ASPECTS OF SOLID-SOLID REACTIONS

1. ASPECTS OF SOLID-SOLID REACTIONS • Conventional solid state synthesis - heating mixtures of two or more solids to form a solid phase product. • Unlike gas phase and solution reactions • Limiting factor in solid-solid reactions usually diffusion, driven thermodynamically by a concentration gradient. • Fick’s law : J = -D(dc/dx) • J = Flux of diffusing species (#/cm2s) • D = Diffusion coefficient (cm2/s) • (dc/dx) = Concentration Gradient (#/cm4)

2. ASPECTS OF SOLID-SOLID REACTIONS • The average distance a diffusing species will travel <x> • <x> » (2Dt)1/2 where t is the time. • To obtain good rates of reaction you typically need the diffusion coefficient D to be larger than ~ 10-12 cm2/s. • D = Doexp(-Ea/RT) diffusion coefficient increases with temperature, rapidly as you approach the melting point. • This concept leads to empirical Tamman’s Rule : Extensive reaction will not occur until temperature reaches at least 1/3 of the melting point of one or more of the reactants.

3. RATES OF REACTIONS IN SOLID STATE SYNTHESIS ARE CONTROLLED BY THREE MAIN FACTORS 1. Contact area: surface area of reacting solids 2. Rates of diffusion: of ions through various phases, reactants and products 3. Rate of nucleation: of product phase Let us examine each of the above in turn

4. SURFACE AREA OF PRECURSORS • Seems trivial - vital consideration in solid state synthesis • Consider MgO, 1 cm3 cubes, density 3.5 gcm-3 • 1 cm cubes: SA 6x10-4 m2/g • 10-3 cm cubes: SA 6x10-1 m2/g (109x6x10-6/104) • 10-6 cm cubes: SA 6x102 m2/g (1018x6x10-12/104) • The latter is equal to a 100 meter running track!!! • Clearly reaction rate influenced by SA of precursors as contact area depends roughly on SA of the particles

5. EXTRA CONSIDERATIONS IN SOLID STATE SYNTHESIS – GETTING PRECURSORS TOGETHER • High pressure squeezing of reactive powders into pellets, for instance using 105 psi to reduce inter-grain porosity and enhance contact area between precursor grains • Pressed pellets still 20-40% porous • Hot pressing improves densification • Note: contact area NOT in planar layer lattice diffusion model for thickness change with time, dx/dt = k/x

6. EXTRA CONSIDERATIONS IN SOLID STATE SYNTHESIS • x(thickness planar layer) µ 1/A(contact area) • A(contact area) µ 1/d(particle size) • Thus particle sizes and surface area connected • Hence x µ d • Therefore A and d affect interfacial thickness x!!! • These relations suggest some strategies for rate enhancement in direct solid state reactions by controlling diffusion lengths!!!

7. Particle surface area A Product interface thickness x Particle size d dx/dt = k/x = k’A =k"/d Decreasing particle size to nanocrystalline range Hot pressing densification of particles Atomic mixing in composite precursor compounds Coated particle mixed component reagents, corona/core precursors All aimed to increase A and decrease x and minimize diffusion length scale MINIMIZING DIFFUSION LENGTHS<x> » (2Dt)1/2FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T

8. Core-corona reactants in intimate contact, made by salt precipitation, sol-gel deposition, CVD All aimed to increase A and decrease x and minimize diffusion length scale COATED PARTICLE SOLID STATE REAGENTS MINIMIZING DIFFUSION LENGTHS<x> » (2Dt)1/2FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T

9. MINIMIZING DIFFUSION LENGTHS<x> » (2Dt)1/2FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T • Johnson superlattice precursor • Deposition of thin film reactants • Controlled thickness, composition • Metals, semiconductors, oxides • Binary, ternary compounds • Modulated structures • Solid solutions (statistical reagent mixing) • Diffusion length x control • Thickness control of reaction rate • Low T solid state reaction • Designer element precursor layers • Coherent directed product nucleation • Oriented product crystal growth • LT metastable hetero-structures • HT thermodynamic product SUPERLATTICE REAGENTS

10. ELEMENTALLY MODULATED SUPERLATTICES -DEPOSITED AND THERMALLY POST TREATED TO GIVE LAYERED METAL DICHALCOGENIDES MX2 COMPUTER MODELLING OF SOLID STATE REACTION OF JOHNSON SUPERLATTICE

11. ELEMENTALLY MODULATED SUPERLATTICES • Several important synthetic parameters and in situ probes. • Reactants prepared using thin film deposition techniques and consist of nm scale layers of the elements to be reacted. • One element easily substituted for another • Allows rapid surveys over a class of related reactions and synthesis of iso-structural compounds.

12. ELEMENTALLY MODULATED SUPERLATTICES • Diffusion distance is determined by the multilayer repeat distance which can be continuously varied. • An important advantage, allowing experimental demonstration of changes in reaction mechanism as a function of inter-diffusion distance and temperature. • Multi-layer repeat distances can be easily verified in the prepared reactants and products made under different conditions using low angle X-ray diffraction.

13. MINIMIZING DIFFUSION LENGTHS<x> » (2Dt)1/2FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T Johnson superlattice reagent design {(Ti-2Se)6(Nb-2Se)6}n Low T annealing reaction {(TiSe2)6(NbSe2)6}n Metastable ternary modulated layered metal dichalcogenide (hcp Se2- layers, Ti4+/Nb4+ Oh/D3h interlayer sites) superlattice well defined PXRD Confirms correlation between precursor heterostructure sequence and superlattice ordering of final product SUPERLATTICE REAGENTS YIELD SUPERLATTICE ARTIFICIAL CRYSTAL PRODUCT

14. Superlattice precursor sequence 6(Ti-2Se)-6(Nb-2Se) yields ternary modulated superlattice composition {(TiSe 2)6(NbSe 2)6}nwith 62 well defined PXRD reflections – good exercise – give it a try Confirms correlation between precursor heterostructure sequence and superlattice ordering of final product

15. MINIMIZING DIFFUSION LENGTHS<x> » (2Dt)1/2FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T John superlattice reagent design {(Ti-2Se)6(Nb-2Se)6}n High T annealing reaction {(Ti0.5Nb0.5Se2)}n Thermodynamic linear Vegard type solid solution ternary metal dichalcogenide product with identical layers Properties of ternary product is the atomic fraction weighted average of binary end member components P(TixNb(1-x)Se2) = xP(TiSe2) + (1-x)PNbSe2 SUPERLATTICE REAGENTS YIELD HOMOGENEOUS SOLID SOLUTION PRODUCT

16. S Co V[Co] e(-) Co(2+) S(2-) Co2S3 NANOCLUSTER PRECURSOR BASED KIRKENDALL SYNTHESIS OF HOLLOW NANOCLUSTERS • Synthesis of surfactant-capped cobalt nanoclusters: • Co(3+)/BH4(-) reduction in oleic acid, oleylamine  ConLm in a high temperature surfactant solvent, • surfactant-sulfur injection, coating of sulfur shell on nanocluster • cobalt sesquisulfide product shell layer formed at interface • counter-diffusion of Co(2+)/2e(-) and S(2-) across thickening shell • faster diffusion of Co(2+) than S(2-) creates V[Co] in core • vacancies agglomerate in core • hollow core created which grows as the product shell thickens • end result – a hollow nanosphere made of cobalt sesquisulfide Co2S3

17. TURNING NANOSTRUCTURES INSIDE-OUT • Kirkendall effect a well-known phenomenon discovered in 1930’s. • Occurs during reaction of two solid-state materials and involves the counter diffusion of reactant species, like ions, across product interface usually at different rates. • Special case of movement of fast-diffusing component cannot be balanced by movement of slow component the net mass flow is accompanied by a net flow of atomic vacancies in the opposite direction. • Leads to Kirkendall porosity, formed through super-saturation of vacancies into hollow pores • When starting with perfect building blocks such as monodisperse cobalt nanocrystals a reaction meeting the Kirkendall criteria can lead to super-saturation of vacancies exclusively in the center of the nanocrystal. • General route to hollow nanocrystals of almost any given material • Proof-of-concept - synthesis of Co2S3 nanoshell starting from Co nanocluster.

18. Time evolution of a hollow Co2S3 nanocrystal grown from a Co nanocrystal via the nanoscale Kirkendall effect Science 2004, 304, 711

19. NANOSCALE PATTERNING OF SHAKE-AND-BAKE SOLID-STATE CHEMISTRY MINIMIZING DIFFUSION LENGTHS <x> » (2Dt)1/2 FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T Younan Xia

20. PDMS MASTER Whitesides

21. PDMS MASTER Whitesides • Schematic illustration of the procedure for casting PDMS replicas from a master having relief structures on its surface. • The master is silanized and made hydrophobic by exposure to CF3(CF2)6(CH2)2SiCl3 vapor • SiCl bind to surface OH groups and anchor perfluoroalkylsilane to surface of silicon master CF3(CF2)6(CH2)2SiO3for easy removal of PDMS mold • Each master can be used to fabricate more than 50 PDMS replicas. • Representative ranges of values forh, d, and lare0.2 - 20, 0.5 - 200, and 0.5 - 200 mmrespectively.

22. NANOSCALE PATTERNING OF SHAKE-AND-BAKE SOLID-STATE CHEMISTRY Younan Xia

23. NANOSCALE PATTERNING OF SHAKE-AND-BAKE SOLID-STATE CHEMISTRY (A) Optical micrograph (dark field) of an ordered 2-D array of nanoparticles of Co(NO3)2 that was fabricated on a Si/SiO2 substrate by selective de-wetting from a 0.01 M nitrate solution in 2-propanol. The surface was patterned with an array of hydrophilic Si-SiO2 grids of 5 x 5 mm2 in area and separated by 5 mm. (B) An SEM image of the patterned array shown in (A), after the nitrate had been decomposed into Co3O4 by heating the sample in air at 600 °C for 3 h. These Co3O4 particles have a hemispherical shape (see the inset for an oblique view). (C) An AFM image (tapping mode) of the 2-D array shown in (B), after it had been heated in a flow of hydrogen gas at 400 °C for 2 h. These Co particles were on average 460 nm in lateral dimensions and 230 nm in height. Co(NO3)2 Co3O4 Co

24. NANOSCALE PATTERNING OF SHAKE-AND-BAKE SOLID-STATE CHEMISTRY AFM image of an ordered 2-D array of (A) MgFe2O4and (B) NiFe2O4 that was fabricated on the surface of a Si/SiO2 substrate by selective de-wetting from the 2-propanol solution (0.02 M) that contained a mixture of two nitrates [e.g. 1:2 between Mg(NO3)2 and Fe(NO3)3]. The PDMS stamp contained an array of parallel lines that were 2 mm in width and separated by 2 mm. Twice stamped orthogonally.Citric acid HOC(CH2CO2H)3 forms mixed Mg(II)/Fe(III) complex - added to reduce the reaction temperature between these two nitrate solids in forming the ferrite. Ferrite nanoparticles ~300 nm in lateral dimensions and ~100 nm in height. MgFe2O4 NiFe2O4

25. MgO ccp O(2-) with Mg(2+) diffusion Al2O3 hcp O(2-) with Al(3+) diffusion Nucleation at interface favored by structural similarity of reagents and products Minimal structural reorganization Promotes nucleation and growth Both MgO and MgAl2O4 similar O(2-) ccp Spinel lattice nuclei matches MgO at interface Essentially continuous across reaction interface STRUCTURAL SIMILARITY OF REACTANTS AND PRODUCTS PROMOTES NUCLEATION RATE AND RATE OF PRODUCT GROWTH NUCLEATION OF PRODUCT PHASE

26. O2- Mg 2+ Mg 2+ O2- O2- Mg 2+ Mg 2+ Mg 2+ O2- O2- O2- Mg 2+ Mg 2+ Mg 2+ Mg 2+ Mg 2+ Mg 2+ Mg 2+ Mg 2+ O2- O2- O2- O2- O2- O2- O2- O2- Mg 2+ O2- Mg 2+ O2- O2- O2- Mg 2+ {100} face {111} face {111} face Mg 2+ Mg 2+ SURFACE STRUCTURE AND REACTIVITY EFFECTS ON DIRECT REACTION OF SOLIDS Nucleation depends on surface structure of reacting phases - crystal faces in contact - MgO rock salt - different Miller index faces exposed - ion arrangements in crystal face different - distinct crystal habits (octahedral, cubooctahedral, cubic) possible depending on growth conditions and additives - {100} alternating Mg(2+) and O(2-) at corners of square grid - {111} Mg(2+) or O(2-) in hexagonal arrangement - implies different surface structures, energies and reactivities

27. DIRECT REACTION OF SOLIDS - “SHAKE-AND-BAKE” SOLID STATE SYNTHESIS • Although this approach may seem to be ad hoc and a little irrational at times, the technique has served solid state chemistry for well over the past 50 years • It has given birth to the majority of high technology devices and products that we take for granted every day of our lives • Thus it behooves us to look critically and carefully at the methods used if one is to move beyond trial-and-error methods to the new chemistry and a rational and systematic approach to the synthesis of materials

28. THINKING ABOUT REAGENTS • Drying reagents MgO/Al2O3 200-800°C, maximum SA • In situ decomposition of precursors at 600-800°C MgCO3/Al(OH)3MgO/Al2O3 • Intimate mixing of precursor reagents • Homogenization of reactants using organic solvents, grinding, ball milling, ultra-sonification

29. THINKING ABOUT CONTAINER MATERIALS • Chemically inert crucibles, boats • Noble metals Nb, Ta, Au, Pt, Ni, Rh, Ir • Refractories, alumina, zirconia, silica, boron nitride, graphite • Reactivity with containers at high temperatures needs to be carefully evaluated for each system

30. THINKING ABOUT SOLID STATE SYNTHESIS HEATING PROGRAM • Furnaces, RF, microwave, lasers, ion and electron beams • Prior reactions and frequent cooling, grinding and regrinding, boost SA of reacting grains • Overcoming sintering, grain growth, brings up SA, fresh surfaces, enhanced contact area • Pellet and hot press reagents – densification and porosity reduction, higher surface contact area, enhances rate, extent of reaction • Care with unwanted preferential component volatilization if T too high, composition dependent • Need INERT atmosphere for unstable oxidation states

31. PRECURSOR SOLID STATE SYNTHESIS METHOD • Co-precipitation, high degree of homogenization, high reaction rate - applicable to nitrates, acetates, citrates, carboxylates, oxalates, alkoxides, b-diketonates, glycolates • Concept: precursors to magnetic Spinels - recording media • Zn(CO2)2/Fe2[(CO2)2]3/H2O 1 : 1 solution phase mixing • H2O evaporation, salts co-precipitated – solid solution mixing on atomic/molecular scale, filter, calcine in air • Zn(CO2)2 + Fe2[(CO2)2]3 ZnFe2O4 + 4CO + 4CO2 • High degree of homogenization, smaller diffusion lengths, fast rate at lower reaction temperature

32. PROBLEMS WITH CO-PRECIPITATION METHOD • Co-precipitation requires: • Similar salt solubilities • Similar precipitation rates • Avoid super-saturation as poor control of co-precipitation • Useful for synthesizing Spinels, Perovskites • Disadvantage: often difficult to prepare high purity, accurate stoichiometric phases

33. DOUBLE SALT PRECURSORS • Known stoichiometry double salts having controlled stoichiometry • Ni3Fe6(CH3CO2)17O3(OH).12Py • Basic double acetate pyridinate • Burn off organics at 200-300oC, then calcine at 1000oC in air for 2-3 days • Product highly crystalline phase pure NiFe2O4 spinel

34. Good way to make chromite Spinels, important tunable magnetic materials - juggling electronic-magnetic properties of the A Oh and B Td ions in the Spinel lattice DOUBLE SALT PRECURSORS • Chromite Spinel Precursor compound Ignition T, oC • MgCr2O4 (NH4)2Mg(CrO4)2.6H2O 1100-1200 • NiCr2O4 (NH4)2Ni(CrO4)2.6H2O 1100 • MnCr2O4 MnCr2O7.4C5H5N 1100 • CoCr2O4 CoCr2O7.4C5H5N 1200 • CuCr2O4 (NH4)2Cu(CrO4)2.2NH3 700-800 • ZnCr2O4 (NH4)2Zn(CrO4)2. 2NH3 1400 • FeCr2O4 (NH4)2Fe(CrO4)2 1150

35. PEROVSKITE FERROELECTRICS BARIUM TITANATE • Control of grain size determines ferroelectric properties, important for capacitors, microelectronics • Direct heating of solid state precursors is of limited value in this respect – lack of size and morphology control • BaCO3(s) + TiO2(s)  BaTiO3(s) • Sol-gel reagents useful to create single source barium titanate precursor with correct stoichiometry

36. SINGLE SOURCE PRECURSOR SYNTHESIS OF BARIUM TITANATE - FERROELECTRIC MATERIAL • Ti(OBu)4(aq) + 4H2O  Ti(OH)4(s) + 4BuOH(aq) • Ti(OH)4(s) + C2O42-(aq)  TiO(C2O4)(aq) + 2OH-(aq) + H2O • Ba2+(aq) + C2O42-(aq) + TiO(C2O4)(aq)  Ba[TiO(C2O4)2](s) • Precipitate contains barium and titanium in correct ratio and at 920C decomposes to barium titanate according to: • Ba[TiO(C2O4)2](s)  BaTiO3(s) + 2CO(g) + 2CO2(g) • Grain size importantfor control of ferroelectric properties • Used to grow single crystals hydrothermally

37. BASICS: FERROELECTRIC BARIUM TITANATE Cubic perovskite equivalent O-Ti-O bonds in BaTiO3 Tetragonal perovskite long-short axial O-Ti—O bonds in BaTiO3 Small grains, tetragonal to cubic surface gradients, ferroelectricity particle size dependent Multidomain ferroelectric dipoles align in E field and/or below Tc Multidomain paraelectric above Tc Cooperative electric dipole interactions within each domain – aligned in domain but random between Single domain superparaelectric

38. SOL-GEL SINGLE SOURCE PRECURSORS TO LITHIUM NIOBATE - NLO MATERIAL • LiOEt + EtOH + Nb(OEt)5 LiNb(OEt)6 LiNbO3 • LiNb(OEt)6 + H2O  LiNb(OEt)n(OH)6-n   gel • LiNb(OEt)n(OH)6-n + D + O2LiNbO3 • Lithium niobate, ferroelectric Perovskite, nonlinear optical NLO material, used as electrooptical switch • Bimetallic alkoxides - single source precursor • Sol-gel chemistry - hydrolytic polycondensation  gel • MOH + M’OH  MOM’ + H2O • Yields glassy product • Sintering product in air - induces crystallization

39. INDIUM TIN OXIDE -ITO • Indium sesquioxide In2O3 (wide Eg semiconductor) electrical conductivity enhanced by p-doping with (10%) Sn(4+) • ITO is SnnIn2-nO3 • ITO is optically transparent, electrically conducting, thin films are vital as electrode material for solar cells, electrochromic windows/mirrors, LEDs, LC displays, electronic ink, photonic crystal ink and so forth • Precursors - EtOH solution of (2-n)In(OBu)3/nSn(OBu)4 • Hydrolytic poly-condensation to form gel, spin coat gel onto glass substrate to make thin film • Dry gel at 50-100C, heat at 350C in air to produce ITO • Check electrical conductivity and optical transparency

40. SUB -10 NM NANOSCALE DIRECT SOLID STATE REACTION – TiO2 Electron Beam Nanolithography of Spin-Coated Sol-Gel TiO2 Based Resists benzoyl acetone tetrabutoxyorthotitanate Choosing the right solid state precursor to make resist

41. SUB -10 NM NANOSCALE DIRECT SOLID STATE REACTION Electron Beam Nanolithography Using Spin-Coated TiO2 Resists • Utilization of spin-coated sol gel based TiO2 resists by chemically reacting titanium n-butoxide with benzoylacetone in methyl alcohol. • They have an electron beam sensitivity of 35 mC cm-2 and are >107 times more sensitive to an electron beam than sputtered TiO2 and crystalline TiO2 films. Choosing the right solid state precursor

42. Sub-10 nm Electron Beam Nanolithography Using Spin-Coated TiO2 Resists • Fourier transform infrared studies suggest that exposure to an electron beam results in the gradual removal of organic material from the resist. • This makes the exposed resist insoluble in organic solvents such as acetone, thereby providing high-resolution negative patterns as small as 8 nm wide. • Such negative patterns can be written with a pitch as close as 30 nm. Choosing the right solid state precursor

43. Nanometer scale precision structures Nanoscale TiO2 structures offer new opportunities for developing next generation solar cells, optical wave-guides, gas sensors, electrochromic displays, photocatalysts, photocatalytic mCP, battery materials

44. Nanometer scale tolerances