A statistical study on the measurability of Bijvoet differences in crystals with type-I and type-II degree of centrosymmetry

Abstract

The probability distributions of the normalized Bijvoet differences x and A are derived for non-centrosymmetric crystals with type-I and type-II degree of centrosymmetry assuming that there is a single anomalous scatterer in the unit cell besides a sufficiently large number of similar normal scatterers. The theoretical results are used to study the influence of degree of centrosymmetry on the measurability of Bijvoet differences. It is found that, for given values of k and a 22, the measurability is in general poorer in the type-I case than in the type-II case.

Bioactive Glasses: A Promising Therapeutic Ion Release Strategy for Enhancing Wound Healing

“…On the other hand, nonbridging oxygen is not shared between two tetrahedra anymore. It is noteworthy to mention that the glass properties are directly influenced by the charge-to-size ratio of the modifier cations . As mentioned before, intermediate oxides such as MgO, ZnO, Al 2 O 3 , TiO 2 , and ZrO 2 act as network modifiers or network former, depending upon the glass composition. , …”

“…It is noteworthy to mention that the glass properties are directly influenced by the chargeto-size ratio of the modifier cations. 115 As mentioned before, intermediate oxides such as MgO, ZnO, Al 2 O 3 , TiO 2 , and ZrO 2 act as network modifiers or network former, depending upon the glass composition. 112,116 The structural change that occurs due to the addition of network modifiers in silicate-based glasses can be suggested by eq 1:…”

Thermodynamics of CeSiO4: Implications for Actinide Orthosilicates

“…Cerium was selected as the surrogate for Pu, due to the similarity in structure, and the ionic radii of the A-site cations and chemical properties (i.e., multiple valence states) [38][39][40][41] . Ce 4+ in the eight-coordination environment has an ionic radius of 0.97 Å, which is very close to that of eight-coordinated Pu 4+ (0.96 Å) 42 , therefore Ce in the solid-state system can be used to simulate Pu. Pure synthetic CeSiO 4 has been successfully prepared by both direct and indirect hydrothermal methods in 2019 43,44 and has been used for the thermodynamic study in this paper.…”

“…By using the experimentally determined ΔH f, ox of CeSiO 4 (27.5 ± 3.1 kJ/mol), USiO 4 (25.6 ± 3.9 kJ/mol 48 ) and ThSiO 4 (-6.4 ± 5.7 kJ/mol 8 ) and the ionic radii (Å) of metal cations in an eight-fold coordination environment 42 , a near linear trend is found between ΔH f, ox and the ionic radius r (Å), ΔH f, ox = (-446.3 ± 152.5) r -(464.9 ± 153.6), with an adjusted R 2 = 0.79096. From the obtained linear regression, we obtained the ΔH f, ox for the other actinide (Pa, Np, Pu, Am, Cm, Bk, Cf) orthosilicates ( Figure 2).…”

“…However, thorite is relatively easier to synthesize by various solid-state and aqueous-chemistry methods [51][52][53][54] , despite of the ionic similarity in Th 4+ (1.05 Å) and U 4+ (1.00 Å) 42 , the less difficult synthesis is consistent with its negative value of ΔH f,ox , -6.4 ± 5.7 kJ/mol 8 Secondly, the natural mineral occurrence of CeSiO 4 , stetindite, was discovered in 2009 in a granitic pegmatite in Norway 55 . However, there are no studies of its thermodynamic stability.…”