1 "HEAT-AND-BEAT" or "SHAKE-AND-BAKE“ Solid state reactions At least one of the reactants and one of the products are solid Reactions in a lattice of atoms Atomic mobility No mobility without defects – perfect crystal = no chemistry High temperatures Reactions on the interphase between phases Microstructure - crystallite size, shape, defects Diffusion controls the reaction rate Direct Reactions of Solids 2 Reaction Types Solid - solid synthesis - addition A + B  AB MgO(s) + Al2O3(s)  MgAl2O4(s) MgO(s) + SiO2(s)  MgSiO3(s) or Mg2SiO4(s) Solid - solid synthesis – exchange, metathesis AB + C  AC + B CaCO3(s) + SiO2(s)  CaSiO3(s) + CO2(g) Ge(s) + 2 MoO3(s)  GeO2(s) + 2 MoO2(s) Solid - solid synthesis – exchange and addition PbSO4 + ZrO2 + K2CO3  K2SO4 + PbZrO3 + CO2 Solid - solid synthesis - dissociation AB  A + B Ca3SiO5(s)  Ca2SiO4(s) + CaO(s) 3 Reaction Types Solid - solid synthesis - addition A + B  AB MgO(s) + Al2O3(s)  MgAl2O4(s) MgO(s) + SiO2(s)  MgSiO3(s) or Mg2SiO4(s) Solid - solid synthesis – exchange, metathesis AB + C  AC + B CaCO3(s) + SiO2(s)  CaSiO3(s) + CO2(g) Ge(s) + 2 MoO3(s)  GeO2(s) + 2 MoO2(s) Solid - solid synthesis - dissociation AB  A + B Ca3SiO5(s)  Ca2SiO4(s) + CaO(s) 4 Reaction Types Solid – gas synthesis A + B  AB 2 Fe3O4(s) + 1/2 O2(g) 3 Fe2O3(s) 2 SiCl4(g) + 4 H2(g) + Mo(s) MoSi2(s) + 8 HCl(g) High temperature corrosion of metals in air Solid – gas dissociation AB  A + B CaCO3(s)  CaO(s) + CO2(g) Al4Si4O10(OH)8(s) Al4(Si4O10)O4(s) + 4 H2O(g) Kaolinite Metakaolinite 5 Other Examples 873 K 1223 K Oxides BaCO3 + TiO2 BaTiO3 + BaTi2O5 + CO2 UF6 + H2 + 2 H2O UO2 (powder) + 6 HF dust = radiological hazard, milling, sintering to UO2 pellets YBCO 123 Superconductor (1987) Y2O3 + BaCO3 + CuO YBa2Cu3O7-x Tl2O3 + 2BaO + 3CaO + 4CuO Tl2Ba2Ca3Cu4O12 473 K air O2 1130 K Reaction Types 6 Pnictides Na3E + ME + E Na2M3E4 M = Eu, Sr, E = P, As Metals UF4 + 2 Ca U + 2 CaF2 Manhattan Project 1100 K Reaction Types Other classes than oxides 7 Chlorides 3 CsCl + 2 ScCl3 Cs3Sc2Cl9 6 NH4Cl + Y2O3 2 YCl3 + 3 H2O + 6 NH3 6 NH4Cl + Y (NH4)3YCl6 + 1.5 H2 + 3 NH3 4 NH4Cl + 3 NH4ReO4 3 Re + 12 H2O + 3.5 N2 + 4 HCl Aluminosilicates NaAlO2 + SiO2 NaAlSiO4 Chalcogenides Pb + Mo + S PbMo6S8 Chevrel phases (MxMo6X8, M = RE, Sn, Pb, Cu, X = S, Se, Te) 1400 K Reaction Types 8 Experimental Considerations Powder Mixing Method Precise weighing for exact stoichiometry Mixing (components, dopants, additives) Milling or grinding (ball mill, mortar) Compaction (pelleting, organic binders) Calcination @ high temperature (> 1000 °C) Firing/grinding cycles 9 Planetary ball mill Planetary ball mill Rotation and counter-wise spining Milling Rotation speed: up to 400 rpm Milling jars: alumina, YSZ, tungsten carbide, agate 10 Milling Atritor mill 11 Compaction - Pressing Hydraulic Uniaxial Press Maximum pressure: 120 MPa Warm Isostatic Press Max. pressure: 400 MPa Max. temperature: 80 oC Volume: 2,5 l Hot press Max. temperature: 1250 °C Max. pressure: 100 MPa Max. diameter: 25 mm 12 Calcination Tube Furnace in air and in controled atmosphere Maximum temperature: 1450 oC or 1600 °C Furnace-tube diameter: up to 75 mm Vacuum Furnace in vacuum or Ar, N2, O2 atmosphere Maximum temperature: 1200 °C Chamber Dimensions: 150x200x250 mm3 13 Advantages simple equipment low cost and easily accessible starting materials well studied Disadvantages impurities from grinding (Fe, Cr, …) broad particle size distribution some phases unstable @ high T, decomposition formation of undesirable phases slow formation, diffusion, long reaction times large grain size poor chemical homogeneity: poor mixing of large crystallites (milling lower limit ~ 100 nm) volatility of some components (Na2O, PbO, …) uptake of ambient gas (O2 in superconductors) Direct Reactions of Solids 14 Experimental Considerations  Reagents Drying, fine grain powders for maximum SA, surface activation (Mo + H2), in situ decomposition (CO3 2-, OH-, O2 2-, C2O4 2-) for intimate mixing, precursor reagents, homogenization, organic solvents, grinding, ball milling, ultrasonication  Prior decomposition Initial cycle at lower temperature to prevent spillage or volatilization, frequent cycles of heating, cooling, grinding, boost SA. Overcoming sintering, grain growth, fresh surfaces. Pelleting, hot pressing, enhanced contact area increases rate and extent of reaction  Container Materials Chemically inert crucibles, boats, ampoules (open, sealed, welded) Noble metals: Au, Ag, Pt, Ni, Rh, Ir, Nb, Ta, Mo, W Refractories: alumina, zirconia, silica, BN, graphite Reactivities with containers at high temperatures needs to be carefully evaluated for each system, pelleting minimizes contact with container, sacrificial pellet 15 Properties of Common Container Materials Material Maximum Working Temp., K Thermal Shock Resistance Thermal Conductivity, W m-1 K-1 Coefficient of Linear Expansion x106 , K-1 Other Properties Pyrex 770 GOOD 1.13 3.2 Permeable to air at high T CaF2 1420 FAIR - 24 SiO2 1530 VERY GOOD 1.38 - 2.67 0.4 - 0.6 Permeable to air at high T, devitrification above 1670 K Si3N4 1770 FAIR 10 - 33 6.4 Pt 1950 VERY GOOD 73 9.11 Plastic at high T BN 1970 VERY GOOD 5.02 0.2-3 Oxidizes in air above 970 K Vitreous C 2070 GOOD 4.19 - 8.37 2-3.5 Oxidizes in air above 900 K Al2O3 2170 FAIR 35 - 39 8 Reacts with metals above 1800 K AlN 2270 FAIR 50 - 170 5.7 BeO 2570 GOOD 230 8.4 Reacts with metals above 1800 K ZrO2 2570 GOOD 1.97 4.5 Ir 2600 VERY GOOD 148 6.8 MgO 2870 FAIR 37.7 25 High vapor pressure ThO2 3070 FAIR 4.19 6 Reacts with C above 2290 K 16 Experimental Considerations  Controlled atmosphere oxidizing, reducing, inert or vacuum. Unstable oxidation states, preferential component volatilization if T is too high, composition dependent atmosphere (O2, NH3, H2S, …)  Heating Program Slow or fast heating, cooling, holding at a set point temperature. Furnaces, RF, microwave, lasers, ion or electron beam Tammann’s rule: Tr  2/3 Tm Factors Influencing Direct Reactions of Solids 17 CONTACT AREA Surface area of reactants Particle size Pelleting, pressing, precursors DIFFUSION RATE Diffusion rates of atoms, ions, molecules in solids Reaction temperature, pressure, atmosphere Diffusion length, particle size Defect concentration, defect type Reaction mechanism NUCLEATION RATE Nucleation of product phase within the reactant with similar crystal structure Epitactic and topotactic reactions Surface structure and reactivity of different crystal planes/faces 18 KEY FACTORS IN SOLID STATE SYNTHESIS CONTACT AREA and surface area (SA) of reacting solids control: Rates of diffusion of ions through various phases, reactants and products Rate of nucleation of the product phase Reaction rate is greatly influenced by the SA of precursors as contact area depends roughly on SA of the particles Surface Area (SA) of Precursors spherical particles, radius r [nm], density  [g/cm3 ] SA = A/m = = 3000/r [m2 /g] 4r2 4/3r3 . Direct Reactions of Solids 19 Direct Reactions of Solids Silicanumber of cubes edge length SA, m2/g 1 1 cm 6.10-4 103 1 mm 6.10-3 1012 1 m 6 1021 1 nm 6000 Consider 1 g of a material, density 1.0 g/cm3 , cubic crystallites 20 Direct Reactions of Solids Contact area not in reaction rate expression for product layer thickness versus time: dx/dt = k/x But for a constant product volume (V = x A) : x ~ 1/Acontact and furthermore Acontact ~ 1/dparticle Thus particle sizes and surface area inextricably connected and obviously x ~ d and SA particle size affect the interfacial thickness 21 These relations suggest some strategies for rate enhancement in direct reactions: Hot pressing densification of particles High pressure squeezing of reactive powders into pellets (700 atm) Pressed pellets still 20-40% porous. Hot pressing improves densification Atomic mixing in composite precursor compounds Coated particle mixed component reagents, corona/core precursors Decreasing particle size, nanocrystalline precursors Aimed to increase interfacial reaction area A and decrease interface thickness x, minimizes diffusion length scales dx/dt = k/x = k’A = k"/d Direct Reactions of Solids Direct Reactions of Solids 22 DIFFUSION RATE Fick’s law J = - D(dc/dx) J = flux of diffusing species, #/cm2 s (dc/dx) = concentration gradient, #/cm4 D = diffusion coefficient, cm2 /s, for good reaction rates  10-12 D increases with temperature, rapidly as you approach the melting point Tammann’s rule: Extensive reaction will not occur until the temperature reaches at least 2/3 ot the melting point of one or more of the reactants. Factors influencing cation diffusion rates: Charge, mass and temperature Interstitial versus substitutional diffusion Number and types of defects in reactant and product phases All types of defects enhance diffusion of ions (intrinsic or extrinsic, vacancies, interstitials, lines, planes, dislocations, grain boundaries)         RT Q DD exp 23 Reaction Paths between Two Solids gas phase diffusion volume diffusion interface diffusion surface diffusion A B 24 Direct Reactions of Solids Ax By Oz Stoichiometric formula of spinel ccp O2A occupy 1/8 Td B occupy 1/2 Oh 25 The Spinel Structure: (A)[B2]O4 fcc array of O2- ions, A occupies 1/8 of the tetrahedral and B 1/2 of the octahedral holes  normal spinel: AB2O4 Co3O4, GeNi2O4, WNa2O4  inverse spinel: B[AB]O4 Fe3O4: Fe3+[Fe2+Fe3+]O4, TiMg2O4, NiLi2F4  basis structure for several magnetic materials 26 The Spinel Structure: MgAl2O4 (A)[B2]O4 27 The Spinel Structure: MgAl2O4 I II I II • = Mg x = O = Al (A)[B2]O4 28 Model reaction, well studied: MgO + Al2O3  MgAl2O4 Spinel (ccp O2, Mg2+ 1/8 Td, Al3+ 1/2 Oh) Single crystals of precursors, interfaces between reactant grains On reaction, new reactant-product MgO/MgAl2O4 and Al2O3/MgAl2O4 interfaces are formed Free energy negative, favors reaction but extremely slow at normal temperatures (several days at 1500 o C) Interfacial growth rates 3 : 1 Linear dependence of interface thickness x2 versus t Easily monitored rates with colored product at interface, T and t NiO + Al2O3  NiAl2O4 MgO + Fe2O3  MgFe2O4 Direct Reactions of Solids 29 Model for a classical solid-solid reaction (below melting point !): Planar interface between two crystals MgO + Al2O3  MgAl2O4 (Spinel) Phase 1: nucleation Phase 2: growth of nuclei MgO Al2O3 MgO Al2O3 Direct Reactions of Solids MgAl2O4 x 30 Direct Reactions of Solids  Structural differences between reactants and products, major structural reorganization in forming product spinel MgO ccp O2-, Mg2+ in Oh sites Al2O3 hcp O2-, Al3+ in 2/3 Oh sites MgAl2O4 ccp O2-, Mg2+ 1/8 Td, Al3+ 1/2 Oh Making and breaking many strong bonds (mainly ionic), high temperature process as D(Mg2+) and D(Al3+) large for small highly charged cations Long range counter-diffusion of Mg2+ and Al3+ cations across interface, usually RDS (= rate determining step), requires ionic conductivity, substitutional or interstitial hopping of cations from site to site to effect mass transport Nucleation of product spinel at interface, ions diffuse across thickening interface, oxide ion reorganization at nucleation site  Decreasing rate as spinel product layer thickens Parabolic rate law: dx/dt = k/x x2 = kt 31 Kinetics: Linear x2 vs. t plots observed ln k vs. 1/T experiments provide Arrhenius activation energy Ea for the solid-state reaction Reaction mechanism requires charge balance to be maintained in the solid state interfacial reaction: 3Mg2+ diffuse in opposite way to 2Al3+ MgO/MgAl2O4 Interface: 2Al3+ -3Mg2+ + 4MgO  1MgAl2O4 MgAl2O4/Al2O3 Interface: 3Mg2+ -2Al3+ + 4Al2O3  3MgAl2O4 Overall Reaction: 4MgO + 4Al2O3  4MgAl2O4 the Kirkendall Effect : RHS/LHS growth rate of interface = 3/1 Direct Reactions of Solids 32 Al2O3 MgOMgAl2O4 interface I interface II 2 Al3+ 3 Mg2+ 1/2 O2 1/2 O2 Al2O3 MgOMgAl2O4 interface I interface II 2 Al3+ 2 Mg2+ 2 e-O2- O2Reaction Mechanism 33 Thermodynamic and kinetic factors 10 0 0       PP PP e t Pt = the value of a property at time t P0 = the value of a property at the beginning Pe = the value of a property at the end Direct Reactions of Solids      fTk dt d       dtTkg f d      e.g. Pt = mass loss, x, …… – the molar fraction of the reacted product at a time t k(T) – the rate constant of the process General kinetic expression Reaction rate Rate constant Reaction order Experimentally evaluate at different t Fit data into a g() = k(T) t expression to obtain k(T) and the type of mechanism model 34 Direct Reactions of Solids Decreasing reaction rate as spinel product layer (x) thickens Here  = x Parabolic rate law: dx/dt = k/x x2 = kt g() = k(T) dt g() = k(T) t      fTk dt d     dtTk f d     MgO Al2O3 MgAl2O4 x 10 0 0       PP PP e t 35 Mechanism model g() Diffusion controlled One-dimensional 2 Two-dimensional  ln  Three-dimensional, Jander [)1/3 ]2/3 Three-dimensional, Ginstling (1 – 2/3) – (1  )2/3 Three-dimensional, Carter (1 + )2/3 + (1  )2/3 Growth controlled General [)1-n ] First order, n = 1 [ ln ] Nucleation controlled Power law 1/n Nucleation-Growth controlled Avrami [ ln ]1/2 Erofeev [ ln ]1/3 Planar boundary 1)1/2 Spherical boundary 1)1/3 36 Avrami Plot α,Fractionreacted Conversion is 50% Complete is the time required for 50% conversion | Incubation Time | t, Time (s) α =1 exp[(kt)n] k = rate constant n = exponent 37 Direct Reactions of Solids Perform the measurements in a range of temperatures T use Arrhenius equation to evaluate the activation energy Ea k(T) = k0 exp(Ea/RT) FractionTransformed 135 C 120 C 80 C Time, s 38 Cation Diffusion in LaCoO3 La2O3 CoO DCo >> DLa Rate-determining step: Diffusion of Co cations Marker experiments LaCoO3 39 Growth Kinetics of LaCoO3 Parabolic rate law valid = diffusion controlled process x2 = kt In air 1673 K 1573 K 1478 K 1370 K 40 Growth Kinetics of LaCoO3 EA = (250 ± 10) kJ mol-1 k(T) = k0 exp(Ea/RT) log k = log k0  Ea/RT 41 Nucleation Homogeneous nucleation Liquid melt to crystalline solid Cluster formation Gv = driving force for solidification (negative) below the equilibrium melting temperature, Tm T = undercooling, Hv = enthalpy of solidification (negative) Small clusters of crystallized solid form in a melt because of the random motion of atoms within the liquid Driving force is opposed by the increase in energy due to the creation of a new solid-liquid interface SL = the solid/liquid interfacial energy m V V T TH G   42 r: radius of spheric seed r*: critical radius GN: total free energy change Gs: surface free energy change Gv: volume free energy change GN = 4r2SL + 4/3r3GV Nucleation G G N 43 Critical Radius r* The critical radius r* = the radius at which GN is maximum The energy barrier to homogeneous nucleation The temperature-dependence r* = 1/T G*r = 1/T2 44 Nucleation a nucleus stable for r >r* the stable nucleus continues to grow a sub-critical cluster unstable for r < r* the cluster re-dissolves Increasing r G > 0 Increasing r G < 0 45 Nucleation rate n Liquid to solid GN = thermodynamic barrier to nucleation GD = kinetic barrier to diffusion across the liquid/nucleus interface Assume, that solid phase nucleates as spherical clusters of radius r GN = the net (excess) free energy change for a single nucleus GN = GS + 4/3r3GV GS = 4r2SL surface free energy change positive 4/3r3GV volume free energy change negative, l to s lowers the energy Nucleation rate n           kT GG nn DN exp0 46 Heterogeneous Nucleation Nuclei can form at preferential sites: flask wall, impurities, catalysts, ….. The energy barrier to nucleation, G*, is substantially reduced The critical nucleus size, r* is the same for both heterogeneous and homogeneous nucleation 47 Heterogeneous Nucleation a solid cluster forming on a wall: • the newly created interfaces (i.e. solid-liquid and solid-wall) • the destroyed interface (liquid-wall) 48 Heterogeneous Nucleation  = wetting angle Shape factor S() SL WSWL     cos 49 Wetting Angle GL SLGS SLGLGS        cos cos Force equilibrium 50 Heterogeneous Nucleation The critical radius r* is the same for both homogeneous and heterogeneous nucleation The volume of a critical nucleus and G* can be significantly smaller for heterogeneous nucleation due to the shape factor, depending on the wetting angle,  51 Direct Reactions of Solids Solidification G = 4/3  r3 Gv +4  r2 SL – Volume free energy + surface energy One solid phase changing to another G = 4/3  r3 Gv +4  r2 SL + 4/3  r3  – Volume energy + surface energy + strain energy – the new solid does not take up the same volume as the old solid – a misfit strain energy term, Gs = V  αβ = the α/β interfacial energy 52 Nucleation Transformation from liquid to solid phase requires: •Nucleation of new phase •Growth of new phase Nucleation depends on: •driving force toward equilibrium – cooling of a melt increases as we move to lower temperatures •diffusion of atoms into clusters increases at higher temperatures Combination of these two terms (multiplication) determines the total nucleation rate 53 Nucleation rate I         kT G nn * 0 * exp Nucleation rate [m-3 s-1] I = β n* n* = the steady-state population of critical nuclei (m-3) n0 = the number of potential nucleation sites per unit volume G* = the critical free energy of nucleation β = the rate at which atoms join critical nuclei (s-1), thereby making them stable, a diffusion-dependent term  = temperature independent term incorporating vibrational frequency and the area to which atoms can join the critical nucleus Q = an activation energy for atomic migration 54 Nucleation rate I n* = the steady-state population of critical nuclei (m-3) 55 Nucleation 56 Nucleation vs. Growth Growth Rate Nucleatio n Rate Overall Transformation Rate Temperature Rate Equilibrium transformation temperature 57 Undercooling – cooling below the melting point relations between undercooling, nucleation rate and growth rate of the nuclei large undercooling: many small nuclei (spontaneous nucleation) growth rate small - high viscosity, slow diffusion small undercooling: few (evtl. small) nuclei growth rate high – fast diffusion close to the m.p. Nucleation vs. Crystal Growth (solution or melt) 58 Nucleation vs. Crystal Growth Rate of nucleation Rate of growth Ta = small undercooling, slow cooling rate Fast growth, slow nucleation = Few coarse crystals Tb = larger undercooling, rapid cooling rate Rapid nucleation, slow growth = many fine-grained crystals Tc = very rapid cooling Nearly no nucleation = glass 59 DIRECT REACTION OF SOLIDS NUCLEATION RATE Nucleation requires structural similarity of reactants and products less reorganization energy = faster nucleation of product phase within reactants MgO, Al2O3, MgAl2O4 example MgO (rock salt) and MgAl2O4 (spinel) similar ccp O2but distinct to hcp O2in Al2O3 phase Spinel nuclei, matching of structure at MgO interface Oxide arrangement essentially continuous across MgO/MgAl2O4 interface Bottom line: structural similarity of reactants and products promotes nucleation and growth of one phase within another Lattice of oxide anions, mobile Mg2+ and Al3+ cations Topotactic and epitactic reactions Orientation effects in the bulk and surface regions of solids Implies structural relationships between reagent and product Topotaxy occurs in bulk, 1-, 2- or 3-D Epitaxy occurs at interfaces, 2-D 60 DIRECT REACTION OF SOLIDS Epitactic reactions require 2-D structural similarity, lattice matching within 15% to tolerate oriented nucleation otherwise mismatch over large contact area, strained interface, missing atoms Example: MgO/BaO, both rock salt lattices, cannot be lattice matched over large contact area Lattice matched crystalline growth Best with less than 0.1% lattice mismatch. Causes elastic strain at interface Slight atom displacement from equilibrium position. Strain energy reduced by misfit-dislocation Creates dangling bonds, localized electronic states, carrier scattering by defects, luminescence quenching, killer traps, generally reduces efficacy of electronic and optical devices, can be visualized by HRTEM imaging 61 Direct Reactions of Solids Topotactic reactions More specific, require interfacial and bulk crystalline structural similarity, lattice matching Topotaxy: involves lock-and-key ideas of self-assembly, molecule recognition, host-guest inclusion, clearly requires available space or creates space in the process of adsorption, injection, intercalation etc. 62 Surface structure and reactivity Nucleation depends on actual surface structure of reacting phases. Different Miller index faces exposed, atom arrangements different, different surface structures, implies distinct surface reactivities. Direct Reactions of Solids 63 Example: MgO (rock salt) {100} MgO alternating Mg2+ , O2at corners of square grid {111} MgO, Mg2+ or O2hexagonal arrangement Direct Reactions of Solids 64 Direct Reactions of Solids 65 Direct Reactions of Solids Atoms located in (111) and (100) crystal planes for spherical and cuboid particles Model particles = fcc structure of Pt 4 nm size Dark grey = atoms located in (111)-surface Light orange = the (100) face Surface Facet Reactivity 66 Electron tomography and electron energy loss spectroscopy (EELS) map the valency of the Ce ions in CeO2x nanocrystals in 3D. A facet-dependent reduction shell at the surface; {111} facets show a low surface reduction, whereas at {001} surface facets, the cerium ions are more reduced. Work function of different crystal planes 67 68 69 Different crystal habits possible, depends on rate of growth of different faces, octahedral, cubooctahedral, cubic possible and variants in between CRYSTAL GROWTH Most prominent surfaces, slower growth Growth rate of specific surfaces controls morphology Depends on area of a face, structure of exposed face, accessibility of a face, adsorption at surface sites, surface defects Play major role in reactivity, nucleation, crystal growth, materials properties (electronic, optical, magnetic, charge-transport, mechanical, thermal, acoustical etc) Direct Reactions of Solids 70 DIRECT REACTION OF SOLIDS Azide Method 3 NaN3 + NaNO2 2 Na2O + 5 N2 5 NaN3 + NaNO3 3 Na2O + 8 N2 9 NaN3 + 3 NaNO2 + 2 ZnO 2 Na6ZnO4 + 15 N2 8 NaN3 + 4 NaNO2 + Co3O4 3 Na4CoO4 + 14 N2 2 NaN3 + 4 CuO 2 NaCu2O2 + 3 N2 71 Self-Sustained High-Temperature Synthesis (SHS) Mixing Metal powders (Ti, Zr, Cr, Mo, W, ....) + other reactants Pressing into pellets Ignition by energy pulse (W wire) S.S. reactor, under Ar Exothermic reaction Byproduct removal 72 DIRECT REACTION OF SOLIDS SHS reactions:  heterogeneous  exothermic, high temperatures, Tf = 1500 - 3000 C  high thermal gradients  redox  frontal mode, reaction wave velocity u = 1 - 10 mm.s-1  metastable phases State of the substance in the reaction front: solid (Tf  Tm, p  p0) „solid flame“ liquid, melt (Tf  Tm) gaseous Thermite reaction Zr + Fe2O3 Zr1-xFexO2 + Fe Ti + C TiC Ti + B TiB 73 Grinding of components in a glove box addition of NaCl, KCl or NH4Cl as a heat sink, S.S. vessel, ignition by a resistively heated wire, reaction time 1 s, washing products with MeOH, water, drying 3 ZrCl4 + 4 Na3P 3 c-ZrP + 12 NaCl + P 3 HfCl4 + 4 Li3P 3 c-HfP + 12 LiCl + P c-ZrP and c-HfP hard and chemically inert materials, hexagonal to cubic transitions: ZrP 1425 C, HfP 1600 C Self-Propagating Metathesis 74 DIRECT REACTION OF SOLIDS Silicon production Na2SiF6 + 4 Na 6 NaF + Si Hard materials production TaCl5 + Li3N + NaN3 + NH4Cl c-TaN + LiCl + NaCl + N2 + HCl CrCl3 + Li3N + NH4Cl Cr + Cr2N + c-CrN CrI3 + Li3N Cr2N CrI3 + Li3N + NH4Cl c-CrN MoCl5 + Li3N explosive MoCl5 + Ca3N2 + NH4Cl cubic -Mo2N Self-Propagating Metathesis 75 Oxidizing reagents (metal nitrates) mixed with fuel (urea, glycine) by melting or in solution drying combustion ignited at 300-500 C exothermic self-propagating non-explosive reaction (excess of fuel) reaction time 1 min, flame temperature 1000 C product dry foam, crumbles to a fine powder. Zn(NO3)2.6H2O + CO(NH2)2 ZnO + N2 + CO2 + H2O Combustion Synthesis 76 ZnO(90%) - Bi2O3 - Sb2O3 Non-Ohmic behavior I = (U/C)a C, a = constants, a = 50 Voltage stabilization, surge absorption Examples Combustion Synthesis 77 Combustion Synthesis Reaction front propagation: glycine-iron nitrate 78 Self-Propagating Metathesis 79 Examples LiNO3 + NH4VO3 + (NH4)2MoO4 + glycine  LiVMoO6 mixing 1:1:1 in aqueous solution, drying at 90 C combustion at 250 C calcination to LiVMoO6 cathode material for Li-ion Combustion Synthesis 80 Yttrium Iron Garnet (YIG) Y3Fe5O12 Metal nitrates (MN) = oxidants • Y(NO3)3·6H2O • Fe(NO3)3·9H2O Citric acid monohydrate (CA) = fuel Solution in water Y:Fe = 3:5 The solution evaporated at 85 C stirrred until viscous gel Increasing the temperature up to 250  C ignition of the gel MN/CA ratio controls the size Solution Combustion Synthesis 81 DIRECT REACTION OF SOLIDS Carbothermal Reduction Acheson SiO2 + 3 C 2 CO + SiC H = 478 kJ 3 SiO2 + 6 C + 2 N2 6 CO + Si3N4 2000 K C + SiO2 SiO(g) + CO SiO2 + CO SiO + CO2 C + CO2 2 CO 2 C + SiO SiC + CO 82 DIRECT REACTION OF SOLIDS Carbothermal Reduction Borides TiO2 + B2O3 + 5 C 5 CO + TiB2 2 TiO2 + B4C + 3 C 4 CO + 2 TiB2 Al2O3 + 12 B2O3 + 39 C 2 AlB12 + 39 CO Carbides 2 Al2O3 + 9 C Al4C3 + 6 CO 2 B2O3 + 7 C B4C + 6 CO WO3 + 4 C WC + 3 CO Nitrides Al2O3 + N2 + 3 C 2 AlN + 3 CO 2 TiO2 + N2 + 4 C 2 TiN + 4 CO 1300 K 2300 K 1820 K 2220 K 1820 K 970 K 1970 K 1820 K 83 DIRECT REACTION OF SOLIDS Fusion-Crystallization from Glass Glass is a non-equilibrium, non-crystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent supercooled liquids (SCL), and they spontaneously relax toward the SCL state. Their ultimate fate, in the limit of infinite time, is to crystallize. 84 DIRECT REACTION OF SOLIDS Fusion-Crystallization from Glass Mixing powders Melting to glass: single phase, homogeneous (T, C), amorphous Temperature limits: • mp of reagents • volatility of reagents Nucleation agent Homogeneous nucleation, few crystal seeds Slow transport of precursors to seed Lowest possible crystallization temperature Crystallizing a glass above its glass transition Metastable phases accessible, often impossible to prepare by other methods 85 DIRECT REACTION OF SOLIDS Fusion-Crystallization from Glass Production of window glass Abrasive grains Al2O3 + MgO melt, solidify, crush, size Crystallizing an inorganic glass, lithium disilicate Li2O + 2SiO2 + Al2O3 Li2Si2O5 Li2Si2O5 forms as a melt. Hold at 1100o C for 2-3 hrs. Homogeneous, rapid cooling, fast viscosity increase, quenches transparent glass Li2Si2O5, glass 500-700o C, Tg ~ 450o C from DSC  Li2Si2O5, crystals in 2-3 hrs., principle of crystallizing a glass above its glass transition 1300 K, Pt crucible 2100 K Fusion-Crystallization from Glass 86 DIRECT REACTION OF SOLIDS Fusion-Crystallization from Glass Glass Ceramics polyxtalline materials made by controlled xtallization of glasses Cooking utensils Li2O/SiO2/Al2O3(>10%) nucl. TiO2 -spodumene Vacuum tube components Li2O/SiO2/Al2O3(<10%) nucl. P2O5 Li-disilicate, quartz Missile radomes MgO/SiO2/Al2O3 nucl. TiO2 cordierite, cristobalite Fusion-Crystallization from Glass 87 Cements 5600 BC - the floor of a villa in Serbia, a red lime binder (calcium oxide). Lime obtained by burning gypsum, limestone or chalk 2589-2566 BC - Egypt, the Great Pyramid of Cheops, gypsum-derived binders 800 BC the Greeks, 300 BC the Romans, limestone-derived cements became widespread Vitruvius, De Architectura the Appian Way, the Coliseum, the Pantheon cements based on a mixture of natural and synthetic aluminosilicates with lime - pozzolan 1756 John Smeaton, lighthouse, a pozzolanic binder from lime, volcanic ash and copper slag, able to withstand the harsh coastal environment 1824 Joseph Aspdin, Leeds, England, developed and patented Portland cement. Portland cement - made by heating at 1450°C chalk, shale, and clay or limestone in a kiln to form a partially fused mixture – clinker, which is then finely ground with gypsum 88 Cements Hydraulic cements - materials that set and harden by reacting with water, produce an adhesive matrix, combined with other materials, are used to form structural composite materials. Non-hydraulic cements - lime and gypsum plasters, set by drying out, must be kept dry, gain strength slowly by absorption of CO2 to form calcium carbonate through carbonatation Concrete - a mixture of cement (binding agent) and water with aggregate (varying amounts of coarse and fine sand and stone). Consumption of concrete - 2.5 tonnes per person per year. Mortar - used to bind bricks together, made from cement but with finer grade of added materials. Portland cement Component Formula Phase wt% Tricalcium silicate C3S Ca3SiO5 Alite 50-70 Β-dicalcium silicate C2S Ca2SiO4 Belite 15-30 Tricalcium aluminate C2A Ca3Al2O6 Aluminate 5-10 Tetracalcium aluminoferrite C4AF Ca2(Al/Fe)O5 Ferrite 5-15 89 S SiO2 C CaO A Al2O3 F Fe2O3 T TiO2 M MgO K K2O N Na2O H H2O CO2 SO3 Chemical Cement Nomenclature