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
The fractional deposition rates can be used as measures of the local fractional composition in a deposited layer at a certain thickness or time.
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
(5-54)
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