Conventional solid state synthesis techniques involve heating mixtures of two or more solids to form a solid phase product. Unlike gas phase and solution reactions, the limiting factor in solid-solid reactions is usually diffusion.

Fick’s law :

J = -D(dc/dx)

J = Flux of diffusing species (#/cm²-s)
D = Diffusion coefficient (cm²/s)
(dc/dx) = Concentration Gradient (#/cm⁴)

The average distance a diffusing species will travel, <x>, is given by:

<x> » (2Dt)^1/2

where t is the time.

To obtain good rates of reaction you typically need the diffusion constant to be larger than ~ 10^-12 cm²/s.

The diffusion coefficient increases with temperature, rapidly as you approach the melting point. This concept is leads to Tamman’s Rule : Extensive reaction will not occur until the temperature reaches at least 2/3 of the melting point of one or more of the reactants.

Rates of Reaction are controlled by three factors:

(1) The area of contact between reacting solids

(a) To maximize this we want to use starting reagents with large surface area.

^{Consider the effect of reducing the edge length of a hypothetical collection of crystallites, while keeping the mass constant (beginning from a single cubic crystal with 1 cm edges)}
 

Edge Length	1 cm	10 mm	100Å
# of Crystallites	1	109	1018
Surface Area	6 cm2	6x103 cm2	6x106 cm2

(b) Pelletize to encourage intimate contact between cyrstallites.

(2) The rate of diffusion

(a) Increase temperature
(b) Introduce defects (start with reagents that decompose prior to or during reaction like carbonates or nitrates)

(3) The rate of nucleation of the product phase

Use reactants with crystal structures similar to that of the product (topotactic, epitactic reactions)
 

Types of Solid State Materials

There are several forms solid state materials can adapt
 

• Single Crystal - Preferred for characterization of structure and properties.
• Polycrystalline Powder (Highly crystalline) - Used for characterization when single xtal can not be easily obtained, preferred for industrial production and certain applications.
• Polycrystalline Powder (Large Surface Area) - Desirable for further reactivity and certain applications such as catalysis and electrode materials
• Amorphous (Glass) - No long range translational order.
• Thin Film - Widespread use in microelectronics, telecommunications, etc.

Single Crystal

• Czochralski Method (399)
• Zone Melting (35)
• Verneuil Method (9)
• Molten Flux Growth (10)
• Vapor Transport (101)
• Skull Melting (2)
• Hydrothermal (56)
• Electrochemical (52)

• Traditional Ceramic Routes
• Precursor Routes [Coprecipitation (129), sol-gel (976), Alkoxide-hydroxide (2), etc.]
• Chimie Douce [cation exchange, dehydration, hydrolosis, intercalation (574), etc.]
• Metathesis Reactions (6)
• High Pressure-High Temperature (4)
• Hydrothermal (56)
• Molten Flux (52)

• Chemical Vapor Deposition (CVD) (3782)
• Physical Vapor Deposition (PVD) (116)
• Laser Ablation (432)
• Sputtering (2275)
• Molecular Beam Epitaxy (MBE) (2051)
• Liquid Phase Epitaxy (LPE) (326)
• Modulated Reactant Precursors (1)

(1) Select appropriate starting materials
        (a) Fine grain powders to maximize surface area
        (b) Reactive starting reagents are better than inert
        (c) Well defined compositions

(2) Weigh out starting materials

(3) Mix starting materials together
        (a) Agate mortar and pestle (organic solvent optional)
        (b) Ball Mill (Especially for large preps > 20g)
(4) Pelletize
        (a) Enhances intimate contact of reactants
        (b) Minimizes contact with the crucible
        (c) Organic binder may be used to help keep pellet together

(5) Select sample container
        Reactivity, strength, cost, ductility all important
        (a) Ceramic refractories (crucibles and boats)
            Al₂O₃             1950° C     $30/(20 ml)
            ZrO₂/Y₂O₃     2000° C     $94/(10 ml)
        (b) Precious Metals (crucibles, boats and tubes)
            Pt 1770° C $500/(10 ml)
            Au 1063° C $340/(10 ml)
            Ag 960° C $ 43/(10 ml)
            Ir 2450° C $930/(10 ml)
        (c) Sealed Tubes
            SiO₂- Quartz
            Au, Ag, Pt
            Nb, Ta, Mo, W

(6) Heat
        (a) Factors influencing choice of temperature include Tamman’s
             rule and potential for volatilization Initial heating cycle to
             lower temperature can help to prevent spillage and volatilization
        (b) Atmosphere is also critical

                Oxides
                        Oxidizing Cond. – Air, O₂, Low Temps
                        Reducing Cond. – H₂/Ar, CO/CO₂, High T

                Nitrides – NH₃ or Inert (N₂, Ar, etc.)
                Sulfides – H₂S
                Sealed tube reactions, Vacuum furnaces

(7) Grind product and analyze (x-ray powder diffraction)

(8) If reaction incomplete return to step 4 and repeat.
 

(1) Possible starting reagents

Sr Metal – Hard to handle, prone to oxidation
SrO - Picks up CO₂ & water, mp = 2430° C
Sr(NO₃)₂ – mp = 570° C, may pick up some water
SrCO₃ – decomposes to SrO at 1370° C

Ta Metal – mp = 2996° C
Ta₂O₅ – mp = 1800° C

Cr Metal – Hard to handle, prone to oxidation
Cr₂O₃ – mp = 2435° C
Cr(NO₃)_3*nH₂O – mp = 60° C, composition inexact
 

(2) Weigh out starting reagents

To make 5.04 g of Sr₂CrTaO₆ (FW = 504.2 g/mol; 0.01 mol) to complete the reaction:

(4) Applying Tamman’s rule to each of the reagents:

SrCO₃ ® SrO 1370° C (1643 K)

SrO mp = 2700 K ²/₃ mp = 1527° C
Ta₂O₅ mp = 2070 K ²/₃ mp = 1107° C
Cr₂O₃ mp = 2710 K ²/₃ mp = 1532° C

Although you may get a complete reaction by heating to 1150° C, in practice there will still be a fair amount of unreacted Cr₂O₃. Therefore, to obtain a complete reaction it is best to heat to 1500-1600° C. The initial heating cycle should be slow, or a preliminary fire at 1400° C should be used to prevent the SrCO₃ from violently decomposing and spilling out of the crucible.

(5) If the sample is pelletized the reaction with an alumina crucible should be rather small. For the highest purity products a sacrificial pellet should be used, or a platinum crucible.

(6) All of the elements are in stable highly oxidized states in the product, so that heating in air should be appropriate.

Obstacle : Solid state reaction rates are typically diffusion limited.

Solution : Decrease diffusion distances through intimate mixing of cations.

Advantages : Lower reaction temps, possibly stabilize metastable phases, eliminate intermediate impurity phases, produce products with small crystallites/high surface area.

Disadvantages : Reagents are more difficult to work with, can be hard to control exact stoichiometry in certain cases, sometimes it is not possible to find compatible reagents.

Methods : All precursor routes (sol-gel, coprecipitation, alkoxide-hydroxide, etc.) involve the following steps:

• Mixing the starting reagents together in solution.
• Remove the solvent, leaving behind an amorphous mixture of cations and one or more of the following anions: acetate, citrate, hyroxide, oxalate, alkoxide, etc.
• Heat the resulting gel or powder to induce reaction to the desired product.

Coprecipitation Synthesis of ZnFe₂O₄

Mix the oxalates of zinc and iron together in water in a 1:1 ratio. Heat to evaporate off the water, as the amount of H₂O decreases a mixed Zn/Fe acetate (probably hydrated) precipitates out.

Fe₂((COO)₂)₃ + Zn(COO)₂ ® Fe₂Zn((COO)₂)_5*xH₂O

After most of the water is gone, filter off the precipitate and calcine it (1000° C).

Fe₂Zn((COO)₂)₅ ® ZnFe₂O₄ + 4CO + 4CO₂

This method is easy and effective when it works. It is not suitable when

• Reactants of comparable water solubility cannot be found.
• The precipitation rates of the reactants is markedly different.

Sol-Gel Synthesis of Metastable ScMnO₃

Begin by dissolving Sc₂O₃ and MnCO₃, separately, in heated aqueous solutions of formic acid to form the formate salts:

Sc₂O₃ + 6HCOOH ® 2Sc(HCOO)₃ + 3H₂O
MnCO₃ + 2HCOOH + 2H₂O ® Mn(COOH)_2*2H₂O + H₂CO₃

Addition of Sc(HCOO)₃ and Mn(COOH)_2*2H₂O to melted citric acid monohydrate results in the formation of a (Sc,Mn) citrate polymer.

Heat to 180° C ® Removal of excess water and organics
Heat to 450° C ® Formation of an amorphous oxide product
Heat to 690° C ® Formation of crystalline ScMnO₃

Direct reaction of the formates at 700° C simply gives the a mixture of the binary oxides:

2Sc(HCOO)₃ + 2Mn(COOH)_2*2H₂O ® Sc₂O₃ + Mn₂O₃ + 5CO₂ + 2H₂O + H₂

Alkoxide-Hydroxide Synthesis of Sr₂AlTaO₆

Reflux a mixture of Ta(OC₂H₅)₅ and Al(OC₂H₅)₃ overnight in a solution of ethanol. This results in the formation of polymeric (Ta,Al) ethoxide species

Add a stoichiometric quantity of Sr(OH)_2*8H₂O in acetone, mix well and reflux overnight. The hydroxide ions and water of hydration are sufficient to trigger a slow precipitation

Filter off the solution and heat at 120° C to drive off remaining solvent

Heat to 1200-1400° C to form highly crystalline Sr₂AlTaO₆ or heat to 800-1000° C to form high surface area Sr₂AlTaO₆

Direct reaction of the oxides also results in formation of Sr₂AlTaO₆, but minor Sr/Ta/O impurity phases are always present.

The alkoxides are often hygroscopic and air sensitive, consequently it can be difficult to weigh out accurate quantities. Furthermore, they are rather expensive.

A metathesis reaction between two salts merely involves an exchange of anions, although in the context we will use there can also be a redox component. If the appropriate starting materials are chosen, a highly exothermic reaction can be devised.

MoCl₅ + ⁵/₂ Na₂S ® MoS₂ + 5NaCl + ½ S

The enthalpy of this reaction is DH_rxn = -213 kcal/mol

Due to the highly exothermic nature of this reaction, once it is started (by grinding, spark, etc.) the heat generated by the reaction itself leads to a rapid increase in temperature.

• The maximum temperature attained is ~ 1700 K.
• The reaction is completed in < 4 s.
• The percent yield is typically 80% of theoretical.

• Reduces cost and time associated with synthesis
• Fast cooling can lead to high surface area products

• Incomplete conversion to products
• Applicability unclear for complex materials

Chimie Douce reactions are carried out under moderate conditions (typically T < 500° C)

Chimie Douce reactions are topotactic, meaning that structural elements of the reactants are preserved in the product.

Chimie Douce Methods

(1) Intercalation
 

• Involves inserting ions into an existing structure, this leads to a reduction (cations inserted) or an oxidation (anions inserted) of the host
• Typically carried out on layered materials (strong covalent bonding within layers, weak van der Waals type bonding between layers, i.e. graphite, clays, dicalchogenides, etc.)
• Performed via electrochemistry or via chemical reagents as in the n-butyl Li technique

TiS₂ + nBu-Li ® LiTiS₂
b-ZrNCl + Naph-Li ® b-Li_xZrNCl

(2) Deintercalation
 

• The reverse of intercalation, also performed using either electrochemical methods or with reactive chemical species

NiMo₃S₄ ® Mo₃S₄ (Wash with HNO₃)
In₂Mo₆S₆ + 6HCl (g) ® Mo₆S₆ + 2InCl₃ (g) + 3H₂ (g)

This approach can often lead to new phases (structures) of previously known compounds, for example

CuTi₂S₄ ® cubic TiS₂
KCrSe₂ ® layered CrSe₂
Li₂FeS₂ ® FeS₂

(3) Dehydration
 

• By removing water and/or hydroxide groups from a compound, you can often perform redox chemistry and maintain a structural framework not accessible using conventional synthesis approaches

Ti₄O₇(OH)_2*nH₂O ® TiO₂ (B) (500° C)
2KTi₄O₈(OH)_*nH₂O ® K₂Ti₈O₁₇ (500° C)
 

(4) Ion Exchange

• Exchange charge compensating, ionically bonded cations (easiest for monovalent cations)

LiNbWO₆ + H₃O⁺ ® HNbWO₆ + Li⁺
Cubic-KSbO₃ + Na⁺ ® Cubic-NaSbO₃ + K⁺
 

Chimie Douce Methods

Useful for

• Modifying the electronic structure of solids (doping)
• Design of new metastable compounds (structural motif can be selected by choice of precursor, may have unusual properties)
• Preparing reactive and/or high surface area materials used in heterogeneous catalysis, batteries and sensors

• Sometimes difficult to find appropriate precursor
• Metastable products are often unstable in applications where high temperatures are used or single xtals are needed

• Earlier when we discussed precursor routes the first step was generally to dissolve the reactants in solution (typically aqueous or organic based), thereby promoting mixing and diffusion
• Unfortunately, most inorganic reactants are highly insoluble in water and/or organic solvents. This limits the applicability of the precursor methods
• Hydrothermal Conditions and Molten Fluxes are two approaches to circumventing this problem

• Reaction takes place in superheated water, in a closed reaction vessel (150 < T < 500° C; 100 < P < 2000 atm)
• The conditions help to solubilize reagents, and the high pressures can also help to stabilize new phases
• Seed crystals and a temperature gradient can be used for growing crystals
• Particularly common approach to synthesis of zeolites

6CaO + 6SiO₂ ® Ca₆Si₆O₁₇(OH)₂ (150-350° C)
 
 

Molten Salt Fluxes

Solubilize reactants ® Enhance diffusion ® Reduce reaction temperature

This reduces/overcomes problems with

• Incorporating volatile species (i.e. alkali metals)
• Stabilizing cations in high oxidation states
• Avoiding stable intermediate impurity phases

Examples :

4SrCO₃ + Al₂O₃ + Ta₂O₅ ® Sr₂AlTaO₆ (SrCl₂ flux, 900° C)

• Powder sample, wash away SrCl₂ with weakly acidic H₂O
• Direct synthesis requires T > 1400° C and Sr₂Ta₂O₇ impurities persist even at 1600° C

• Volatility of potassium plagues direct reaction
• Single crystal products

• Example of reactive A₂Q_x (A = alkali metal, Q = S, Se, Te) flux
• single crystal products

To encourage reaction and increase reaction rates

(1) Increase diffusion rates
            (a) Increase temperature
            (b) Use reactants which decompose
            (c) Carry out reactions in solution
                        (i)  Hydrothermal conditions
                        (ii) Molten Salt Fluxes

(2) Decrease diffusion distances
            (a) Decrease reactant particle size
            (b) Intimate mixing – precursor routes

(3) Promote nucleation
            (a) Topotactic reactions
            (b) Chimie Douce
 

Other Considerations

If all else is equal, favor the easy and cheap routes

Low temperature routes are good for :

• incorporating volatile species
• stabilizing unusually high oxidation states
• formation of metastable phases
• small crystallites (high surface area)