Some Examples
Manganese
zinc ferrite
Che5700 陶瓷粉末處理
Liquid Phase Synthesis
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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 (?)
Che5700 陶瓷粉末處理
Process Introduction
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Precursor in solvent (aqueous or organic)  one or
several precursors  chemical reaction (additive,
temp., etc.)  separation from solvent  postprocessing (washing, drying, etc.)  product powder
Precipitation method: co-precipitation, homogeneous
precipitation, emulsion precipitation, hydrothermal
precipitation, hydrolytic precipitation (referring to solgel, 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 NH4F
Complex 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.
reaction
* Taken from JS Reed; precipitation occurs when two
chemical reacting with each other, formation of particles –
described by the theory of nucleation and growth
Che5700 陶瓷粉末處理
Expression of supersaturation
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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
 

(  i   i ) &  i   i  RT ln a i
eq
i
o
a i   i xi & xi   i x
    {1  ln(   /   ) / ln( x / x )} RT ln( 1   x )
eq
eq
Che5700 陶瓷粉末處理
Electrolytic Solutions
• 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□) νwhere 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 zi2 Mi (over all ions);
α: parameter of system = f(T, solvent) (find it out in
handbooks for common solvents)
=RT ln;  = (i/Ksp)
 = i
Ksp: ionic product at equilibrium; i = current
ionic product; ratio of these two values ~
supersaturation
1/;
Solubility
 Thermodynamic data: mainly affected by
temperature, and solution environment (e.g. other
ions, pH,…)
 G  (  2   1 )   RT ln(
S 
C
Co

a
ao
a
ao
)
Solubility (2)
Temp. & pH effect: DCP =
dicalcium phosphate; HAP =
hydroxyapatite;
System of: Ca(OH)2-H3PO4 –
KOH – HNO3 – CO2 – H2O;
Ca/P = 1
A
2

 2 B  AB 2 ( s )
K sp  [ A
S  [A
2
2

]o [ B ]

2
2
o
][ B ] / K sp
• 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”)
Che5700 陶瓷粉末處理
Nucleation
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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=
Che5700 陶瓷粉末處理
Kinetic Expression of Nucleation
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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)
df i / dt  C i 1 f i 1  E i f i  C i f i  E i 1 f i 1  I ( i  1, t )  I ( i.t )
I   ao P /
2 mkT ( a o  / 9 kT )
1/ 2
I   Z ( i *) C ( i *) n ( i *)
exp(  4 a o  / 27 k T (ln P / Pe ) )
3
3
3
3
Zeldovich factor
2
Che5700 陶瓷粉末處理
Solute Clustering & Nucleation
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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
Che5700 陶瓷粉末處理
Heterogeneous Nucleation
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
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Complex ions
can increase size
of cluster, closer
to critical
nucleus size,
helpful to
nucleation;
Impurity also
influence
structure (phase)
of product
Che5700 陶瓷粉末處理
More on Nucleation
Taken from
TA Ring,
1996; data
for BaSO4
Che5700 陶瓷粉末處理
Secondary Nucleation
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 MTj (rpm)h; where MT = quantity of
suspending particles
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A Model on Secondary Nucleation
Taken from Botsaris, et. al. Chem. Eng. Sci., 52(20), 34293440, 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 bigger
Theory of rapid coagulation: - dn/dt = 8D 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
Che5700 陶瓷粉末處理
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
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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
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Crystal growth: mass transfer, heat transfer can not be
neglected; species entering structure, may also the rate
determining step
Relation between size and solubility: OstwaldFreundlich 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
ln( X / X eq )  2 M   / 3 LRT
•Growth steps:
•Diffusion to surface; Adsorption; Desolvation;
(dehydration); Surface diffusion; Integration at kink site
•terminology: ledge, step and kink
F = surface energy
xL/ xeq = a
measure
of supersaturation
It shows small size, large solubility; for low surface energy,
size effect less significant (see Kelvin equation)
Che5700 陶瓷粉末處理
Growth Rates
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
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Can be
classified as:
linear, parabolic,
and
exponential law
(growth rate
and
supersaturation)
Che5700 陶瓷粉末處理
More on Growth Rates
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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
(  H / M ) G  C  h i (T i  T )
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
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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
 S / L (1) A (1)   S / L ( 2 ) A ( 2 )  ...  const .
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
Che5700 陶瓷粉末處理
Ostwald Ripening
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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
C s ( r )  C   C  [exp( a / r )  1]
a  2 V M /  RT
(from Wikipedia)
* Ostwald ripening (often water-inoil system) vs flocculation (oil-inwater 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 – ao3 = [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 superlattice – look like reversible crystallization);