Download Lecture 4 (version 2016-03-21)

Lecture 4: Synthesis of solid state
materials. Phase diagrams
Figure: West
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Phase diagrams
– Phase rule
– Basic phase diagrams for one- and
two-component systems
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Synthesis of solid state materials
– Shake ’n bake / heat ’n beat
– Low temperature
– Gas gas phase
– Crystal growth
Figure: Kraft
Figure: http://lulelaboratory.blogspot.fi/
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Some definitions
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Phase is a physically separable part of a system with distinct physical and chemical
properties.
A system consists of one or more phases
For example, NaCl-H2O system:
– If all of the salt is dissolved: one phase (salt solution).
– If all salt is not dissolved: 2 phases, solid NaCl and solution.
– If system is heated under sealed conditions: 3 phases (solid + solution + gas)
Each phase in the system is composed of one or more components. The number of
components is the minimum number of constituents needed in order to describe
completely the compositions of the phases present
– The NaCl-H2O system has two components NaCl an H2O (binary system)
– All other combinations can be described with these formula.
Pure water would be an unary (one-component) system
Three components -> ternary system; four components -> quaternary system
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Gibbs Phase Rule
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Applies to non-reactive multi-component heterogeneous systems in
thermodynamic equilibrium
– Pressure p and temperature T are constant in the system
– The chemical potentials of the components are the same in each phase
F=C–P+2
– P is the number of phases present in equilibrium
– C is the number of components needed to describe the system
– F is the number of degrees of freedom or independent variables taken from
temperature, pressure, and composition of the phases present
In many cases, pressure is constant and the condensed phase rule is used:
– F=C–P+1
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Phase rule in practice
1. A solid solution in the system Al2O3–Cr2O3 (C = 2) has one composition variable
because the Al2O3:Cr2O3 ratio can be varied
– If a sample has x% of Al2O3, then the Cr2O3 content is fixed as (100 – x)%
– The temperature of the single-phase solid solution can also be varied
– F = C – P + 1 = 2 – 1 + 1 = 2 (Al2O3:Cr2O3 ratio and T)
– If pressure is taken into account, F = 3
2. A partially melted solid (e.g. ice) in a one-component system (e.g. H2O), in
equilibrium at its melting point (ignoring pressure)
– F=C–P+1=1–2+1=0
– If the temperature changes, the number of phases must change
3. Boiling water = H2O (l) and H2O (g) in equilibrium (C = 1)
– F=C–P+2=1–2+2=1
– Boiling point depends on vapour pressure and there is only one degree of
freedom
– For example, Mount Everest: 8848 m; p = 34 kPa -> boiling point of H2O=71 °C
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Equilibrium
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In using phase diagrams, it is important to understand what is meant by
equilibrium
The equilibrium state is always that which has the lowest Gibbs free energy G
– Other free energy minima may exist but not be as deep as the equilibrium well
– If there is a considerable energy barrier involved in moving from a metastable
state to the stable state, the reaction product may stay in its metastable state
A good example of a thermodynamically metastable but kinetically stable state is
the metastability of diamond (C) relative to graphite (C) at room temperature
Important point: phase diagrams give no information concerning kinetics of
reactions or transformations!
G
Ref: West p. 329
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One-component systems (1)
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The composition is fixed at C = 1 and the independent variables are T and p
– F = C – P + 2 <=> F + P = 3
– The system is bivariant (F = 2) if one phase is present, univariant (F = 1) if two
are present and invariant (F = 0) if three are present
In the schematic example below, the possible phases are two crystalline
polymorphs (X and Y), liquid, and gas
Each phase occupies an area or field on the diagram since F = 2 when P = 1 (both p
and T are needed to describe a point in one of these fields
Ref: West p. 331
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One-component systems (2)
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Each single-phase region is separated from neighboring single-phase regions by
univariant curves (P = 2 and F = 1): If p is fixed then T is fixed and vice versa
The univariant curves on the diagram represent the following equilibria:
– BE – transition temperature between polymorphs X and Y; it gives the change
of transition temperature with pressure
– FC – change of melting point of polymorph Y with pressure
– AB, BC – sublimation curves for X and Y, respectively
– CD – change of boiling point of liquid with pressure
On heating, X can either sublime at a pressure
below P1 or transform to polymorph Y at
pressures above. It cannot melt directly.
Two invariant points B and C for which P = 3 and
F = 0 are also called triple points.
Ref: West p. 331
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H 2O
Figure: Wikipedia
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SiO2
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Silica is the main component of many ceramic materials in addition to being the
most common oxide in the Earth’s crust
Complex polymorphism at atmospheric pressure:
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With increasing pressure, the polymorphs with higher density are favored
Ref: West p. 332
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Binary eutectic system (1)
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Binary systems (C = 2) have 3 independent variables: p, T and composition
Let’s consider condensed phases (ignoring pressure): F = C – P + 1 = 3 – P
– Invariant point (F = 0) occurs when three phases coexist, a univariant curve for
two phases and a bivariant condition for one phase
Conventionally, temperature is the vertical axis and composition is the horizontal
axis in binary phase diagrams
The simplest two-component condensed system is the eutectic system below
– Occurs whenever two non-interacting solids, A and B, that can melt without
decomposition, are mixed
– No compounds or solid solutions are formed but the mixtures melt at lower
temperatures than either pure solid
Ref: West p. 334
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Binary eutectic system (2)
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The liquidus curve (xyz) gives the highest temperatures at which crystals can exist
– Shows the effect of soluble impurities on the melting points of pure compounds
– Familiar practical example: In the binary system H2O–NaCl, addition of NaCl
lowers the melting point of ice as the system contains an eutectic at –21°C.
The solidus curve (cyd) gives the lowest temperatures at which liquids can exist
Point y is an invariant point at which three phases, A, B and liquid, coexist
– F=C–P+1=2–3+1=0
– Called the eutectic point
– The lowest temperature at which a composition can be completely liquid
Ref: West p. 334
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Binary system with a compound (1)
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A stoichiometric binary compound such as AB is represented by a vertical line. This
shows the range of temperatures over which it is stable
Compound AB melts congruently in Fig. 7.8(a) because it changes directly from
solid AB to liquid of the same composition at temperature T3.
– Important for understanding crystallization paths
In Fig. 7.8(c), compound AB melts incongruently at T2 to give a mixture of A and
liquid of composition x
Ref: West p. 338
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Binary system with a compound (2)
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Sometimes, compounds decompose before melting, as shown for AB in Fig. 7.9(a)
– In this case, compound AB has an upper limit of stability
– At temperature T1 it disproportionates into a mixture of A and B;
– At higher temperatures the system is simple eutectic in character
There are also systems containing compounds with a lower limit of stability
– Below a certain temperature, AB decomposes into a mixture of A and B
Ref: West p. 339
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Binary systems with solid solutions
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The simplest solid solution system is one that shows
complete miscibility in both solid and liquid states
The melting point of one end member, A, is depressed
by addition of the other end member, B
The liquidus and solidus are smooth curves which meet
only at the end-member compositions A and B
At low temperatures, a single-phase solid solution
exists and is bivariant (C = 2, P = 1, and F = C – P + 1 = 2)
At high temperatures, a single-phase liquid solution
exists and is similarly bivariant
At intermediate temperatures, a two-phase region of
solid solution + liquid exists
Ref: West p. 340
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Yttria-stabilized Zirconia (YSZ)
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Zirconia, ZrO2, is potentially a very useful ceramic material with a high melting
point of ∼2700 ◦C but on cooling it undergoes a series of phase transitions:
The tetragonal to monoclinic transition is associated with an increase in unit cell
volume by ∼9% -> ceramic bodies fabricated at high T shatter on cooling
The transitions can be avoided by creating a solid solution ZrO2–Y2O3
~15% Y2O3
Ref: West p. 355
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Fe-C phase diagram
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”The most important phase diagram in the history of civilization”(?)
For some hands-on exercises on phase diagrams, see:
http://www.southampton.ac.uk/~pasr1/index.htm
Figure + explanation: http://www.calphad.com/iron-carbon.html
Steel
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Ternary phase diagrams
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Ternary phase diagrams are much more complicated than binary diagrams
One reasonable visualization is to show the diagram just for one temperature
Resource for binary and ternary phase diagrams (requires subscription):
http://www1.asminternational.org/AsmEnterprise/APD/default.aspx
Figure: ASM Handbook of Alloy Phase Diagrams
Stainless steel phase diagram at 900°C (ASM 1-27)
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Synthesis of solid state materials
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The products are typically single crystals,
powders or thin films
Solid State Reaction / Shake ’n Bake Methods
Low Temperature / Soft Chemistry Methods
Gas-Phase methods
High-Pressure methods (Lecture 6)
Crystal Growth
Recipes? Journal papers!
Figure: Aalto University
Figure: Aalto University
Figure: http://lulelaboratory.blogspot.fi/
Figure: University of Warwick
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Shake ’n Bake methods
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The oldest, simplest and still most widely used method to make inorganic solids
– Mix together powdered reactants (and possibly press them into pellets)
– Heat in a furnace for prolonged periods
• Based on solid state reactions that are intrinsically slow
– Although the reactants may be well mixed at the level of individual particles
(e.g. μm scale), they are very inhomogeneous on the atomic level
• Solid state counter-diffusion of ions between different particles or liquid- or gasphase transport is necessary to bring together reactants
• Let’s consider a solid state reaction of MgO and Al2O3 powders to MgAl2O4 spinel
close-packed anions in all three
Al
O
O
Mg
Figures: AJK
MgO (Fm-3m)
Al2O3(R-3c)
MgAl2O4 (Fd-3m)
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MgAl2O4 spinel from MgO and Al2O3
Ref: West p. 188-189
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MgAl2O4 spinel from MgO and Al2O3
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Although the first few atomic layers of product nuclei may form easily, subsequent
growth or thickening of the product is more difficult because effectively,
– The two reactants, MgO and Al2O3, are no longer in contact but are separated
by a rather impenetrable spinel layer.
A complex counter-diffusion process is then required in which Mg2+ ions diffuse
away from, and Al3+ ions diffuse towards, the MgO/MgAl2O4 interface, and vice
versa for the MgAl2O4/Al2O3 interface
As reaction proceeds, the spinel layer thickens, the diffusion pathlength increases
and reaction slows (Mg2+ and Al3+ diffuse very slowly)
Heating for 1 week at 1500°C would be required to form a fairly pure spinel product
Ref: West p. 190
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Some practical considerations
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The problems associated with spinel synthesis are particularly difficult since both
reagents, MgO and Al2O3, are very stable, inert, non-reactive solids
Solid state reactions may be easier if one or more of the starting materials is
chemically reactive and/or contains ions that can diffuse easily
Other problems may arise, however, such as
– potential loss of reactants by evaporation (e.g. alkali metal oxides, Tl2O, PbO,
Bi2O3, HgO) or
– reactivity towards the container (e.g. transition metal-containing materials).
With attention to synthesis procedures, these problems can usually be avoided
There are four main issues for consideration in planning a solid state reaction:
– Choice of starting materials (purity / reactivity)
– Mixing method (high-energy ball milling may open up new possibilities mechanosynthesis)
– Container (Pt / Ta / Au / Al2O3 / SiO2 / graphite)
– Heat treatment conditions (temperature program)
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Few solid state reaction examples
Ref: West p. 193
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Low temperature methods (1)
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Low temperature methods to achieve atomic scale mixing of reactants, in gas,
liquid or even solid phases
– Final heating at high temperature may be needed, especially for ceramic
products
May enable higher purity products, especially if prolonged heating at high
temperature can be avoided (no contamination from container materials and
furnace atmosphere)
Products with high chemical homogeneity are usually obtained
– Often leads to improved properties or better understanding of the
dependence of properties on structure, composition and dopants
Disadvantages:
– Reagents are often costly and difficult to handle on a large scale
– Considerable research may be required to optimize the synthesis of a
particular material
– Once suitable conditions have been found, they may not be readily applicable
to the synthesis of related materials
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Low temperature methods (2)
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Sol–gel method
Use of homogeneous, single-source precursors
Hydrothermal and solvothermal synthesis
Microwave synthesis
Intercalation and deintercalation (Lecture 11)
Molten salt synthesis
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Alkoxide sol–gel method (1)
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The first stage is to prepare a homogeneous solution containing all the cationic
ingredients in the desired ratio
The solution is gradually dried and, depending on the species present, should
transform
– First to a viscous sol (particles of colloidal dimensions, ~1-1000 nm)
– Finally to a transparent, homogeneous, amorphous solid known as a gel
– Without precipitation of any crystalline phases
The gel is then heated at high temperatures to remove volatile components
trapped in the pores of the gel or chemically bonded hydroxyl and organic sidegroups and to crystallize the final product.
Organometallic precursors, particularly alkoxides, are widely used for the smallscale synthesis of known or new materials
– Alkoxide: R-O--M+ (e.g. CH3-O-Na+; Si(OCH2CH3)4 – source of SiO2)
The alkoxide-based sol–gel method is extremely versatile and can incorporate
most elements of the periodic table
Ref: West p. 196
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Alkoxide sol–gel method (2)
TEOS = Tetraethyl orthosilicate
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Use of homogeneous, singlesource precursors
A solid state analogue of the sol–gel method is to prepare a crystalline,
homogeneous, single-phase precursor material that contains all the required
cations in the correct ratio
This precursor should not be particularly stable and on heating decomposes to
give the desired product
Ba2+
Ref: West p. 201
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Hydrothermal and solvothermal
synthesis (1)
Hydrothermal synthesis involves heating reactants in water/steam
at high pressures and temperatures
The water has two functions pressure-transmitting medium and as
a solvent, in which the solubility of the reactants is (p,T)-dependent
The reactants and water are placed inside a PTFE-lined cylinder
(autoclave / ‘bomb’) which is either sealed or connected to an
external pressure control
The bomb is placed in an oven, usually at a temperature in the
range 100–500°C
A temperature gradient is maintained between the opposite ends
of the growth chamber
At the hotter end the nutrient solute dissolves, while at the cooler
end it is deposited on a seed crystal, growing the desired crystal
Solvothermal synthesis is similar to hydrothermal synthesis but uses
supercritical solvents or solvent mixtures
– Supercritical fluid: Distinct liquid and gas phases do not exist
– In water, the critical point occurs at around 374 °C and 22 MPa
Ref: West p. 202
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Hydrothermal and solvothermal
synthesis (2)
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Microwave synthesis
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Ref: West p. 204
The use of microwave heating is well established in organic chemistry and is
increasingly used in the inorganic synthesis, especially at the nanolevel
Reaction times are orders of magnitude less than required for solid state reaction
and side reactions are less problematic
– Improved yield and reproducibility
The microwave region covers the range 0.3 GHz (1 m)–300 GHz (1 mm), but most
ovens are restricted to the frequency 2.45 GHz
– Absorption at the range of molecular rotations -> increase in temperature
Microwaves are absorbed and the sample is heated, to a certain penetration depth
– Conventional heating, by contrast, requires in-diffusion of heat
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From elemental Li and Ge to novel
allotropes of germanium
Chemistry of Materials, 2011, 23, 4578–4586.
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Li7Ge12 precursor
Li7Ge12 precursor (P2/n)
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From Li7Ge12 to m-allo-Ge (1)
H2O / EtOH
Removal (deintercalation) of Li
Ge atoms with two, three
or four bonds
Li7Ge12 precursor (P2/n)
Oxidative coupling of the layers
m-allo-Ge
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From Li7Ge12 to m-allo-Ge (2)
Li7Ge12 precursor (P2/n)
m-allo-Ge
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From m-allo-Ge to 4H-Ge and α-Ge
140°C
400°C
α-Ge (Fd-3m)
m-allo-Ge
(stacking faulted)
4H-Ge (P63/mmc)
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Gas-Phase methods
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Chemical vapour deposition (CVD)
– Atomic Layer deposition (ALD)
Sputtering and evaporation
Aerosol synthesis and spray pyrolysis
Vapor-phase transport
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Chemical Vapor Deposition (1)
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Extremely important technique of making high-purity thin films and coatings for
– Industrial applications, especially in electronics,
– Fundamental scientific research
Precursor molecules containing the elements of interest are decomposed in the
gas phase and the products deposit as thin films.
Example of a simple, volatile precursor molecule:
– SiH4 -> Si (polycrystalline) + 2H2
To deposit compounds, e.g. GaAs, a mixture of precursors is needed
– An alternative is to use (organometallic) single-source precursors which
contain all the elements of interest and in the correct ratio
Figure: WIkipedia
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Chemical Vapor Deposition (2)
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Examples of CVD processes:
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New single-source precursors are
being continually developed for
metal-organic CVD (MOCVD) ->
Ref: West p. 217
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Atomic Layer Deposition (1)
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Atomic Layer Deposition (2)
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Atomic Layer Deposition (3)
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Based on sequential, self-limiting reactions
– Offers exceptional conformality on high
aspect ratio structures
– Thickness control at the Angstrom level
(usually ~10-100 nm thickness; max ~1 μm)
– Tunable film composition
Powerful tool for many industrial and research
applications
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Sputtering and evaporation
Pressure 10-1 .. 10-2 Torr of inert gas (e.g. Ar, Xe)
Sputtering involves the transfer of momentum
from the gaseous ions to the cathode in such a
way that atoms or ions are ejected (sputtered)
from the cathode to the substrate
Figure: Wikipedia
Vacuum evaporation method: High
vacuum of 10-6 Torr or better
Heating / electron bombardment
Physical Vapor
Deposition (PVD)
Ref: West p. 222
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Crystal Growth
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Crystals may be grown from vapor, liquid or solid phases
– Usually, only the vapor and liquid routes give crystals
of sufficient size for applications or property
measurements
Czochralski method
Bridgman and Stockbarger methods
Zone melting method
Precipitation from solution or melt: flux method
13 gram single crystal of
Ba8Ga16Ge30 (Christensen et al.
Nature Mater. 2008, 7, 811)
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Czochralski method
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A crystal is grown from a melt of the same
composition by starting with a seed crystal in
contact with the melt, whose temperature is
maintained slightly above its melting point
As the seed is gradually pulled out of the melt,
the melt solidifies on the surface of the seed to
give a rod-shaped crystal in the same
crystallographic orientation as the original seed
The melt and growing crystal are usually rotated
counter-clockwise during pulling
Widely used for semiconducting materials: Si,
Ge, GaAs, etc.
Ref: West p. 226
Figure: Wikipedia
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Bridgman and Stockbarger methods
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Based on the solidification of a
stoichiometric melt
Crystallisation is controlled by passing the
melt through a temperature gradient such
that crystallization occurs at the cooler
end
This is achieved in the Stockbarger
method by arranging displacement of the
melt within a temperature gradient
In the Bridgman method, the melt is
inside a temperature gradient furnace and
the furnace is gradually cooled so that
solidification begins at the cooler end
In both methods, it is advantageous to use
a seed crystal
Ref: West p. 228
(a) Stockbarger method. Tm = crystal melting point.
(b) Bridgman method
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Zone melting method
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Related to the Stockbarger method but the thermal profile through the furnace is
such that only a small part of the charge is molten at any one time
Initially that part of the charge in contact with the seed crystal is melted
As the boat is pulled through the furnace, oriented solidification onto the seed
occurs and, at the same time, more of the charge melts
A well-known method for purification of solids, the zone-refining technique
Makes use of the principle that impurities usually concentrate in the liquid rather
than in the solid phase
Impurities are “swept out” of the crystal by the moving molten zone
Ref: West p. 228
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Precipitation from solution or melt:
Flux method
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In contrast to the above methods in which crystals have the same composition as
the melt, precipitation methods involve the growth of crystals from a solvent of
different composition
The solvent may be one of the constituents of the desired crystal,
– e.g. crystallization of salt hydrate crystals from water,
– or the solvent may be an entirely separate liquid in which the crystals of
interest are partially soluble, e.g. various high-melting silicates may be
precipitated from low-melting borate or halide melts
In these cases, the solvent melts are often referred to as fluxes since they
effectively reduce the melting point of the crystals by a considerable amount.
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Growing Si single
crystals at lower
temperature with
the help of Al flux
Figure: Athena S. Sefat, Oak Ridge
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