Some Examples

Manganese zinc ferrite

Che5700 陶瓷粉末處理

Liquid Phase Synthesis

Very common; simple; cheap; (will generate waste water)

Easy to get multi-component product, high uniformity, dispersion in atomic scale;

Often more steps; complex inter-relationship; often need calcination to get final useful product

Classification: (the way to remove solvent) Solvent evaporation: spray drying, spray decomposition,

evaporative decomposition of solutions EDS; emulsion drying, freeze drying

Precipitation-filtration: ordinary process; homogeneous precipitation

Solvent extraction: salting out; sol-gel (?)

Process Introduction

Che5700 陶瓷粉末處理

Precursor in solvent (aqueous or organic) one or several precursors chemical reaction (additive, temp., etc.) separation from solvent post-processing (washing, drying, etc.) product powder

Precipitation method: co-precipitation, homogeneous precipitation, emulsion precipitation, hydrothermal precipitation, hydrolytic precipitation (referring to sol-gel, alkoxide was hydrolyzed)

Important parameters: pH, temperature, time, precipitation agent, quantity, rate of addition, method of addition, type of cation, type of solvent and quantity, reactor size and shape, other additives, stirring, atmosphere and pressure (e.g. in autoclave) VERY COMPLEX; often rely on experimental design

UO2 nuclear fuel rod material;

Reaction: UO2F2 + (NH4)2CO3 (NH4)4UO2(CO3

)3 + 2 NH4FComplex steps experimental design to find optimal condition quickly, e.g. Taguchi method, Plackett – Burman etc.

•Top figure: a,b,c (in sequence)– particle size distribution after precipitation, washing/drying and calcination, agglomeration during washing and drying is obvious

•Bottom figure: relation between average size (after calcination) and sintered density; only qualitative in nature.

* Taken from JS Reed; precipitation occurs when two chemical reacting with each other, formation of particles – described by the theory of nucleation and growth

reaction

Expression of supersaturation

Che5700 陶瓷粉末處理

ioii

eqiii aRT ln&)(

xxxa iiiii &

)1ln()}/ln(/)/ln(1{ xeqeq RTxx

supersaturation: C = C – C or m, x Supersaturation ratio: = C/C Relative supersaturation: C = C/C; x + 1 = x/x Dimensionless growth affinity: = /RT For Activity & activity coefficient of ions: thermodynamic

equations such as Debye-Huckel equation

Electrolytic Solutions

Che5700 陶瓷粉末處理

• Behavior of ions: non-ideal solution; due to strong interaction between ions• electrical neutrality: z+ NA + z- NB = 0 (Aν+Bν- = ν+

A z+ +ν- Bz-; ν+ z+ +ν- z- = 0;)• mean ionic activity coefficient: γ±ν = (γA

□) ν+ (γB□) ν-

where ν=ν+ +ν-

• mean ionic molality: M±ν=MA ν+ MB

ν-

• Debye-Huckel limiting law: ln γ± = - α z+ z- √I; ∣ ∣where I = ionic strength = ½ Σ zi

2 Mi (over all ions); α: parameter of system = f(T, solvent) (find it out in handbooks for common solvents)

=RT ln; = (i/Ksp) 1/; = i

Ksp: ionic product at equilibrium; i = current ionic product; ratio of these two values ~ supersaturation

Solubility

Thermodynamic data: mainly affected by temperature, and solution environment (e.g. other ions, pH,…)

oo

o

a

a

C

CS

a

aRTG

)ln()( 12

Solubility (2)

sp

oosp

s

KBAS

BAK

ABBA

/]][[

][][

2

22

22

)(22

Temp. & pH effect: DCP = dicalcium phosphate; HAP = hydroxyapatite; System of: Ca(OH)2-H3PO4 – KOH – HNO3 – CO2 – H2O; Ca/P = 1

• ΔT: also used as a measure of supersaturation (as shown in figure);

•Solubility often increase with temperature; (there are also contrary cases, e.g. CaCO3 solubility in water decrease with temperature; the reason we get “scales”)

Nucleation

Che5700 陶瓷粉末處理

Several cases: homogeneous nucleation, heterogeneous nucleation, secondary nucleation

For homogeneous nucleation: for its rate, we have thermodynamic model or kinetic model

Thermodynamic model: changes between surface energy and bulk energy, energy of formation of new crystals = Ac – ( - ) Mc [Ac: crystal surface area; Mc: crystal mass) when nucleus size reach some critical value d /d(d) = 0 to get critical nucleus size d* = 4 Vm /(RT ln)

Finally to derive the rate equation: Bo = C exp(- */kT) & * = 32 b 3 Vm2/(RT ln)2

S =

Kinetic Expression of Nucleation

).(),1(/ 1111 tiItiIfEfCfEfCdtdf iiiiiiiii

))/(ln27/4exp()9/(2/ 233332/1eooo PPTkakTamkTPaI

*)(*)(*)( iniCiZI Zeldovich factor

Che5700 陶瓷粉末處理

Kinetic viewpoint: A1 + A1 = A2 + A1 = A3 …. A i+1 +.. A1 = monomer Then the following kinetic equations Ci = condensation rate; Ei = evaporation rate Under steady state d fi/dt = 0, and B.C. f1 = n1 =

constant; fG = 0 or constant (G: some critical size, e.g. critical nucleus size)

Solute Clustering & Nucleation

Che5700 陶瓷粉末處理

Taken from JCG, 89, 202-208, 1988. Main viewpoint: solute molecules aggregate to form

clusters (precursor to nuclei), surface energy of cluster may differ from large particles (different structure).

At 0oC, for water, 76% exist as clusters One method to study cluster size and conc. : let

supersaturated solution stand for very long time develop spatial distribution of clusters of different size, measurement by density or opacity difference.

Indirectly, width for metastable zone, provide information on cluster (narrow: cluster already exist, easy to nucleation)

Typical cluster size: 4-10nm, ~ 103 molecules

Heterogeneous Nucleation

Che5700 陶瓷粉末處理

Reasons to heterogeneous nucleation: larger complex size; impurity; wall of container;

liquid/air interface Due to lowering of surface energy, (lowering

barrier to nucleation) In a sense, co-precipitation: similar effect Epitaxial growth: similar structure between nuclei

and impurity surface, therefore growth of nuclei on this impurity surface

Used to make core-shell particles, core as seed to shell particles

Complex ions can increase size of cluster, closer to critical nucleus size, helpful to nucleation;

Impurity also influence structure (phase) of product

More on Nucleation

Che5700 陶瓷粉末處理

Taken from TA Ring, 1996; data for BaSO4

Secondary Nucleation

Che5700 陶瓷粉末處理

Under-saturated condition, existing nuclei induce new nucleation – secondary nucleation

Reasons include: Initial breeding; Needle breeding Contact breeding; Fluid shear etc. parameters: degree of supersaturation, stirring,

collision between suspending particles (frequency, energy, material of container etc)

Empirical relation: secondary nucleation rate Bo ~ (S-1)b MT

j (rpm)h; where MT = quantity of suspending particles

A Model on Secondary Nucleation

Taken from Botsaris, et. al. Chem. Eng. Sci., 52(20), 3429-3440, 1996; Their concept: in supersaturated solution, existing embryos (may be viewed as a result of coagulation between clusters), they aggregate (due to van der Waals forces attractive forces), if also seed, embryos move to seed, in the neighbor of seed: high embryo concentration, they will aggregate to form new nuclei, swept by fluid to become secondary nuclei, some may aggregate with seed to make it biggerTheory of rapid coagulation: - dn/dt = 8D r n2 = (4kT/3) n2 (by Smoluchowski) (particle movement by Brownian motion; n: particle conc. r particle radius; D diffusion coefficient)

Botsaris: estimate secondary nucleation rate near a seed; curve 7: assume cluster g = 622; At = seed surface area = 1.67 cm2/cm3; system: KCl-H2O; curve 6 first half: contact nucleation; second half: similar to Botsaris’ theory

LH left-hand左旋光結構

To demonstrate relation between seed and nuclei: use chiral compound; low supersaturation: some effect, middle: significant; high supersaturation: homogeneous nucleation

This impurity show inhibiting effect

Induction Times

• From start of generation of supersaturation until observation of crystals, - induction time

• Techniques to observe crystals: turbidity, visual observation, conductivity, or properties related to concentration

• It include three parts: ti = tr + tn + tg

ti : induction time; tr: time required for attainment of stationary embryo

distribution (relaxation time) tn: time for the formation of nucleus tg: time for nucleus to grow into detectable crystals* One possible barrier to nucleation: dehydration

reaction of ions

Che5700 陶瓷粉末處理

More on Induction Times

If tn: major part, nucleation dominate, tn ~ 1/Bo then ln(tn) or ln(ti) vs ln() -2 should be linear

If tg: major, ti often becomes very long, its growth may be limited by surface nucleation ln(ti) vs ln() -1 will be linear

sometimes, embryo structure differs from crystal, phase change may become barrier

Che5700 陶瓷粉末處理

Crystal Growth

Che5700 陶瓷粉末處理

LRTMXX eq 3/2)/ln(

Crystal growth: mass transfer, heat transfer can not be neglected; species entering structure, may also the rate determining step

Relation between size and solubility: Ostwald-Freundlich law, similar to Kelvin equation; small size (L small) high solubility

surface nucleation mechanism birth and spread screw dislocation mechanism Impurity effect: often inhibit growth by adsorption on

specific site (surface), often change morphology

•Growth steps:•Diffusion to surface; Adsorption; Desolvation; (dehydration); Surface diffusion; Integration at kink site•terminology: ledge, step and kink

F = surface energy

It shows small size, large solubility; for low surface energy, size effect less significant (see Kelvin equation)

xL/ xeq = a measure of super-saturation

Growth Rates

Che5700 陶瓷粉末處理

Different mechanism, different equations to show relation between growth rate and supersaturation: e.g.

Birth & Spread mechanism (2D nucleation model): growth rate ~ (step height) x (step velocity) 2/3 x

(#critical nuclei formed/area-time) 1/3 G = A i 5/6 exp(-B/i)

General empirical equation: G = k n

Note: can be supersaturation with respect to bulk, or to surface

Can be classified as: linear, parabolic, and exponential law (growth rate and supersaturation)

More on Growth Rates

)()/( TThGMH iiC

Che5700 陶瓷粉末處理

Growth rate may depend upon size, I.e. G = f(L) Growth rate dispersion: due to different residence time,

or due to surface structure & perfection Too fast growth rate, easy to trap mother liquid

(inclusion) Heat production: interface temperature may affect

solubility near interface i.e. super-saturation, or growth rate

In general: linear growth rate = mass transfer or adsorption effect

parabolic rate = spiral steps exponential rate = polynuclear surface control

Growth rate proportional to density of defects (screw dislocation)

Accumulation of supersaturation nucleation supersaturation decrease nucleation stops growth continue end

Summary on Particle Formation

Reaction formation of some “species” (reaction kinetics) supersaturation (induction times) Nucleation (home-, hetero- ..) (critical nucleus size, nucleation rate) growth (growth rate, crystal habit, …) agglomeration (rate of adsorption of dispersing agent) final particle size distribution and morphology

Veiled: 蓋面紗的 , 遮蔽的

Crystal Habit

....)2()2()1()1( // constAA LSLS

Equilibrium shape versus growth shape Former: surface energy of each surface Latter: relative growth of each surface,

depending on growth environment Equilibrium shape: ( Wulff theorem: following

equation) large surface energy, small surface area, I.e. easy to disappear

equilibrium shape;

Elimination of high energy surface via growth

Different morphology: obtained under different supersaturation (AgBr);

From octahedron (only 111 surface), gradually change to tetradecahedron (showing 100 surface), finally to cubic (with only 100 surfaces)

Taken from TA Ring, 1996; by adsorbing impurity species to control morphology

Ostwald Ripening

Che5700 陶瓷粉末處理

]1)/[exp()( raCCrCs

RTVa M /2

An aging process, often cause coarsening of large particles at the expense of small ones

Driving force: difference between solubility between sizes (thermodynamically-driven); Gibbs-Thompson equation; also influenced by mass transfer and growth kinetics

(from Wikipedia)

* Ostwald ripening (often water-in-oil system) vs flocculation (oil-in-water system)* Diffusion is often rate controlling process

Oil droplet in pastis mixed with water grow by Ostwald ripening

Taken from 游佩青博士論文稿 ( 成大資源工程系 ; p.16; 2008)* Maximum growth rate size ~ 2 x average size (where growth rate = zero)a3 – ao

3 = [6 D co γM/(ρ2RT)] (t – to) where a = average size, D = diffusion coefficient; co = solubility at interface; γ=interfacial energy;

Digestive Ripening

Source: Langmuir, 2002, 18, 7515-7520 * Transform polydispersed particle to monodispersed Au colloids after ageing in the presence of dispersive agents

* These monodispersed colloids may be stable only at high temperature, will form ordered precipitate when temperature cools down;

Taken from: New Journal of Chemistry, 35, 755-763, 2011•Possible mechanism: dispersion molecule (surfactant) may penetrate large colloids to adsorb on the surface and to create small colloids; • When the chain length of dispersion molecule decrease, the attractive force between two particle will increase and tend to form precipitate (self-assemble into 3D super-lattice – look like reversible crystallization);