Abstract
Diamond detectors are increasingly employed in dosimetry. Their response has been investigated by means of Monte Carlo (MC) methods, but there is no consensus on what mass density ρ, mean excitation energy I and number of conduction electrons per atom n ce to use in the simulations. The ambiguity occurs due to its seeming similarity with graphite (both are carbon allotropes). Except for the difference in ρ between crystalline graphite (2.265 g cm−3) and diamond (3.515 g cm−3), their dielectric properties are assumed to be identical. This is incorrect, and the two materials should be distinguished: (ρ = 2.265 g cm−3, I = 81.0 eV, n ce = 1) for graphite and (ρ = 3.515 g cm−3, I = 88.5 eV, n ce = 0) for diamond. Simulations done with the MC code penelope show that the energy imparted in diamond decreases by up to 1% with respect to ‘pseudo-diamond’ (ρ = 3.515 g cm−3, I = 81.0 eV, n ce = 0) depending on the beam quality and cavity thickness. The energy imparted changed the most in cavities that are small compared with the range of electrons. The difference in the density-effect term relative to graphite was the smallest for diamond owing to an interplay effect that ρ, I and n ce have on this term, in contrast to pseudo-diamond media when either ρ or I alone were adjusted. The study also presents a parameterized density-effect correction function for diamond that may be used by MC codes like EGSnrc. The estar program assumes that n ce = 2 for all carbon-based materials, hence it delivers an erroneous density-effect correction term for graphite and diamond. Despite the small changes of the energy imparted in diamond simulated with two different I values and expected close-to-negligible deviation from the published small-field output correction data, it is important to pay attention to material properties and model the medium faithfully.
Highlights
Clinical dosimetry in radiation therapy was traditionally based on cavity theory where the absorbed dose to the detector cavity medium is converted to absorbed dose to water by means of the ratio of mass electronic stopping powers of water to detector cavity medium (Bragg–Gray and Spencer–Attix cavity theories), the ratio of mass energyabsorption coefficients, or both (Burlin cavity theory) (Andreo et al 2017)
This approximate method avoids the need of knowing the full optical energy-loss function (OELF) and it has been exploited in International Commission on Radiation units and Measurements (ICRU) Reports 37 and 49 (ICRU 1984, 1993) as well as in the new ICRU Report 90 (ICRU 2016)
Graphite and diamond do not share the same physical properties, in particular the mass density and the dielectric response function (DRF), and different sets of (ρ, I, nce) values affect the energy deposition in the medium depending on beam quality and cavity thickness via the I-value directly and via the density-effect term
Summary
Clinical dosimetry in radiation therapy was traditionally based on cavity theory where the absorbed dose to the detector cavity medium is converted to absorbed dose to water by means of the ratio of mass electronic stopping powers of water to detector cavity medium (Bragg–Gray and Spencer–Attix cavity theories), the ratio of mass energyabsorption coefficients (large cavity theory), or both (Burlin cavity theory) (Andreo et al 2017). Modelling of the most common detectors with cavities made of, for instance, air, silicon, or lithium fluoride, is rather straightforward because their values of ρ and I are well established This is not the case for diamond detectors, which have gained interest and are being employed in high-energy photon- and electronbeam dosimetry (Laub and Crilly 2014, Ralston et al 2014, Di Venanzio et al 2015, De Coste et al 2017) as well as in proton (Gomaet al 2016) and carbon (Rossomme et al 2016, Marsolat et al 2016) beam dosimetry. At ultrarelativistic energies (β → 1) the δ-term dominates in equation (1) and approaches the asymptotic form δ(β) → 2 ln √ 1 Ωp − 1,
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