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 High temperatures No mobility without defects ­ perfect crystal = no chemistry Reactions on the interphase between phases Microstructure Diffusion controls the reaction rate Direct Reactions of Solids 2 Point Defects Schottky-imperfection: vacancy, missing ions moved to the surface Frenkel-imperfection: vacancy, missing ions on interstitial positions 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 Direct Reactions of Solids 6 Pnictides Na3E + ME + E Na2M3E4 M = Eu, Sr, E = P, As Metals UF4 + 2 Ca U + 2 CaF2 Manhattan Project 1100 K Direct Reactions of Solids 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 Direct Reactions of Solids 8 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 Direct Reactions of Solids 9 DIRECT REACTION OF SOLIDS Planetary ball mill 10 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 11 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 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 Direct Reactions of Solids 12 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 13 Heating Program Slow or fast heating, cooling, holding at a set point temperature Tammann's rule: Tr > 2/3 Tm Furnaces, RF, microwave, lasers, ion or electron beam 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 Controlled atmosphere (oxidizing, reducing, inert) or vacuum. Unstable oxidation states, preferential component volatilization if T too high, composition dependent atmosphere (O2, NH3, H2S, ...) Direct Reactions of Solids 14 Possible reaction paths between two solid grains A and B gas phase diffusion volume diffusion interface diffusion surface diffusion A B 15 Thermodynamic and kinetic factors General kinetic expression g() = k(T) dt g() = k(T) t ­ the molar fraction of the reacted product at a time t k(T) ­ the rate constant of the process Experimentally evaluate at different t Fit data into a g() = k(T) t expression to obtain k(T) and the type of mechanism model 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 16 Mechanism model g() Diffusion controlled One-dimensional 2 Two-dimensional + (1 - ) ln (1 - ) Three-dimensional, Jander [1 - (1 - )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 - (1 - )1-n ] First order, n = 1 [- ln (1 - )] Nucleation controlled Power law 1/n Nucleation-Growth controlled Avrami [- ln (1 - )]1/2 Erofeev [- ln (1 - )]1/3 Planar boundary 1 - (1 - )1/2 Spherical boundary 1 - (1 - )1/3 17 Avrami Plot ,Fractionreacted Conversion is 50% Complete is the time required for 50% conversion | Incubation Time | Time (s) =1- exp(-ctn) 18 Growth Rate Nucleatio n Rate Overall Transformation Rate Temperature Rate Equilibrium transformation temperature 19 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) 20 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 21 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 22 The Spinel Structure: AB2O4 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 23 The spinel structure: MgAl2O4 24 The spinel structure: MgAl2O4 I II I II ˇ = Mg x = O = Al 25 Why is nucleation, mass transport so difficult? 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 Structural differences between reactants and products, major structural reorganization in forming product spinel 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 Direct Reactions of Solids 26 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 27 FACTORS INFLUENCING REACTIONS OF SOLIDS 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 28 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] 4r2 4/3r3 . Direct Reactions of Solids 29 Consider 1 g of a material, density 1.0 g/cm3 , cubic crystallites number of cubes edge length, cm SA, m2 /g 1 1 6.10-4 109 10-3 0.6 1018 10-6 600 Contact area not in reaction rate expression for product layer thickness versus time: dx/dt = k/x But for a constant product volume 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 Direct Reactions of Solids 30 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 31 DIRECT REACTION OF SOLIDS 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) 32 Direct Reactions of Solids Typical diffusion coefficients for ions (atoms) in a solid at room temperature 10-13 cm2 s-1 In solid state ionic conductors (e.g. Ag-ions in -AgI) the values are greater by orders of magnitude ( 10-6 cm2 s-1) Knowledge of D allows an estimation of the average diffusion length for the migrating particles: = 2Dt (: average square of diffusion area; t: time) 33 Diffusion Diffusion coefficients show an exponential temperature dependence (Arrhenius type): D = D exp(-Q/kT) D: D for T , Q: activation energy of diffusion k: Boltzmann constant The logarithmic representation of D verus 1/T is linear the slope corresponds to the activation energy Q and the intercept to D . 34 Diffusion Ag in AgC in Fe 35 NUCLEATION RATE Nucleation rate =const. x exp{­ (GN + GD)/kT} GN = thermodynamic barrier to nucleation GD = kinetic barrier to diffusion across the liquid/nucleus interface GN = GS + 4/3r3GV GS = 4r2 surface free energy change positive 4/3r3GV volume free energy change negative, l to s lowers energy Direct Reactions of Solids 36 NUCLEATION RATE r: radius of spheric seed r*: critical radius (r>r* seed grows by itself) GN: total free energy change Gs: surface free energy change Gv: volume free energy change GN = 4r2 + 4/3r3GV Direct Reactions of Solids 37 Direct Reactions of Solids Solidification G = 4/3 r3 Gv +4 r2 ­ Volume free energy + surface energy One solid phase changing to another G = 4/3 r3 Gv +4 r2 + 4/3 r3 ­ Volume energy + surface energy + strain energy ­ the new solid does not take up the same volume as the old solid 38 Nucleation versus crystal growth (solution or melt) - relations between undercooling, nucleation and growth rate of the nuclei large undercooling: many small nuclei (spontaneous nucleation) growth rate small small undercooling: few (evtl. small) nuclei growth rate high 39 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 O2- but 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 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 40 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 HR- TEM imaging 41 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. Direct Reactions of Solids 42 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 43 Example: MgO (rock salt) {100} MgO alternating Mg2+ , O2- at corners of square grid {111} MgO, Mg2+ or O2- hexagonal arrangement Direct Reactions of Solids 44 Direct Reactions of Solids 45 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 46 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 47 DIRECT REACTION OF SOLIDS Self-Sustained High-Temperature Synthesis (SHS) Metal powders (Ti, Zr, Cr, Mo, W, ....) + other reactants mixing, pressing into pellets, ignition by energy pulse (W wire), S.S. reactor, under Ar, exothermic, byproduct removal 48 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 49 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 50 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 51 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 52 ZnO(90%) - Bi2O3 - Sb2O3 Non-Ohmic behavior I = (U/C)a C, a = constants, a = 50 Voltage stabilization, surge absorption Examples Combustion Synthesis 53 Combustion Synthesis Reaction front propagation: glycine-iron nitrate 54 55 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 56 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 57 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 58 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 59 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 60 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