Boundary clearing thresholds

Clearly, the phase boundaries lie on top of each other. A closer look reveals a slight decrease in the slope r0 of Eq. (26) according to Ca2+>Sr2+>-Ba2+, which indicates that the larger the bivalent earth alkaline cation is, the smaller is the stoichiometric amount of M2+ necessary to precipitate NaPA. Although based on a different method, the present results suggest a comparison with data from Pochard et al. [73]. In doing so, we have to keep in mind that our own r0 values are of fair accuracy at best because they were evaluated from slopes based on a few data points only. Still, this trend in rQ is the opposite to the observation of Pochard et al. [73]. They found a decrease of the amount of M2+ per COO function at the precipitation threshold, if Ca2+... 

Tis Pity too is interested in borders, as we see when the boundary of civil jurisdiction conies to an abrupt end when the officers of the watch try to pursue the murderer Grimaldi once he has safely passed the threshold of his uncle Ae Cardinal, and the Cardinal abruptly prevents them (3.9.30-41). What we see in this scene is not a national border, but it does nevertheless clearly mark a boimdaiy of another sort, where civic power and jurisdiction run up slap against that of the chinch, and in this world of invisible and ill-defined borders, sexual transgression flourishes. 

The right-hand side of expression (3.409) is always less than unity it tends to 1 as L —> 00 and to zero as L 0. Thus Hi is a critical threshold value such that for H > Hi the above solution (3.399) exists with the distance L between disclinations being determined by the value of if L can be calculated implicitly via the expression (3.409) once values have been inserted for the various physical constants Xa> 7> P) 9i and Ci. It is clear that L 0 as if 00 and L — 00 as fi — Hf hence increasing if decreases the distance between disclinations on the boundary surface. In the special case for a free surface with we can... 

A comparison of our results to the preferred coordination numbers determined by Brown [35] in 1985 cf. Fig. 13) based on the smaller set of reference structures available at that time shows that for high Ac, the values determined by the approach presented here tend to be higher than those reported by Brown. This is mainly an expected result of the different approach in defining the boundary of the first coordination shell. For lower Ac the results of both studies are not significantly different, as the clear gap between the bond lengths of nearest and second-nearest neighboring shells of anions around a cation make the detailed choice of the threshold value less relevant. 

---