RESUMO
Molecular dynamic (MD) calculations were performed to investigate the thermodynamic and structural properties of lead fluoride (PbF2) by using a proposed inter-ionic temperature-dependent potential. This potential allows calculating with high precision the linear thermal expansivity and the lattice parameter as a temperature function. In addition, the potential can be represented as a sum of two contributions, a temperature-independent potential added to another temperature-dependent potential, considered last as a correction justified by the one-dimensional Newtonian quantum equation. Two fitting regions were considered, the first region from 300 to 700 K and the other one from 700 to 900 K. These regions arise naturally due to the smooth and continuous transition that PbF2 undergoes until it reaches the superionic state and, allows us to model with high precision the anomaly in the dependence of the lattice parameter with the temperature of this material, a feature that until now under the molecular dynamic method has not been studied. These results are all in good agreement with the experimental measurements.
RESUMO
PURPOSE: Cherenkov radiation has recently received attention due to its prompt emission phenomenon, which has the potential to improve the timing performance of radiation detectors dedicated to positron emission tomography (PET). In this study, a Cherenkov-based three-dimensional (3D) position-sensitive radiation detector was proposed, which is composed of a monolithic lead fluoride (PbF2 ) crystal and a photodetector array of which the signals can be readout independently. METHODS: Monte Carlo simulations were performed to estimate the performance of the proposed detector. The position- and time resolution were evaluated under various practical conditions. The radiator size and various properties of the photodetector, e.g., readout pitch and single photon timing resolution (SPTR), were parameterized. The single photon time response of the photodetector was assumed to be a single Gaussian for the simplification. The photo detection efficiency of the photodetector was ideally 100% for all wavelengths. Compton scattering was included in simulations, but partly analyzed. To estimate the position at which a γ-ray interacted in the Cherenkov radiator, the center-of-gravity (COG) method was employed. In addition, to estimate the depth-of-interaction (DOI) principal component analysis (PCA), which is a multivariate analysis method and has been used to identify the patterns in data, was employed. The time-space distribution of Cherenkov photons was quantified to perform PCA. To evaluate coincidence time resolution (CTR), the time difference of two independent γ-ray events was calculated. The detection time was defined as the first photon time after the SPTR of the photodetector was taken into account. RESULTS: The position resolution on the photodetector plane could be estimated with high accuracy, by using a small number of Cherenkov photons. Moreover, PCA showed an ability to estimate the DOI. The position resolution heavily depends on the pitch of the photodetector array and the radiator thickness. If the readout pitch were ideally 0 and practically 3 mm, a full-width at half-maximum (FWHM) of 0.348 and 1.92 mm was achievable with a 10-mm-thick PbF2 crystal, respectively. Furthermore, first-order correlation could be observed between the primary principal component and the true DOI. To obtain a coincidence timing resolution better than 100-ps FWHM with a 20-mm-thick PbF2 crystal, a photodetector with SPTR of better than σ = 30 ps was necessary. CONCLUSIONS: From these results, the improvement of SPTR allows us to achieve CTR better than 100-ps FWHM, even in the case where a 20-mm-thick radiator is used. Our proposed detector has the potential to estimate the 3D interaction position of γ-rays in the radiator, using only time and space information of Cherenkov photons.