Factors Influencing the Dispersion of Lengths of Interatomic Vectors

Table 2.1 presents empirical estimates of the first two central moments of interatomic vector lengths with the described properties. In this case terminal monatomic entities belong to a certain type. The dispersion of lengths of these vectors expressed by the second central moment m₂ shows the value of 7.383 Å2 for the sample of vector lengths of Zn2+ → 0, this value being much higher than 5.192 Å2 for the sample of vector lengths for Zn2+ → S. In the case of such great sample sizes the variance equality of these data sets can be tested using sample characteristics of $$F = S_1^2/S_2^2:$$$${H_0}:\sigma _1^2 = \sigma _2^2against{H_1}:\sigma _1^2 \ne \sigma _2^2$$We will use the estimate of the above characteristics F₁= m₂(Zn2+ → 0)/m₂(Zn2+ → S) = 1.422. The critical Fvalue on the significance level of α = 0.05 for v₁ = n(Zn2+ → 0) — 1 and v₂ = n(Zn2+ →S) — 1 is 1.011 [1]. Since F > F_crit the hypothesis H₀ of the equality of dispersions can be rejected. The vector lengths of Co3+ → Cl and Co3+ → N also show a significant difference between their dispersions. In both cases of central monatomic entities one could explain the differences between the dispersions of interatomic vector lengths with different qualities of their terminal entities. The values of m₂ of the samples of vectors of Zn2+ → S and Zn2+ → N exhibit, however, only a small difference (0.139 Å2). Similarly, the estimates of the second central moments of samples Cu2+ →Cl and Cu2+ → N are comparatively near.