Theoretical Wood Densitometry: I Mass Attenuation Equations and Wood Density Models
Keywords:Wood densitometry, attenuation coefficients, transmission probability, wood density, X-radiation, atomic parameters, mathematical modeling
AbstractTheoretical linear and mass attenuation equations that model X-ray attenuation processes of both monoatomic and polyatomic absorbers with homogeneous or heterogeneous structures have been derived. The reaction mechanisms of photons to atoms, as well as relevant atomic parameters, have been used in the development of parametric expressions that relate attenuation coefficients to important radiation parameters—including X-ray energy, absorber thickness, incident angle, and absorber density. To better understand the physical process to be modeled, systematic analyses and critical comparisons of attenuation equations of different X-ray sources and various absorbers are reported in simple physical and mathematical contexts. To address the wood densitometric problems that we encounter, theoretical formulas for transmission probabilities and wood density calculation have also been developed. Examples are provided to demonstrate uses of these theoretical models in calculating (1) atomic mass attenuation coefficients for major elements as well as minor ash elements in wood, (2) mass attenuation coefficients of coniferous wood, (3) transmission probabilities under various combinations of radiation parameters, and (4) wood density of pine heartwood. Throughout this mathematical treatment, emphases have been placed on the microscopic point of view for modeling and the parametric formulation for describing X-ray transmission experiments.
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