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 3 Reaction Types Solid – gas synthesis – addition 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 synthesis – dissociation AB  A + B CaCO3(s)  CaO(s) + CO2(g) Al4Si4O10(OH)8(s)  Al4(Si4O10)O4(s) + 4 H2O(g) Kaolinite Metakaolinite Solid – solid synthesis – dissociation AB  A + B Ca3SiO5(s)  Ca2SiO4(s) + CaO(s) 4 Solid State Reactions Oxides BaCO3 + TiO2  BaTiO3 + BaTi2O5 + CO2 UF6 + H2 + 2 H2O  UO2 (powder) + 6 HF at 873 K dust = radiological hazard, milling, sintering to UO2 pellets YBCO 123 Superconductor (1987) Y2O3 + BaCO3 + CuO  YBa2Cu3O7-x 1223 K in air, then 473 K in oxygen Tl2O3 + 2BaO + 3CaO + 4CuO  Tl2Ba2Ca3Cu4O12 at 1130 K Aluminosilicates NaAlO2 + SiO2  NaAlSiO4 5 Solid State Reactions Pnictides Na3E + ME + E  Na2M3E4 at 1100 K M = Eu, Sr, E = P, As Metals UF4 + 2 Ca  U + 2 CaF2 Manhattan Project Chlorides 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 Chalcogenides Pb + Mo + S  PbMo6S8 Chevrel phases (MxMo6X8, M = RE, Sn, Pb, Cu, X = S, Se, Te) 6 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 7 Planetary ball mill Rotation and counter-wise spining Milling Rotation speed: up to 400 rpm Milling jars: alumina, YSZ, tungsten carbide, agate 8 Milling Atritor mill 9 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 10 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 11 Direct Reactions of Solids 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) 12 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  Reaction Process 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 13 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 14 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 Parameters in Direct Reactions of Solids 15 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 16 SA = A/m = = 3000/r [m2 /g] 4r2 4/3r3 . Parameters in Direct Reactions of Solids 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] 17 Parameters in 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 The smaller the particle size, the larger the surface area 18 Parameters in Direct Reactions of Solids Contact area not in reaction rate expression for product layer thickness, x, versus time: dx/dt = k/x But for a constant product volume (V = x  Acontact ) : x ~ 1/Acontact and furthermore Acontact ~ 1/dparticle Thus particle sizes and surface area inextricably connected and obviously x ~ dparticle and SA particle size affect the interfacial thickness Acontact ~ 1/ dparticle x 19 Parameters in Direct Reactions of Solids 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 - 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 Parameters in Direct Reactions of Solids 20         RT Q DD exp DIFFUSION RATE Fick’s law J = - D(dc/dx) J = flux of diffusing species, #/cm2s (dc/dx) = concentration gradient, #/cm4 D = diffusion coefficient, cm2/s For good reaction rates D  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 of 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) 21 Reaction Paths between Two Solids gas phase diffusion volume diffusion interface diffusion surface diffusion A B 22 Direct Reactions of Solids (A) [B]2 O4 Stoichiometric formula of spinel ccp array of O2(A) occupy 1/8 Td [B] occupy 1/2 Oh normal spinels: (A) [B]2 O4 - MgAl2O4, Co3O4 inverse spinel: (B) [AB] O4 - Fe3O4: Fe3+[Fe2+Fe3+]O4 23 The Spinel Structure: MgAl2O4 I II • = Mg x = O = Al (A)[B]2O4 I II 24 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 Model reaction, well studied: MgO + Al2O3  MgAl2O4 (Spinel) Single crystals of precursors, interfaces between reactant grains On reaction, new reactant-product MgO/MgAl2O4 and Al2O3/MgAl2O4 interfaces are formed Free energy is negative, favors reaction but extremely slow at normal temperatures (several days at 1500 oC) 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 25 Direct Reactions of Solids x NiO Al2O3 dx/dt = k/x 26 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 27 Kinetics of Reactions in Solids Linear dependency of x2 vs. t plots observed ln k vs. 1/T experiments provide Arrhenius activation energy Ea for the solid-state reaction k(T) = k0 exp(Ea/RT) Reaction mechanism requires charge and mass balance to be maintained in the solid state interfacial reaction: 3 Mg2+ diffuse in opposite direction to 2 Al3+ MgAl2O4/Al2O3 Interface (I): 3 Mg2+ - 2 Al3+ + 4 Al2O3  3 MgAl2O4 MgO/MgAl2O4 Interface (II): 2 Al3+ - 3 Mg2+ + 4 MgO  1 MgAl2O4 Overall Reaction: 4 MgO + 4 Al2O3  4 MgAl2O4 the Kirkendall Effect : growth rate of interfaces = 3/1 28 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 the Kirkendall Effect : growth rate of interfaces = 3/1 29 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 Kinetics of Reactions in 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: k(T) = k0 exp(Ea/RT) 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 30 Kinetics of Reactions in Solids Decreasing reaction rate dx/dt 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 31 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 Reaction Mechanism g() = k(T) dt g() = k(T) t 32 Kinetics of Reactions in Solids α,Fractionreacted Conversion is 50% Complete t is the time required for 50% conversion | Incubation Time | t, Time (s) α =1 exp[(kt)n] k = rate constant n = exponent Avrami Plot 33 Kinetics of Reactions in 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 34 Cation Diffusion in LaCoO3 La2O3 CoO DCo >> DLa Rate-determining step is the diffusion of Co cations Marker experiments Experimental result: LaCoO3 35 Growth Kinetics of LaCoO3 Parabolic rate law valid = process is controlled by onedimensional diffusion = rate limiting step x2 = kt In air 1673 K 1573 K 1478 K 1370 K Evaluate k as the slope at several temperatures 36 Growth Kinetics of LaCoO3 Ea = (250 ± 10) kJ mol-1 k(T) = k0 exp(Ea/RT) log k = log k0  Ea/RT 37 Nucleation Homogeneous nucleation Liquid melt to crystalline solid Cluster formation on cooling Gv = driving force for solidification (negative) Spontaneous below the equilibrium melting temperature, Tm T = 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   38 GN = 4r2SL + 4/3r3GV r: radius of spherical seed r*: critical radius GN: total free energy change Gs: surface free energy change Gv: volume free energy change Nucleation G GN 39 Critical Radius r* 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 40 Critical Radius r* The critical radius r* = the radius at which GN is maximum The energy barrier to homogeneous nucleation The temperature-dependence (T = Tm  T = undercooling) r* = 1/T G*r = 1/T2 41 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 = 4r2SL + 4/3r3GV 4r2SL = surface free energy change, positive 4/3r3GV = volume free energy change, negative, transition from (l) to (s) lowers the energy Nucleation Rate n           kT GG nn DN exp0 42 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 a solid cluster forming on a wall: • the newly created interfaces (i.e., solid-liquid and solid-wall) • the destroyed interface (liquid-wall) 43 Wetting Angle GL SLGS SLGLGS        cos cos Force equilibrium 44 Heterogeneous Nucleation  = wetting angle W = wall SL WSWL     cos Critical radius r* The energy barrier to heterogeneous nucleation Shape factor S() 45 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,  46 Direct Reactions of Solids Solidification G = 4/3  r3 Gv + 4  r2 SL – Volume free energy + surface energy One solid phase changing to another (α to β) 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 47 Nucleation Transformation from liquid to solid phase requires: • Nucleation of a new phase • Growth of a 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 Tm 48 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 49 Nucleation rate I n* = the steady-state population of critical nuclei (m-3)         kT G nn * 0 * exp I = β n* β = the rate at which atoms join critical nuclei (s-1) = growth rate 50 Undercooling = cooling below the melting point Relations between undercooling, nucleation rate and growth rate of the nuclei Ta = small undercooling: few nuclei, growth rate high – fast diffusion close to the m.p. = few coarse crystals Tb = large undercooling: rapid spontaneous nucleation, slow growth rate - high viscosity, slow diffusion = many small nuclei, nanocrystals Tc = very rapid cooling, nearly no nucleation = glass Nucleation vs. Crystal Growth (solution or melt) Direct Reactions of Solids 51 Nucleation requires structural similarity of reactants and products Less reorganization energy = faster nucleation of product phase within reactants Example: MgO, Al2O3, MgAl2O4 MgO (rock salt) and MgAl2O4 (spinel) similar ccp O2but distinct to hcp O2- in 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 Epitactic Reactions 52 Lattice-matched crystalline growth Require 2-D structural similarity, lattice matching within 15% to tolerate oriented nucleation, otherwise mismatch over large contact area, strained interface, missing atoms Best with less than 0.1% lattice mismatch, causes elastic strain at interface, slight atom displacement from equilibrium position, strain energy reduced by misfitdislocation, 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 HR-TEM imaging 53 Topotactic Reactions Orientation effects in the bulk regions of solids Implies structural relationships between reagent and product Topotaxy occurs in bulk, 1-, 2- or 3-D 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. 54 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 55 Surface Structure and Reactivity Example: MgO (rock salt) {100} MgO alternating Mg2+, O2- at corners of square grid {111} MgO, Mg2+ or O2- hexagonal arrangement 56 Surface Structure and Reactivity 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 57 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 Surface Structure and Reactivity 58 Work function of different crystal planes of W 59 Crystal Growth Growth rate of specific surfaces controls morphology Different crystal habits possible, depends on rate of growth of different faces = octahedral, cubooctahedral, cubic possible and variants in between 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) 60 Fusion-Crystallization from Glass Glass = a non-equilibrium, noncrystalline condensed state of matter that exhibits a glass transition The structure of glasses is similar to that of their parent supercooled liquids Spontaneously relax ultimately, in the limit of infinite time, crystallize 61 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 62 Fusion-Crystallization from Glass Production of abrasive grains Al2O3 + MgO  melt at 2100 K, solidify, crush, size Crystallizing an inorganic glass, lithium disilicate Li2O + 2 SiO2 + Al2O3  Li2Si2O5 at 1300 K, Pt crucible Li2Si2O5 forms as a melt, hold at 1100 C for 2-3 h Homogeneous, rapid cooling, fast viscosity increas Quenches to transparent glass Li2Si2O5, Tg ~ 450 C glass, hold at 500 - 700 C, Li2Si2O5 crystals in 2-3 h Crystallizing a glass above its glass transition 63 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 Carbothermal Reduction 64 High-temperature process Acheson process SiO2 + 3 C  2 CO + SiC at 2000 K, H = 478 kJ C + SiO2 ⇄ SiO(g) + CO SiO2 + CO ⇄ SiO + CO2 C + CO2 ⇄ 2 CO 2 C + SiO ⇄ SiC + CO 3 SiO2 + 6 C + 2 N2  6 CO + Si3N4 Carbothermal Reduction 65 Borides TiO2 + B2O3 + 5 C  5 CO + TiB2 at 1300 K 2 TiO2 + B4C + 3 C  4 CO + 2 TiB2 at 2300 K Al2O3 + 12 B2O3 + 39 C  2 AlB12 + 39 CO at 1820 K Carbides 2 Al2O3 + 9 C  Al4C3 + 6 CO at 2200 K 2 B2O3 + 7 C  B4C + 6 CO at 1820 K WO3 + 4 C  WC + 3 CO at 970 K Nitrides Al2O3 + N2 + 3 C  2 AlN + 3 CO at 1970 K 2 TiO2 + N2 + 4 C  2 TiN + 4 CO at 1820 K Direct Reactions of Solids 66 Heat from chemical reaction energy 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 Driving force - enthalpic and entropic ? 67 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 redox reaction - high temperatures, Tf = 1500-3000 C Frontal mode, reaction wave velocity u = 1 - 10 mm.s-1 High thermal gradients - metastable phases Byproduct removal - washing State of the substance in the reaction front: • solid (Tf < Tm) „solid flame“ • liquid, melt (Tf > Tm) • gaseous Thermite reaction: Zr + Fe2O3  Zr1-xFexO2 + Fe 68 Self-Propagating Metathesis Alkali metal halides as products - large lattice energy 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 69 Self-Propagating Metathesis Silicon production: Na2SiF6 + 4 Na  6 NaF + Si Hard materials production: TaCl5 + Li3N + NaN3 + NH4Cl  c-TaN + LiCl + NaCl + N2 + HCl Chemical control of the reaction: CrCl3 + Li3N + NH4Cl  Cr + Cr2N + c-CrN CrI3 + Li3N  Cr2N CrI3 + Li3N + NH4Cl  c-CrN MoCl5 + Li3N  explosion MoCl5 + Ca3N2 + NH4Cl  cubic -Mo2N 70 Combustion Synthesis 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)2ꞏ6H2O + CO(NH2)2  ZnO + N2 + CO2 + H2O (Balance this equation) 71 Combustion Synthesis Varistors ZnO(90%) - Bi2O3 - Sb2O3 Non-Ohmic behavior I = (U/C)a C, a = constants, a = 50 Voltage stabilization, surge absorption 72 Combustion Synthesis Reaction front propagation: glycine-iron nitrate 73 Combustion Synthesis 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 74 Yttrium Iron Garnet (YIG) Y3Fe5O12 Metal nitrates (MN) = oxidants • Y(NO3)3ꞏ6H2O • Fe(NO3)3ꞏ9H2O 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 Combustion Synthesis