handbook of carbon, graphite, diamond and fullerenes

Pyrolytlc Graphite 145
AG Calculation: The first step is to ensure that the desired CVD
reaction will take place in a given temperature range. This will happen if the
thermodynamics is favorable, that is, if the transfer of energy (i.e., the freeenergy
change of the reaction, known as AGr) is negative. To calculate AGr,
it is necessary to know the thermodynamic properties of each component,
specifically their free-energy of formation (also known as Gibbs free
energy), AGf. The values of AGr of the reactants and products for each
temperature can be obtained from thermodynamic-data tables such as the
JANAF Thermochemical Tables and others. 16 '^
It should be noted that the negative free-energy change is a valid
criterionforthefeasibility of areaction only if the reaction as written contains
the major species that exist at equilibrium.
2.3 Minimization of Gibbs Free Energy
Experimentation shows that the best, fully dense, and homogeneous
carbon deposits are produced at an optimum negative value of AG. For
smaller negative values, the reaction rate is very low and, for higher
negative values, vapor-phase precipitation and the formation of soot can
occur. Such factors are not revealed in the simple free-energy change
calculation. A more complete analysis is often necessary.
A method of analysis is the minimization of the Gibbs free energy, a
calculation based on the rule of thermodynamics which states that a
system will be in equilibrium when the Gibbs free energy is at a minimum.
The objective then is the minimization of the total free energy of the system
and the calculation of equilibria at constant temperature and volume or
constant pressure. It is a complicated and lengthy operation but, fortunately,
computer programs are now available that simplify the task
considerably.^ 8 ]! 9 '
These programs provide the following information:
• The composition and amount of deposited material that
is theoretically possible at a given temperature, pressure,
and concentration of input gases
• The existence of gaseous species and their equilibrium
partial pressures
• The possibility of multiple reactions with the inclusion of
the substrate as a possible reactant