Aspects of Solid-Solid Reactions

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 coefficient 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

To maximize the contact between reactants we want to use starting reagents with large surface area. Consider the numbers for a 1 cm³ volume of a reactant

Edge Length = 1 cm
# of Crystallites = 1
Surface Area = 6 cm²

Edge Length = 10 mm
# of Crystallites = 10⁹
Surface Area = 6 ´ 10³ cm²

Edge Length = 100Å
# of Crystallites = 10¹⁸
Surface Area = 6 ´ 10⁶ cm²

Pelletize to encourage intimate contact between crystallites.

2) The rate of diffusion

Two ways to increase the rate of diffusion are to

• Increase temperature
• Introduce defects by starting with reagents that decompose prior to or during reaction, such as carbonates or nitrates.

3) The rate of nucleation of the product phase

We can maximize the rate of nucleation by using reactants with crystal structures similar to that of the product (topotactic and epitactic reactions).

What are the consequences of high reaction temperatures?

To speed the rate of diffusion conventional solid state synthetic preps are usually carried out at high temperature. This has the following disadvantages:

• It can be difficult to incorporate ions that readily form volatile species (i.e. Ag⁺),
• It is not possible to access low temperature, metastable (kinetically stabilized) products. For example the C-H-O phase diagram (organic chemistry) is pretty simple at 1200° C,
• High (cation) oxidation states are often unstable at high temperature, due to the thermodynamics of the following reaction: