Therefore, Figure 5 clearly indicates that MNBs in the wastewater trapped impurities existed around them on their surfaces and concentrated impurities during their residence time until quenching.
Figure2a presents the results corresponding to integrating Equations 5 to 7 using these parameter values, for the areal density of trapped impurities at the entrance of the channel n(x = 0,t) and at its exit point n(x = L t) and also for the global average areal density of trapped impurities n ̄ ( t ) = L − 1 ∫ 0 L n ( x, t ) d x.
Indeed, z e will depend on the areal density of already trapped impurities n (which will screen out the wall) and also on the chemistry specifics of the wall and impurities.
The effective radiuses re and ρe vary as trapped impurities cover the inner wall, via their dependences on, respectively, the areal density n of trapped impurities and on the areal density ze of effective charge of the inner wall.
Extrinsic gettering refers to gettering that employs external means to create the damage or stress in the silicon lattice in such a way that extended defects needed for trapping impurities are formed.
Stiffness in these grains may be associated to the trapped impurities at the subsurface region such as oxygen and/or argon atoms might explain the differences in stiffness in these grains.
(a) Results, obtained by integrating Equations 5 to 7, for the time dependence of the areal density of trapped impurities (continuous lines) at the entrance of the channel n(x = 0,t) and at its exit point n(x = L,t), and also the global average areal density of trapped impurities n ̄ ( t ) = L − 1 ∫ 0 L n ( x, t ) d x.
The model also predicts the time evolution of the trapped impurity concentration and of the filtering capability, including three successive regimes: a linear regime, a logarithmic regime, and the saturated limit.
Some of those impurities will become trapped by the inner wall of the channel, then reducing its effective radius to a value r e (x,t) = r0−r1n x,t), where t is the time, n is the number areal density of trapped impurities in the inner wall, and r1is a constant proportional to the average volume of impurities.
