Particles and Spacetime Diagrams

This chapter begins the process of making a 3D interpretation of the plaid model. The idea is to group together certain of the light points and think of them as instances of 1-dimensional worldlines rather than as a succession of points. It fixes an even rational parameter p/q and uses the notation from Section 1.2, i.e., ω‎ = p + q. Section 4.2 explains a different notion of adjacency for the ω‎ × ω‎ blocks, dividing up the plaid model. Section 4.3 says what it means for two horizontal light points in remotely adjacent blocks to be different instances of the same particle. Section 4.4 does the same for the vertical particles. Section 4.5 shows a few pictures of spacetime diagrams and discuss their symmetries. Section 4.6 proves a technical lemma, the Bad Tile Lemma, which is very similar in spirit to Theorem 1.4.

Interpretation of Changes in Peak Shape and Position of the Oxygen Kα Characteristic X-Ray Line

Changes in shape and position of long-wavelength X-ray lines measured by wavelength dispersive spectrometry (WDS) reflect changes in the density of bonding states of the emitting atom. However, some features of soft X-ray spectra are not due to bonding. For example, small peaks on the shorter-wavelength side of a characteristic peak probably arise from double ionization, absorption effects must be considered and there may be artefacts from the diffracting crystal itself. Nonetheless, when there are dramatic shape changes, spectrometry of soft X-rays can usefully augment microanalysis particularly in the study of tiny particulates which may be difficult to prepare for transmission microscopy.5 Two examples of spectrometry of O Kα follow.Oxidation of very fine TiB2 particulates is a problem in the ceramics industry. The backscattered electron (BSE) micrograph in fig. 1 shows a particle section with a central core of TiB2 and a darker, oxidised rim analysing roughly like a borate, interspersed with brighter regions, probably TiO2.