A Universal Equation for the Emission Range of X Rays from Bulk Specimens
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Bibliographic record
Abstract
The derivation of a universal equation to compute the range of emitted X rays is presented for homogeneous bulk materials. This equation is based on two fundamental assumptions: the varphi(rhoz) curve of X-ray generation is constant and the ratio of the emitted to the generated X-ray range is equal to the ratio of the emitted to the generated X-ray intensity. An excellent agreement is observed with data obtained from Monte Carlo simulations of 200,000 electron trajectories in C, Al, Cu, Ag, Au, and an Fe-B alloy with boron weight fractions equal to 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 0.99, performed with the electron beam energy varied from 1 to 30 keV in 1-keV steps. When the ratio of the generated X-ray range to the photon mean free path is much smaller than one, the emission X-ray range is equal to the generated X-ray range, but when this ratio is much greater than one, the emission X-ray range is constant and is given by the product of the effective photon mean free path multiplied by the sine of the take-off angle.
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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 it