Possible Correction of Preferential Orientation of Crystallites in Quantitative X-ray Determination by Means of Basal Reflections

In a previously published work1 we have described a method by which the intensity of an X-ray reflection that has been strengthened by preferential crystallite orientation can be corrected by measuring its ratio to the intensity of a reflection that is weakened by the same effect. In this way the intensity can be corrected to that given by a sample with a selected define degree of preferential orientation and then applied in quantitative analysis

Correction of Preferential Crystallite Orientation in X-ray Quantitative Analysis. Quantitative X:ray Determination of Ca (OH)2

The work deals with the problem of preferential orientation of crystallites in quantitafrwe X-ray analysis. A n ew method has been worked out theoretically. and practically for the correction of reflection intensities from \u27polycrystalline samples w ith preferentially oriented crystallites. Equations are included for the determination of correction parameters. Practical a pplication of the new method is demonstrated on quantitative X-ray analysis of calcium hydroxide. The work includes a calibration graph for the determination of coefficient a, comparing corrected and uncorrecte d values of analytical intensities of Ca(OH)2

Electrical Conductivity of Borax

The crystal structure of .sodium tetraborate decahydrate (borax) solved in 1956 by Morimoto 1 lead to the actual formula of this compound as B40 5(0H)i · Na2 8 H 2 0. The anionic part of the structure is composed of B,05(0H)4-polyions linked by hydrogen bonds, while the cationic set of the chains is formed by sodium ions surrounded octahedrally with water molecules. These two types of chains are. connected through hydrogen bonds running throughout the crystal parallel to its z-axis

Crystal Structure Investigation of Calcium Aluminium Sulphate Hydrate- Ettringite

Calcium threesulphoalun:iinate hydrate - ettringite , the general formula of which is 3Ca0 · Al20 8 • 3CaS04 • 32H20 occurs as natural mineral. This compound is, however, more important and better known as an ingredient of set Portland cement

Determination of Correction Factor for Preferential Crystallite Orientation in Quantitative X-ray Analysis of Calcium Hydroxide

In the work of A. Bezjak and I. Jelenic1 an expression was derived for correcting the intensities of .X-ray reflections from samples with preferential crystallite orientation

An X-ray and Proton Magnetic Resonance Study of the Dehydration and Deuteration of Borax, Na2[B40s(OH)4] · 8 H20

A quantitative powder-x-ray analysis was developed for this case by which it was shown that carefully prepared borax dehydrates directly into an unhydrous amorphous phase. Eight molecul es of water are quantitatively lost on complete dehydration (below 50°C) as required by the structural formula.. The proton m agnetic resonance results agree with these findings showing also that the spectrum due to OH-groups changes considerably on dehydration. This was used ~n following deuteration (solid/gas) of dehydrated borax. The p.m.r. spectra, the x-ray di agrams, and the measured regain indicate ·a reconshltution of the borax- lattice towards the formula Na2,[B 40 5(0H) 4] • 8D 20

Crystal Structure Investigation of Calcium Aluminium Sulphate Hydrate- Ettringite

Calcium threesulphoalun:iinate hydrate - ettringite , the general formula of which is 3Ca0 · Al20 8 • 3CaS04 • 32H20 occurs as natural mineral. This compound is, however, more important and better known as an ingredient of set Portland cement

Influence of Particle size in Quantitative X-Ray Analysis of Substances with a Pronounced Disposition for Preferential Orientation of Crystallites. Quantitative X-Ray Determination of Calcium Hydroxide

The paper deals with the influence of particle size in quantitative X-ray analysis of substances with a pronounced disposition of crystallites to orient prefe rentially. Dep endence of the broadening of diffraction maxima on the degree of preferential orientation of crystallites is proved experimentally. An equation has been derived to correct the broadening of diffraction maxima to the value belonging to randomly oriented specimen. Such a correction is needed to find out the dependence of the coefficient of proportionality a (reflectio n intensity/weight fraction) on the particle size of c rystallites . This dependence is expressed by equation B 1 • u. = cons t. which is the result of experiments carried out in quantitative X-ray analysis of calcium hydroxide

Electrical Conductivity of Borax

The crystal structure of .sodium tetraborate decahydrate (borax) solved in 1956 by Morimoto 1 lead to the actual formula of this compound as B40 5(0H)i · Na2 8 H 2 0. The anionic part of the structure is composed of B,05(0H)4-polyions linked by hydrogen bonds, while the cationic set of the chains is formed by sodium ions surrounded octahedrally with water molecules. These two types of chains are. connected through hydrogen bonds running throughout the crystal parallel to its z-axis

A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator