Optimization of quantitative X-ray phase analysis by Monte Carlo methods

Abstract

Present methods for quantitative X-ray phase analysis make extensive use of multilinear regression. Practical application of these methods compels workers to make a choice among many different sets of experimental conditions such as the number, identity and relative concentration of the phases in the synthetic mixtures used for the solution of the regression problem; the number and extent of the angular regions within which X-ray intensities are to be measured; and so on. There are as yet no general criteria for this selection, and classical statistical experimental methods, even such effective ones as SIMPLEX, are very time consuming. In the present work a Monte Carlo method is proposed for optimization of the reproducibility and detection limit for a completely general quantitative X-ray phase analysis. A system of three computer programs to this end is developed and applied to X-ray phase analysis of laterites, illustrating the choice of a set of performing conditions among 20 of them.

Study of the Adsorption Space of Modified Clinoptilolites

“…Further, the X-ray diffraction data (Figs. 1b and 1c) allowed the calculation of the phase composition of the modified clinoptilolites by means of standards [21] by applying a previously developed methodology [56,57]. In the present case the standard was the sample NH 4 -CSW.…”

Foundations of thermo-dielectrical analysis

“…The dependence between the apparent permittivity of powdered homoionic Na-HEU, Ca-HEU Na-MOR (homoionized natural clinoptilolite and mordenite with 75 and 85 weight per cent, respectively, of zeolite phase and the remainder quartz, calcite, montmorillonite and volcanic glass [25,26], Na-PHI and Na-FAU (Phillipsite and faujasite synthesized in our laboratory (27)) and the frequency (0.04 to 100 kHz) was measured with a measuring device [1,28,29] consisting of an operational amplifier which compares the capacities of a standard and a sample capacitor. By using the relation e ( w ) = -~o x, where Cx is the capacity of the condenser full of sample and Ce is the capacity of the empty capacitor, and the relation e ( w ) = e ( oo ) + X' ( w ), it is possible to fit the experimental data with the real part of Eq.…”

Foundations of thermo-dielectrical analysis

“…Dielectrical spectrometry is by itself an analytical method as was shown [11][12][13], but the interpretation of the results Zeolites were used as model material because of the presence of all the effects in its thermal curves i. e.: water polarization, cationic polarization and cationic conduction by cation hopping, the possibility of changing the cation present in the zeolite, the quantity of water or other sorbed phase. moreover zeolite structures are well documented [14,15], in our laboratory are developed the analytical methods for its study [16][17][18][19] and synthesis [8] and its dielectrical properties are not completely unknown, i. e. the dielectrical response of zeolites, is the result of a variety of individual factors which behave differently under the influence of: frequency, temperature, humidity, electric field, etc. Among these factors are" the very rapid electronic polarization, lattice polarization and the slow dipolar response, the last mechanism includes cation hopping [20] in both hydrated and dehydrated zeolites and water polarization [21,32].…”