves have the same phase inphase Destructive interference When the waves have different phases outofphase 63 64 Xray Diffraction AB BC 2dsin e For constructive interference the path difference should be gig equal to an integer number of wavelengths A c I 11 Let s say the direction of the 9 9 l first layer is 111 B Q Then what is the direction of the second layer in this picture A Huge number of xrays hit a huge number of planes with the same direction and then make only one dot in the xray diffraction pattern Xray Diffraction In x ray diffraction pattern Each bright point is made by all the re ections of xrays with the constructive interference from the huge number of planes of the same direction 66 Xray Diffraction Real Space and Reciprocal Space Their relationship eXp27Z39iK R 1 r2gtltr3 K k1 k2 k3 a position vector in the reciprocal space r1r2gtltr3 R r1 r2 r3 a position vector in the real space r3gtltr1 r2r3xr1 1 lKl m k3 r1gtltr2 r3r1xr2 All the planes with the same direction are mapped to just one point Q The best mathematical way to handle this type of mapping is Fourier Transform 67 Xray Diffraction Fourier Transform Joseph Fourier FK j fReXp27ziK RclR Things in real space 9 Things in reciprocal space Fourier Inverse Transform fR j FKexp 27ziKRdK K Things in reciprocal space 9 Things in real space as Ewald sphere Convenient Device helps us think about the xray diffraction Conceived by Paul Peter Ewald 1 The radius of Ewald sphere I Incident X ray 32 1 2 whatever 7 ism 6 plane 2quot Bragg s Law whatever crystal Only when diffracted beam meets the Ewald sphere reflection sphere The diffraction point can be observed Ewald sphere Convenient Device helps us think about the xray diffraction We have a piece of crystal in real space 9 We have also reciprocal space corresponding to the real space Only the point where reciprocal lattice point meet the Ewald sphere can be observed in the pattern It is because of the reciprocal length of wavelength of xray lattice Reciprocal lattice Each reciprocal lattice point is mapped to the plane inside the crystal in real space 70 Question How can we obtain sufficient amount of diffraction points 1 Use different wavelength 2 Rotate the crystal httpwwwphysicsbyuedufacuItycampbexraydiffractionaspx 7 1 One crystal in real space brings its reciprocal lattice together 2 Once the wavelength is selected 7 the Ewald sphere is determined with the radius of 17 3 The points of reciprocal lattice met by the Ewald sphere can be observed when xray is radiated OONFDQ39IbS ONT Chapter 2 Atomic Scale Structures Introduction Atomic Structure Thermodynamics and Kinetics Primary Bonds BondEnergy Curve Atomic Packing Secondary Bonds Mixed Bonds Introductory Remarks for Chapter 2 Atomic Scale Structures Why do certain materials have particular sets of properties Why are metals good electrical conductors while plastics and ceramics are good insulators Why are some materials stiff and what controls the stiffness Why do some materials expand with temperature while others do not Introductory Remarks for Chapter 2 Atomic Scale Structures Although properties depend on all levels of structure many are determined by the atomic scale The types of atoms present The types of bonds in the material The way the atoms are packed In Chapter 2 we review Structure of the atom Basic concepts from thermodynamics and kinetics Types of bonds Xenon on Nickel 110 STM Scanning Tunneling Microscope Au 111 surface AFM Atomic Force Microscope Atom All matter is composed of atoms Atom All atoms are composed of nucleus and electrons All nucleus consist of protons and neutrons Properties of an atom are determined by 1 number of electrons or protons in a neutral atom 2 mass 3 distribution of electrons in orbits 4 energy of electrons fl Electron Neils Bohr Albert Einstein Louise de Broglie Werner Heisenberg Erwin Schrodinger 5 ease of adding or removing electrons to create a charged ion Properties of materials depend on what atoms they are made of and how these atoms are arranged Atom Neis Bohr Werner Heisenberg Nobel Prize in Physics 1922 Nobel Prize in Physics 1932 electron Uncertainty Principle Apxmz Bohr Model Atom Duality of Light and Duality of Matter Light consists of particles called photons with ener equal to Elv Ezhvz As well as Emc2 Prince LouiseVictor Pierre Raymond De Broglie Nobel Prize in Physics 1929 h h i77 p ZnIEf h Planck constant 4 663 x1044 sec Albert Einstein Nobel Prize in Physics 1921 Inside an Atom Atom Quantum Mechanics Hamiltonian h nuclei 1 2 electrom nucleielectmm Z H i2 Mivi hz Vi2 62 Z 2 A 87r A A 87r me i A i VA nuclear kinetic electron kinetic nuclearelectron potential 2 electromelectromi nucleirmcleiZ Z 62 Z Z A B 6 A BgtA RAB i jgti Vi nuclearnuclear potential electronelectron potential h Planck constant Z atomic number e electron charge rAa distance separating nucleusA and electron a me electron mass RAB distance separating nuclei A and B M nuclear mass rab distance separating electrons a and b Schrodinger Equation Hmta I mtanuclet electrons E I totalnuclei electrons WaVefuncjt ior I BornOppenheimer Approximation Tram nuclei electrons LPelectroanLPn1tclei r V H 2 h2 electrons 62 nucleielectronsziA Erwin Schrodinger 87t2me 139 A i rAi Nobel Prize in Physics 1933 nucleinuclei electronselectrons 1 e2 z 2 L423 e2 Z 2 i A BgtA RAB i jgti 7 1 parameterization N1 N M Z N N 1 2 A Helectron ZiVi Z Z Z 27 i12 i1A1 79A i1jgtirij H LP r ELPelectronR9 739 electron electron 5 Her SamE FOR Ej 9 Quantum Number In the solution to the Schrodinger equation three quantum numbers arise from the space geometry of the solution and a fourth arises from electron spin Z J N 39H V The three spherical coordinates are associated with the three spatial uantum numbers Rr Principal quantum number n1 2 3 0 6 Angular momentum to 1 2 a Orbital quantum number qgt magic quantum m z 51 0 m 51 T l Spin quantum number ms 12 12 9 The quantum numbers set limits on the number of electrons which can occupy a given state and therefore give insight into the building up of the periodic table of the elements 9 of electron at each shell 2 2 51 Get back to old Bohr Model 11 a Zinc Atom of electrons at each shell 22I 1 where I 0 52 1 I0 6 I 2 d 10 I 3 f14 Q Electrons Zn Atomic number 30 Shell amp Orbital Energy Level Energy f d f d E p f 8 s d S d p S p 1 2 3 4 5 6 7 Prmcnpal quantum number n Schematic representation of the relative energies of the electrons for the various shells and subshells The Aufbau building up Principle 1 The number of electrons in an atom is equal to the atomic number 2 Each added electron will enter the orbitals in the order of increasing energy 3 An orbital cannot take more than 2 electrons Order of filling 1s 25 2p 3s 3p 45 3d 4p 55 4d 5p 65 4f 5d 6p 75 5f 6d Hwy m 1 fr 513cLl 139 pr w 1 fl ll 39 7 i r 7 gel ll 7 swxll Lilal All 4 J Hall r J l39 L 1 L 7 7 sl V VL vs 7 quotu go u 15739 t 13 2 mi 3439 39539 v 1 u c ll ll r fur ll glL l alllgol Mlhlnl Mlle lLllw lLllll 1 nuttyquot Hg 3 H w lllnl gllllng 5 Mi ll d orbitals shown with correct electron arrangement d orbitals shown with incorrect electron arrangement Electronic Structure Compare the electronic structures of Silicon anol Germanium with Carbon Atomic number of Carbon 6 Atomic number of Silicon 14 Atomic number of Germanium 32 These electronic configurations lead to similar crystal structure for the three 13 IIIB VB VB elements S as wage a 4 4 019mm 9 3m 8 o a Electronic Structure Order of filling 13232p33p4s3d4p5s 4d 5p 63 4f 5d 6p 73 5f 6d ggx 8p 8d 8f 2252 2Sp34 The same hybridization gt gt SP3 Silicon 14 electrons quot When hybridized 1S2 2522p6 3sp34 Germanium 32 electrons i 397 is gar1C4 When hybridized 182 252 2p6 3S2 3p6 3d 4sp34 PERIODIC TABLE GROUP gt A LIA 111A IVA VA VIA VUA VIHA 13 IE IIIB IVB VB VlB VUB 1 Transition Elements Atomic numba39 Gas Liqui f Transnion Elements Atomic mass 9 molquot 39Lanmanides 58 60 1 52 S 64 5 66 67 68 6 7 71 Rare Earlhs Ge W N Pm 539quot Equot Gd Tb Dy Ho Er Tm Vb Lu uolz 1mm my mm 15135 15197 x5715 1539 mm I653 15725 1539 173m 17497 quotAclinides Th Pa U Np Pu Am Cm Bk cf Es Fm Md No Lr Thermodynamics The study of the relationships between the thermal properties of matter and the external system variables such as pressure temperature and composition Thermodynamic considerations are fundamental in determining whether chemical and physical reactions can occur Kinetics Regarding how rapidly reactions can proceed 9 Reaction Rate X Properties and Behaviors of Materials Thermodynamics The study of the relationships between the thermal properties of matter and the external system variables such as pressure temperature and composition The study of the changes in the state or condition of a substance when changes in its temperature state of aggregation or its internal energy are important Thermodynamic states amp changes between such states Properties such as temperature pressure internal energy and entropy Universe System Surroundings System Surroundings System Isolated amp nonisolate 9 Interaction Open amp Closed mass Adiabatic amp Diabatic Energy The Laws of Thermodynamics 20 They are obtained from a wide variety of observations and ultimately justified by the agreement of the conclusions drawn from them with experiment 0 Zeroth law of thermodynamics stating that thermodynamic equilibrium is an equivalence relation If two thermodynamic systems are separately in thermal equilibrium with a third they are also in thermal equilibrium with each other B A IEquil Equil C B IEquil C 1 First law of thermodvnamics about the conservation of energy The change in the internal energy U of a closed thermodynamic system is equal to the sum of the amount of heat energy Q supplied to the system and the work wl done on the system dUde dw 21 The Laws of Thermodynamics 2 Second law of thermodynamics about entropy S The total entropy of any isolated thermodynamic system tends to increase over time approaching a maximum value T Classical thermodynamics Statistical thermodynamics 3 Third law of thermodynamics about absolute zero temperature As a system asymptotically approaches absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value also stated as quotthe entropy of all systems and of all states of a system is zero at absolute zeroquot or equivalently quotit is impossible to reach the absolute zero of temperature by any finite number of processesquot the Unattainability of Absolute Zero Definition Of Temperature Function of pressure and density temperatur e f pressure density Thermodynamics State Functions Useful Relation dU dQ dw 1st and 2nd law of Thermodynamics 9 d5 dQT a w pdV dU TdS pdV H Enthalpy H E U HltSaPgt dH TdS Vdp A Helmholtz Free Energy Why do we need A E U these different state functions ATv dA SdT pdV G Gibbs Free Energy G E H TS GTP dG SdT Vdp Properties of the Gibbs function 1 The Gibbs free energy is a state function 2 At equilibrium the Gibbs free energy of the phases are all equal 3 For a spontaneous process the change in the Gibbs free energy is less than zero 23 24 Thermodynamics 3 dG SdT VdP L 3 LU Sod Ice 1 i a I I AtTltTmGSltG39 I the transformation of liquid 8 to solid is a spontaneous Liquid c2 process water 9 I Tmelting Temperature gt At constant P 25 Kinetics A stable state A to another stable state B Equilibrium Between Two States Kinetics Tracking the center of gravity as the block goes from one equilibrium state to the other The potential energy of position 1 and 5 are the same 26 Kinetics A metastable state A to a stable state B Metastable Relationship Between Metastable nd Equilibrium States Equilibrium 28 Metastable Equilibrium Tracking the center of gravity as the block goes from the metastable state 1 to the equilibrium state 6 The potential energy of position 1 is higher than position 6 Energy Kinetics Activation Energy Reaction without catalyst Reaction with catalyst Ea RT Reaction Rate C eXp Arrhenius equation Reaction path Primary Bonds Ionic Bond Electron transfer From the extremes of the periodic chart ieGroups IA and VllANaCl arge difference in electronegativity boundary approximately 17 see Appendix B Covalent Bond Sharing electrons in an attempt to make a complete shell Group IV elements C Si Ge and diatomic elements such as H2 Cl2 and F2 Metallic Bond Shared by all the atoms in the substance 30 Stable Electronic Configuration II H II J 1 Hasacomplete s and p subshells 2 Tends to be inert Atomic Number Element Configuration 2 He Helium 182 10 Ne Neon 152 252 2p6 18 Ar Argon 152 232 2p6 332 3p6 36 Kr Krypton 152 232 2p6 332 3p6 432 3d10 4p6 339 Ionic Bond An ion is an atom or group of bonded atoms which have lost or gained one or more electrons making them negatively or positively charged rCI 0107nm rNa 0186nm Ionization potential Electron affinit rNa 0098nm ror 0181nm Energy required 514 eV Energy released 402 eV Ionic Bond FIGURE 24 1 An exampte of an ionic bond showing electron transfer from Na to CI to form the Na cation and CI anion pair Etectron trans1b 33 Nucleus Ionic bond a bond between ions What is the driving force for the formation of ionic bond N39l C1 Na 11 331 CI 17 382 3P5 4 Attractive force Fat f 2122 24778M392 Cl Na NeIike configuration CI39 Ar Iike configuration 1 Bond between Electroneqative nonmetal atom and Electropositive metal atom 2 The electronegativity difference between the pair is big gt17 3 They may participate in bond as ionic species 9 Once they form a bond they are not ions any more lt 34 Covalent Bond Covalent bond is a chemical bond that is characterized by the sharing of pairs of electrons between atoms or between atoms and other covalent bonds When they form a bond they participate the bond as radical Ions 9 ionic bond Metal 9 metal bond Radical 9 covalent bond Radical Atom or chemical species that has unpaired electron Octet Rule is a simple chemical rule of thumb Sham 69m that states that atoms tend to mm combine in such a way that they each have eight electrons in their valence shells giving them the same electronic configuration as a noble gas Shared electron from hydrogen 1 Bond between Electronegative atoms 2 The electronegativity difference between the pair is small lt 17 3 Thev mav participate in bond as radical species 9 Once thev form a bond thev are not radicals anv more Covalent Bond When a carbon meets 4 hydrogens C 152 252 2p2 gt C 152 25p31 25p31 25p312sp31 H radical H1 III H gt Clt H E l E gl B C radical More frequently H E lt Hgt H HE C a a H El Hradical E H H E C E H CH3 El radical H H E CEH E H Now it completed the sp3 hybridization 36 Metallic Bond Example SOdIUm 1 valence electron Bond between metal Electropositive atoms Metal Na atom likes Noblegaslike 39 Ne like configuration in some conditions can be Viewed as Valence electrons have a role of glue for ion cores Isolated Na Valence electrons run freely through the system Delocalized valence electron 9 free electron Many free electrons 9 sea of electrons Many Na atoms combine to form a solid metal