First-principles X-ray absorption dose calculation for time-dependent mass and optical density
Bibliographic record
Abstract
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 + aexp(-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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".