1
Naica Cave, Mexico
5 My, 50 C
CaSO4·2H2O
1.2 × 15 m
2
High temperature methods
Czochralski
Stockbarger and Bridgman
Verneuil
Zone melting
Medium temperature methods
Fluxes, Ionic Liquids
Electrochemical from melts
Hydrothermal
Vapor phase transfer
Sublimation
Low temperature methods
Solution
Gel
Growth of Single Crystals
3
Many different crystal growing techniques exist, hence one must
think very carefully as to which method is the most appropriate for
the material under consideration, size of crystal desired, stability in
air, morphology or crystal habit required
Growth of Single Crystals
Crystallization techniques: vapor, liquid, solid phase
Single crystals
vital for meaningful property measurements of materials
allow measurement of anisotropic phenomena (electrical, optical, magnetic,
mechanical, thermal) in anisotropic crystals (symmetry lower than cubic)
 fabrication of devices
Y3Al5O12 (YAG = yttrium aluminum garnet) and beta-beryllium borate (BBO) for
doubling and tripling the frequency of CW or pulsed laser light
SiO2 (quartz) crystal oscillators for mass monitors
lithium niobate for photorefractive applications
4
Thermodynamics and Kinetics of Crystallization
As a material cools off the average kinetic energy drops
Boltzman
Distribution
T1 > T2
5
Stages of Crystallization
• Nucleation – formation of nuclei of critical size
• Growth – diffusion of material toward the critical nuclei, depositon
vs. dissolution, crystal growth
6
Formation of Nuclei
Molecules are always bumping into each other – sometimes they stick
At lower kinetic energies more molecules stick together = form nuclei
Cooling
Addition of monomer
7
Transformation from Liquid to Solid
VOLUME
The energy of a crystalline phase is less than that of a liquid
The difference = the volume free energy Gv (a negative value)
As the solid grows in size, the magnitude of the total volume free energy
increases
The volume free energy Gv drives crystallization
SURFACE
When solids form in a liquid there is an interface created
The surface free energy, SL = the solid/liquid interfacial energy associated
with this interface (changed in different solvents)
As the solid grows, the total surface free energy increases (a positive value)
The surface free energy hinders crystallization
8
Thermodynamics of Nucleation
The driving force = the supersaturated solution is not stable in energy.
The total change in free energy for the nucleating system is the sum of the two factors.
For spherical nuclei
GT = 4/3 r 3Gv + r 2 SL
The volume free energy goes up with the cube of the radius
The surface free energy goes up with the square of the radius
GT has a maximum at a critical radius – critical free energy GN
If just a few molecules stick together, they will redissolve
If enough molecules stick together, the embryo will grow
9
r: radius of spherical nuclei
r*: critical radius
(r>r* seed grows by itself)
GT: total free energy change
Gs: surface free energy change
Gv: volume free energy change
GN: critical free energy change
(activation energy to nucleation)
GT = 4r2SL + 4/3r3GV
Nucleation
G
GN
10
Volume Free Energy
m
V
V
SRT
G
ln

ΔGV – the free energy change between the ‘monomer’ in solution and in
a unit volume of bulk crystal
S – supersaturation = the quotient of the actual concentration [M] and
the concentration of the respective species at equilibrium with the
flat crystal surface [M], indicates how far away from equilibrium
the system is:
Vm – molar volume of the monomer composing the bulk crystal
 
 

M
M
S
11
Total Free Energy of a Solid-Liquid System
Surface Energy
Volume Energy
Critical Radius
rc 4/3 r 3Gv
r2 SL
G

 2
3
4
3
ln4
r
V
SRTr
G
m
T 
12
Supersaturated Solutions
If the liquid is just at the freezing point, only a few molecules stick, because
they have comparatively high energy.
As the liquid is cooled, more molecules can form into nuclei.
When the nucleus is big enough (because of undercooling) the supercooled
liquid suddenly changes to a solid.
13
Nucleation - Critical Radius rc
rc critical nuclei radius is:
S = supersaturation SRT
V
G
r mSL
V
SL
c
ln
22 



At larger supersaturation, the critical radius of nuclei is smaller

 2
3
4
3
ln4
r
V
SRTr
G
m
T  0
)(


dr
Gd T
14
Nucleation - Critical Free Energy GN
 2
23
ln3
16
SRT
V
G mSL
N

 The free energy necessary to form stable nuclei
Thermodynamic barrier to nucleation
15
Rate of Nucleation
ΔGN – the free energy barrier to nucleation
S – supersaturation
Vm – molar volume of the bulk crystal
Arrhenius
 
  










 
 2233
23
ln3
16
expexp
SNTk
V
A
kT
G
A
dt
Nd
A
mSLN 
16
Homogeneous Nucleation
The process of solid formation from liquid phase = homogeneous nucleation
It only occurs if the material is very pure
The size of the critical radius is:
T is the undercooling
Metals often experience undercooling of 50 to 500 ºC
TH
T
r
f
mSL


2*
17
La Mer Plot
Burst nucleation - many nuclei generated at the same time, then the nuclei grow
without additional nucleation, all of the particles nucleate simultaneously, their
growth histories are the same.
Control of the size distribution of the ensemble of particles during growth synthesis
of monodisperse nanocrystals
18
The concentration of “monomer”, (the minimum subunit of bulk crystal) constantly
increases with time.
Stage I precipitation does not occur even under supersaturated conditions
(S > 1), the energy barrier for spontaneous homogeneous nucleation is too high.
Stage II nucleation occurs, the degree of supersaturation is high enough to overcome the
energy barrier for nucleation, the formation and accumulation of stable nuclei. The rate
of monomer consumption exceeds the rate of monomer supply, the monomer
concentration decreases until it reaches the level at which the nucleation rate is zero.
Stage III the growth stage, nucleation stopped, the particles keep growing as long as the
solution is supersaturated
19
Growth
Growth by diffusion
the growth rate of spherical particles (dr/dt)
depends only on the flux of the monomers to the particles (J)
dt
dr
V
r
J
m
2
4

dx
dC
DxJ 2
4
  sCC
rr
DJ 

 


4
 
 
 C
C
r
r s
dC
J
D
x
dx 4
2
20
Heterogeneous Nucleation
Homogeneous nucleation usually only occurs under very clean
conditions
Impurities provide a “seed” for nucleation
Solidification can start on a wall
It’s like cloud seeding, or water condensing on the side of a glass
Adding impurities on purpose = inoculation
21
Growth and Solidification - Grain Size
Solidification caused by homogeneous nucleation occurs suddenly, and only produces a
few grains
In heterogeneous nucleation, solidification occurs on many “seeds”, so the grains are
smaller, and more uniform
If a melt is cooled slowly, and the temperature is the same throughout, solidification
occurs with equal probability everywhere in the melt.
Metals are usually cooled from the container walls – so solidification starts on the walls
22
Nucleation vs. Crystal Growth
(solution or melt)
Undercooling – cooling below the melting point
relations between undercooling, nucleation rate and growth rate of the nuclei
large undercooling: many small nuclei
(spontaneous nucleation)
growth rate small
small undercooling: few (evtl. small) nuclei
growth rate high
23
Nucleation vs. Crystal Growth
Rate of nucleation
Rate of growth
Ta = small undercooling, slow cooling
rate
Fast growth, slow nucleation = Few
coarse crystals
Tb = larger undercooling, rapid
cooling rate
Rapid nucleation, slow growth =
many fine-grained crystals
Tc = very rapid cooling
Nearly no nucleation = glass
24
Heat of Fusion
When the liquid solidifies, energy must be removed.
In planar growth the energy is conducted into the solid and out through the walls of the
container
If the melt is not well inoculated
Solidification starts on the walls
The surrounding liquid is supercooled, so the solid quickly grows
All heat that is evolved is hard to conduct away
Some of it is absorbed by the surrounding liquid which then heats up
25
CZOCHRALSKI or KYROPOULOS METHOD
Jan Czochralski
(1885 – 1953)
Growth of Single Crystals
1917
Crystal pulling technique
Single crystal growth from the melt precursor(s)
Crystal seed placed in contact with surface of melt
Temperature of melt held just above melting point =
highest viscosity, lowest vapor pressure
Seed gradually pulled out of the melt, 1 mm per hour
Melt solidifies on surface of seed
Melt and seed usually rotated counterclockwise with
respect to each other to maintain constant temperature
and to facilitate uniformity of the melt during crystal
growth, 10 rpm
Produces higher quality crystals, less defects
Inert atmosphere, often under pressure around growing
crystal and melt to prevent any materials loss
26
CZOCHRALSKI or KYROPOULOS METHOD
Growth of Single Crystals
27
Diam 300 mm
Length 2 m
Weight 265 kg
28
Growing bimetallic crystals like GaAs
Layer of molten inert oxide like B2O3 spread on to the molten feed
material to prevent preferential volatilization of the more volatile
component of the bimetal
critical for maintaining precise stoichiometry
for example Ga1+xAs and GaAs1+x which are respectively rich in Ga
and As, become p-doped and n-doped
Growth of Single Crystals
29
The Czochralski crystal pulling technique for growing large single
crystals in the form of a rod
subsequently cut and polished for various applications
Si
Ge
GaAs
LiNbO3
SrTiO3
NdCa(NbO3)2
Growth of Single Crystals
30
Six steps in the CZ growth of a silicon
single crystal:
a) Evacuation and heating of the
polycrystalline silicon (“pumping”)
b) Setting the temperature of the Si melt
just above 1414 ºC (“melting”)
c) Dipping the thin Si seed crystal into
the homogeneous Si melt (“dipping”)
d) Initiating crystallization at the neck
of the thin Si seed (“necking”)
e) Adjustment of the shoulder of the
desired single crystal diameter
(“shoulder”; four positions which
portray the fourfold drawing axis [100]
are visible at the hot, light marginal
zone of the single crystal)
f) Growing phase of the single crystal
with constant diameter (“body”).
31
STOCKBARGER AND BRIDGMAN METHODS
Stockbarger method is based on a crystal growing from the melt,
involves the relative displacement of melt and a temperature
gradient furnace, fixed gradient and a moving melt/crystal
Growth of Single Crystals
32
Bridgman method is again based on crystal growth from a melt, but
now a temperature gradient furnace is gradually cooled and
crystallization begins at the cooler end, fixed crystal and changing
temperature gradient
STOCKBARGER AND BRIDGMAN METHODS
Growth of Single Crystals
33
Both methods are founded on the controlled solidification of a
stoichiometric melt of the material to be crystallized
Enables oriented solidification
Melt passes through a temperature gradient
Crystallization occurs at the cooler end
Both methods benefit from seed crystals and controlled atmospheres
(sealed containers)
Mylar0.5-1.5-189Ar (!)
Pyrex1-5434AgBr
graphite6-601083Cu
Ir5-101790FeAl2O4
Mo2-8 mm h-12037Al2O3
container materialvelocity of
grad.
mp (oC)crystal
34
Zone Melting
Purification of solids
Crystal growth
Thermal profile furnace, RF, arc, electron beam heating
Material contained in a boat (must be inert to the melt)
Only a small region of the charge is melted at any one time
Initially part of the melt is in contact with the seed
Boat containing sample pulled at a controlled velocity
through the thermal profile furnace - zone of material melted
Oriented solidification of crystal occurs on the seed
35
Zone Melting
Zone refining methods for
purifying solids
Partitioning of impurities occurs
between melt and the crystal
Impurities concentrate in liquid
more than the solid phase, swept
out of crystal by moving the liquid
zone
Used for purifying materials like
W, Si, Ge to ppb level of
impurities, often required for
device applications
36
- a small slice of the sample is molten and moved
continuously along the sample
- impurities normally dissolve preferably in the melt
(!! icebergs in salt water don‘t
contain any salt !!)
- segregation coefficient k:
k = csolid/cliquid
(c: concentration of an impurity)
only impurities with k < 1 can be removed by zone melting !!
Zone Melting
37
Zone Melting
38
FLOATING ZONE METHOD
Molten zone is confined by surface tension between a polycrystalline
ingot and a single-crystal seed
Zone Melting
Verneuil Fusion Flame Method
39
1902 - French chemist Auguste Verneuil
the first commercially successful method of manufacturing synthetic
gemstones - ruby, sapphire, diamond simulants rutile and strontium
titanate
Verneuil Fusion Flame Method
40
Useful for growing crystals
of extremely high melting metal oxides
Examples include:
Ruby from Cr3+
/Al2O3 powder
Sapphire from Cr2
6+
/Al2O3 powder
Spinel, CoO, ferrites
Starting material fine powder
Passed through O2/H2 flame or plasma torch
Melting of the powder occurs in the flame
Molten droplets fall onto the surface of a seed or growing crystal
Controlled crystal growth
Lowered 10 mm/hour
41
THE FLUX METHOD
Material dissolved in a suitable flux = solvent (metals, fluorides,
oxides), lower melting point than the pure solute
Single crystals grown from supersaturated solution
Suitable for materials which:
 vaporize or dissociate at temperatures above their mp
 there are no suitable containers at elevated temperatures
Material Flux
As Ga
B Pt
Si, Ge Pb, Zn, Sn
GaAs, GaP Pb, Zn, Sn
BaTiO3 KF
ZnO PbF2
ZnS SnF2
MgFe2O4 NaF
Co3O4 B2O3 – PbO
Fe2O3 Na2B4O7
TiO2 Na2B4O7 – B2O3
42
THE FLUX METHOD
AlF3
2.0 g of AlF3, 25.0 g of PbCl2, 2.5 g PbF2
24 h at 1200 K, cooled at 4 deg h1 down to 723 K
thick platelets and small cubes
43
THE SOLUTION METHOD
Suitable for materials with a reasonable solubility in the selected
solvent: water, organic solvents, NH3(l) , HF, SO2(l)
Nucleation homogeneous
heterogeneous
Dilute solution, solvent with low solubility for given solute
Supersaturated solution, seed crystals
Single crystals grown at constant supersaturation
Techniques:
 slow evaporation
 slow cooling
 vapor diffusion
 solvent diffusion
 reactant diffusion
 recirculation, thermal differential, convection
 cocrystallants (OPPh3 for organic proton donors)
 counterion, similar size of cation and anion least soluble
 ionization of neutral compounds, protonation/deprotonation,
hydrogen bonding
Rochelle salt: d-NaKC4H4O6.4H2O (tartrate)
KDP
alum
44
KDP crystals (KH2PO4)
grown from supersaturated solution
crystal seed
slow cooling
a frequency converter converts
the infrared light at
1053 nm into the ultraviolet at
351 nm
Hydrothermal Synthesis
45
1957 - Bell Labs
Water medium
High temperature growth, above normal boiling point
Water acts as a pressure transmitting agent
Water functions as solubilizing phase
Often a mineralizing agent is added to assist with the
transport of reactants and crystal growth
Speeds up chemical reactions between solids
Crystal growth hydrothermally involves:
Temperature gradient reactor = autoclave (a bomb !!)
Dissolution of reactants at one end
Transport with help of mineralizer to seed at the other
end
Crystallization at the other end
Hydrothermal Synthesis
46
Useful technique for the synthesis and crystal growth of phases that
are unstable in a high temperature preparation in the absence of
water
materials with low solubility in water below 100 o
C
Some materials have negative solubility coefficients,
crystals can grow at the hotter end in a temperature gradient
hyrdothermal reactor
Example: -AlPO4 (Berlinite) important for its high piezoelectric
coefficient (larger than -quartz with which it is isoelectronic) used
as a high frequency oscillator
Hydrothermal growth of quartz crystals
Water medium, nutrients 400 o
C, seed 360 o
C, pressure 1.7 kbar
Mineralizer 1M NaOH
Uses of single crystal quartz: Radar, sonar, piezoelectric
transducers, monochromators, XRD
Annual global production hundreds of tons of quartz crystals
Hydrothermal Synthesis
47
Hydrothermal crystal growth is also suitable for growing single
crystals of:
Ruby: Cr3+
/Al2O3
Corundum: -Al2O3
Sapphire: Cr2
6+
/Al2O3
Emerald: Cr3+
/Be3Al2Si6O18
Berlinite: -AlPO4
Metals: Au, Ag, Pt, Co, Ni, Tl, As
Role of the mineralizer:
Control of crystal growth rate:
choice of mineralizer, temperature and pressure
Solubility of quartz in water is important
48
HYDROTHERMAL SYNTHESIS
SiO2 + 2H2O Si(OH)4
0.3 wt% even at supercritical temperatures >374 o
C
A mineralizer is a complexing agent (not too stable) for the
reactants/precursors that need to be solublized (not too much) and
transported to the growing crystal
Some mineralizing reactions:
NaOH mineralizer, dissolving reaction, 1.3-2.0 kbar
3SiO2 + 6OH
Si3O9
6+
3H2O
Na2CO3 mineralizer, dissolving reaction, 0.7-1.3 kbar
SiO2 + 2OH
SiO3
2+
H2O
CO3
2+
H2O  HCO3
+
OHNaOH
creates growth rates about 2x greater than with Na2CO3
because of different concentrations of hydroxide mineralizer
49
HYDROTHERMAL SYNTHESIS
Examples of hydrothermal crystal growth and mineralizers
Berlinite -AlPO4
Powdered AlPO4 cool end of reactor
negative solubility coefficient!!!
H3PO4/H2O mineralizer, AlPO4 seed crystal at hot end
Emeralds Cr3+
/Be3Al2Si6O18
SiO2 powder at hot end 600 o
C, NH4Cl or HCl/H2O mineralizer, 0.7-
1.4 kbar, cool central region for seed, 500 o
C, Al2O3/BeO/Cr3+
dopant powder mixture at other hot end 600 o
C
6SiO2 + Al2O3 + 3BeO  Be3Al2Si6O18
Beryl contains Si6O18
12six
rings
50
HYDROTHERMAL SYNTHESIS
Metal crystals
Metal powder at cool end 480 o
C, Mineralizer 10M HI/I2
Metal seed at hot end 500 o
C.
Dissolving reaction that also transports Au to the seed crystal:
Au + 3/2I2 + I
AuI4
Metal
crystals grown this way include Au, Ag, Pt, Co, Ni, Tl, As at
480-500 o
C
Diamonds
Ni + C + H2O diamond
800 C, 140 MPa
51
Carbon films on SiC fibers
SiC + 2 H2O C + 2 H2 + SiO2
Zeolites
Al(OH)3, SiO2, NaOH, template
Mx/n [(AlO2)x(SiO2)y]. mH2O
100 MPa
300-600C
HYDROTHERMAL SYNTHESIS
52
HYDROTHERMAL SYNTHESIS
necessitates knowledge of what is going on in an autoclave under
different degrees of filling and temperature
Pressure, volume, temperature tables of dense fluids like water
Critical point of water: 374.2 o
C, 218.3 bar
Density of liquid water decreases with T
Density of water vapor increases with T
Density of gas and liquid water the same 0.32 gcm-3
, at the critical
point
Liquid level in autoclave rises for > 32% volume filling
Autoclave filled at 250 o
C for > 32% volume filling
For 32% volume filling liquid level remains unchanged and becomes
fluid at critical temperature
53
HYDROTHERMAL SYNTHESIS
54
HYDROTHERMAL SYNTHESIS
Tables of pressure versus temperature for different initial volume
filling of autoclave must be consulted to establish a particular set of
reaction conditions for a hydrothermal synthesis or crystallization
Safety: if this is not done correctly, with proper protection
equipment in place, you can have an autoclave explosion that can
kill!!!
55
BULK-MATERIAL DISSOLUTION TECHNIQUE
large zeolite crystals: up to 3 mm, SOD, MFI, ANA,CAN, JBW
autoclave, PTFE liner
quartz tube (SiO2) TPAOH, HF, H2O 200 C, 25-50 days
ceramic tube (SiO2, Al2O3) NaOH, H2O 100-200 C, 7-20 days
Small surface area, low dissolution rate, saturation concentration
maintained, only a few nuclei are produced at the beginning, no large
crystals formed in the stirred reactions, concentration gradients
56
DECOMPLEXATION CRYSTALLIZATION
crystallization under ambient conditions, low temperature and
pressure, provides kinetic products, control of crystal size and
morphology, habit
AgX, X = Cl, Br, I
MX, M = H, Na, K, NH4
AgI + HI H+
+ [AgI2]aqueous
solution
overlayer absolute ethanol, HI diffusion, decomplexation of AgI,
hexagonal plates 5 mm
AgX + 2 NH3 [Ag(NH3)2]+
+ XX
= Cl, Br, slow evaporation (3-5 days), AgX crystals
57
AgI + KI K+
+ [AgI2]
concentration gives K[AgI2] crystals
 dilution by slow diffusion gives 20 mm AgI crystals
 warming gives AgI crystals (inverse temperature
dependence of AgI solubility in KI)
CuCl + HCl H+
+ [CuCl2]-
CuCl
HgI2 + KI [HgI3]-
[HgI4]2-
HgI2
PbO + hot KOH solution, slow cooling provides PbO
as 2 mm yellow needles and 1 mm red blocks
58
COMPLEXATION-MEDIATED CRYSTALLIZATION
Salts with high lattice energy
fluorides, carbonates, acetates
Solubilized in organic solvents by crown ethers
Crystallization provides uncomplexed salts
NaOOCCH3.3H2O dissolves in cyclohexane with 15-crown-5
prismatic crystals
59
COMPLEXATION-MEDIATED REACTION CRYSTALLIZATION
Two soluble salts react to produce an insoluble phase
 aqueous solutions
 nonaqueous solvents
CaCO3 calcite TD stable phase at room temp., in H2O
vaterite kinetic product
aragonite TD stable at high temperature
CaCl2 (in MeOH) + NaHCO3 (in MeOH, 18-crown-6)
microcrystalline calcite
upon aging converts to nanocrystalline vaterite, surface stabilization by
surface chelatation
60
THE GEL METHOD
Large single crystals
 hydrogels: silicagel (water glass), polyvinyl alcohol, gelatin, agar
Silicate gel
Impregnation with metal or ligand, setting the gel = condensation,
crosslinking, pH control of the condensation rate
Layered with the solution of ligand or metal
Slow diffusion, xtal growth
CuSO4 + [NH3OH]Cl Cu
Pb(OAc)2 + Zn Pb + Zn(OAc)2
Pb(OAc)2 + KI PbI2 + 2 KOAc
Liesegang rings, agates
RbSnBr3, CsSb2I5 semiconductors
61
THE GEL METHOD
 nonaqueous gels
PEO (MW = 100 000) in 1,2-dichloroethane + MeOH, EtOH, PrOH,
DMF, CH3CN, DMSO
Impregnation with metal or ligand
Layered with the solution of ligand or metal
Slow diffusion, crystal growth
U-tube, counter-diffusion
Concentration programming, increasing concentrations
Ostwald rippening = larger xtals grow, smaller dissolve
62
ELECTROCHEMICAL REDUCTIVE SYNTHESIS, CRYSTAL
GROWTH
Molten mixtures of precursors, product crystallizes from melt
Melt electrochemistry: Electrochemical reduction
CaTi(IV)O3 (perovskite)/CaCl2 (850 o
C)  CaTi(III)2O4 (spinel)
Na2Mo(VI)O4/Mo(VI)O3 (675 o
C)  Mo(IV)O2 (large crystals)
Li2B4O7/LiF/Ta(V)2O5 (950 o
C)  Ta(II)B2
Na2B4O7/NaF/V(V)2O5/Fe(III)2O3 (850 o
C)  Fe(II)V(III)2O4
(spinel)
Na2CrO4/Na2SiF6 (T o
C)  Cr3Si
Na2Ge2O5/NaF/NiO  Ni2Ge
63
ELECTROCHEMICAL REDUCTIVE SYNTHESIS, CRYSTAL
GROWTH
Phosphates  phosphides
Carbonates  carbides
Borates  borides
Sulfates  sulfides
Silicates  silicides
Germanates  germides
64
Synthesis of amorphous materials
Quenching of molten mixture of metal oxide with a glass former
(P2O5, V2O5, Bi2O3, SiO2, CaO, …), large cooling rates required (>107 K s1)
Ion beam sputtering
Thermal evaporation
Thermal decomposition of organometallic precursors (Fe(CO)5, …)
Cr2O3, MnO2, PbO2, V2O5, Fe2O3
Sonochemical decomposition of organometallic precursors
(Fe(CO)5, M(acac)n,…
Precipitation on metal hydroxides, transformation to hydrous oxides
MW heating of metal salt solution
Cr2O3, Fe2O3