Various interference reactions producing unwanted Ar isotopes from K, Ca, Cl and Ar require correction to satisfy the ⁴⁰Ar/³⁹Ar age equation. Using GEANT4, we design and build a model Cadmium Lined In Core Irradiation Tube (CLICIT) irradiation facility, as used in the Oregon State TRIGA Reactor (OSTR). We illustrate the complexity of the irradiation of geologic samples within this framework and determine an overlooked production channel of ³⁶Ar. The production of ³⁶Ar is fed from the ³⁹K(n,α)³⁶Cl nuclear channel, ³⁶Cl subsequently decays to ³⁶Ar (³⁹K(n,α,β) ³⁶Ar). Simulations in this work using a ²³⁵U fission neutron energy spectrum and modelled CLICIT facility, determine a production ratio for this reaction (³⁶Cl/³⁹Ar)_K = 0.40 ± 0.01 (1σ); greater than an order of magnitude larger than any other K interference. The magnitude of the resulting age bias for an unknown sample will be a function of the integrated neutron flux, the length of irradiation (fluence), the time elapsed since irradiation, and the age relationship between the unknown and neutron fluence monitor. We show using the raw data of (Niespolo et al., 2017) that the age of Alder Creek sanidine can be modified to be ca. 0.1% older (1σ), at the 2σ level of current analytical precision for the Alder Creek age for this study. The ³⁹K(n,α,β)³⁶Ar inference should be incorporated into routine data analysis and may be especially important in the intercalibration of the ⁴⁰Ar/³⁹Ar system with other chronometers (e.g., ²⁰⁶Pb/²³⁸U).