Governing Equations for the Bulk Concentrations
Bulk Species Rates and Growth Velocity
The reaction rate for a bulk species of index k, being added to the bulk due to surface reactions is defined as Rb,k (SI unit: mol/(s·m2)).
The reaction rate in mass basis, rb,k (SI unit: kg/(s·m2)) for species k, is given by:
with Mk (SI unit: kg/mol) being the molar mass of the species.
Based on this, the species contribution to the bulk growth velocity, vk (SI unit: m/s), is given by:
where ρk is the species density (SI unit: kg/m3).
Total Rates and Velocity
To get the corresponding total values, a summation for all bulk species is made according to:
Fractional Rates and Velocity
The fractional deposition rates are calculated by:
Accumulated Bulk Quantities
By solving for the bulk species concentrations for each time step, the accumulated mass and thickness changes of the bulk material can be calculated.
The bulk concentration, cb,k (SI unit: mol/m2), for species k is governed by the equation:
(5-53)
The bulk concentration in mass basis, mb,k (SI unit: kg/m2) for a species k, can be derived from:
leading to the bulk thickness sb,k (SI unit: m) of species k according to:
Total Bulk Quantities
The total bulk concentration is calculated according to:
The deposited total mass, mb,tot (SI unit: kg/m2) is
and the total bulk thickness, stot (SI unit: m) is
Fractional Quantities
The fractional bulk concentration, bulk mass, and thickness (all dimensionless) are calculated according to: