Context. The bulk abundances of CHNOS-bearing species of a planet have a profound effect on its interior structure and evolution. Therefore, it is key to investigate the behavior of the local abundances of these elements in the solid phase in the earliest stages of planet formation, where micrometer-sized dust grows into larger and larger aggregates. However, the physical and chemical processes occurring in planet-forming disks that shape these abundances are highly coupled and nonlocal. Aims. We aim to quantify the effects of the interplay between dynamical processes (turbulent diffusion, dust settling and radial drift), collision processes (coagulation and fragmentation), and the adsorption and desorption of ices on the abundances of CHNOS in local disk solids as a function of position throughout the planet-forming region. Methods. We used SHAMPOO (Stochastic Monomer Processor), which tracks the ice budgets of CHNOS-bearing molecules of a dust monomer as it undergoes nonlocal disk processing in a Class I disk. We used a large set of individual monomer evolutionary trajectories to make inferences about the properties of the local dust populations via a stochastic analysis of 64 000 monomers on a preexisting spatial grid. Results. We find that spatially, monomers can travel larger distances farther out in the disk, leading to a larger spread in positions of origin for a dust population at, for example, r = 50 AU compared to r = 2 AU. However, chemically, the inner disk (r ≲ 10 AU) is more nonlocal due to the closer spacing of ice lines in this disk region. Although to zeroth order the bulk ice mantle composition of icy dust grains remains similar compared to a fully local dust population, the ice mass associated with individual chemical species can change significantly. The largest differences with local dust populations were found near ice lines where the collisional timescale is comparable to the adsorption and desorption timescales. Here, aggregates may become significantly depleted in ice as a consequence of microscopic collisional mixing, a previously unknown effect where monomers are stored away in aggregate interiors through rapid cycles of coagulation and fragmentation. Conclusions. Nonlocal ice processing in a diffusion-dominated, massive, smooth disk has the most significant impact on the inner disk (r ≲ 10 AU). Furthermore, microscopic collisional mixing can have a significant effect on the amounts of ice of individual species immediately behind their respective ice lines. This suggests that ice processing is highly coupled to collisional processing in this disk region, which implies that the interiors of dust aggregates must be considered and not just their surfaces.
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