tokens: ); and r is the distance from one specific location in the silicate's interior to its surface. 3. Results 3.1. Boundary Conditions In the standard case, we assumed spherical orthopyroxene minerals with radii of 50 μ m (Figures 2 (a)–(c)) and 500 μ m (Figures 2 (d)–(f)) condense in a region with a heliocentric distance of 1 au from the proto-Sun. The minerals are implanted by the protons in the solar nebula for 1 day, 1 month (30 days), 1 year (365 days), and 10 years (3650 days). For both silicates, the simulations were run with retention coefficients ( N R ) of 0.01, 0.1, and 0.5. Other critical boundary conditions applied for our standard case are listed in Table 1 . Figure 2. Simulated concentration profiles of water in the interior of the silicates. Spherical silicates with radii of 50 μ m (a)–(c) and 500 μ m (d)–(f) are assumed to be implanted with nebular plasma hydrogen for 1 day, 1 month (30 days), 1 year (365 days), and 10 years (3650 days). Three retention coefficients ( N R ), i.e., 0.01, 0.1, and 0.5, are applied for the implantation. With the same retention coefficient (e.g., N R = 0.01), it takes a longer time for 500 μ m sized silicate (d) to evenly distribute the projectile ions than the 50 μ m sized silicate (a). The higher retention coefficient leads to the larger production of water. For instance, implantation with a retention coefficient of 0.5 can produce more than 1000 ppm water in one year in the 50 μ m sized silicate (c), whereas when the retention coefficient is 0.01, the production is less than 200 ppm (b). The gray shaded area indicates the range of previously reported water contents (200–1000 ppm) of the ordinary chondritic minerals, which can be well produced by the implantation–diffusion processes with 0.1 ((b), (c), (e), (f)). Boundary conditions for the simulations are listed in Table 1 . Table 1 Boundary Conditions Applied for the Standard Case References. (1) Wu Judge ( 1979 ), (2) Lewis ( 1972 ), (3) Fromang et al. ( 2002 ), (4) Öberg et al. ( 2011 ), (5) Stalder Skogby ( 2003 ), (6) Dürr Höfer ( 2006 ). We first adopt a high nebular gas pressure ( P = 10 −3 bar) for the chondrule formation (Galy et al. 2000 ). The ambient temperature when chondrule minerals formed was characterized by a range of temperatures, from 600 K to >900 K (Rubin 2000 ). The presence of a primary trolite in type 3 ordinary chondrites indicates an ambient nebular temperature of 650 K (Rubin et al. 1999 ). Accordingly, we select this value as the background temperature for the implantation and diffusion. In previous studies, the ionization fraction ( f ion ) of protoplanetary disks have been reported to be with orders between 10 −12 and 10 −10 (Fromang et al. 2002 ; Öberg et al. 2011 ) and we adopt a median value of 10 −11 . Due to the lack of the parameters applicable to the low-temperature (650 ± 100 K) diffusion of hydrogen in nominally anhydrous silicate minerals, here we use the diffusion coefficient ( D 0 ) and activation energy ()
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