
First‐principles X‐ray absorption dose calculation for time‐dependent mass and optical density
Author(s) -
Berejnov Viatcheslav,
Rubinstein Boris,
Melo Lis G. A.,
Hitchcock Adam P.
Publication year - 2018
Publication title -
journal of synchrotron radiation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.172
H-Index - 99
ISSN - 1600-5775
DOI - 10.1107/s1600577518002655
Subject(s) - absorption (acoustics) , exponential function , kinetics , photon energy , order (exchange) , photon , function (biology) , physics , materials science , computational physics , chemistry , optics , mathematics , mathematical analysis , quantum mechanics , evolutionary biology , economics , biology , finance
A dose integral of time‐dependent X‐ray absorption under conditions of variable photon energy and changing sample mass is derived from first principles starting with the Beer–Lambert (BL) absorption model. For a given photon energy the BL dose integral D ( e , t ) reduces to the product of an effective time integral T ( t ) and a dose rate R ( e ). Two approximations of the time‐dependent optical density, i.e. exponential A ( t ) = c + a exp(− bt ) for first‐order kinetics and hyperbolic A ( t ) = c + a /( b + t ) for second‐order kinetics, were considered for BL dose evaluation. For both models three methods of evaluating the effective time integral are considered: analytical integration, approximation by a function, and calculation of the asymptotic behaviour at large times. Data for poly(methyl methacrylate) and perfluorosulfonic acid polymers measured by scanning transmission soft X‐ray microscopy were used to test the BL dose calculation. It was found that a previous method to calculate time‐dependent dose underestimates the dose in mass loss situations, depending on the applied exposure time. All these methods here show that the BL dose is proportional to the exposure time D ( e , t ) ≃ K ( e ) t .