CHARGE BALANCE IN SOLID STATE INTERFACIAL REACTIONS 3Mg(2+) diffuse in opposite way to 2Al(3+)...

CHARGE BALANCE IN SOLID STATE INTERFACIAL REACTIONS

• 3Mg(2+) diffuse in opposite way to 2Al(3+)

• MgO/MgAl2O4 Interface

• 2Al(3+) - 3Mg(2+) + 4MgO MgAl2O4 LHS

• MgAl2O4/Al2O3 Interface

• 3Mg(2+) - 2Al(3+) + 4Al2O3 3 MgAl2O4 RHS

• Overall Reaction

• 4MgO + 4Al2O3 4 MgAl2O4

• RHS/LHS growth rate of interface = 3/1 Kirkendall Effect

KIRKENDALL EFFECT

OTHER SOLID STATE REACTIONS

• MgO + Fe2O3 MgFe2O4

• Different color interfaces

• Easily monitored rates

• Other examples - calculate the Kirkendall ratio:

• SrO + TiO2 SrTiO3 Perovskite, AMO3 (type ReO3)

• 2KF + NiF2 K2NiF4 Corner Sharing Oh NiF6(2-) Sheets, Inter-sheet K(+)

• 2SiO2 + Li2O Li2Si2O5

ROCK SALT CRYSTAL STRUCTURE

OO

MM

x

y

RUTILE CRYSTAL STRUCTURE

x

y

z

PEROVSKITE CRYSTAL STRUCTURE

AA

OO

MM

PEROVSKITE MATERIALS: STRUCTURE-PROPERTY-FUNCTION-UTILITY RELATIONS

• LiNbO3 non-linear optical ferroelectric - E-field RI control - electrooptical switch

• SrTiO3 dye sensitized semiconductor liquid junction photocathode - solar cell

• HxWO3 proton conductor - hydrogen/oxygen fuel cell electrolyte

• BaY2Cu3O7 high Tc superconductor - magnetic levitation - detector/SQUIDS

• BaTiO3 ferroelectric high dielectric capacitor, photorefractive – holography

• CaxLa1-xMnO3 x control F-metal, P-semiconductor - GMR - data storage

• SrxLa1-xMnO3 x control e-/oxide ion conductor - solid oxide fuel cell cathode

• PbZrxTi1-xO3 piezoelectric - oscillator, nano-positioner

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.

• 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 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 turn

SURFACE AREA OF PRECURSORS

• Seems trivial - vital consideration in solid state synthesis

• Consider MgO, 1cm3 cubes, density 3.5 gcm-3

• 1 cm cubes: SA 6x10-4 m2/g • 10-3 cm cubes: SA 6x10-1 m2/g • 10-6 cm cubes: SA 6x102 m2/g

• The latter is equal to a 100 metre 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

• High pressure squeezing of reactive powders into pellets, for instance using 105 psi

• 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

EXTRA CONSIDERATIONS IN SOLID STATE SYNTHESIS

• x 1/A(contact)

• A(contact) 1/d(particle)

• Thus particle sizes and surface area connected

• Hence x d therefore A and d affect interfacial thickness

• These relations suggest some strategies for rate enhancement in direct reactions

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 size 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)1/2 FOR RAPID AND COMPLETE DIRECT REACTION BETWEEN

SOLID STATE MATERIALS AT LOWEST T

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

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

COATED PARTICLE SOLID STATE REAGENTS

MINIMIZING DIFFUSION LENGTHS <x> (2Dt)1/2 FOR 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•Diffusion length 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 heterostructures•HT thermodynamic product

SUPERLATTICE REAGENTS

ELEMENTALLY MODULATED

SUPERLATTICES -DEPOSITED AND

THERMALLY POST TREATED

COMPUTER MODELLING OF SOLID STATE REACTION OF

JOHNSON SUPERLATTICE

• Give 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 can be easily substituted for another, allowing rapid surveys over a class of related reactions and synthesis of isostructural compounds.

ELEMENTALLY MODULATED SUPERLATTICES

ELEMENTALLY MODULATED SUPERLATTICES

• The 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.

• Multi-layer repeat distances can be easily verified in the prepared reactants using low angle X-ray diffraction.

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

SOLID STATE MATERIALS AT LOWEST T

Johnson superlattice reagent design

{(Ti2Se)6(Nb2Se)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 - PTO

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

SUPERLATTICE REAGENTS YIELD SUPERLATTICE ARTIFICIAL CRYSTAL PRODUCT

Superlattice sequence 6(Ti2Se)-6(Nb2Se) yields ternary modulated superlattice composition {(TiSe 2)6(NbSe 2)6}n

with 62 well defined PXRD reflections

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

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

SOLID STATE MATERIALS AT LOWEST T

John superlattice reagent design

{(Ti2Se)6(Nb2Se)6}n

High T annealing reaction

{(Ti0.5Nb0.5Se2)}n

Thermodynamic 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

SUPERLATTICE REAGENTS YIELD HOMOGENEOUS SOLID SOLUTION PRODUCT

NANOCLUSTER KIRKENDALL SYNTHESIS OF HOLLOW NANOCLUSTERS

V[Co]

Co(2+)

S(2-)

e(-)

Co

S

Co2S3

Capped cobalt nanoclusters in a high temperature solvent, sulfur injection, coating of sulfur 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+) 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

TURNING NANOSTRUCTURES INSIDE-OUT

• The Kirkendall effect is a well-known phenomenon discovered in the 1930’s. • It occurs during the reaction of two solid-state materials and involves the

diffusion of reactant species, like ions, across the product interface usually at different rates.

• In the special case when the movement of the fast-diffusing component cannot be balanced by the movement of the slow component the net mass flow is accompanied by a net flow of atomic vacancies in the opposite direction.

• This effect leads to Kirkendall porosity, formed through supersaturation of vacancies into hollow pores

• When starting with perfect building blocks such as cobalt nanocrystals a reaction meeting the Kirkendall criteria can lead to supersaturation of vacancies exclusively in the center of the nanocrystal.

• This provides a general route to hollow nanocrystals out of almost any given material

• Proof-of-concept - synthesis of a cobalt sulfide nanoshell starting from a cobalt nanocluster.

Time evolution of a hollow cobalt sulfide nanocrystal grown from a cobalt nanocrystal via the nanoscale Kirkendall effect

Science 2004, 304, 711

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 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

• 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 m respectively.

Whitesides

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

Younan Xia

NANOCALE 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 dewetting 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

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

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 dewetting 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 m in width and separated by 2 m. Citric acid was also 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

SIZE, DISPERSITY, SHAPE AND ORIENTATION CONTROL OF NANOCRYSTAL SUPERLATTICE

• Shape is critical for command of structural, physical, chemical properties of nanocrystals and their arrays

• Shape determines electrical, optical, magnetic behavior• Magnetic anisotropy control of nanocrystals crucial for aligning easy

axis of magnetization of nanocrystal necessary for magnetic applications like data storage

• Magnetic spinels test case for shape-controlled synthesis• Fe(acac)3 + Mn(acac)2 + 1,2-hexadecanediol + oleic acid +

oleylamine + benzylether (high boiling solvent) 12 nm MnFe2O4

• Size command by concentration of metal acetylacetonate precursors

• Shape control by amount of stabilizing surfactant capping agents 1,2-hexadecanediol, oleic acid, oleylamine – selective adsorption on different crystal faces and growth of those facets

SIZE, DISPERSITY, SHAPE AND ORIENTATION CONTROL OF NANOCRYSTAL SUPERLATTICE

• TEM low and high resolution images of 12 nm MnFe2O4 cube and polyhedral nanocrystal superlattices

• Grown on Si(100) substrate by EISA from hexane dispersion

• Showing control over size, dispersity, shape and orientation

SIZE, DISPERSITY, SHAPE AND ORIENTATION CONTROL OF NANOCRYSTAL SUPERLATTICE

• TEM and PXRD of 12 nm MnFe2O4 cube and polyhedral nanocrystal superlattices

• Grown on Si(100) substrate by EISA from hexane dispersion

• Showing control over size, dispersity, shape and orientation

NUCLEATION OF PRODUCT PHASE

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 reorganizationPromotes nucleation and growthBoth MgO and MgAl2O4 similar O(2-) ccpSpinel lattice nuclei matches MgO at interfaceEssentially continuous across reaction interface

STRUCTURAL SIMILARITY OF REACTANTS AND PRODUCTS PROMOTES NUCLEATION RATE AND PRODUCT GROWTH

FACTORS INFLUENCING CATION DIFFUSION RATES IN SOLID STATE REACTIONS: MgO+Al2O3

• Lattice of oxide anions, mobile Mg(2+) and Al(3+) cations

• Factors influencing cation diffusion rates

• Charge, mass and temperature

• Interstitial Frenkel versus substitutional Schottky diffusion

• Depends on number and types of defects in reactant and product phases

• Point, line, planar defects, grain boundaries

• Enhanced ionic diffusion with defects and grain boundaries

TOPOTACTIC AND EPITACTIC REACTIONS

• What about orientation effects on reactivity in the bulk and surface regions of solids?

• Implies structural relationships between two phases

• Topotactic reactions occur in bulk materials with 1D, 2D or 3-D structures - 1D TiS3, 2D MoO3, 3D WO3

• Topotaxy more specific, require interfacial and bulk crystalline structural similarity, lattice matching

TOPOTAXY: HOST-GUEST INCLUSION

1D- Tunnel Structures

-TiS3

2D- Layered Structures

-Graphite-TiS2

-KxMnO2

-FeOCl-HxMoO3

-LiCoO2

3D-Frameworks

- LiMn2O4

- WO3

Pivotal topotactic materials properties for functional utility in e.g., Li solid state batteries, electrochromic mirrors and windows, fuel cell electrolytes, chemical sensors, superconductors

TOPOTACTIC AND EPITACTIC REACTIONS

• Topotaxy: involves host-guest inclusion

• Requires available space or creates space in the process of adsorption and injection

• Epitactic reactions occurs at interfaces, inherently a 2-D phenomenon

• Epitactic reactions requires structural similarity in 2-D

EFFECT OF LATTICE MATCHING IN REACTIVITY OF SOLIDS - EPITACTIC AND TOPOTACTIC REACTIONS

Lattice A unit cell dimension a

Structural relationship between two phases - topotaxy in bulk, epitaxy at interfaces - epitaxy requires interfacial structural similarity - lattice matching <15% to tolerate oriented nucleation and growth - otherwise mismatch over large contact areas - strained interfaces, missing atoms, misfit dislocation

Missing atom - interfacial vacancy

Lattice B unit cell dimension a’

EFFECT OF LATTICE MATCHING IN REACTIVITY OF SOLIDS - EPITACTIC AND TOPOTACTIC REACTIONS

Lattice A unit cell dimension a

Causes elastic strain at interface - even lattice mismatch < 0.1% - slight atom displacement from equilibrium position in lattice - strain energy reduced by misfit dislocation - creates dangling bonds, localized electronic states, charge carrier scattering by defects, luminescence quenching - reduces efficacy of devices - visualized by TEM imaging

Missing atom - interfacial vacancy

Lattice B unit cell dimension a’