ASPECTS OF SOLID-SOLID REACTIONS

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)

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.

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 turnLet us examine each of the above in turn

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

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

A, d, x Relations

Small d Large d

Large SA/V Small SA/V

Small x Large x

EXTRA CONSIDERATIONS IN SOLID STATE SYNTHESIS

• x(thickness planar layer) 1/A(contact area)

• A(contact area) 1/d(particle size)

• Thus particle sizes and surface area connectedThus particle sizes and surface area connected

• Hence x 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!!! controlling diffusion lengths!!!

MINIMIZING DIFFUSION LENGTHS <x> (2Dt)1/2 FOR RAPID AND COMPLETE DIRECT REACTION

BETWEEN SOLID STATE MATERIALS AT LOWEST T

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 scale mixing in composite precursor compounds Coated particle mixed component reagents, corona/core precursorsJohnson superlattice layered precursors

All aimed to increase A and decrease x and minimize diffusion length scale



All aimed to increase A and decrease x and minimize diffusion length scale

Core-corona reactants in intimate contact, made by precursor precipitation, sol-gel deposition, CVD

COATED PARTICLE MIXED SOLID STATE REAGENTS

SYNTHESIS OF COMPOSITION TUNABLE MONODISPERSE ZnxCd1-xSe ALLOY NANOCRYSTALS –

ELECTRONIC BAND GAP ENGINEERING

x controlled by size of core and corona more on this later



•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 SUPERLATTICE REAGENTSREAGENTS

ELEMENTALLY MODULATED

SUPERLATTICES -DEPOSITED AND

THERMALLY POST TREATED TO GIVE LAYERED METAL

DICHALCOGENIDES MX2

COMPUTER MODELLING OF

SOLID STATE REACTION OF

JOHNSON SUPERLATTICE



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

AT LOW T THE SUPERLATTICE REAGENTS YIELD SUPERLATTICE ARTIFICIAL CRYSTAL PRODUCT

Superlattice precursor sequence 6(Ti-2Se)-6(Nb-2Se) yields ternary modulated superlattice composition {(TiSe 2)6(NbSe 2)6}n with 62 well defined PXRD reflections – good exercise – give it a try

Confirms correlation between precursor heterostructure sequence and superlattice ordering of final product



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 “alloy” product with identical layers

Properties of ternary product is the atomic fraction weighted average of binary end member components – Vegard Law

P(TixNb(1-x)Se2) = xP(TiSe2) + (1-x)PNbSe2

AT HIGH T THE SUPERLATTICE REAGENTS YIELD HOMOGENEOUS SOLID SOLUTION PRODUCT

• Several important synthetic parameters and in situ probes

• Reactants prepared using thin film deposition techniques – more on this later - and consist of nm scale layers of the elements to be reacted.

• Elements easily substituted for another

• Allows rapid surveys over a class of related reactions and synthesis of iso-structural compounds.

ELEMENTALLY MODULATED ELEMENTALLY MODULATED SUPERLATTICESSUPERLATTICES

ELEMENTALLY MODULATED ELEMENTALLY MODULATED SUPERLATTICESSUPERLATTICES

• Diffusion distance is determined by the multilayer repeat distance which can be continuously varied

• An important advantage, allowing experimental probe of 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

• Think about how to make a BaTiO3-SrTiO3 Perovskite superlattice or a MgAl2O4-ZnAl2O4 Spinel superlattice and why would you do this ???

CORE-CORONA NANOCLUSTER PRECURSOR BASED KIRKENDALL SYNTHESIS OF HOLLOW NANOCLUSTERS

V[Co]

Co(3+)

S(2-)

e(-)

Co

S

Co2S3• Synthesis of surfactant-capped cobalt nanoclusters:

• Co(3+)/BH4(-) reduction in oleic acid, oleylamine ConLm • arrested nucleation and growth of ligand capped cobalt nanoclusters• surfactant functions as high temperature capping ligand and solvent• surfactant-sulfur injection, coating of sulfur shell on nanocluster• cobalt sesquisulfide product shell layer formed at interface

CORE-CORONA NANOCLUSTER PRECURSOR BASED KIRKENDALL SYNTHESIS OF HOLLOW NANOCLUSTERS

V[Co]

Co(3+)

S(2-)

e(-)

Co

S

Co2S3

• counter-diffusion of Co(3+)/2e(-) and S(2-) across thickening shell• faster diffusion of Co(3+) than S(2-) creates vacancies 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

THINGS ARE NEVER THAT SIMPLE!!!

Different diffusion processes in the growth of hollow nanostructuresinduced by the

Kirkendall effect

Small Sept 2007 asap web

Time evolution of a hollow Co2S3 nanocrystal grown from a Co nanocrystal via the nanoscale Kirkendall effect

Science 2004, 304, 711

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 and shape – like nanorods – see next example

• Proof-of-concept - synthesis of Co2S3 nanoshell starting from Co nanocluster.

Time evolution of a hollow CoSehollow CoSe22 nanocrystal magnetic nanocrystal magnetic

dipole chaindipole chain grown from a Co nanocrystal and selenium in surfactant capping ligand and solvent via the

nanoscale Kirkendall effect – Small September 2007

Works for Hollow ZnAl2O4 Spinel Nanotubes!!!

Li2NH Hollow Nanospheres from the Kirkendall Reaction of Li Nanospheres

and Ammonia - Hydrogen Storage Materials with Superior Adsorption-

Desorption Kinetics

Chemistry Materials December 9th 2007

SYNTHESIS OF Li2NH HOLLOW NANOSPHERES AND THEIR REVERSIBLE REACTION WITH H2

• Vaporization of Li metal as spherical nanodroplets

• Reaction of nanodroplets with gaseous NH3

• Kirkendall effect of small fast diffusing Li reacting with NH3 forms shell of Li2NH and core of vacancies which coalesce

• Li2NH hollow nanospheres with high surface area and thin shell enables fast H2 adsorption kinetics (6wt%, 470K, Ea 106 kJ/mole) to form LiNH2 and LiH and fast de-sorption kinetics 503K for reaction of LiNH2 with LiH enabled by small diffusion lengths

• Significantly improved kinetics compared to micron size particles of Li2NH (610K, Ea 225kJ/mole ads, 618K des)

SYNTHESIS OF Li2NH HOLLOW NANOSPHERES AND THEIR REVERSIBLE REACTION WITH H2 WITH SHAPE RETENTION

• (a) SEM image• (b) TEM image (inset:

magnified TEM image) of the as-prepared Li2NH hollow nanospheres

• (c) TEM image of the Li2NH hollow nanospheres annealing at 573 K under vacuum for 1 h

• (d) TEM image of the Li2NH hollow nanospheres after hydrogenated at 573 K under 35 bar of hydrogen for 1 h.

PXRD Characterization

• XRD patterns of (a) Li2NH hollow nanospheres

• (b) Li2NH hollow nanospheres after hydrogenated at 573 K under 35 bar of hydrogen for 1 h.

DSC Characterization

• (a) DSC curves of hydrogenation at a heating rate of 10 K/min under 35 bar of H2 and

• (b) DSC curves of desorption at a heating rate of 10 K/min under flowing Ar after hydrogenated under 35 bar of H2 at 573K for 1 h.

• N ) Li2NH hollow nanospheres, and M ) Li2NH micrometer particles.

Adsorption Characterization

• Hydrogenation absorption curves of the obtained samples at different temperature under an initial hydrogen pressure about 35 bar of H2 of (N) Li2NH hollow nanospheres and (M) Li2NH micrometer particles.

Pressure Hydrogen Content Temperature Behaviour of Li2NH Hollow Nanospheres

NANOSCALE PATTERNING OF SHAKE-AND-BAKE SOLID-STATE CHEMISTRY

Younan Xia

MINIMIZING DIFFUSION LENGTHS <x> (2Dt)1/2 FOR RAPID AND COMPLETE

DIRECT REACTION BETWEEN SOLID STATE MATERIALS AT LOWEST T

PDMS MASTER FOR SOFT LITHOGRAPHY MICROCONTACT PRINTING

Whitesides

PDMS MASTER

• 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)2SiO3 for easy removal of PDMS mold

• Each master can be used to fabricate more than 50 PDMS replicas.

• Representative ranges of values for h, d, and l are 0.2 - 20, 0.5 - 200, and 0.5 - 200 mm respectively.

Whitesides


Younan Xia


(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 m2 in area and separated by 5 m.

(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


AFM image of an ordered 2-D array of (A) MgFe2O4 and (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

ACTUALLY DOING IT IN THE LAB

DIRECT REACTION OF SOLIDS - “SHAKE-AND-BAKE” SOLID STATE SYNTHESISDIRECT 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 in the lab if one is to move beyond trial-and-error methods to the new solid state chemistry and a rational and systematic approach to synthesis of materials

THINKING ABOUT MIXINGMIXING SOLID 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

THINKING ABOUT CONTAINERCONTAINER 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

THINKING ABOUT SOLID STATE SYNTHESIS HEATINGHEATING 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

PRECURSORPRECURSOR SOLID STATE SYNTHESIS METHOD

• Co-precipitation, high degree of homogenization, high reaction rate - applicable to nitrates, acetates, citrates, carboxylates, oxalates, alkoxides, -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

PROBLEMS WITH CO-PRECIPITATION METHOD

• Co-precipitation requirements:

• 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

DOUBLE SALTDOUBLE SALT PRECURSORS

• Known stoichiometry double salts have controlled element 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

Good way to make chromite Spinels, important tunable magnetic materialsjuggling electronic-magnetic properties of the A Ojuggling electronic-magnetic properties of the A Ohh and B T and B Tdd ions in the Spinel lattice ions in the Spinel lattice

• 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

DOUBLE SALTDOUBLE SALT PRECURSORS

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 stoichiometry, size and morphology lack of stoichiometry, size and morphology controlcontrol

• BaCO3(s) + TiO2(s) BaTiO3(s)

• Sol-gel reagents useful to create single source barium titanate precursor with correct stoichiometry

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 920Precipitate contains barium and titanium in correct ratio and at 920 C C decomposes to barium titanate according to:decomposes to barium titanate according to:

• Ba[TiO(C2O4)2](s) BaTiO3(s) + 2CO(g) + 2CO2(g)

• Grain size important for control of ferroelectric properties

• Used to grow single crystals hydrothermally

BASICS: FERROELECTRIC BARIUM TITANATE

CubicCubic perovskite equivalent O-Ti-O bonds in BaTiO3

TetragonalTetragonal perovskite long-short axial O-Ti—O bonds in BaTiO3

Multidomain paraelectric above Curie Tc Cooperative electric dipole interactions within each domain – aligned in domain but random between

Multidomain ferroelectric dipoles align in E field and/or below Tc

Single domain superparaelectric

Small grains, tetragonal to cubic surface gradients, ferroelectricity particle size dependent

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 + + O2 LiNbO3

• Lithium niobate, ferroelectric Perovskite, nonlinear optical NLO material, used as electrooptical switch – voltage control of refractive index – random vs aligned electric dipoles

• 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

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: InOH + HOSn InOSn

• Dry gel at 50-100C, heat at 350C in air to produce ITO

• Check electrical conductivity and optical transparency

SUB -10 NM NANOSCALE DIRECT SOLID STATE REACTION – TiO2

Electron Beam Nanolithography of Spin-Coated Sol-Gel TiO2 Based Resists LOCALIZED HEATING AT THE NANOMETER SCALE

Choosing the right solid state precursor to make resist

benzoyl acetone

tetrabutoxyorthotitanate

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

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, unexposed is soluble, 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

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

Nanometer scale tolerances

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ASPECTS OF SOLID-SOLID REACTIONS